From 2b40c5c3de1ee2caca2c0072f812fea04b5a0238 Mon Sep 17 00:00:00 2001 From: Nadrieril Date: Mon, 27 May 2024 14:59:10 +0200 Subject: tests: Merge the hashmap test files --- tests/coq/hashmap/Hashmap_Funs.v | 72 +- tests/coq/hashmap/Hashmap_FunsExternal.v | 21 + tests/coq/hashmap/Hashmap_FunsExternal_Template.v | 23 + tests/coq/hashmap/Hashmap_Types.v | 6 +- tests/coq/hashmap/Hashmap_TypesExternal.v | 13 + tests/coq/hashmap/Hashmap_TypesExternal_Template.v | 15 + tests/coq/hashmap_main/HashmapMain_Funs.v | 589 ------------- tests/coq/hashmap_main/HashmapMain_FunsExternal.v | 24 - .../HashmapMain_FunsExternal_Template.v | 26 - tests/coq/hashmap_main/HashmapMain_Types.v | 40 - tests/coq/hashmap_main/HashmapMain_TypesExternal.v | 14 - .../HashmapMain_TypesExternal_Template.v | 15 - tests/coq/hashmap_main/Makefile | 23 - tests/coq/hashmap_main/Primitives.v | 981 --------------------- tests/coq/hashmap_main/_CoqProject | 12 - tests/fstar/hashmap/Hashmap.Clauses.Template.fst | 18 +- tests/fstar/hashmap/Hashmap.Funs.fst | 69 +- tests/fstar/hashmap/Hashmap.FunsExternal.fsti | 16 + tests/fstar/hashmap/Hashmap.Properties.fst | 48 + tests/fstar/hashmap/Hashmap.Types.fst | 5 +- tests/fstar/hashmap/Hashmap.TypesExternal.fsti | 10 + .../hashmap_main/HashmapMain.Clauses.Template.fst | 72 -- tests/fstar/hashmap_main/HashmapMain.Clauses.fst | 61 -- tests/fstar/hashmap_main/HashmapMain.Funs.fst | 446 ---------- .../hashmap_main/HashmapMain.FunsExternal.fsti | 18 - .../fstar/hashmap_main/HashmapMain.Properties.fst | 48 - tests/fstar/hashmap_main/HashmapMain.Types.fst | 24 - .../hashmap_main/HashmapMain.TypesExternal.fsti | 10 - tests/fstar/hashmap_main/Makefile | 49 - tests/fstar/hashmap_main/Primitives.fst | 929 ------------------- tests/lean/Hashmap/Funs.lean | 70 +- tests/lean/Hashmap/FunsExternal.lean | 19 + tests/lean/Hashmap/FunsExternal_Template.lean | 17 + tests/lean/Hashmap/Types.lean | 5 +- tests/lean/Hashmap/TypesExternal.lean | 7 + tests/lean/Hashmap/TypesExternal_Template.lean | 9 + tests/lean/HashmapMain.lean | 1 - tests/lean/HashmapMain/Funs.lean | 463 ---------- tests/lean/HashmapMain/FunsExternal.lean | 17 - tests/lean/HashmapMain/FunsExternal_Template.lean | 18 - tests/lean/HashmapMain/Opaque.lean | 18 - tests/lean/HashmapMain/Types.lean | 23 - tests/lean/HashmapMain/TypesExternal.lean | 7 - tests/lean/HashmapMain/TypesExternal_Template.lean | 9 - tests/lean/lakefile.lean | 1 - tests/src/hashmap.rs | 29 +- tests/src/hashmap_main.rs | 22 - tests/src/hashmap_utils.rs | 13 - 48 files changed, 366 insertions(+), 4079 deletions(-) create mode 100644 tests/coq/hashmap/Hashmap_FunsExternal.v create mode 100644 tests/coq/hashmap/Hashmap_FunsExternal_Template.v create mode 100644 tests/coq/hashmap/Hashmap_TypesExternal.v create mode 100644 tests/coq/hashmap/Hashmap_TypesExternal_Template.v delete mode 100644 tests/coq/hashmap_main/HashmapMain_Funs.v delete mode 100644 tests/coq/hashmap_main/HashmapMain_FunsExternal.v delete mode 100644 tests/coq/hashmap_main/HashmapMain_FunsExternal_Template.v delete mode 100644 tests/coq/hashmap_main/HashmapMain_Types.v delete mode 100644 tests/coq/hashmap_main/HashmapMain_TypesExternal.v delete mode 100644 tests/coq/hashmap_main/HashmapMain_TypesExternal_Template.v delete mode 100644 tests/coq/hashmap_main/Makefile delete mode 100644 tests/coq/hashmap_main/Primitives.v delete mode 100644 tests/coq/hashmap_main/_CoqProject create mode 100644 tests/fstar/hashmap/Hashmap.FunsExternal.fsti create mode 100644 tests/fstar/hashmap/Hashmap.Properties.fst create mode 100644 tests/fstar/hashmap/Hashmap.TypesExternal.fsti delete mode 100644 tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst delete mode 100644 tests/fstar/hashmap_main/HashmapMain.Clauses.fst delete mode 100644 tests/fstar/hashmap_main/HashmapMain.Funs.fst delete mode 100644 tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti delete mode 100644 tests/fstar/hashmap_main/HashmapMain.Properties.fst delete mode 100644 tests/fstar/hashmap_main/HashmapMain.Types.fst delete mode 100644 tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti delete mode 100644 tests/fstar/hashmap_main/Makefile delete mode 100644 tests/fstar/hashmap_main/Primitives.fst create mode 100644 tests/lean/Hashmap/FunsExternal.lean create mode 100644 tests/lean/Hashmap/FunsExternal_Template.lean create mode 100644 tests/lean/Hashmap/TypesExternal.lean create mode 100644 tests/lean/Hashmap/TypesExternal_Template.lean delete mode 100644 tests/lean/HashmapMain.lean delete mode 100644 tests/lean/HashmapMain/Funs.lean delete mode 100644 tests/lean/HashmapMain/FunsExternal.lean delete mode 100644 tests/lean/HashmapMain/FunsExternal_Template.lean delete mode 100644 tests/lean/HashmapMain/Opaque.lean delete mode 100644 tests/lean/HashmapMain/Types.lean delete mode 100644 tests/lean/HashmapMain/TypesExternal.lean delete mode 100644 tests/lean/HashmapMain/TypesExternal_Template.lean delete mode 100644 tests/src/hashmap_main.rs delete mode 100644 tests/src/hashmap_utils.rs diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v index 778b9d56..89f90210 100644 --- a/tests/coq/hashmap/Hashmap_Funs.v +++ b/tests/coq/hashmap/Hashmap_Funs.v @@ -8,15 +8,17 @@ Import ListNotations. Local Open Scope Primitives_scope. Require Import Hashmap_Types. Include Hashmap_Types. +Require Import Hashmap_FunsExternal. +Include Hashmap_FunsExternal. Module Hashmap_Funs. (** [hashmap::hash_key]: - Source: 'tests/src/hashmap.rs', lines 35:0-35:32 *) + Source: 'tests/src/hashmap.rs', lines 37:0-37:32 *) Definition hash_key (k : usize) : result usize := Ok k. (** [hashmap::{hashmap::HashMap}::allocate_slots]: loop 0: - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) + Source: 'tests/src/hashmap.rs', lines 60:4-66:5 *) Fixpoint hashMap_allocate_slots_loop (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n1 : usize) : result (alloc_vec_Vec (List_t T)) @@ -34,7 +36,7 @@ Fixpoint hashMap_allocate_slots_loop . (** [hashmap::{hashmap::HashMap}::allocate_slots]: - Source: 'tests/src/hashmap.rs', lines 58:4-58:76 *) + Source: 'tests/src/hashmap.rs', lines 60:4-60:76 *) Definition hashMap_allocate_slots (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n1 : usize) : result (alloc_vec_Vec (List_t T)) @@ -43,7 +45,7 @@ Definition hashMap_allocate_slots . (** [hashmap::{hashmap::HashMap}::new_with_capacity]: - Source: 'tests/src/hashmap.rs', lines 67:4-71:13 *) + Source: 'tests/src/hashmap.rs', lines 69:4-73:13 *) Definition hashMap_new_with_capacity (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) : @@ -62,13 +64,13 @@ Definition hashMap_new_with_capacity . (** [hashmap::{hashmap::HashMap}::new]: - Source: 'tests/src/hashmap.rs', lines 83:4-83:24 *) + Source: 'tests/src/hashmap.rs', lines 85:4-85:24 *) Definition hashMap_new (T : Type) (n : nat) : result (HashMap_t T) := hashMap_new_with_capacity T n 32%usize 4%usize 5%usize . (** [hashmap::{hashmap::HashMap}::clear]: loop 0: - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) + Source: 'tests/src/hashmap.rs', lines 90:4-98:5 *) Fixpoint hashMap_clear_loop (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (i : usize) : result (alloc_vec_Vec (List_t T)) @@ -91,7 +93,7 @@ Fixpoint hashMap_clear_loop . (** [hashmap::{hashmap::HashMap}::clear]: - Source: 'tests/src/hashmap.rs', lines 88:4-88:27 *) + Source: 'tests/src/hashmap.rs', lines 90:4-90:27 *) Definition hashMap_clear (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) := hm <- hashMap_clear_loop T n self.(hashMap_slots) 0%usize; @@ -105,13 +107,13 @@ Definition hashMap_clear . (** [hashmap::{hashmap::HashMap}::len]: - Source: 'tests/src/hashmap.rs', lines 98:4-98:30 *) + Source: 'tests/src/hashmap.rs', lines 100:4-100:30 *) Definition hashMap_len (T : Type) (self : HashMap_t T) : result usize := Ok self.(hashMap_num_entries) . (** [hashmap::{hashmap::HashMap}::insert_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) + Source: 'tests/src/hashmap.rs', lines 107:4-124:5 *) Fixpoint hashMap_insert_in_list_loop (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) : result (bool * (List_t T)) @@ -133,7 +135,7 @@ Fixpoint hashMap_insert_in_list_loop . (** [hashmap::{hashmap::HashMap}::insert_in_list]: - Source: 'tests/src/hashmap.rs', lines 105:4-105:71 *) + Source: 'tests/src/hashmap.rs', lines 107:4-107:71 *) Definition hashMap_insert_in_list (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) : result (bool * (List_t T)) @@ -142,7 +144,7 @@ Definition hashMap_insert_in_list . (** [hashmap::{hashmap::HashMap}::insert_no_resize]: - Source: 'tests/src/hashmap.rs', lines 125:4-125:54 *) + Source: 'tests/src/hashmap.rs', lines 127:4-127:54 *) Definition hashMap_insert_no_resize (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) : result (HashMap_t T) @@ -180,7 +182,7 @@ Definition hashMap_insert_no_resize . (** [hashmap::{hashmap::HashMap}::move_elements_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) + Source: 'tests/src/hashmap.rs', lines 193:4-206:5 *) Fixpoint hashMap_move_elements_from_list_loop (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) : result (HashMap_t T) @@ -198,7 +200,7 @@ Fixpoint hashMap_move_elements_from_list_loop . (** [hashmap::{hashmap::HashMap}::move_elements_from_list]: - Source: 'tests/src/hashmap.rs', lines 191:4-191:72 *) + Source: 'tests/src/hashmap.rs', lines 193:4-193:72 *) Definition hashMap_move_elements_from_list (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) : result (HashMap_t T) @@ -207,7 +209,7 @@ Definition hashMap_move_elements_from_list . (** [hashmap::{hashmap::HashMap}::move_elements]: loop 0: - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) + Source: 'tests/src/hashmap.rs', lines 181:4-190:5 *) Fixpoint hashMap_move_elements_loop (T : Type) (n : nat) (ntable : HashMap_t T) (slots : alloc_vec_Vec (List_t T)) (i : usize) : @@ -233,7 +235,7 @@ Fixpoint hashMap_move_elements_loop . (** [hashmap::{hashmap::HashMap}::move_elements]: - Source: 'tests/src/hashmap.rs', lines 179:4-179:95 *) + Source: 'tests/src/hashmap.rs', lines 181:4-181:95 *) Definition hashMap_move_elements (T : Type) (n : nat) (ntable : HashMap_t T) (slots : alloc_vec_Vec (List_t T)) (i : usize) : @@ -243,7 +245,7 @@ Definition hashMap_move_elements . (** [hashmap::{hashmap::HashMap}::try_resize]: - Source: 'tests/src/hashmap.rs', lines 148:4-148:28 *) + Source: 'tests/src/hashmap.rs', lines 150:4-150:28 *) Definition hashMap_try_resize (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) := max_usize <- scalar_cast U32 Usize core_u32_max; @@ -275,7 +277,7 @@ Definition hashMap_try_resize . (** [hashmap::{hashmap::HashMap}::insert]: - Source: 'tests/src/hashmap.rs', lines 137:4-137:48 *) + Source: 'tests/src/hashmap.rs', lines 139:4-139:48 *) Definition hashMap_insert (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) : result (HashMap_t T) @@ -288,7 +290,7 @@ Definition hashMap_insert . (** [hashmap::{hashmap::HashMap}::contains_key_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) + Source: 'tests/src/hashmap.rs', lines 216:4-229:5 *) Fixpoint hashMap_contains_key_in_list_loop (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool := match n with @@ -305,14 +307,14 @@ Fixpoint hashMap_contains_key_in_list_loop . (** [hashmap::{hashmap::HashMap}::contains_key_in_list]: - Source: 'tests/src/hashmap.rs', lines 214:4-214:68 *) + Source: 'tests/src/hashmap.rs', lines 216:4-216:68 *) Definition hashMap_contains_key_in_list (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool := hashMap_contains_key_in_list_loop T n key ls . (** [hashmap::{hashmap::HashMap}::contains_key]: - Source: 'tests/src/hashmap.rs', lines 207:4-207:49 *) + Source: 'tests/src/hashmap.rs', lines 209:4-209:49 *) Definition hashMap_contains_key (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result bool := hash <- hash_key key; @@ -326,7 +328,7 @@ Definition hashMap_contains_key . (** [hashmap::{hashmap::HashMap}::get_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) + Source: 'tests/src/hashmap.rs', lines 234:4-247:5 *) Fixpoint hashMap_get_in_list_loop (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T := match n with @@ -341,14 +343,14 @@ Fixpoint hashMap_get_in_list_loop . (** [hashmap::{hashmap::HashMap}::get_in_list]: - Source: 'tests/src/hashmap.rs', lines 232:4-232:70 *) + Source: 'tests/src/hashmap.rs', lines 234:4-234:70 *) Definition hashMap_get_in_list (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T := hashMap_get_in_list_loop T n key ls . (** [hashmap::{hashmap::HashMap}::get]: - Source: 'tests/src/hashmap.rs', lines 247:4-247:55 *) + Source: 'tests/src/hashmap.rs', lines 249:4-249:55 *) Definition hashMap_get (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T := hash <- hash_key key; @@ -362,7 +364,7 @@ Definition hashMap_get . (** [hashmap::{hashmap::HashMap}::get_mut_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) + Source: 'tests/src/hashmap.rs', lines 255:4-264:5 *) Fixpoint hashMap_get_mut_in_list_loop (T : Type) (n : nat) (ls : List_t T) (key : usize) : result (T * (T -> result (List_t T))) @@ -388,7 +390,7 @@ Fixpoint hashMap_get_mut_in_list_loop . (** [hashmap::{hashmap::HashMap}::get_mut_in_list]: - Source: 'tests/src/hashmap.rs', lines 253:4-253:86 *) + Source: 'tests/src/hashmap.rs', lines 255:4-255:86 *) Definition hashMap_get_mut_in_list (T : Type) (n : nat) (ls : List_t T) (key : usize) : result (T * (T -> result (List_t T))) @@ -397,7 +399,7 @@ Definition hashMap_get_mut_in_list . (** [hashmap::{hashmap::HashMap}::get_mut]: - Source: 'tests/src/hashmap.rs', lines 265:4-265:67 *) + Source: 'tests/src/hashmap.rs', lines 267:4-267:67 *) Definition hashMap_get_mut (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result (T * (T -> result (HashMap_t T))) @@ -427,7 +429,7 @@ Definition hashMap_get_mut . (** [hashmap::{hashmap::HashMap}::remove_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) + Source: 'tests/src/hashmap.rs', lines 275:4-301:5 *) Fixpoint hashMap_remove_from_list_loop (T : Type) (n : nat) (key : usize) (ls : List_t T) : result ((option T) * (List_t T)) @@ -455,7 +457,7 @@ Fixpoint hashMap_remove_from_list_loop . (** [hashmap::{hashmap::HashMap}::remove_from_list]: - Source: 'tests/src/hashmap.rs', lines 273:4-273:69 *) + Source: 'tests/src/hashmap.rs', lines 275:4-275:69 *) Definition hashMap_remove_from_list (T : Type) (n : nat) (key : usize) (ls : List_t T) : result ((option T) * (List_t T)) @@ -464,7 +466,7 @@ Definition hashMap_remove_from_list . (** [hashmap::{hashmap::HashMap}::remove]: - Source: 'tests/src/hashmap.rs', lines 302:4-302:52 *) + Source: 'tests/src/hashmap.rs', lines 304:4-304:52 *) Definition hashMap_remove (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result ((option T) * (HashMap_t T)) @@ -502,8 +504,18 @@ Definition hashMap_remove end . +(** [hashmap::insert_on_disk]: + Source: 'tests/src/hashmap.rs', lines 335:0-335:43 *) +Definition insert_on_disk + (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) := + p <- hashmap_utils_deserialize st; + let (st1, hm) := p in + hm1 <- hashMap_insert u64 n hm key value; + hashmap_utils_serialize hm1 st1 +. + (** [hashmap::test1]: - Source: 'tests/src/hashmap.rs', lines 323:0-323:10 *) + Source: 'tests/src/hashmap.rs', lines 350:0-350:10 *) Definition test1 (n : nat) : result unit := hm <- hashMap_new u64 n; hm1 <- hashMap_insert u64 n hm 0%usize 42%u64; diff --git a/tests/coq/hashmap/Hashmap_FunsExternal.v b/tests/coq/hashmap/Hashmap_FunsExternal.v new file mode 100644 index 00000000..bcf12c17 --- /dev/null +++ b/tests/coq/hashmap/Hashmap_FunsExternal.v @@ -0,0 +1,21 @@ +(** [hashmap]: external functions. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Require Export Hashmap_Types. +Import Hashmap_Types. +Module Hashmap_FunsExternal. + +(** [hashmap::hashmap_utils::deserialize]: + Source: 'tests/src/hashmap.rs', lines 330:4-330:47 *) +Axiom hashmap_utils_deserialize : state -> result (state * (HashMap_t u64)). + +(** [hashmap::hashmap_utils::serialize]: + Source: 'tests/src/hashmap.rs', lines 325:4-325:46 *) +Axiom hashmap_utils_serialize : HashMap_t u64 -> state -> result (state * unit) +. + +End Hashmap_FunsExternal. diff --git a/tests/coq/hashmap/Hashmap_FunsExternal_Template.v b/tests/coq/hashmap/Hashmap_FunsExternal_Template.v new file mode 100644 index 00000000..c35b8e14 --- /dev/null +++ b/tests/coq/hashmap/Hashmap_FunsExternal_Template.v @@ -0,0 +1,23 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap]: external functions. +-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Require Import Hashmap_Types. +Include Hashmap_Types. +Module Hashmap_FunsExternal_Template. + +(** [hashmap::hashmap_utils::deserialize]: + Source: 'tests/src/hashmap.rs', lines 330:4-330:47 *) +Axiom hashmap_utils_deserialize : state -> result (state * (HashMap_t u64)). + +(** [hashmap::hashmap_utils::serialize]: + Source: 'tests/src/hashmap.rs', lines 325:4-325:46 *) +Axiom hashmap_utils_serialize : HashMap_t u64 -> state -> result (state * unit) +. + +End Hashmap_FunsExternal_Template. diff --git a/tests/coq/hashmap/Hashmap_Types.v b/tests/coq/hashmap/Hashmap_Types.v index 8a8137d5..452d56f8 100644 --- a/tests/coq/hashmap/Hashmap_Types.v +++ b/tests/coq/hashmap/Hashmap_Types.v @@ -6,10 +6,12 @@ Require Import Coq.ZArith.ZArith. Require Import List. Import ListNotations. Local Open Scope Primitives_scope. +Require Import Hashmap_TypesExternal. +Include Hashmap_TypesExternal. Module Hashmap_Types. (** [hashmap::List] - Source: 'tests/src/hashmap.rs', lines 27:0-27:16 *) + Source: 'tests/src/hashmap.rs', lines 29:0-29:16 *) Inductive List_t (T : Type) := | List_Cons : usize -> T -> List_t T -> List_t T | List_Nil : List_t T @@ -19,7 +21,7 @@ Arguments List_Cons { _ }. Arguments List_Nil { _ }. (** [hashmap::HashMap] - Source: 'tests/src/hashmap.rs', lines 43:0-43:21 *) + Source: 'tests/src/hashmap.rs', lines 45:0-45:21 *) Record HashMap_t (T : Type) := mkHashMap_t { hashMap_num_entries : usize; diff --git a/tests/coq/hashmap/Hashmap_TypesExternal.v b/tests/coq/hashmap/Hashmap_TypesExternal.v new file mode 100644 index 00000000..0aa52a5d --- /dev/null +++ b/tests/coq/hashmap/Hashmap_TypesExternal.v @@ -0,0 +1,13 @@ +(** [hashmap]: external types. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Module Hashmap_TypesExternal. + +(** The state type used in the state-error monad *) +Axiom state : Type. + +End Hashmap_TypesExternal. diff --git a/tests/coq/hashmap/Hashmap_TypesExternal_Template.v b/tests/coq/hashmap/Hashmap_TypesExternal_Template.v new file mode 100644 index 00000000..a8051adb --- /dev/null +++ b/tests/coq/hashmap/Hashmap_TypesExternal_Template.v @@ -0,0 +1,15 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap]: external types. +-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Module Hashmap_TypesExternal_Template. + +(** The state type used in the state-error monad *) +Axiom state : Type. + +End Hashmap_TypesExternal_Template. diff --git a/tests/coq/hashmap_main/HashmapMain_Funs.v b/tests/coq/hashmap_main/HashmapMain_Funs.v deleted file mode 100644 index f6467d5a..00000000 --- a/tests/coq/hashmap_main/HashmapMain_Funs.v +++ /dev/null @@ -1,589 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: function definitions *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Import HashmapMain_Types. -Include HashmapMain_Types. -Require Import HashmapMain_FunsExternal. -Include HashmapMain_FunsExternal. -Module HashmapMain_Funs. - -(** [hashmap_main::hashmap::hash_key]: - Source: 'tests/src/hashmap.rs', lines 35:0-35:32 *) -Definition hashmap_hash_key (k : usize) : result usize := - Ok k. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::allocate_slots]: loop 0: - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) -Fixpoint hashmap_HashMap_allocate_slots_loop - (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize) - : - result (alloc_vec_Vec (hashmap_List_t T)) - := - match n with - | O => Fail_ OutOfFuel - | S n2 => - if n1 s> 0%usize - then ( - slots1 <- alloc_vec_Vec_push (hashmap_List_t T) slots Hashmap_List_Nil; - n3 <- usize_sub n1 1%usize; - hashmap_HashMap_allocate_slots_loop T n2 slots1 n3) - else Ok slots - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::allocate_slots]: - Source: 'tests/src/hashmap.rs', lines 58:4-58:76 *) -Definition hashmap_HashMap_allocate_slots - (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n1 : usize) - : - result (alloc_vec_Vec (hashmap_List_t T)) - := - hashmap_HashMap_allocate_slots_loop T n slots n1 -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::new_with_capacity]: - Source: 'tests/src/hashmap.rs', lines 67:4-71:13 *) -Definition hashmap_HashMap_new_with_capacity - (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize) - (max_load_divisor : usize) : - result (hashmap_HashMap_t T) - := - slots <- - hashmap_HashMap_allocate_slots T n (alloc_vec_Vec_new (hashmap_List_t T)) - capacity; - i <- usize_mul capacity max_load_dividend; - i1 <- usize_div i max_load_divisor; - Ok - {| - hashmap_HashMap_num_entries := 0%usize; - hashmap_HashMap_max_load_factor := (max_load_dividend, max_load_divisor); - hashmap_HashMap_max_load := i1; - hashmap_HashMap_slots := slots - |} -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::new]: - Source: 'tests/src/hashmap.rs', lines 83:4-83:24 *) -Definition hashmap_HashMap_new - (T : Type) (n : nat) : result (hashmap_HashMap_t T) := - hashmap_HashMap_new_with_capacity T n 32%usize 4%usize 5%usize -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::clear]: loop 0: - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) -Fixpoint hashmap_HashMap_clear_loop - (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) : - result (alloc_vec_Vec (hashmap_List_t T)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in - if i s< i1 - then ( - p <- - alloc_vec_Vec_index_mut (hashmap_List_t T) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots - i; - let (_, index_mut_back) := p in - i2 <- usize_add i 1%usize; - slots1 <- index_mut_back Hashmap_List_Nil; - hashmap_HashMap_clear_loop T n1 slots1 i2) - else Ok slots - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::clear]: - Source: 'tests/src/hashmap.rs', lines 88:4-88:27 *) -Definition hashmap_HashMap_clear - (T : Type) (n : nat) (self : hashmap_HashMap_t T) : - result (hashmap_HashMap_t T) - := - hm <- hashmap_HashMap_clear_loop T n self.(hashmap_HashMap_slots) 0%usize; - Ok - {| - hashmap_HashMap_num_entries := 0%usize; - hashmap_HashMap_max_load_factor := self.(hashmap_HashMap_max_load_factor); - hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := hm - |} -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::len]: - Source: 'tests/src/hashmap.rs', lines 98:4-98:30 *) -Definition hashmap_HashMap_len - (T : Type) (self : hashmap_HashMap_t T) : result usize := - Ok self.(hashmap_HashMap_num_entries) -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) -Fixpoint hashmap_HashMap_insert_in_list_loop - (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) : - result (bool * (hashmap_List_t T)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match ls with - | Hashmap_List_Cons ckey cvalue tl => - if ckey s= key - then Ok (false, Hashmap_List_Cons ckey value tl) - else ( - p <- hashmap_HashMap_insert_in_list_loop T n1 key value tl; - let (b, tl1) := p in - Ok (b, Hashmap_List_Cons ckey cvalue tl1)) - | Hashmap_List_Nil => - Ok (true, Hashmap_List_Cons key value Hashmap_List_Nil) - end - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_in_list]: - Source: 'tests/src/hashmap.rs', lines 105:4-105:71 *) -Definition hashmap_HashMap_insert_in_list - (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) : - result (bool * (hashmap_List_t T)) - := - hashmap_HashMap_insert_in_list_loop T n key value ls -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_no_resize]: - Source: 'tests/src/hashmap.rs', lines 125:4-125:54 *) -Definition hashmap_HashMap_insert_no_resize - (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) : - result (hashmap_HashMap_t T) - := - hash <- hashmap_hash_key key; - let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in - hash_mod <- usize_rem hash i; - p <- - alloc_vec_Vec_index_mut (hashmap_List_t T) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) - self.(hashmap_HashMap_slots) hash_mod; - let (l, index_mut_back) := p in - p1 <- hashmap_HashMap_insert_in_list T n key value l; - let (inserted, l1) := p1 in - if inserted - then ( - i1 <- usize_add self.(hashmap_HashMap_num_entries) 1%usize; - v <- index_mut_back l1; - Ok - {| - hashmap_HashMap_num_entries := i1; - hashmap_HashMap_max_load_factor := - self.(hashmap_HashMap_max_load_factor); - hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := v - |}) - else ( - v <- index_mut_back l1; - Ok - {| - hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries); - hashmap_HashMap_max_load_factor := - self.(hashmap_HashMap_max_load_factor); - hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := v - |}) -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) -Fixpoint hashmap_HashMap_move_elements_from_list_loop - (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) : - result (hashmap_HashMap_t T) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match ls with - | Hashmap_List_Cons k v tl => - ntable1 <- hashmap_HashMap_insert_no_resize T n1 ntable k v; - hashmap_HashMap_move_elements_from_list_loop T n1 ntable1 tl - | Hashmap_List_Nil => Ok ntable - end - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements_from_list]: - Source: 'tests/src/hashmap.rs', lines 191:4-191:72 *) -Definition hashmap_HashMap_move_elements_from_list - (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) : - result (hashmap_HashMap_t T) - := - hashmap_HashMap_move_elements_from_list_loop T n ntable ls -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements]: loop 0: - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) -Fixpoint hashmap_HashMap_move_elements_loop - (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) - (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) : - result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - let i1 := alloc_vec_Vec_len (hashmap_List_t T) slots in - if i s< i1 - then ( - p <- - alloc_vec_Vec_index_mut (hashmap_List_t T) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots - i; - let (l, index_mut_back) := p in - let (ls, l1) := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in - ntable1 <- hashmap_HashMap_move_elements_from_list T n1 ntable ls; - i2 <- usize_add i 1%usize; - slots1 <- index_mut_back l1; - hashmap_HashMap_move_elements_loop T n1 ntable1 slots1 i2) - else Ok (ntable, slots) - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements]: - Source: 'tests/src/hashmap.rs', lines 179:4-179:95 *) -Definition hashmap_HashMap_move_elements - (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) - (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) : - result ((hashmap_HashMap_t T) * (alloc_vec_Vec (hashmap_List_t T))) - := - hashmap_HashMap_move_elements_loop T n ntable slots i -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::try_resize]: - Source: 'tests/src/hashmap.rs', lines 148:4-148:28 *) -Definition hashmap_HashMap_try_resize - (T : Type) (n : nat) (self : hashmap_HashMap_t T) : - result (hashmap_HashMap_t T) - := - max_usize <- scalar_cast U32 Usize core_u32_max; - let capacity := - alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in - n1 <- usize_div max_usize 2%usize; - let (i, i1) := self.(hashmap_HashMap_max_load_factor) in - i2 <- usize_div n1 i; - if capacity s<= i2 - then ( - i3 <- usize_mul capacity 2%usize; - ntable <- hashmap_HashMap_new_with_capacity T n i3 i i1; - p <- - hashmap_HashMap_move_elements T n ntable self.(hashmap_HashMap_slots) - 0%usize; - let (ntable1, _) := p in - Ok - {| - hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries); - hashmap_HashMap_max_load_factor := (i, i1); - hashmap_HashMap_max_load := ntable1.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := ntable1.(hashmap_HashMap_slots) - |}) - else - Ok - {| - hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries); - hashmap_HashMap_max_load_factor := (i, i1); - hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := self.(hashmap_HashMap_slots) - |} -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert]: - Source: 'tests/src/hashmap.rs', lines 137:4-137:48 *) -Definition hashmap_HashMap_insert - (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) : - result (hashmap_HashMap_t T) - := - self1 <- hashmap_HashMap_insert_no_resize T n self key value; - i <- hashmap_HashMap_len T self1; - if i s> self1.(hashmap_HashMap_max_load) - then hashmap_HashMap_try_resize T n self1 - else Ok self1 -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) -Fixpoint hashmap_HashMap_contains_key_in_list_loop - (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match ls with - | Hashmap_List_Cons ckey _ tl => - if ckey s= key - then Ok true - else hashmap_HashMap_contains_key_in_list_loop T n1 key tl - | Hashmap_List_Nil => Ok false - end - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key_in_list]: - Source: 'tests/src/hashmap.rs', lines 214:4-214:68 *) -Definition hashmap_HashMap_contains_key_in_list - (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool := - hashmap_HashMap_contains_key_in_list_loop T n key ls -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key]: - Source: 'tests/src/hashmap.rs', lines 207:4-207:49 *) -Definition hashmap_HashMap_contains_key - (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : - result bool - := - hash <- hashmap_hash_key key; - let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in - hash_mod <- usize_rem hash i; - l <- - alloc_vec_Vec_index (hashmap_List_t T) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) - self.(hashmap_HashMap_slots) hash_mod; - hashmap_HashMap_contains_key_in_list T n key l -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) -Fixpoint hashmap_HashMap_get_in_list_loop - (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match ls with - | Hashmap_List_Cons ckey cvalue tl => - if ckey s= key - then Ok cvalue - else hashmap_HashMap_get_in_list_loop T n1 key tl - | Hashmap_List_Nil => Fail_ Failure - end - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_in_list]: - Source: 'tests/src/hashmap.rs', lines 232:4-232:70 *) -Definition hashmap_HashMap_get_in_list - (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T := - hashmap_HashMap_get_in_list_loop T n key ls -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get]: - Source: 'tests/src/hashmap.rs', lines 247:4-247:55 *) -Definition hashmap_HashMap_get - (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T := - hash <- hashmap_hash_key key; - let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in - hash_mod <- usize_rem hash i; - l <- - alloc_vec_Vec_index (hashmap_List_t T) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) - self.(hashmap_HashMap_slots) hash_mod; - hashmap_HashMap_get_in_list T n key l -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) -Fixpoint hashmap_HashMap_get_mut_in_list_loop - (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : - result (T * (T -> result (hashmap_List_t T))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match ls with - | Hashmap_List_Cons ckey cvalue tl => - if ckey s= key - then - let back := fun (ret : T) => Ok (Hashmap_List_Cons ckey ret tl) in - Ok (cvalue, back) - else ( - p <- hashmap_HashMap_get_mut_in_list_loop T n1 tl key; - let (t, back) := p in - let back1 := - fun (ret : T) => - tl1 <- back ret; Ok (Hashmap_List_Cons ckey cvalue tl1) in - Ok (t, back1)) - | Hashmap_List_Nil => Fail_ Failure - end - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut_in_list]: - Source: 'tests/src/hashmap.rs', lines 253:4-253:86 *) -Definition hashmap_HashMap_get_mut_in_list - (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : - result (T * (T -> result (hashmap_List_t T))) - := - hashmap_HashMap_get_mut_in_list_loop T n ls key -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut]: - Source: 'tests/src/hashmap.rs', lines 265:4-265:67 *) -Definition hashmap_HashMap_get_mut - (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : - result (T * (T -> result (hashmap_HashMap_t T))) - := - hash <- hashmap_hash_key key; - let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in - hash_mod <- usize_rem hash i; - p <- - alloc_vec_Vec_index_mut (hashmap_List_t T) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) - self.(hashmap_HashMap_slots) hash_mod; - let (l, index_mut_back) := p in - p1 <- hashmap_HashMap_get_mut_in_list T n l key; - let (t, get_mut_in_list_back) := p1 in - let back := - fun (ret : T) => - l1 <- get_mut_in_list_back ret; - v <- index_mut_back l1; - Ok - {| - hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries); - hashmap_HashMap_max_load_factor := - self.(hashmap_HashMap_max_load_factor); - hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := v - |} in - Ok (t, back) -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) -Fixpoint hashmap_HashMap_remove_from_list_loop - (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : - result ((option T) * (hashmap_List_t T)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match ls with - | Hashmap_List_Cons ckey t tl => - if ckey s= key - then - let (mv_ls, _) := - core_mem_replace (hashmap_List_t T) (Hashmap_List_Cons ckey t tl) - Hashmap_List_Nil in - match mv_ls with - | Hashmap_List_Cons _ cvalue tl1 => Ok (Some cvalue, tl1) - | Hashmap_List_Nil => Fail_ Failure - end - else ( - p <- hashmap_HashMap_remove_from_list_loop T n1 key tl; - let (o, tl1) := p in - Ok (o, Hashmap_List_Cons ckey t tl1)) - | Hashmap_List_Nil => Ok (None, Hashmap_List_Nil) - end - end -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove_from_list]: - Source: 'tests/src/hashmap.rs', lines 273:4-273:69 *) -Definition hashmap_HashMap_remove_from_list - (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : - result ((option T) * (hashmap_List_t T)) - := - hashmap_HashMap_remove_from_list_loop T n key ls -. - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove]: - Source: 'tests/src/hashmap.rs', lines 302:4-302:52 *) -Definition hashmap_HashMap_remove - (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : - result ((option T) * (hashmap_HashMap_t T)) - := - hash <- hashmap_hash_key key; - let i := alloc_vec_Vec_len (hashmap_List_t T) self.(hashmap_HashMap_slots) in - hash_mod <- usize_rem hash i; - p <- - alloc_vec_Vec_index_mut (hashmap_List_t T) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) - self.(hashmap_HashMap_slots) hash_mod; - let (l, index_mut_back) := p in - p1 <- hashmap_HashMap_remove_from_list T n key l; - let (x, l1) := p1 in - match x with - | None => - v <- index_mut_back l1; - Ok (None, - {| - hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries); - hashmap_HashMap_max_load_factor := - self.(hashmap_HashMap_max_load_factor); - hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := v - |}) - | Some x1 => - i1 <- usize_sub self.(hashmap_HashMap_num_entries) 1%usize; - v <- index_mut_back l1; - Ok (Some x1, - {| - hashmap_HashMap_num_entries := i1; - hashmap_HashMap_max_load_factor := - self.(hashmap_HashMap_max_load_factor); - hashmap_HashMap_max_load := self.(hashmap_HashMap_max_load); - hashmap_HashMap_slots := v - |}) - end -. - -(** [hashmap_main::hashmap::test1]: - Source: 'tests/src/hashmap.rs', lines 323:0-323:10 *) -Definition hashmap_test1 (n : nat) : result unit := - hm <- hashmap_HashMap_new u64 n; - hm1 <- hashmap_HashMap_insert u64 n hm 0%usize 42%u64; - hm2 <- hashmap_HashMap_insert u64 n hm1 128%usize 18%u64; - hm3 <- hashmap_HashMap_insert u64 n hm2 1024%usize 138%u64; - hm4 <- hashmap_HashMap_insert u64 n hm3 1056%usize 256%u64; - i <- hashmap_HashMap_get u64 n hm4 128%usize; - if negb (i s= 18%u64) - then Fail_ Failure - else ( - p <- hashmap_HashMap_get_mut u64 n hm4 1024%usize; - let (_, get_mut_back) := p in - hm5 <- get_mut_back 56%u64; - i1 <- hashmap_HashMap_get u64 n hm5 1024%usize; - if negb (i1 s= 56%u64) - then Fail_ Failure - else ( - p1 <- hashmap_HashMap_remove u64 n hm5 1024%usize; - let (x, hm6) := p1 in - match x with - | None => Fail_ Failure - | Some x1 => - if negb (x1 s= 56%u64) - then Fail_ Failure - else ( - i2 <- hashmap_HashMap_get u64 n hm6 0%usize; - if negb (i2 s= 42%u64) - then Fail_ Failure - else ( - i3 <- hashmap_HashMap_get u64 n hm6 128%usize; - if negb (i3 s= 18%u64) - then Fail_ Failure - else ( - i4 <- hashmap_HashMap_get u64 n hm6 1056%usize; - if negb (i4 s= 256%u64) then Fail_ Failure else Ok tt))) - end)) -. - -(** [hashmap_main::insert_on_disk]: - Source: 'tests/src/hashmap_main.rs', lines 13:0-13:43 *) -Definition insert_on_disk - (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) := - p <- hashmap_utils_deserialize st; - let (st1, hm) := p in - hm1 <- hashmap_HashMap_insert u64 n hm key value; - hashmap_utils_serialize hm1 st1 -. - -(** [hashmap_main::main]: - Source: 'tests/src/hashmap_main.rs', lines 22:0-22:13 *) -Definition main : result unit := - Ok tt. - -End HashmapMain_Funs. diff --git a/tests/coq/hashmap_main/HashmapMain_FunsExternal.v b/tests/coq/hashmap_main/HashmapMain_FunsExternal.v deleted file mode 100644 index fb5f23cd..00000000 --- a/tests/coq/hashmap_main/HashmapMain_FunsExternal.v +++ /dev/null @@ -1,24 +0,0 @@ -(** [hashmap_main]: external function declarations *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Export HashmapMain_Types. -Import HashmapMain_Types. -Module HashmapMain_FunsExternal. - -(** [hashmap_main::hashmap_utils::deserialize]: forward function - Source: 'src/hashmap_utils.rs', lines 10:0-10:43 *) -Axiom hashmap_utils_deserialize - : state -> result (state * (hashmap_HashMap_t u64)) -. - -(** [hashmap_main::hashmap_utils::serialize]: forward function - Source: 'src/hashmap_utils.rs', lines 5:0-5:42 *) -Axiom hashmap_utils_serialize - : hashmap_HashMap_t u64 -> state -> result (state * unit) -. - -End HashmapMain_FunsExternal. diff --git a/tests/coq/hashmap_main/HashmapMain_FunsExternal_Template.v b/tests/coq/hashmap_main/HashmapMain_FunsExternal_Template.v deleted file mode 100644 index 66835e8c..00000000 --- a/tests/coq/hashmap_main/HashmapMain_FunsExternal_Template.v +++ /dev/null @@ -1,26 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: external functions. --- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Import HashmapMain_Types. -Include HashmapMain_Types. -Module HashmapMain_FunsExternal_Template. - -(** [hashmap_main::hashmap_utils::deserialize]: - Source: 'tests/src/hashmap_utils.rs', lines 11:0-11:43 *) -Axiom hashmap_utils_deserialize - : state -> result (state * (hashmap_HashMap_t u64)) -. - -(** [hashmap_main::hashmap_utils::serialize]: - Source: 'tests/src/hashmap_utils.rs', lines 6:0-6:42 *) -Axiom hashmap_utils_serialize - : hashmap_HashMap_t u64 -> state -> result (state * unit) -. - -End HashmapMain_FunsExternal_Template. diff --git a/tests/coq/hashmap_main/HashmapMain_Types.v b/tests/coq/hashmap_main/HashmapMain_Types.v deleted file mode 100644 index 5656bd9c..00000000 --- a/tests/coq/hashmap_main/HashmapMain_Types.v +++ /dev/null @@ -1,40 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: type definitions *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Import HashmapMain_TypesExternal. -Include HashmapMain_TypesExternal. -Module HashmapMain_Types. - -(** [hashmap_main::hashmap::List] - Source: 'tests/src/hashmap.rs', lines 27:0-27:16 *) -Inductive hashmap_List_t (T : Type) := -| Hashmap_List_Cons : usize -> T -> hashmap_List_t T -> hashmap_List_t T -| Hashmap_List_Nil : hashmap_List_t T -. - -Arguments Hashmap_List_Cons { _ }. -Arguments Hashmap_List_Nil { _ }. - -(** [hashmap_main::hashmap::HashMap] - Source: 'tests/src/hashmap.rs', lines 43:0-43:21 *) -Record hashmap_HashMap_t (T : Type) := -mkhashmap_HashMap_t { - hashmap_HashMap_num_entries : usize; - hashmap_HashMap_max_load_factor : (usize * usize); - hashmap_HashMap_max_load : usize; - hashmap_HashMap_slots : alloc_vec_Vec (hashmap_List_t T); -} -. - -Arguments mkhashmap_HashMap_t { _ }. -Arguments hashmap_HashMap_num_entries { _ }. -Arguments hashmap_HashMap_max_load_factor { _ }. -Arguments hashmap_HashMap_max_load { _ }. -Arguments hashmap_HashMap_slots { _ }. - -End HashmapMain_Types. diff --git a/tests/coq/hashmap_main/HashmapMain_TypesExternal.v b/tests/coq/hashmap_main/HashmapMain_TypesExternal.v deleted file mode 100644 index 28651c14..00000000 --- a/tests/coq/hashmap_main/HashmapMain_TypesExternal.v +++ /dev/null @@ -1,14 +0,0 @@ -(** [hashmap_main]: external types. --- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Module HashmapMain_TypesExternal. - -(** The state type used in the state-error monad *) -Axiom state : Type. - -End HashmapMain_TypesExternal. diff --git a/tests/coq/hashmap_main/HashmapMain_TypesExternal_Template.v b/tests/coq/hashmap_main/HashmapMain_TypesExternal_Template.v deleted file mode 100644 index 391b2775..00000000 --- a/tests/coq/hashmap_main/HashmapMain_TypesExternal_Template.v +++ /dev/null @@ -1,15 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: external types. --- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Module HashmapMain_TypesExternal_Template. - -(** The state type used in the state-error monad *) -Axiom state : Type. - -End HashmapMain_TypesExternal_Template. diff --git a/tests/coq/hashmap_main/Makefile b/tests/coq/hashmap_main/Makefile deleted file mode 100644 index 1a5aee4a..00000000 --- a/tests/coq/hashmap_main/Makefile +++ /dev/null @@ -1,23 +0,0 @@ -# This file was automatically generated - modify ../Makefile.template instead -# Makefile originally taken from coq-club - -%: Makefile.coq phony - +make -f Makefile.coq $@ - -all: Makefile.coq - +make -f Makefile.coq all - -clean: Makefile.coq - +make -f Makefile.coq clean - rm -f Makefile.coq - -Makefile.coq: _CoqProject Makefile - coq_makefile -f _CoqProject | sed 's/$$(COQCHK) $$(COQCHKFLAGS) $$(COQLIBS)/$$(COQCHK) $$(COQCHKFLAGS) $$(subst -Q,-R,$$(COQLIBS))/' > Makefile.coq - -_CoqProject: ; - -Makefile: ; - -phony: ; - -.PHONY: all clean phony diff --git a/tests/coq/hashmap_main/Primitives.v b/tests/coq/hashmap_main/Primitives.v deleted file mode 100644 index b29fce43..00000000 --- a/tests/coq/hashmap_main/Primitives.v +++ /dev/null @@ -1,981 +0,0 @@ -Require Import Lia. -Require Coq.Strings.Ascii. -Require Coq.Strings.String. -Require Import Coq.Program.Equality. -Require Import Coq.ZArith.ZArith. -Require Import Coq.ZArith.Znat. -Require Import List. -Import ListNotations. - -Module Primitives. - - (* TODO: use more *) -Declare Scope Primitives_scope. - -(*** Result *) - -Inductive error := - | Failure - | OutOfFuel. - -Inductive result A := - | Ok : A -> result A - | Fail_ : error -> result A. - -Arguments Ok {_} a. -Arguments Fail_ {_}. - -Definition bind {A B} (m: result A) (f: A -> result B) : result B := - match m with - | Fail_ e => Fail_ e - | Ok x => f x - end. - -Definition return_ {A: Type} (x: A) : result A := Ok x. -Definition fail_ {A: Type} (e: error) : result A := Fail_ e. - -Notation "x <- c1 ; c2" := (bind c1 (fun x => c2)) - (at level 61, c1 at next level, right associativity). - -(** Monadic assert *) -Definition massert (b: bool) : result unit := - if b then Ok tt else Fail_ Failure. - -(** Normalize and unwrap a successful result (used for globals) *) -Definition eval_result_refl {A} {x} (a: result A) (p: a = Ok x) : A := - match a as r return (r = Ok x -> A) with - | Ok a' => fun _ => a' - | Fail_ e => fun p' => - False_rect _ (eq_ind (Fail_ e) - (fun e : result A => - match e with - | Ok _ => False - | Fail_ e => True - end) - I (Ok x) p') - end p. - -Notation "x %global" := (eval_result_refl x eq_refl) (at level 40). -Notation "x %return" := (eval_result_refl x eq_refl) (at level 40). - -(* Sanity check *) -Check (if true then Ok (1 + 2) else Fail_ Failure)%global = 3. - -(*** Misc *) - -Definition string := Coq.Strings.String.string. -Definition char := Coq.Strings.Ascii.ascii. -Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte. - -Definition core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) . - -Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }. -Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }. - -(*** Scalars *) - -Definition i8_min : Z := -128%Z. -Definition i8_max : Z := 127%Z. -Definition i16_min : Z := -32768%Z. -Definition i16_max : Z := 32767%Z. -Definition i32_min : Z := -2147483648%Z. -Definition i32_max : Z := 2147483647%Z. -Definition i64_min : Z := -9223372036854775808%Z. -Definition i64_max : Z := 9223372036854775807%Z. -Definition i128_min : Z := -170141183460469231731687303715884105728%Z. -Definition i128_max : Z := 170141183460469231731687303715884105727%Z. -Definition u8_min : Z := 0%Z. -Definition u8_max : Z := 255%Z. -Definition u16_min : Z := 0%Z. -Definition u16_max : Z := 65535%Z. -Definition u32_min : Z := 0%Z. -Definition u32_max : Z := 4294967295%Z. -Definition u64_min : Z := 0%Z. -Definition u64_max : Z := 18446744073709551615%Z. -Definition u128_min : Z := 0%Z. -Definition u128_max : Z := 340282366920938463463374607431768211455%Z. - -(** The bounds of [isize] and [usize] vary with the architecture. *) -Axiom isize_min : Z. -Axiom isize_max : Z. -Definition usize_min : Z := 0%Z. -Axiom usize_max : Z. - -Open Scope Z_scope. - -(** We provide those lemmas to reason about the bounds of [isize] and [usize] *) -Axiom isize_min_bound : isize_min <= i32_min. -Axiom isize_max_bound : i32_max <= isize_max. -Axiom usize_max_bound : u32_max <= usize_max. - -Inductive scalar_ty := - | Isize - | I8 - | I16 - | I32 - | I64 - | I128 - | Usize - | U8 - | U16 - | U32 - | U64 - | U128 -. - -Definition scalar_min (ty: scalar_ty) : Z := - match ty with - | Isize => isize_min - | I8 => i8_min - | I16 => i16_min - | I32 => i32_min - | I64 => i64_min - | I128 => i128_min - | Usize => usize_min - | U8 => u8_min - | U16 => u16_min - | U32 => u32_min - | U64 => u64_min - | U128 => u128_min -end. - -Definition scalar_max (ty: scalar_ty) : Z := - match ty with - | Isize => isize_max - | I8 => i8_max - | I16 => i16_max - | I32 => i32_max - | I64 => i64_max - | I128 => i128_max - | Usize => usize_max - | U8 => u8_max - | U16 => u16_max - | U32 => u32_max - | U64 => u64_max - | U128 => u128_max -end. - -(** We use the following conservative bounds to make sure we can compute bound - checks in most situations *) -Definition scalar_min_cons (ty: scalar_ty) : Z := - match ty with - | Isize => i32_min - | Usize => u32_min - | _ => scalar_min ty -end. - -Definition scalar_max_cons (ty: scalar_ty) : Z := - match ty with - | Isize => i32_max - | Usize => u32_max - | _ => scalar_max ty -end. - -Lemma scalar_min_cons_valid : forall ty, scalar_min ty <= scalar_min_cons ty . -Proof. - destruct ty; unfold scalar_min_cons, scalar_min; try lia. - - pose isize_min_bound; lia. - - apply Z.le_refl. -Qed. - -Lemma scalar_max_cons_valid : forall ty, scalar_max ty >= scalar_max_cons ty . -Proof. - destruct ty; unfold scalar_max_cons, scalar_max; try lia. - - pose isize_max_bound; lia. - - pose usize_max_bound. lia. -Qed. - -Definition scalar (ty: scalar_ty) : Type := - { x: Z | scalar_min ty <= x <= scalar_max ty }. - -Definition to_Z {ty} (x: scalar ty) : Z := proj1_sig x. - -(** Bounds checks: we start by using the conservative bounds, to make sure we - can compute in most situations, then we use the real bounds (for [isize] - and [usize]). *) -Definition scalar_ge_min (ty: scalar_ty) (x: Z) : bool := - Z.leb (scalar_min_cons ty) x || Z.leb (scalar_min ty) x. - -Definition scalar_le_max (ty: scalar_ty) (x: Z) : bool := - Z.leb x (scalar_max_cons ty) || Z.leb x (scalar_max ty). - -Lemma scalar_ge_min_valid (ty: scalar_ty) (x: Z) : - scalar_ge_min ty x = true -> scalar_min ty <= x . -Proof. - unfold scalar_ge_min. - pose (scalar_min_cons_valid ty). - lia. -Qed. - -Lemma scalar_le_max_valid (ty: scalar_ty) (x: Z) : - scalar_le_max ty x = true -> x <= scalar_max ty . -Proof. - unfold scalar_le_max. - pose (scalar_max_cons_valid ty). - lia. -Qed. - -Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool := - scalar_ge_min ty x && scalar_le_max ty x . - -Lemma scalar_in_bounds_valid (ty: scalar_ty) (x: Z) : - scalar_in_bounds ty x = true -> scalar_min ty <= x <= scalar_max ty . -Proof. - unfold scalar_in_bounds. - intros H. - destruct (scalar_ge_min ty x) eqn:Hmin. - - destruct (scalar_le_max ty x) eqn:Hmax. - + pose (scalar_ge_min_valid ty x Hmin). - pose (scalar_le_max_valid ty x Hmax). - lia. - + inversion H. - - inversion H. -Qed. - -Import Sumbool. - -Definition mk_scalar (ty: scalar_ty) (x: Z) : result (scalar ty) := - match sumbool_of_bool (scalar_in_bounds ty x) with - | left H => Ok (exist _ x (scalar_in_bounds_valid _ _ H)) - | right _ => Fail_ Failure - end. - -Definition scalar_add {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x + to_Z y). - -Definition scalar_sub {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x - to_Z y). - -Definition scalar_mul {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x * to_Z y). - -Definition scalar_div {ty} (x y: scalar ty) : result (scalar ty) := - if to_Z y =? 0 then Fail_ Failure else - mk_scalar ty (to_Z x / to_Z y). - -Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (Z.rem (to_Z x) (to_Z y)). - -Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)). - -Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *) -Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *) -Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *) -Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *) -Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *) - -(** Cast an integer from a [src_ty] to a [tgt_ty] *) -(* TODO: check the semantics of casts in Rust *) -Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) := - mk_scalar tgt_ty (to_Z x). - -(* This can't fail, but for now we make all casts faillible (easier for the translation) *) -Definition scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) := - mk_scalar tgt_ty (if x then 1 else 0). - -(** Comparisons *) -Definition scalar_leb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool := - Z.leb (to_Z x) (to_Z y) . - -Definition scalar_ltb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool := - Z.ltb (to_Z x) (to_Z y) . - -Definition scalar_geb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool := - Z.geb (to_Z x) (to_Z y) . - -Definition scalar_gtb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool := - Z.gtb (to_Z x) (to_Z y) . - -Definition scalar_eqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool := - Z.eqb (to_Z x) (to_Z y) . - -Definition scalar_neqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool := - negb (Z.eqb (to_Z x) (to_Z y)) . - - -(** The scalar types *) -Definition isize := scalar Isize. -Definition i8 := scalar I8. -Definition i16 := scalar I16. -Definition i32 := scalar I32. -Definition i64 := scalar I64. -Definition i128 := scalar I128. -Definition usize := scalar Usize. -Definition u8 := scalar U8. -Definition u16 := scalar U16. -Definition u32 := scalar U32. -Definition u64 := scalar U64. -Definition u128 := scalar U128. - -(** Negaion *) -Definition isize_neg := @scalar_neg Isize. -Definition i8_neg := @scalar_neg I8. -Definition i16_neg := @scalar_neg I16. -Definition i32_neg := @scalar_neg I32. -Definition i64_neg := @scalar_neg I64. -Definition i128_neg := @scalar_neg I128. - -(** Division *) -Definition isize_div := @scalar_div Isize. -Definition i8_div := @scalar_div I8. -Definition i16_div := @scalar_div I16. -Definition i32_div := @scalar_div I32. -Definition i64_div := @scalar_div I64. -Definition i128_div := @scalar_div I128. -Definition usize_div := @scalar_div Usize. -Definition u8_div := @scalar_div U8. -Definition u16_div := @scalar_div U16. -Definition u32_div := @scalar_div U32. -Definition u64_div := @scalar_div U64. -Definition u128_div := @scalar_div U128. - -(** Remainder *) -Definition isize_rem := @scalar_rem Isize. -Definition i8_rem := @scalar_rem I8. -Definition i16_rem := @scalar_rem I16. -Definition i32_rem := @scalar_rem I32. -Definition i64_rem := @scalar_rem I64. -Definition i128_rem := @scalar_rem I128. -Definition usize_rem := @scalar_rem Usize. -Definition u8_rem := @scalar_rem U8. -Definition u16_rem := @scalar_rem U16. -Definition u32_rem := @scalar_rem U32. -Definition u64_rem := @scalar_rem U64. -Definition u128_rem := @scalar_rem U128. - -(** Addition *) -Definition isize_add := @scalar_add Isize. -Definition i8_add := @scalar_add I8. -Definition i16_add := @scalar_add I16. -Definition i32_add := @scalar_add I32. -Definition i64_add := @scalar_add I64. -Definition i128_add := @scalar_add I128. -Definition usize_add := @scalar_add Usize. -Definition u8_add := @scalar_add U8. -Definition u16_add := @scalar_add U16. -Definition u32_add := @scalar_add U32. -Definition u64_add := @scalar_add U64. -Definition u128_add := @scalar_add U128. - -(** Substraction *) -Definition isize_sub := @scalar_sub Isize. -Definition i8_sub := @scalar_sub I8. -Definition i16_sub := @scalar_sub I16. -Definition i32_sub := @scalar_sub I32. -Definition i64_sub := @scalar_sub I64. -Definition i128_sub := @scalar_sub I128. -Definition usize_sub := @scalar_sub Usize. -Definition u8_sub := @scalar_sub U8. -Definition u16_sub := @scalar_sub U16. -Definition u32_sub := @scalar_sub U32. -Definition u64_sub := @scalar_sub U64. -Definition u128_sub := @scalar_sub U128. - -(** Multiplication *) -Definition isize_mul := @scalar_mul Isize. -Definition i8_mul := @scalar_mul I8. -Definition i16_mul := @scalar_mul I16. -Definition i32_mul := @scalar_mul I32. -Definition i64_mul := @scalar_mul I64. -Definition i128_mul := @scalar_mul I128. -Definition usize_mul := @scalar_mul Usize. -Definition u8_mul := @scalar_mul U8. -Definition u16_mul := @scalar_mul U16. -Definition u32_mul := @scalar_mul U32. -Definition u64_mul := @scalar_mul U64. -Definition u128_mul := @scalar_mul U128. - -(** Xor *) -Definition u8_xor := @scalar_xor U8. -Definition u16_xor := @scalar_xor U16. -Definition u32_xor := @scalar_xor U32. -Definition u64_xor := @scalar_xor U64. -Definition u128_xor := @scalar_xor U128. -Definition usize_xor := @scalar_xor Usize. -Definition i8_xor := @scalar_xor I8. -Definition i16_xor := @scalar_xor I16. -Definition i32_xor := @scalar_xor I32. -Definition i64_xor := @scalar_xor I64. -Definition i128_xor := @scalar_xor I128. -Definition isize_xor := @scalar_xor Isize. - -(** Or *) -Definition u8_or := @scalar_or U8. -Definition u16_or := @scalar_or U16. -Definition u32_or := @scalar_or U32. -Definition u64_or := @scalar_or U64. -Definition u128_or := @scalar_or U128. -Definition usize_or := @scalar_or Usize. -Definition i8_or := @scalar_or I8. -Definition i16_or := @scalar_or I16. -Definition i32_or := @scalar_or I32. -Definition i64_or := @scalar_or I64. -Definition i128_or := @scalar_or I128. -Definition isize_or := @scalar_or Isize. - -(** And *) -Definition u8_and := @scalar_and U8. -Definition u16_and := @scalar_and U16. -Definition u32_and := @scalar_and U32. -Definition u64_and := @scalar_and U64. -Definition u128_and := @scalar_and U128. -Definition usize_and := @scalar_and Usize. -Definition i8_and := @scalar_and I8. -Definition i16_and := @scalar_and I16. -Definition i32_and := @scalar_and I32. -Definition i64_and := @scalar_and I64. -Definition i128_and := @scalar_and I128. -Definition isize_and := @scalar_and Isize. - -(** Shift left *) -Definition u8_shl {ty} := @scalar_shl U8 ty. -Definition u16_shl {ty} := @scalar_shl U16 ty. -Definition u32_shl {ty} := @scalar_shl U32 ty. -Definition u64_shl {ty} := @scalar_shl U64 ty. -Definition u128_shl {ty} := @scalar_shl U128 ty. -Definition usize_shl {ty} := @scalar_shl Usize ty. -Definition i8_shl {ty} := @scalar_shl I8 ty. -Definition i16_shl {ty} := @scalar_shl I16 ty. -Definition i32_shl {ty} := @scalar_shl I32 ty. -Definition i64_shl {ty} := @scalar_shl I64 ty. -Definition i128_shl {ty} := @scalar_shl I128 ty. -Definition isize_shl {ty} := @scalar_shl Isize ty. - -(** Shift right *) -Definition u8_shr {ty} := @scalar_shr U8 ty. -Definition u16_shr {ty} := @scalar_shr U16 ty. -Definition u32_shr {ty} := @scalar_shr U32 ty. -Definition u64_shr {ty} := @scalar_shr U64 ty. -Definition u128_shr {ty} := @scalar_shr U128 ty. -Definition usize_shr {ty} := @scalar_shr Usize ty. -Definition i8_shr {ty} := @scalar_shr I8 ty. -Definition i16_shr {ty} := @scalar_shr I16 ty. -Definition i32_shr {ty} := @scalar_shr I32 ty. -Definition i64_shr {ty} := @scalar_shr I64 ty. -Definition i128_shr {ty} := @scalar_shr I128 ty. -Definition isize_shr {ty} := @scalar_shr Isize ty. - -(** Small utility *) -Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x). - -(** Notations *) -Notation "x %isize" := ((mk_scalar Isize x)%return) (at level 9). -Notation "x %i8" := ((mk_scalar I8 x)%return) (at level 9). -Notation "x %i16" := ((mk_scalar I16 x)%return) (at level 9). -Notation "x %i32" := ((mk_scalar I32 x)%return) (at level 9). -Notation "x %i64" := ((mk_scalar I64 x)%return) (at level 9). -Notation "x %i128" := ((mk_scalar I128 x)%return) (at level 9). -Notation "x %usize" := ((mk_scalar Usize x)%return) (at level 9). -Notation "x %u8" := ((mk_scalar U8 x)%return) (at level 9). -Notation "x %u16" := ((mk_scalar U16 x)%return) (at level 9). -Notation "x %u32" := ((mk_scalar U32 x)%return) (at level 9). -Notation "x %u64" := ((mk_scalar U64 x)%return) (at level 9). -Notation "x %u128" := ((mk_scalar U128 x)%return) (at level 9). - -Notation "x s= y" := (scalar_eqb x y) (at level 80) : Primitives_scope. -Notation "x s<> y" := (scalar_neqb x y) (at level 80) : Primitives_scope. -Notation "x s<= y" := (scalar_leb x y) (at level 80) : Primitives_scope. -Notation "x s< y" := (scalar_ltb x y) (at level 80) : Primitives_scope. -Notation "x s>= y" := (scalar_geb x y) (at level 80) : Primitives_scope. -Notation "x s> y" := (scalar_gtb x y) (at level 80) : Primitives_scope. - -(** Constants *) -Definition core_u8_max := u8_max %u32. -Definition core_u16_max := u16_max %u32. -Definition core_u32_max := u32_max %u32. -Definition core_u64_max := u64_max %u64. -Definition core_u128_max := u64_max %u128. -Axiom core_usize_max : usize. (** TODO *) -Definition core_i8_max := i8_max %i32. -Definition core_i16_max := i16_max %i32. -Definition core_i32_max := i32_max %i32. -Definition core_i64_max := i64_max %i64. -Definition core_i128_max := i64_max %i128. -Axiom core_isize_max : isize. (** TODO *) - -(*** core *) - -(** Trait declaration: [core::clone::Clone] *) -Record core_clone_Clone (self : Type) := { - clone : self -> result self -}. - -Definition core_clone_impls_CloneBool_clone (b : bool) : bool := b. - -Definition core_clone_CloneBool : core_clone_Clone bool := {| - clone := fun b => Ok (core_clone_impls_CloneBool_clone b) -|}. - -Definition core_clone_impls_CloneUsize_clone (x : usize) : usize := x. -Definition core_clone_impls_CloneU8_clone (x : u8) : u8 := x. -Definition core_clone_impls_CloneU16_clone (x : u16) : u16 := x. -Definition core_clone_impls_CloneU32_clone (x : u32) : u32 := x. -Definition core_clone_impls_CloneU64_clone (x : u64) : u64 := x. -Definition core_clone_impls_CloneU128_clone (x : u128) : u128 := x. - -Definition core_clone_impls_CloneIsize_clone (x : isize) : isize := x. -Definition core_clone_impls_CloneI8_clone (x : i8) : i8 := x. -Definition core_clone_impls_CloneI16_clone (x : i16) : i16 := x. -Definition core_clone_impls_CloneI32_clone (x : i32) : i32 := x. -Definition core_clone_impls_CloneI64_clone (x : i64) : i64 := x. -Definition core_clone_impls_CloneI128_clone (x : i128) : i128 := x. - -Definition core_clone_CloneUsize : core_clone_Clone usize := {| - clone := fun x => Ok (core_clone_impls_CloneUsize_clone x) -|}. - -Definition core_clone_CloneU8 : core_clone_Clone u8 := {| - clone := fun x => Ok (core_clone_impls_CloneU8_clone x) -|}. - -Definition core_clone_CloneU16 : core_clone_Clone u16 := {| - clone := fun x => Ok (core_clone_impls_CloneU16_clone x) -|}. - -Definition core_clone_CloneU32 : core_clone_Clone u32 := {| - clone := fun x => Ok (core_clone_impls_CloneU32_clone x) -|}. - -Definition core_clone_CloneU64 : core_clone_Clone u64 := {| - clone := fun x => Ok (core_clone_impls_CloneU64_clone x) -|}. - -Definition core_clone_CloneU128 : core_clone_Clone u128 := {| - clone := fun x => Ok (core_clone_impls_CloneU128_clone x) -|}. - -Definition core_clone_CloneIsize : core_clone_Clone isize := {| - clone := fun x => Ok (core_clone_impls_CloneIsize_clone x) -|}. - -Definition core_clone_CloneI8 : core_clone_Clone i8 := {| - clone := fun x => Ok (core_clone_impls_CloneI8_clone x) -|}. - -Definition core_clone_CloneI16 : core_clone_Clone i16 := {| - clone := fun x => Ok (core_clone_impls_CloneI16_clone x) -|}. - -Definition core_clone_CloneI32 : core_clone_Clone i32 := {| - clone := fun x => Ok (core_clone_impls_CloneI32_clone x) -|}. - -Definition core_clone_CloneI64 : core_clone_Clone i64 := {| - clone := fun x => Ok (core_clone_impls_CloneI64_clone x) -|}. - -Definition core_clone_CloneI128 : core_clone_Clone i128 := {| - clone := fun x => Ok (core_clone_impls_CloneI128_clone x) -|}. - -(** [core::option::{core::option::Option}::unwrap] *) -Definition core_option_Option_unwrap (T : Type) (x : option T) : result T := - match x with - | None => Fail_ Failure - | Some x => Ok x - end. - -(*** core::ops *) - -(* Trait declaration: [core::ops::index::Index] *) -Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index { - core_ops_index_Index_Output : Type; - core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output; -}. -Arguments mk_core_ops_index_Index {_ _}. -Arguments core_ops_index_Index_Output {_ _}. -Arguments core_ops_index_Index_index {_ _}. - -(* Trait declaration: [core::ops::index::IndexMut] *) -Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut { - core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx; - core_ops_index_IndexMut_index_mut : - Self -> - Idx -> - result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) * - (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self)); -}. -Arguments mk_core_ops_index_IndexMut {_ _}. -Arguments core_ops_index_IndexMut_indexInst {_ _}. -Arguments core_ops_index_IndexMut_index_mut {_ _}. - -(* Trait declaration [core::ops::deref::Deref] *) -Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref { - core_ops_deref_Deref_target : Type; - core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target; -}. -Arguments mk_core_ops_deref_Deref {_}. -Arguments core_ops_deref_Deref_target {_}. -Arguments core_ops_deref_Deref_deref {_}. - -(* Trait declaration [core::ops::deref::DerefMut] *) -Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut { - core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self; - core_ops_deref_DerefMut_deref_mut : - Self -> - result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) * - (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self)); -}. -Arguments mk_core_ops_deref_DerefMut {_}. -Arguments core_ops_deref_DerefMut_derefInst {_}. -Arguments core_ops_deref_DerefMut_deref_mut {_}. - -Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range { - core_ops_range_Range_start : T; - core_ops_range_Range_end_ : T; -}. -Arguments mk_core_ops_range_Range {_}. -Arguments core_ops_range_Range_start {_}. -Arguments core_ops_range_Range_end_ {_}. - -(*** [alloc] *) - -Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Ok x. -Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) := - Ok (x, fun x => Ok x). - -(* Trait instance *) -Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {| - core_ops_deref_Deref_target := Self; - core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self; -|}. - -(* Trait instance *) -Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {| - core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self; - core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self; -|}. - - -(*** Arrays *) -Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}. - -Lemma le_0_usize_max : 0 <= usize_max. -Proof. - pose (H := usize_max_bound). - unfold u32_max in H. - lia. -Qed. - -Lemma eqb_imp_eq (x y : Z) : Z.eqb x y = true -> x = y. -Proof. - lia. -Qed. - -(* TODO: finish the definitions *) -Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n. - -(* For initialization *) -Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n. - -Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T. -Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n). - -Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) : - result (T * (T -> result (array T n))) := - match array_index_usize T n a i with - | Fail_ e => Fail_ e - | Ok x => Ok (x, array_update_usize T n a i) - end. - -(*** Slice *) -Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}. - -Axiom slice_len : forall (T : Type) (s : slice T), usize. -Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T. -Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T). - -Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) : - result (T * (T -> result (slice T))) := - match slice_index_usize T s i with - | Fail_ e => Fail_ e - | Ok x => Ok (x, slice_update_usize T s i) - end. - -(*** Subslices *) - -Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T). -Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n). - -Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) : - result (slice T * (slice T -> result (array T n))) := - match array_to_slice T n a with - | Fail_ e => Fail_ e - | Ok x => Ok (x, array_from_slice T n a) - end. - -Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T). -Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n). - -Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T). -Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T). - -(*** Vectors *) - -Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }. - -Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v. - -Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)). - -Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max). - -Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max. -Proof. - unfold alloc_vec_Vec_length, usize_min. - split. - - lia. - - apply (proj2_sig v). -Qed. - -Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize := - exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v). - -Fixpoint list_update {A} (l: list A) (n: nat) (a: A) - : list A := - match l with - | [] => [] - | x :: t => match n with - | 0%nat => a :: t - | S m => x :: (list_update t m a) -end end. - -Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) := - l <- f (alloc_vec_Vec_to_list v) ; - match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with - | left H => Ok (exist _ l (scalar_le_max_valid _ _ H)) - | right _ => Fail_ Failure - end. - -Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) := - alloc_vec_Vec_bind v (fun l => Ok (l ++ [x])). - -Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) := - alloc_vec_Vec_bind v (fun l => - if to_Z i result (alloc_vec_Vec T))) := - match alloc_vec_Vec_index_usize v i with - | Ok x => - Ok (x, alloc_vec_Vec_update_usize v i) - | Fail_ e => Fail_ e - end. - -(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *) -Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit. - -(* Trait declaration: [core::slice::index::SliceIndex] *) -Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex { - core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self; - core_slice_index_SliceIndex_Output : Type; - core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output); - core_slice_index_SliceIndex_get_mut : - Self -> T -> result (option core_slice_index_SliceIndex_Output * (option core_slice_index_SliceIndex_Output -> result T)); - core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output); - core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output); - core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output; - core_slice_index_SliceIndex_index_mut : - Self -> T -> result (core_slice_index_SliceIndex_Output * (core_slice_index_SliceIndex_Output -> result T)); -}. -Arguments mk_core_slice_index_SliceIndex {_ _}. -Arguments core_slice_index_SliceIndex_sealedInst {_ _}. -Arguments core_slice_index_SliceIndex_Output {_ _}. -Arguments core_slice_index_SliceIndex_get {_ _}. -Arguments core_slice_index_SliceIndex_get_mut {_ _}. -Arguments core_slice_index_SliceIndex_get_unchecked {_ _}. -Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}. -Arguments core_slice_index_SliceIndex_index {_ _}. -Arguments core_slice_index_SliceIndex_index_mut {_ _}. - -(* [core::slice::index::[T]::index]: forward function *) -Definition core_slice_index_Slice_index - (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)) - (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) := - x <- inst.(core_slice_index_SliceIndex_get) i s; - match x with - | None => Fail_ Failure - | Some x => Ok x - end. - -(* [core::slice::index::Range:::get]: forward function *) -Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)). - -(* [core::slice::index::Range::get_mut]: forward function *) -Axiom core_slice_index_RangeUsize_get_mut : - forall (T : Type), - core_ops_range_Range usize -> slice T -> - result (option (slice T) * (option (slice T) -> result (slice T))). - -(* [core::slice::index::Range::get_unchecked]: forward function *) -Definition core_slice_index_RangeUsize_get_unchecked - (T : Type) : - core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) := - (* Don't know what the model should be - for now we always fail to make - sure code which uses it fails *) - fun _ _ => Fail_ Failure. - -(* [core::slice::index::Range::get_unchecked_mut]: forward function *) -Definition core_slice_index_RangeUsize_get_unchecked_mut - (T : Type) : - core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) := - (* Don't know what the model should be - for now we always fail to make - sure code which uses it fails *) - fun _ _ => Fail_ Failure. - -(* [core::slice::index::Range::index]: forward function *) -Axiom core_slice_index_RangeUsize_index : - forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T). - -(* [core::slice::index::Range::index_mut]: forward function *) -Axiom core_slice_index_RangeUsize_index_mut : - forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T * (slice T -> result (slice T))). - -(* [core::slice::index::[T]::index_mut]: forward function *) -Axiom core_slice_index_Slice_index_mut : - forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)), - slice T -> Idx -> - result (inst.(core_slice_index_SliceIndex_Output) * - (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))). - -(* [core::array::[T; N]::index]: forward function *) -Axiom core_array_Array_index : - forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx) - (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output). - -(* [core::array::[T; N]::index_mut]: forward function *) -Axiom core_array_Array_index_mut : - forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx) - (a : array T N) (i : Idx), - result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) * - (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))). - -(* Trait implementation: [core::slice::index::private_slice_index::Range] *) -Definition core_slice_index_private_slice_index_SealedRangeUsizeInst - : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt. - -(* Trait implementation: [core::slice::index::Range] *) -Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) : - core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {| - core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst; - core_slice_index_SliceIndex_Output := slice T; - core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T; - core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T; - core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T; - core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T; - core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T; - core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T; -|}. - -(* Trait implementation: [core::slice::index::[T]] *) -Definition core_ops_index_IndexSliceTIInst (T Idx : Type) - (inst : core_slice_index_SliceIndex Idx (slice T)) : - core_ops_index_Index (slice T) Idx := {| - core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output); - core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst; -|}. - -(* Trait implementation: [core::slice::index::[T]] *) -Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type) - (inst : core_slice_index_SliceIndex Idx (slice T)) : - core_ops_index_IndexMut (slice T) Idx := {| - core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst; - core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst; -|}. - -(* Trait implementation: [core::array::[T; N]] *) -Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize) - (inst : core_ops_index_Index (slice T) Idx) : - core_ops_index_Index (array T N) Idx := {| - core_ops_index_Index_Output := inst.(core_ops_index_Index_Output); - core_ops_index_Index_index := core_array_Array_index T Idx N inst; -|}. - -(* Trait implementation: [core::array::[T; N]] *) -Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize) - (inst : core_ops_index_IndexMut (slice T) Idx) : - core_ops_index_IndexMut (array T N) Idx := {| - core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst); - core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst; -|}. - -(* [core::slice::index::usize::get]: forward function *) -Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T). - -(* [core::slice::index::usize::get_mut]: forward function *) -Axiom core_slice_index_usize_get_mut : - forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))). - -(* [core::slice::index::usize::get_unchecked]: forward function *) -Axiom core_slice_index_usize_get_unchecked : - forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T). - -(* [core::slice::index::usize::get_unchecked_mut]: forward function *) -Axiom core_slice_index_usize_get_unchecked_mut : - forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T). - -(* [core::slice::index::usize::index]: forward function *) -Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T. - -(* [core::slice::index::usize::index_mut]: forward function *) -Axiom core_slice_index_usize_index_mut : - forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))). - -(* Trait implementation: [core::slice::index::private_slice_index::usize] *) -Definition core_slice_index_private_slice_index_SealedUsizeInst - : core_slice_index_private_slice_index_Sealed usize := tt. - -(* Trait implementation: [core::slice::index::usize] *) -Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) : - core_slice_index_SliceIndex usize (slice T) := {| - core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst; - core_slice_index_SliceIndex_Output := T; - core_slice_index_SliceIndex_get := core_slice_index_usize_get T; - core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T; - core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T; - core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T; - core_slice_index_SliceIndex_index := core_slice_index_usize_index T; - core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T; -|}. - -(* [alloc::vec::Vec::index]: forward function *) -Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)) - (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output). - -(* [alloc::vec::Vec::index_mut]: forward function *) -Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)) - (Self : alloc_vec_Vec T) (i : Idx), - result (inst.(core_slice_index_SliceIndex_Output) * - (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))). - -(* Trait implementation: [alloc::vec::Vec] *) -Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type) - (inst : core_slice_index_SliceIndex Idx (slice T)) : - core_ops_index_Index (alloc_vec_Vec T) Idx := {| - core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output); - core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst; -|}. - -(* Trait implementation: [alloc::vec::Vec] *) -Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type) - (inst : core_slice_index_SliceIndex Idx (slice T)) : - core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {| - core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst; - core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst; -|}. - -(*** Theorems *) - -Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a), - alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i = - alloc_vec_Vec_index_usize v i. - -Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a), - alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i = - alloc_vec_Vec_index_mut_usize v i. - -End Primitives. diff --git a/tests/coq/hashmap_main/_CoqProject b/tests/coq/hashmap_main/_CoqProject deleted file mode 100644 index d73541d9..00000000 --- a/tests/coq/hashmap_main/_CoqProject +++ /dev/null @@ -1,12 +0,0 @@ -# This file was automatically generated - see ../Makefile --R . Lib --arg -w --arg all - -HashmapMain_Types.v -HashmapMain_FunsExternal_Template.v -Primitives.v -HashmapMain_Funs.v -HashmapMain_TypesExternal.v -HashmapMain_FunsExternal.v -HashmapMain_TypesExternal_Template.v diff --git a/tests/fstar/hashmap/Hashmap.Clauses.Template.fst b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst index 3119ded8..57003613 100644 --- a/tests/fstar/hashmap/Hashmap.Clauses.Template.fst +++ b/tests/fstar/hashmap/Hashmap.Clauses.Template.fst @@ -7,63 +7,63 @@ open Hashmap.Types #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [hashmap::{hashmap::HashMap}::allocate_slots]: decreases clause - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) + Source: 'tests/src/hashmap.rs', lines 60:4-66:5 *) unfold let hashMap_allocate_slots_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) : nat = admit () (** [hashmap::{hashmap::HashMap}::clear]: decreases clause - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) + Source: 'tests/src/hashmap.rs', lines 90:4-98:5 *) unfold let hashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) : nat = admit () (** [hashmap::{hashmap::HashMap}::insert_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) + Source: 'tests/src/hashmap.rs', lines 107:4-124:5 *) unfold let hashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t) (ls : list_t t) : nat = admit () (** [hashmap::{hashmap::HashMap}::move_elements_from_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) + Source: 'tests/src/hashmap.rs', lines 193:4-206:5 *) unfold let hashMap_move_elements_from_list_loop_decreases (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : nat = admit () (** [hashmap::{hashmap::HashMap}::move_elements]: decreases clause - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) + Source: 'tests/src/hashmap.rs', lines 181:4-190:5 *) unfold let hashMap_move_elements_loop_decreases (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t)) (i : usize) : nat = admit () (** [hashmap::{hashmap::HashMap}::contains_key_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) + Source: 'tests/src/hashmap.rs', lines 216:4-229:5 *) unfold let hashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize) (ls : list_t t) : nat = admit () (** [hashmap::{hashmap::HashMap}::get_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) + Source: 'tests/src/hashmap.rs', lines 234:4-247:5 *) unfold let hashMap_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : list_t t) : nat = admit () (** [hashmap::{hashmap::HashMap}::get_mut_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) + Source: 'tests/src/hashmap.rs', lines 255:4-264:5 *) unfold let hashMap_get_mut_in_list_loop_decreases (t : Type0) (ls : list_t t) (key : usize) : nat = admit () (** [hashmap::{hashmap::HashMap}::remove_from_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) + Source: 'tests/src/hashmap.rs', lines 275:4-301:5 *) unfold let hashMap_remove_from_list_loop_decreases (t : Type0) (key : usize) (ls : list_t t) : nat = diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst index 06cdf7f3..a85be4ed 100644 --- a/tests/fstar/hashmap/Hashmap.Funs.fst +++ b/tests/fstar/hashmap/Hashmap.Funs.fst @@ -3,17 +3,18 @@ module Hashmap.Funs open Primitives include Hashmap.Types +include Hashmap.FunsExternal include Hashmap.Clauses #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [hashmap::hash_key]: - Source: 'tests/src/hashmap.rs', lines 35:0-35:32 *) + Source: 'tests/src/hashmap.rs', lines 37:0-37:32 *) let hash_key (k : usize) : result usize = Ok k (** [hashmap::{hashmap::HashMap}::allocate_slots]: loop 0: - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) + Source: 'tests/src/hashmap.rs', lines 60:4-66:5 *) let rec hashMap_allocate_slots_loop (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) : Tot (result (alloc_vec_Vec (list_t t))) @@ -27,7 +28,7 @@ let rec hashMap_allocate_slots_loop else Ok slots (** [hashmap::{hashmap::HashMap}::allocate_slots]: - Source: 'tests/src/hashmap.rs', lines 58:4-58:76 *) + Source: 'tests/src/hashmap.rs', lines 60:4-60:76 *) let hashMap_allocate_slots (t : Type0) (slots : alloc_vec_Vec (list_t t)) (n : usize) : result (alloc_vec_Vec (list_t t)) @@ -35,7 +36,7 @@ let hashMap_allocate_slots hashMap_allocate_slots_loop t slots n (** [hashmap::{hashmap::HashMap}::new_with_capacity]: - Source: 'tests/src/hashmap.rs', lines 67:4-71:13 *) + Source: 'tests/src/hashmap.rs', lines 69:4-73:13 *) let hashMap_new_with_capacity (t : Type0) (capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) : @@ -54,12 +55,12 @@ let hashMap_new_with_capacity } (** [hashmap::{hashmap::HashMap}::new]: - Source: 'tests/src/hashmap.rs', lines 83:4-83:24 *) + Source: 'tests/src/hashmap.rs', lines 85:4-85:24 *) let hashMap_new (t : Type0) : result (hashMap_t t) = hashMap_new_with_capacity t 32 4 5 (** [hashmap::{hashmap::HashMap}::clear]: loop 0: - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) + Source: 'tests/src/hashmap.rs', lines 90:4-98:5 *) let rec hashMap_clear_loop (t : Type0) (slots : alloc_vec_Vec (list_t t)) (i : usize) : Tot (result (alloc_vec_Vec (list_t t))) @@ -77,18 +78,18 @@ let rec hashMap_clear_loop else Ok slots (** [hashmap::{hashmap::HashMap}::clear]: - Source: 'tests/src/hashmap.rs', lines 88:4-88:27 *) + Source: 'tests/src/hashmap.rs', lines 90:4-90:27 *) let hashMap_clear (t : Type0) (self : hashMap_t t) : result (hashMap_t t) = let* hm = hashMap_clear_loop t self.slots 0 in Ok { self with num_entries = 0; slots = hm } (** [hashmap::{hashmap::HashMap}::len]: - Source: 'tests/src/hashmap.rs', lines 98:4-98:30 *) + Source: 'tests/src/hashmap.rs', lines 100:4-100:30 *) let hashMap_len (t : Type0) (self : hashMap_t t) : result usize = Ok self.num_entries (** [hashmap::{hashmap::HashMap}::insert_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) + Source: 'tests/src/hashmap.rs', lines 107:4-124:5 *) let rec hashMap_insert_in_list_loop (t : Type0) (key : usize) (value : t) (ls : list_t t) : Tot (result (bool & (list_t t))) @@ -105,7 +106,7 @@ let rec hashMap_insert_in_list_loop end (** [hashmap::{hashmap::HashMap}::insert_in_list]: - Source: 'tests/src/hashmap.rs', lines 105:4-105:71 *) + Source: 'tests/src/hashmap.rs', lines 107:4-107:71 *) let hashMap_insert_in_list (t : Type0) (key : usize) (value : t) (ls : list_t t) : result (bool & (list_t t)) @@ -113,7 +114,7 @@ let hashMap_insert_in_list hashMap_insert_in_list_loop t key value ls (** [hashmap::{hashmap::HashMap}::insert_no_resize]: - Source: 'tests/src/hashmap.rs', lines 125:4-125:54 *) + Source: 'tests/src/hashmap.rs', lines 127:4-127:54 *) let hashMap_insert_no_resize (t : Type0) (self : hashMap_t t) (key : usize) (value : t) : result (hashMap_t t) @@ -134,7 +135,7 @@ let hashMap_insert_no_resize else let* v = index_mut_back l1 in Ok { self with slots = v } (** [hashmap::{hashmap::HashMap}::move_elements_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) + Source: 'tests/src/hashmap.rs', lines 193:4-206:5 *) let rec hashMap_move_elements_from_list_loop (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : Tot (result (hashMap_t t)) @@ -148,13 +149,13 @@ let rec hashMap_move_elements_from_list_loop end (** [hashmap::{hashmap::HashMap}::move_elements_from_list]: - Source: 'tests/src/hashmap.rs', lines 191:4-191:72 *) + Source: 'tests/src/hashmap.rs', lines 193:4-193:72 *) let hashMap_move_elements_from_list (t : Type0) (ntable : hashMap_t t) (ls : list_t t) : result (hashMap_t t) = hashMap_move_elements_from_list_loop t ntable ls (** [hashmap::{hashmap::HashMap}::move_elements]: loop 0: - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) + Source: 'tests/src/hashmap.rs', lines 181:4-190:5 *) let rec hashMap_move_elements_loop (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t)) (i : usize) : @@ -175,7 +176,7 @@ let rec hashMap_move_elements_loop else Ok (ntable, slots) (** [hashmap::{hashmap::HashMap}::move_elements]: - Source: 'tests/src/hashmap.rs', lines 179:4-179:95 *) + Source: 'tests/src/hashmap.rs', lines 181:4-181:95 *) let hashMap_move_elements (t : Type0) (ntable : hashMap_t t) (slots : alloc_vec_Vec (list_t t)) (i : usize) : @@ -184,7 +185,7 @@ let hashMap_move_elements hashMap_move_elements_loop t ntable slots i (** [hashmap::{hashmap::HashMap}::try_resize]: - Source: 'tests/src/hashmap.rs', lines 148:4-148:28 *) + Source: 'tests/src/hashmap.rs', lines 150:4-150:28 *) let hashMap_try_resize (t : Type0) (self : hashMap_t t) : result (hashMap_t t) = let* max_usize = scalar_cast U32 Usize core_u32_max in @@ -204,7 +205,7 @@ let hashMap_try_resize else Ok { self with max_load_factor = (i, i1) } (** [hashmap::{hashmap::HashMap}::insert]: - Source: 'tests/src/hashmap.rs', lines 137:4-137:48 *) + Source: 'tests/src/hashmap.rs', lines 139:4-139:48 *) let hashMap_insert (t : Type0) (self : hashMap_t t) (key : usize) (value : t) : result (hashMap_t t) @@ -214,7 +215,7 @@ let hashMap_insert if i > self1.max_load then hashMap_try_resize t self1 else Ok self1 (** [hashmap::{hashmap::HashMap}::contains_key_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) + Source: 'tests/src/hashmap.rs', lines 216:4-229:5 *) let rec hashMap_contains_key_in_list_loop (t : Type0) (key : usize) (ls : list_t t) : Tot (result bool) @@ -227,13 +228,13 @@ let rec hashMap_contains_key_in_list_loop end (** [hashmap::{hashmap::HashMap}::contains_key_in_list]: - Source: 'tests/src/hashmap.rs', lines 214:4-214:68 *) + Source: 'tests/src/hashmap.rs', lines 216:4-216:68 *) let hashMap_contains_key_in_list (t : Type0) (key : usize) (ls : list_t t) : result bool = hashMap_contains_key_in_list_loop t key ls (** [hashmap::{hashmap::HashMap}::contains_key]: - Source: 'tests/src/hashmap.rs', lines 207:4-207:49 *) + Source: 'tests/src/hashmap.rs', lines 209:4-209:49 *) let hashMap_contains_key (t : Type0) (self : hashMap_t t) (key : usize) : result bool = let* hash = hash_key key in @@ -246,7 +247,7 @@ let hashMap_contains_key hashMap_contains_key_in_list t key l (** [hashmap::{hashmap::HashMap}::get_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) + Source: 'tests/src/hashmap.rs', lines 234:4-247:5 *) let rec hashMap_get_in_list_loop (t : Type0) (key : usize) (ls : list_t t) : Tot (result t) (decreases (hashMap_get_in_list_loop_decreases t key ls)) @@ -258,12 +259,12 @@ let rec hashMap_get_in_list_loop end (** [hashmap::{hashmap::HashMap}::get_in_list]: - Source: 'tests/src/hashmap.rs', lines 232:4-232:70 *) + Source: 'tests/src/hashmap.rs', lines 234:4-234:70 *) let hashMap_get_in_list (t : Type0) (key : usize) (ls : list_t t) : result t = hashMap_get_in_list_loop t key ls (** [hashmap::{hashmap::HashMap}::get]: - Source: 'tests/src/hashmap.rs', lines 247:4-247:55 *) + Source: 'tests/src/hashmap.rs', lines 249:4-249:55 *) let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t = let* hash = hash_key key in let i = alloc_vec_Vec_len (list_t t) self.slots in @@ -275,7 +276,7 @@ let hashMap_get (t : Type0) (self : hashMap_t t) (key : usize) : result t = hashMap_get_in_list t key l (** [hashmap::{hashmap::HashMap}::get_mut_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) + Source: 'tests/src/hashmap.rs', lines 255:4-264:5 *) let rec hashMap_get_mut_in_list_loop (t : Type0) (ls : list_t t) (key : usize) : Tot (result (t & (t -> result (list_t t)))) @@ -294,7 +295,7 @@ let rec hashMap_get_mut_in_list_loop end (** [hashmap::{hashmap::HashMap}::get_mut_in_list]: - Source: 'tests/src/hashmap.rs', lines 253:4-253:86 *) + Source: 'tests/src/hashmap.rs', lines 255:4-255:86 *) let hashMap_get_mut_in_list (t : Type0) (ls : list_t t) (key : usize) : result (t & (t -> result (list_t t))) @@ -302,7 +303,7 @@ let hashMap_get_mut_in_list hashMap_get_mut_in_list_loop t ls key (** [hashmap::{hashmap::HashMap}::get_mut]: - Source: 'tests/src/hashmap.rs', lines 265:4-265:67 *) + Source: 'tests/src/hashmap.rs', lines 267:4-267:67 *) let hashMap_get_mut (t : Type0) (self : hashMap_t t) (key : usize) : result (t & (t -> result (hashMap_t t))) @@ -323,7 +324,7 @@ let hashMap_get_mut Ok (x, back) (** [hashmap::{hashmap::HashMap}::remove_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) + Source: 'tests/src/hashmap.rs', lines 275:4-301:5 *) let rec hashMap_remove_from_list_loop (t : Type0) (key : usize) (ls : list_t t) : Tot (result ((option t) & (list_t t))) @@ -346,7 +347,7 @@ let rec hashMap_remove_from_list_loop end (** [hashmap::{hashmap::HashMap}::remove_from_list]: - Source: 'tests/src/hashmap.rs', lines 273:4-273:69 *) + Source: 'tests/src/hashmap.rs', lines 275:4-275:69 *) let hashMap_remove_from_list (t : Type0) (key : usize) (ls : list_t t) : result ((option t) & (list_t t)) @@ -354,7 +355,7 @@ let hashMap_remove_from_list hashMap_remove_from_list_loop t key ls (** [hashmap::{hashmap::HashMap}::remove]: - Source: 'tests/src/hashmap.rs', lines 302:4-302:52 *) + Source: 'tests/src/hashmap.rs', lines 304:4-304:52 *) let hashMap_remove (t : Type0) (self : hashMap_t t) (key : usize) : result ((option t) & (hashMap_t t)) @@ -375,8 +376,16 @@ let hashMap_remove Ok (Some x1, { self with num_entries = i1; slots = v }) end +(** [hashmap::insert_on_disk]: + Source: 'tests/src/hashmap.rs', lines 335:0-335:43 *) +let insert_on_disk + (key : usize) (value : u64) (st : state) : result (state & unit) = + let* (st1, hm) = hashmap_utils_deserialize st in + let* hm1 = hashMap_insert u64 hm key value in + hashmap_utils_serialize hm1 st1 + (** [hashmap::test1]: - Source: 'tests/src/hashmap.rs', lines 323:0-323:10 *) + Source: 'tests/src/hashmap.rs', lines 350:0-350:10 *) let test1 : result unit = let* hm = hashMap_new u64 in let* hm1 = hashMap_insert u64 hm 0 42 in diff --git a/tests/fstar/hashmap/Hashmap.FunsExternal.fsti b/tests/fstar/hashmap/Hashmap.FunsExternal.fsti new file mode 100644 index 00000000..6e3964c7 --- /dev/null +++ b/tests/fstar/hashmap/Hashmap.FunsExternal.fsti @@ -0,0 +1,16 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap]: external function declarations *) +module Hashmap.FunsExternal +open Primitives +include Hashmap.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [hashmap::hashmap_utils::deserialize]: + Source: 'tests/src/hashmap.rs', lines 330:4-330:47 *) +val hashmap_utils_deserialize : state -> result (state & (hashMap_t u64)) + +(** [hashmap::hashmap_utils::serialize]: + Source: 'tests/src/hashmap.rs', lines 325:4-325:46 *) +val hashmap_utils_serialize : hashMap_t u64 -> state -> result (state & unit) + diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar/hashmap/Hashmap.Properties.fst new file mode 100644 index 00000000..0d6372c1 --- /dev/null +++ b/tests/fstar/hashmap/Hashmap.Properties.fst @@ -0,0 +1,48 @@ +(** Properties about the hashmap written on disk *) +module Hashmap.Properties +open Primitives +open Hashmap.Funs + +#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" + +/// Below, we focus on the functions to read from disk/write to disk to showcase +/// how such reasoning which mixes opaque functions together with a state-error +/// monad can be performed. + +(*** Hypotheses *) + +/// [state_v] gives us the hash map currently stored on disk +assume +val state_v : state -> hashMap_t u64 + +/// [serialize] updates the hash map stored on disk +assume +val serialize_lem (hm : hashMap_t u64) (st : state) : Lemma ( + match hashmap_utils_serialize hm st with + | Fail _ -> True + | Ok (st', ()) -> state_v st' == hm) + [SMTPat (hashmap_utils_serialize hm st)] + +/// [deserialize] gives us the hash map stored on disk, without updating it +assume +val deserialize_lem (st : state) : Lemma ( + match hashmap_utils_deserialize st with + | Fail _ -> True + | Ok (st', hm) -> hm == state_v st /\ st' == st) + [SMTPat (hashmap_utils_deserialize st)] + +(*** Lemmas *) + +/// The obvious lemma about [insert_on_disk]: the updated hash map stored on disk +/// is exactly the hash map produced from inserting the binding ([key], [value]) +/// in the hash map previously stored on disk. +val insert_on_disk_lem (key : usize) (value : u64) (st : state) : Lemma ( + match insert_on_disk key value st with + | Fail _ -> True + | Ok (st', ()) -> + let hm = state_v st in + match hashMap_insert u64 hm key value with + | Fail _ -> False + | Ok hm' -> hm' == state_v st') + +let insert_on_disk_lem key value st = () diff --git a/tests/fstar/hashmap/Hashmap.Types.fst b/tests/fstar/hashmap/Hashmap.Types.fst index 962fbee2..818cb9d1 100644 --- a/tests/fstar/hashmap/Hashmap.Types.fst +++ b/tests/fstar/hashmap/Hashmap.Types.fst @@ -2,17 +2,18 @@ (** [hashmap]: type definitions *) module Hashmap.Types open Primitives +include Hashmap.TypesExternal #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [hashmap::List] - Source: 'tests/src/hashmap.rs', lines 27:0-27:16 *) + Source: 'tests/src/hashmap.rs', lines 29:0-29:16 *) type list_t (t : Type0) = | List_Cons : usize -> t -> list_t t -> list_t t | List_Nil : list_t t (** [hashmap::HashMap] - Source: 'tests/src/hashmap.rs', lines 43:0-43:21 *) + Source: 'tests/src/hashmap.rs', lines 45:0-45:21 *) type hashMap_t (t : Type0) = { num_entries : usize; diff --git a/tests/fstar/hashmap/Hashmap.TypesExternal.fsti b/tests/fstar/hashmap/Hashmap.TypesExternal.fsti new file mode 100644 index 00000000..66cb659b --- /dev/null +++ b/tests/fstar/hashmap/Hashmap.TypesExternal.fsti @@ -0,0 +1,10 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap]: external type declarations *) +module Hashmap.TypesExternal +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** The state type used in the state-error monad *) +val state : Type0 + diff --git a/tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst b/tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst deleted file mode 100644 index cdd73210..00000000 --- a/tests/fstar/hashmap_main/HashmapMain.Clauses.Template.fst +++ /dev/null @@ -1,72 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: templates for the decreases clauses *) -module HashmapMain.Clauses.Template -open Primitives -open HashmapMain.Types - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::allocate_slots]: decreases clause - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) -unfold -let hashmap_HashMap_allocate_slots_loop_decreases (t : Type0) - (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::clear]: decreases clause - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) -unfold -let hashmap_HashMap_clear_loop_decreases (t : Type0) - (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) -unfold -let hashmap_HashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) - (value : t) (ls : hashmap_List_t t) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements_from_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) -unfold -let hashmap_HashMap_move_elements_from_list_loop_decreases (t : Type0) - (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements]: decreases clause - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) -unfold -let hashmap_HashMap_move_elements_loop_decreases (t : Type0) - (ntable : hashmap_HashMap_t t) (slots : alloc_vec_Vec (hashmap_List_t t)) - (i : usize) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) -unfold -let hashmap_HashMap_contains_key_in_list_loop_decreases (t : Type0) - (key : usize) (ls : hashmap_List_t t) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) -unfold -let hashmap_HashMap_get_in_list_loop_decreases (t : Type0) (key : usize) - (ls : hashmap_List_t t) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut_in_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) -unfold -let hashmap_HashMap_get_mut_in_list_loop_decreases (t : Type0) - (ls : hashmap_List_t t) (key : usize) : nat = - admit () - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove_from_list]: decreases clause - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) -unfold -let hashmap_HashMap_remove_from_list_loop_decreases (t : Type0) (key : usize) - (ls : hashmap_List_t t) : nat = - admit () - diff --git a/tests/fstar/hashmap_main/HashmapMain.Clauses.fst b/tests/fstar/hashmap_main/HashmapMain.Clauses.fst deleted file mode 100644 index be5a4ab1..00000000 --- a/tests/fstar/hashmap_main/HashmapMain.Clauses.fst +++ /dev/null @@ -1,61 +0,0 @@ -(** [hashmap]: the decreases clauses *) -module HashmapMain.Clauses -open Primitives -open FStar.List.Tot -open HashmapMain.Types - -#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" - -(** [hashmap::HashMap::allocate_slots]: decreases clause *) -unfold -let hashmap_HashMap_allocate_slots_loop_decreases (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) - (n : usize) : nat = n - -(** [hashmap::HashMap::clear]: decreases clause *) -unfold -let hashmap_HashMap_clear_loop_decreases (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) - (i : usize) : nat = - if i < length slots then length slots - i else 0 - -(** [hashmap::HashMap::insert_in_list]: decreases clause *) -unfold -let hashmap_HashMap_insert_in_list_loop_decreases (t : Type0) (key : usize) (value : t) - (ls : hashmap_List_t t) : hashmap_List_t t = - ls - -(** [hashmap::HashMap::move_elements_from_list]: decreases clause *) -unfold -let hashmap_HashMap_move_elements_from_list_loop_decreases (t : Type0) - (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : hashmap_List_t t = - ls - -(** [hashmap::HashMap::move_elements]: decreases clause *) -unfold -let hashmap_HashMap_move_elements_loop_decreases (t : Type0) (ntable : hashmap_HashMap_t t) - (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : nat = - if i < length slots then length slots - i else 0 - -(** [hashmap::HashMap::contains_key_in_list]: decreases clause *) -unfold -let hashmap_HashMap_contains_key_in_list_loop_decreases (t : Type0) (key : usize) - (ls : hashmap_List_t t) : hashmap_List_t t = - ls - -(** [hashmap::HashMap::get_in_list]: decreases clause *) -unfold -let hashmap_HashMap_get_in_list_loop_decreases (t : Type0) (key : usize) (ls : hashmap_List_t t) : - hashmap_List_t t = - ls - -(** [hashmap::HashMap::get_mut_in_list]: decreases clause *) -unfold -let hashmap_HashMap_get_mut_in_list_loop_decreases (t : Type0) - (ls : hashmap_List_t t) (key : usize) : hashmap_List_t t = - ls - -(** [hashmap::HashMap::remove_from_list]: decreases clause *) -unfold -let hashmap_HashMap_remove_from_list_loop_decreases (t : Type0) (key : usize) - (ls : hashmap_List_t t) : hashmap_List_t t = - ls - diff --git a/tests/fstar/hashmap_main/HashmapMain.Funs.fst b/tests/fstar/hashmap_main/HashmapMain.Funs.fst deleted file mode 100644 index c88a746e..00000000 --- a/tests/fstar/hashmap_main/HashmapMain.Funs.fst +++ /dev/null @@ -1,446 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: function definitions *) -module HashmapMain.Funs -open Primitives -include HashmapMain.Types -include HashmapMain.FunsExternal -include HashmapMain.Clauses - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [hashmap_main::hashmap::hash_key]: - Source: 'tests/src/hashmap.rs', lines 35:0-35:32 *) -let hashmap_hash_key (k : usize) : result usize = - Ok k - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::allocate_slots]: loop 0: - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 *) -let rec hashmap_HashMap_allocate_slots_loop - (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) : - Tot (result (alloc_vec_Vec (hashmap_List_t t))) - (decreases (hashmap_HashMap_allocate_slots_loop_decreases t slots n)) - = - if n > 0 - then - let* slots1 = alloc_vec_Vec_push (hashmap_List_t t) slots Hashmap_List_Nil - in - let* n1 = usize_sub n 1 in - hashmap_HashMap_allocate_slots_loop t slots1 n1 - else Ok slots - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::allocate_slots]: - Source: 'tests/src/hashmap.rs', lines 58:4-58:76 *) -let hashmap_HashMap_allocate_slots - (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (n : usize) : - result (alloc_vec_Vec (hashmap_List_t t)) - = - hashmap_HashMap_allocate_slots_loop t slots n - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::new_with_capacity]: - Source: 'tests/src/hashmap.rs', lines 67:4-71:13 *) -let hashmap_HashMap_new_with_capacity - (t : Type0) (capacity : usize) (max_load_dividend : usize) - (max_load_divisor : usize) : - result (hashmap_HashMap_t t) - = - let* slots = - hashmap_HashMap_allocate_slots t (alloc_vec_Vec_new (hashmap_List_t t)) - capacity in - let* i = usize_mul capacity max_load_dividend in - let* i1 = usize_div i max_load_divisor in - Ok - { - num_entries = 0; - max_load_factor = (max_load_dividend, max_load_divisor); - max_load = i1; - slots = slots - } - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::new]: - Source: 'tests/src/hashmap.rs', lines 83:4-83:24 *) -let hashmap_HashMap_new (t : Type0) : result (hashmap_HashMap_t t) = - hashmap_HashMap_new_with_capacity t 32 4 5 - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::clear]: loop 0: - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 *) -let rec hashmap_HashMap_clear_loop - (t : Type0) (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : - Tot (result (alloc_vec_Vec (hashmap_List_t t))) - (decreases (hashmap_HashMap_clear_loop_decreases t slots i)) - = - let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in - if i < i1 - then - let* (_, index_mut_back) = - alloc_vec_Vec_index_mut (hashmap_List_t t) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i - in - let* i2 = usize_add i 1 in - let* slots1 = index_mut_back Hashmap_List_Nil in - hashmap_HashMap_clear_loop t slots1 i2 - else Ok slots - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::clear]: - Source: 'tests/src/hashmap.rs', lines 88:4-88:27 *) -let hashmap_HashMap_clear - (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) = - let* hm = hashmap_HashMap_clear_loop t self.slots 0 in - Ok { self with num_entries = 0; slots = hm } - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::len]: - Source: 'tests/src/hashmap.rs', lines 98:4-98:30 *) -let hashmap_HashMap_len - (t : Type0) (self : hashmap_HashMap_t t) : result usize = - Ok self.num_entries - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 *) -let rec hashmap_HashMap_insert_in_list_loop - (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) : - Tot (result (bool & (hashmap_List_t t))) - (decreases (hashmap_HashMap_insert_in_list_loop_decreases t key value ls)) - = - begin match ls with - | Hashmap_List_Cons ckey cvalue tl -> - if ckey = key - then Ok (false, Hashmap_List_Cons ckey value tl) - else - let* (b, tl1) = hashmap_HashMap_insert_in_list_loop t key value tl in - Ok (b, Hashmap_List_Cons ckey cvalue tl1) - | Hashmap_List_Nil -> Ok (true, Hashmap_List_Cons key value Hashmap_List_Nil) - end - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_in_list]: - Source: 'tests/src/hashmap.rs', lines 105:4-105:71 *) -let hashmap_HashMap_insert_in_list - (t : Type0) (key : usize) (value : t) (ls : hashmap_List_t t) : - result (bool & (hashmap_List_t t)) - = - hashmap_HashMap_insert_in_list_loop t key value ls - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_no_resize]: - Source: 'tests/src/hashmap.rs', lines 125:4-125:54 *) -let hashmap_HashMap_insert_no_resize - (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) : - result (hashmap_HashMap_t t) - = - let* hash = hashmap_hash_key key in - let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in - let* hash_mod = usize_rem hash i in - let* (l, index_mut_back) = - alloc_vec_Vec_index_mut (hashmap_List_t t) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) - self.slots hash_mod in - let* (inserted, l1) = hashmap_HashMap_insert_in_list t key value l in - if inserted - then - let* i1 = usize_add self.num_entries 1 in - let* v = index_mut_back l1 in - Ok { self with num_entries = i1; slots = v } - else let* v = index_mut_back l1 in Ok { self with slots = v } - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 *) -let rec hashmap_HashMap_move_elements_from_list_loop - (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : - Tot (result (hashmap_HashMap_t t)) - (decreases ( - hashmap_HashMap_move_elements_from_list_loop_decreases t ntable ls)) - = - begin match ls with - | Hashmap_List_Cons k v tl -> - let* ntable1 = hashmap_HashMap_insert_no_resize t ntable k v in - hashmap_HashMap_move_elements_from_list_loop t ntable1 tl - | Hashmap_List_Nil -> Ok ntable - end - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements_from_list]: - Source: 'tests/src/hashmap.rs', lines 191:4-191:72 *) -let hashmap_HashMap_move_elements_from_list - (t : Type0) (ntable : hashmap_HashMap_t t) (ls : hashmap_List_t t) : - result (hashmap_HashMap_t t) - = - hashmap_HashMap_move_elements_from_list_loop t ntable ls - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements]: loop 0: - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 *) -let rec hashmap_HashMap_move_elements_loop - (t : Type0) (ntable : hashmap_HashMap_t t) - (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : - Tot (result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t)))) - (decreases (hashmap_HashMap_move_elements_loop_decreases t ntable slots i)) - = - let i1 = alloc_vec_Vec_len (hashmap_List_t t) slots in - if i < i1 - then - let* (l, index_mut_back) = - alloc_vec_Vec_index_mut (hashmap_List_t t) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) slots i - in - let (ls, l1) = core_mem_replace (hashmap_List_t t) l Hashmap_List_Nil in - let* ntable1 = hashmap_HashMap_move_elements_from_list t ntable ls in - let* i2 = usize_add i 1 in - let* slots1 = index_mut_back l1 in - hashmap_HashMap_move_elements_loop t ntable1 slots1 i2 - else Ok (ntable, slots) - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements]: - Source: 'tests/src/hashmap.rs', lines 179:4-179:95 *) -let hashmap_HashMap_move_elements - (t : Type0) (ntable : hashmap_HashMap_t t) - (slots : alloc_vec_Vec (hashmap_List_t t)) (i : usize) : - result ((hashmap_HashMap_t t) & (alloc_vec_Vec (hashmap_List_t t))) - = - hashmap_HashMap_move_elements_loop t ntable slots i - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::try_resize]: - Source: 'tests/src/hashmap.rs', lines 148:4-148:28 *) -let hashmap_HashMap_try_resize - (t : Type0) (self : hashmap_HashMap_t t) : result (hashmap_HashMap_t t) = - let* max_usize = scalar_cast U32 Usize core_u32_max in - let capacity = alloc_vec_Vec_len (hashmap_List_t t) self.slots in - let* n1 = usize_div max_usize 2 in - let (i, i1) = self.max_load_factor in - let* i2 = usize_div n1 i in - if capacity <= i2 - then - let* i3 = usize_mul capacity 2 in - let* ntable = hashmap_HashMap_new_with_capacity t i3 i i1 in - let* p = hashmap_HashMap_move_elements t ntable self.slots 0 in - let (ntable1, _) = p in - Ok - { ntable1 with num_entries = self.num_entries; max_load_factor = (i, i1) - } - else Ok { self with max_load_factor = (i, i1) } - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert]: - Source: 'tests/src/hashmap.rs', lines 137:4-137:48 *) -let hashmap_HashMap_insert - (t : Type0) (self : hashmap_HashMap_t t) (key : usize) (value : t) : - result (hashmap_HashMap_t t) - = - let* self1 = hashmap_HashMap_insert_no_resize t self key value in - let* i = hashmap_HashMap_len t self1 in - if i > self1.max_load then hashmap_HashMap_try_resize t self1 else Ok self1 - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 *) -let rec hashmap_HashMap_contains_key_in_list_loop - (t : Type0) (key : usize) (ls : hashmap_List_t t) : - Tot (result bool) - (decreases (hashmap_HashMap_contains_key_in_list_loop_decreases t key ls)) - = - begin match ls with - | Hashmap_List_Cons ckey _ tl -> - if ckey = key - then Ok true - else hashmap_HashMap_contains_key_in_list_loop t key tl - | Hashmap_List_Nil -> Ok false - end - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key_in_list]: - Source: 'tests/src/hashmap.rs', lines 214:4-214:68 *) -let hashmap_HashMap_contains_key_in_list - (t : Type0) (key : usize) (ls : hashmap_List_t t) : result bool = - hashmap_HashMap_contains_key_in_list_loop t key ls - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key]: - Source: 'tests/src/hashmap.rs', lines 207:4-207:49 *) -let hashmap_HashMap_contains_key - (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result bool = - let* hash = hashmap_hash_key key in - let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in - let* hash_mod = usize_rem hash i in - let* l = - alloc_vec_Vec_index (hashmap_List_t t) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) - self.slots hash_mod in - hashmap_HashMap_contains_key_in_list t key l - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 *) -let rec hashmap_HashMap_get_in_list_loop - (t : Type0) (key : usize) (ls : hashmap_List_t t) : - Tot (result t) - (decreases (hashmap_HashMap_get_in_list_loop_decreases t key ls)) - = - begin match ls with - | Hashmap_List_Cons ckey cvalue tl -> - if ckey = key then Ok cvalue else hashmap_HashMap_get_in_list_loop t key tl - | Hashmap_List_Nil -> Fail Failure - end - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_in_list]: - Source: 'tests/src/hashmap.rs', lines 232:4-232:70 *) -let hashmap_HashMap_get_in_list - (t : Type0) (key : usize) (ls : hashmap_List_t t) : result t = - hashmap_HashMap_get_in_list_loop t key ls - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get]: - Source: 'tests/src/hashmap.rs', lines 247:4-247:55 *) -let hashmap_HashMap_get - (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : result t = - let* hash = hashmap_hash_key key in - let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in - let* hash_mod = usize_rem hash i in - let* l = - alloc_vec_Vec_index (hashmap_List_t t) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) - self.slots hash_mod in - hashmap_HashMap_get_in_list t key l - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 *) -let rec hashmap_HashMap_get_mut_in_list_loop - (t : Type0) (ls : hashmap_List_t t) (key : usize) : - Tot (result (t & (t -> result (hashmap_List_t t)))) - (decreases (hashmap_HashMap_get_mut_in_list_loop_decreases t ls key)) - = - begin match ls with - | Hashmap_List_Cons ckey cvalue tl -> - if ckey = key - then - let back = fun ret -> Ok (Hashmap_List_Cons ckey ret tl) in - Ok (cvalue, back) - else - let* (x, back) = hashmap_HashMap_get_mut_in_list_loop t tl key in - let back1 = - fun ret -> - let* tl1 = back ret in Ok (Hashmap_List_Cons ckey cvalue tl1) in - Ok (x, back1) - | Hashmap_List_Nil -> Fail Failure - end - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut_in_list]: - Source: 'tests/src/hashmap.rs', lines 253:4-253:86 *) -let hashmap_HashMap_get_mut_in_list - (t : Type0) (ls : hashmap_List_t t) (key : usize) : - result (t & (t -> result (hashmap_List_t t))) - = - hashmap_HashMap_get_mut_in_list_loop t ls key - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut]: - Source: 'tests/src/hashmap.rs', lines 265:4-265:67 *) -let hashmap_HashMap_get_mut - (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : - result (t & (t -> result (hashmap_HashMap_t t))) - = - let* hash = hashmap_hash_key key in - let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in - let* hash_mod = usize_rem hash i in - let* (l, index_mut_back) = - alloc_vec_Vec_index_mut (hashmap_List_t t) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) - self.slots hash_mod in - let* (x, get_mut_in_list_back) = hashmap_HashMap_get_mut_in_list t l key in - let back = - fun ret -> - let* l1 = get_mut_in_list_back ret in - let* v = index_mut_back l1 in - Ok { self with slots = v } in - Ok (x, back) - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 *) -let rec hashmap_HashMap_remove_from_list_loop - (t : Type0) (key : usize) (ls : hashmap_List_t t) : - Tot (result ((option t) & (hashmap_List_t t))) - (decreases (hashmap_HashMap_remove_from_list_loop_decreases t key ls)) - = - begin match ls with - | Hashmap_List_Cons ckey x tl -> - if ckey = key - then - let (mv_ls, _) = - core_mem_replace (hashmap_List_t t) (Hashmap_List_Cons ckey x tl) - Hashmap_List_Nil in - begin match mv_ls with - | Hashmap_List_Cons _ cvalue tl1 -> Ok (Some cvalue, tl1) - | Hashmap_List_Nil -> Fail Failure - end - else - let* (o, tl1) = hashmap_HashMap_remove_from_list_loop t key tl in - Ok (o, Hashmap_List_Cons ckey x tl1) - | Hashmap_List_Nil -> Ok (None, Hashmap_List_Nil) - end - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove_from_list]: - Source: 'tests/src/hashmap.rs', lines 273:4-273:69 *) -let hashmap_HashMap_remove_from_list - (t : Type0) (key : usize) (ls : hashmap_List_t t) : - result ((option t) & (hashmap_List_t t)) - = - hashmap_HashMap_remove_from_list_loop t key ls - -(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove]: - Source: 'tests/src/hashmap.rs', lines 302:4-302:52 *) -let hashmap_HashMap_remove - (t : Type0) (self : hashmap_HashMap_t t) (key : usize) : - result ((option t) & (hashmap_HashMap_t t)) - = - let* hash = hashmap_hash_key key in - let i = alloc_vec_Vec_len (hashmap_List_t t) self.slots in - let* hash_mod = usize_rem hash i in - let* (l, index_mut_back) = - alloc_vec_Vec_index_mut (hashmap_List_t t) usize - (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t t)) - self.slots hash_mod in - let* (x, l1) = hashmap_HashMap_remove_from_list t key l in - begin match x with - | None -> let* v = index_mut_back l1 in Ok (None, { self with slots = v }) - | Some x1 -> - let* i1 = usize_sub self.num_entries 1 in - let* v = index_mut_back l1 in - Ok (Some x1, { self with num_entries = i1; slots = v }) - end - -(** [hashmap_main::hashmap::test1]: - Source: 'tests/src/hashmap.rs', lines 323:0-323:10 *) -let hashmap_test1 : result unit = - let* hm = hashmap_HashMap_new u64 in - let* hm1 = hashmap_HashMap_insert u64 hm 0 42 in - let* hm2 = hashmap_HashMap_insert u64 hm1 128 18 in - let* hm3 = hashmap_HashMap_insert u64 hm2 1024 138 in - let* hm4 = hashmap_HashMap_insert u64 hm3 1056 256 in - let* i = hashmap_HashMap_get u64 hm4 128 in - if not (i = 18) - then Fail Failure - else - let* (_, get_mut_back) = hashmap_HashMap_get_mut u64 hm4 1024 in - let* hm5 = get_mut_back 56 in - let* i1 = hashmap_HashMap_get u64 hm5 1024 in - if not (i1 = 56) - then Fail Failure - else - let* (x, hm6) = hashmap_HashMap_remove u64 hm5 1024 in - begin match x with - | None -> Fail Failure - | Some x1 -> - if not (x1 = 56) - then Fail Failure - else - let* i2 = hashmap_HashMap_get u64 hm6 0 in - if not (i2 = 42) - then Fail Failure - else - let* i3 = hashmap_HashMap_get u64 hm6 128 in - if not (i3 = 18) - then Fail Failure - else - let* i4 = hashmap_HashMap_get u64 hm6 1056 in - if not (i4 = 256) then Fail Failure else Ok () - end - -(** [hashmap_main::insert_on_disk]: - Source: 'tests/src/hashmap_main.rs', lines 13:0-13:43 *) -let insert_on_disk - (key : usize) (value : u64) (st : state) : result (state & unit) = - let* (st1, hm) = hashmap_utils_deserialize st in - let* hm1 = hashmap_HashMap_insert u64 hm key value in - hashmap_utils_serialize hm1 st1 - -(** [hashmap_main::main]: - Source: 'tests/src/hashmap_main.rs', lines 22:0-22:13 *) -let main : result unit = - Ok () - diff --git a/tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti b/tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti deleted file mode 100644 index cc20d988..00000000 --- a/tests/fstar/hashmap_main/HashmapMain.FunsExternal.fsti +++ /dev/null @@ -1,18 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: external function declarations *) -module HashmapMain.FunsExternal -open Primitives -include HashmapMain.Types - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [hashmap_main::hashmap_utils::deserialize]: - Source: 'tests/src/hashmap_utils.rs', lines 11:0-11:43 *) -val hashmap_utils_deserialize - : state -> result (state & (hashmap_HashMap_t u64)) - -(** [hashmap_main::hashmap_utils::serialize]: - Source: 'tests/src/hashmap_utils.rs', lines 6:0-6:42 *) -val hashmap_utils_serialize - : hashmap_HashMap_t u64 -> state -> result (state & unit) - diff --git a/tests/fstar/hashmap_main/HashmapMain.Properties.fst b/tests/fstar/hashmap_main/HashmapMain.Properties.fst deleted file mode 100644 index beb3dc2c..00000000 --- a/tests/fstar/hashmap_main/HashmapMain.Properties.fst +++ /dev/null @@ -1,48 +0,0 @@ -(** Properties about the hashmap written on disk *) -module HashmapMain.Properties -open Primitives -open HashmapMain.Funs - -#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" - -/// Below, we focus on the functions to read from disk/write to disk to showcase -/// how such reasoning which mixes opaque functions together with a state-error -/// monad can be performed. - -(*** Hypotheses *) - -/// [state_v] gives us the hash map currently stored on disk -assume -val state_v : state -> hashmap_HashMap_t u64 - -/// [serialize] updates the hash map stored on disk -assume -val serialize_lem (hm : hashmap_HashMap_t u64) (st : state) : Lemma ( - match hashmap_utils_serialize hm st with - | Fail _ -> True - | Ok (st', ()) -> state_v st' == hm) - [SMTPat (hashmap_utils_serialize hm st)] - -/// [deserialize] gives us the hash map stored on disk, without updating it -assume -val deserialize_lem (st : state) : Lemma ( - match hashmap_utils_deserialize st with - | Fail _ -> True - | Ok (st', hm) -> hm == state_v st /\ st' == st) - [SMTPat (hashmap_utils_deserialize st)] - -(*** Lemmas *) - -/// The obvious lemma about [insert_on_disk]: the updated hash map stored on disk -/// is exactly the hash map produced from inserting the binding ([key], [value]) -/// in the hash map previously stored on disk. -val insert_on_disk_lem (key : usize) (value : u64) (st : state) : Lemma ( - match insert_on_disk key value st with - | Fail _ -> True - | Ok (st', ()) -> - let hm = state_v st in - match hashmap_HashMap_insert u64 hm key value with - | Fail _ -> False - | Ok hm' -> hm' == state_v st') - -let insert_on_disk_lem key value st = () diff --git a/tests/fstar/hashmap_main/HashmapMain.Types.fst b/tests/fstar/hashmap_main/HashmapMain.Types.fst deleted file mode 100644 index 85bcaeea..00000000 --- a/tests/fstar/hashmap_main/HashmapMain.Types.fst +++ /dev/null @@ -1,24 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: type definitions *) -module HashmapMain.Types -open Primitives -include HashmapMain.TypesExternal - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [hashmap_main::hashmap::List] - Source: 'tests/src/hashmap.rs', lines 27:0-27:16 *) -type hashmap_List_t (t : Type0) = -| Hashmap_List_Cons : usize -> t -> hashmap_List_t t -> hashmap_List_t t -| Hashmap_List_Nil : hashmap_List_t t - -(** [hashmap_main::hashmap::HashMap] - Source: 'tests/src/hashmap.rs', lines 43:0-43:21 *) -type hashmap_HashMap_t (t : Type0) = -{ - num_entries : usize; - max_load_factor : (usize & usize); - max_load : usize; - slots : alloc_vec_Vec (hashmap_List_t t); -} - diff --git a/tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti b/tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti deleted file mode 100644 index 75747408..00000000 --- a/tests/fstar/hashmap_main/HashmapMain.TypesExternal.fsti +++ /dev/null @@ -1,10 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [hashmap_main]: external type declarations *) -module HashmapMain.TypesExternal -open Primitives - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** The state type used in the state-error monad *) -val state : Type0 - diff --git a/tests/fstar/hashmap_main/Makefile b/tests/fstar/hashmap_main/Makefile deleted file mode 100644 index fa7d1f36..00000000 --- a/tests/fstar/hashmap_main/Makefile +++ /dev/null @@ -1,49 +0,0 @@ -# This file was automatically generated - modify ../Makefile.template instead -INCLUDE_DIRS = . - -FSTAR_INCLUDES = $(addprefix --include ,$(INCLUDE_DIRS)) - -FSTAR_HINTS ?= --use_hints --use_hint_hashes --record_hints - -FSTAR_OPTIONS = $(FSTAR_HINTS) \ - --cache_checked_modules $(FSTAR_INCLUDES) --cmi \ - --warn_error '+241@247+285-274' \ - -FSTAR_EXE ?= fstar.exe -FSTAR_NO_FLAGS = $(FSTAR_EXE) --already_cached 'Prims FStar LowStar Steel' --odir obj --cache_dir obj - -FSTAR = $(FSTAR_NO_FLAGS) $(FSTAR_OPTIONS) - -# The F* roots are used to compute the dependency graph, and generate the .depend file -FSTAR_ROOTS ?= $(wildcard *.fst *.fsti) - -# Build all the files -all: $(addprefix obj/,$(addsuffix .checked,$(FSTAR_ROOTS))) - -# This is the right way to ensure the .depend file always gets re-built. -ifeq (,$(filter %-in,$(MAKECMDGOALS))) -ifndef NODEPEND -ifndef MAKE_RESTARTS -.depend: .FORCE - $(FSTAR_NO_FLAGS) --dep full $(notdir $(FSTAR_ROOTS)) > $@ - -.PHONY: .FORCE -.FORCE: -endif -endif - -include .depend -endif - -# For the interactive mode -%.fst-in %.fsti-in: - @echo $(FSTAR_OPTIONS) - -# Generete the .checked files in batch mode -%.checked: - $(FSTAR) $(FSTAR_OPTIONS) $< && \ - touch -c $@ - -.PHONY: clean -clean: - rm -f obj/* diff --git a/tests/fstar/hashmap_main/Primitives.fst b/tests/fstar/hashmap_main/Primitives.fst deleted file mode 100644 index 9951ccc3..00000000 --- a/tests/fstar/hashmap_main/Primitives.fst +++ /dev/null @@ -1,929 +0,0 @@ -/// This file lists primitive and assumed functions and types -module Primitives -open FStar.Mul -open FStar.List.Tot - -#set-options "--z3rlimit 15 --fuel 0 --ifuel 1" - -(*** Utilities *) -val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) : - ls':list a{ - length ls' = length ls /\ - index ls' i == x - } -#push-options "--fuel 1" -let rec list_update #a ls i x = - match ls with - | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x -#pop-options - -(*** Result *) -type error : Type0 = -| Failure -| OutOfFuel - -type result (a : Type0) : Type0 = -| Ok : v:a -> result a -| Fail : e:error -> result a - -// Monadic return operator -unfold let return (#a : Type0) (x : a) : result a = Ok x - -// Monadic bind operator. -// Allows to use the notation: -// ``` -// let* x = y in -// ... -// ``` -unfold let (let*) (#a #b : Type0) (m: result a) - (f: (x:a) -> Pure (result b) (requires (m == Ok x)) (ensures fun _ -> True)) : - result b = - match m with - | Ok x -> f x - | Fail e -> Fail e - -// Monadic assert(...) -let massert (b:bool) : result unit = if b then Ok () else Fail Failure - -// Normalize and unwrap a successful result (used for globals). -let eval_global (#a : Type0) (x : result a{Ok? (normalize_term x)}) : a = Ok?.v x - -(*** Misc *) -type char = FStar.Char.char -type string = string - -let is_zero (n: nat) : bool = n = 0 -let decrease (n: nat{n > 0}) : nat = n - 1 - -let core_mem_replace (a : Type0) (x : a) (y : a) : a & a = (x, x) - -// We don't really use raw pointers for now -type mut_raw_ptr (t : Type0) = { v : t } -type const_raw_ptr (t : Type0) = { v : t } - -(*** Scalars *) -/// Rem.: most of the following code was partially generated - -assume val size_numbits : pos - -// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t - -let isize_min : int = -9223372036854775808 // TODO: should be opaque -let isize_max : int = 9223372036854775807 // TODO: should be opaque -let i8_min : int = -128 -let i8_max : int = 127 -let i16_min : int = -32768 -let i16_max : int = 32767 -let i32_min : int = -2147483648 -let i32_max : int = 2147483647 -let i64_min : int = -9223372036854775808 -let i64_max : int = 9223372036854775807 -let i128_min : int = -170141183460469231731687303715884105728 -let i128_max : int = 170141183460469231731687303715884105727 -let usize_min : int = 0 -let usize_max : int = 4294967295 // TODO: should be opaque -let u8_min : int = 0 -let u8_max : int = 255 -let u16_min : int = 0 -let u16_max : int = 65535 -let u32_min : int = 0 -let u32_max : int = 4294967295 -let u64_min : int = 0 -let u64_max : int = 18446744073709551615 -let u128_min : int = 0 -let u128_max : int = 340282366920938463463374607431768211455 - -type scalar_ty = -| Isize -| I8 -| I16 -| I32 -| I64 -| I128 -| Usize -| U8 -| U16 -| U32 -| U64 -| U128 - -let is_unsigned = function - | Isize | I8 | I16 | I32 | I64 | I128 -> false - | Usize | U8 | U16 | U32 | U64 | U128 -> true - -let scalar_min (ty : scalar_ty) : int = - match ty with - | Isize -> isize_min - | I8 -> i8_min - | I16 -> i16_min - | I32 -> i32_min - | I64 -> i64_min - | I128 -> i128_min - | Usize -> usize_min - | U8 -> u8_min - | U16 -> u16_min - | U32 -> u32_min - | U64 -> u64_min - | U128 -> u128_min - -let scalar_max (ty : scalar_ty) : int = - match ty with - | Isize -> isize_max - | I8 -> i8_max - | I16 -> i16_max - | I32 -> i32_max - | I64 -> i64_max - | I128 -> i128_max - | Usize -> usize_max - | U8 -> u8_max - | U16 -> u16_max - | U32 -> u32_max - | U64 -> u64_max - | U128 -> u128_max - -type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty} - -let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) = - if scalar_min ty <= x && scalar_max ty >= x then Ok x else Fail Failure - -let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x) - -let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - if y <> 0 then mk_scalar ty (x / y) else Fail Failure - -/// The remainder operation -let int_rem (x : int) (y : int{y <> 0}) : int = - if x >= 0 then (x % y) else -(x % y) - -(* Checking consistency with Rust *) -let _ = assert_norm(int_rem 1 2 = 1) -let _ = assert_norm(int_rem (-1) 2 = -1) -let _ = assert_norm(int_rem 1 (-2) = 1) -let _ = assert_norm(int_rem (-1) (-2) = -1) - -let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - if y <> 0 then mk_scalar ty (int_rem x y) else Fail Failure - -let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - mk_scalar ty (x + y) - -let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - mk_scalar ty (x - y) - -let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - mk_scalar ty (x * y) - -let scalar_xor (#ty : scalar_ty) - (x : scalar ty) (y : scalar ty) : scalar ty = - match ty with - | U8 -> FStar.UInt.logxor #8 x y - | U16 -> FStar.UInt.logxor #16 x y - | U32 -> FStar.UInt.logxor #32 x y - | U64 -> FStar.UInt.logxor #64 x y - | U128 -> FStar.UInt.logxor #128 x y - | Usize -> admit() // TODO - | I8 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 8); - normalize_spec (scalar I8); - FStar.Int.logxor #8 x y - | I16 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 16); - normalize_spec (scalar I16); - FStar.Int.logxor #16 x y - | I32 -> FStar.Int.logxor #32 x y - | I64 -> FStar.Int.logxor #64 x y - | I128 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 128); - normalize_spec (scalar I128); - FStar.Int.logxor #128 x y - | Isize -> admit() // TODO - -let scalar_or (#ty : scalar_ty) - (x : scalar ty) (y : scalar ty) : scalar ty = - match ty with - | U8 -> FStar.UInt.logor #8 x y - | U16 -> FStar.UInt.logor #16 x y - | U32 -> FStar.UInt.logor #32 x y - | U64 -> FStar.UInt.logor #64 x y - | U128 -> FStar.UInt.logor #128 x y - | Usize -> admit() // TODO - | I8 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 8); - normalize_spec (scalar I8); - FStar.Int.logor #8 x y - | I16 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 16); - normalize_spec (scalar I16); - FStar.Int.logor #16 x y - | I32 -> FStar.Int.logor #32 x y - | I64 -> FStar.Int.logor #64 x y - | I128 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 128); - normalize_spec (scalar I128); - FStar.Int.logor #128 x y - | Isize -> admit() // TODO - -let scalar_and (#ty : scalar_ty) - (x : scalar ty) (y : scalar ty) : scalar ty = - match ty with - | U8 -> FStar.UInt.logand #8 x y - | U16 -> FStar.UInt.logand #16 x y - | U32 -> FStar.UInt.logand #32 x y - | U64 -> FStar.UInt.logand #64 x y - | U128 -> FStar.UInt.logand #128 x y - | Usize -> admit() // TODO - | I8 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 8); - normalize_spec (scalar I8); - FStar.Int.logand #8 x y - | I16 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 16); - normalize_spec (scalar I16); - FStar.Int.logand #16 x y - | I32 -> FStar.Int.logand #32 x y - | I64 -> FStar.Int.logand #64 x y - | I128 -> - // Encoding issues... - normalize_spec (FStar.Int.int_t 128); - normalize_spec (scalar I128); - FStar.Int.logand #128 x y - | Isize -> admit() // TODO - -// Shift left -let scalar_shl (#ty0 #ty1 : scalar_ty) - (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) = - admit() - -// Shift right -let scalar_shr (#ty0 #ty1 : scalar_ty) - (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) = - admit() - -(** Cast an integer from a [src_ty] to a [tgt_ty] *) -// TODO: check the semantics of casts in Rust -let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) = - mk_scalar tgt_ty x - -// This can't fail, but for now we make all casts faillible (easier for the translation) -let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) = - mk_scalar tgt_ty (if x then 1 else 0) - -/// The scalar types -type isize : eqtype = scalar Isize -type i8 : eqtype = scalar I8 -type i16 : eqtype = scalar I16 -type i32 : eqtype = scalar I32 -type i64 : eqtype = scalar I64 -type i128 : eqtype = scalar I128 -type usize : eqtype = scalar Usize -type u8 : eqtype = scalar U8 -type u16 : eqtype = scalar U16 -type u32 : eqtype = scalar U32 -type u64 : eqtype = scalar U64 -type u128 : eqtype = scalar U128 - - -let core_isize_min : isize = isize_min -let core_isize_max : isize = isize_max -let core_i8_min : i8 = i8_min -let core_i8_max : i8 = i8_max -let core_i16_min : i16 = i16_min -let core_i16_max : i16 = i16_max -let core_i32_min : i32 = i32_min -let core_i32_max : i32 = i32_max -let core_i64_min : i64 = i64_min -let core_i64_max : i64 = i64_max -let core_i128_min : i128 = i128_min -let core_i128_max : i128 = i128_max - -let core_usize_min : usize = usize_min -let core_usize_max : usize = usize_max -let core_u8_min : u8 = u8_min -let core_u8_max : u8 = u8_max -let core_u16_min : u16 = u16_min -let core_u16_max : u16 = u16_max -let core_u32_min : u32 = u32_min -let core_u32_max : u32 = u32_max -let core_u64_min : u64 = u64_min -let core_u64_max : u64 = u64_max -let core_u128_min : u128 = u128_min -let core_u128_max : u128 = u128_max - -/// Negation -let isize_neg = scalar_neg #Isize -let i8_neg = scalar_neg #I8 -let i16_neg = scalar_neg #I16 -let i32_neg = scalar_neg #I32 -let i64_neg = scalar_neg #I64 -let i128_neg = scalar_neg #I128 - -/// Division -let isize_div = scalar_div #Isize -let i8_div = scalar_div #I8 -let i16_div = scalar_div #I16 -let i32_div = scalar_div #I32 -let i64_div = scalar_div #I64 -let i128_div = scalar_div #I128 -let usize_div = scalar_div #Usize -let u8_div = scalar_div #U8 -let u16_div = scalar_div #U16 -let u32_div = scalar_div #U32 -let u64_div = scalar_div #U64 -let u128_div = scalar_div #U128 - -/// Remainder -let isize_rem = scalar_rem #Isize -let i8_rem = scalar_rem #I8 -let i16_rem = scalar_rem #I16 -let i32_rem = scalar_rem #I32 -let i64_rem = scalar_rem #I64 -let i128_rem = scalar_rem #I128 -let usize_rem = scalar_rem #Usize -let u8_rem = scalar_rem #U8 -let u16_rem = scalar_rem #U16 -let u32_rem = scalar_rem #U32 -let u64_rem = scalar_rem #U64 -let u128_rem = scalar_rem #U128 - -/// Addition -let isize_add = scalar_add #Isize -let i8_add = scalar_add #I8 -let i16_add = scalar_add #I16 -let i32_add = scalar_add #I32 -let i64_add = scalar_add #I64 -let i128_add = scalar_add #I128 -let usize_add = scalar_add #Usize -let u8_add = scalar_add #U8 -let u16_add = scalar_add #U16 -let u32_add = scalar_add #U32 -let u64_add = scalar_add #U64 -let u128_add = scalar_add #U128 - -/// Subtraction -let isize_sub = scalar_sub #Isize -let i8_sub = scalar_sub #I8 -let i16_sub = scalar_sub #I16 -let i32_sub = scalar_sub #I32 -let i64_sub = scalar_sub #I64 -let i128_sub = scalar_sub #I128 -let usize_sub = scalar_sub #Usize -let u8_sub = scalar_sub #U8 -let u16_sub = scalar_sub #U16 -let u32_sub = scalar_sub #U32 -let u64_sub = scalar_sub #U64 -let u128_sub = scalar_sub #U128 - -/// Multiplication -let isize_mul = scalar_mul #Isize -let i8_mul = scalar_mul #I8 -let i16_mul = scalar_mul #I16 -let i32_mul = scalar_mul #I32 -let i64_mul = scalar_mul #I64 -let i128_mul = scalar_mul #I128 -let usize_mul = scalar_mul #Usize -let u8_mul = scalar_mul #U8 -let u16_mul = scalar_mul #U16 -let u32_mul = scalar_mul #U32 -let u64_mul = scalar_mul #U64 -let u128_mul = scalar_mul #U128 - -/// Xor -let u8_xor = scalar_xor #U8 -let u16_xor = scalar_xor #U16 -let u32_xor = scalar_xor #U32 -let u64_xor = scalar_xor #U64 -let u128_xor = scalar_xor #U128 -let usize_xor = scalar_xor #Usize -let i8_xor = scalar_xor #I8 -let i16_xor = scalar_xor #I16 -let i32_xor = scalar_xor #I32 -let i64_xor = scalar_xor #I64 -let i128_xor = scalar_xor #I128 -let isize_xor = scalar_xor #Isize - -/// Or -let u8_or = scalar_or #U8 -let u16_or = scalar_or #U16 -let u32_or = scalar_or #U32 -let u64_or = scalar_or #U64 -let u128_or = scalar_or #U128 -let usize_or = scalar_or #Usize -let i8_or = scalar_or #I8 -let i16_or = scalar_or #I16 -let i32_or = scalar_or #I32 -let i64_or = scalar_or #I64 -let i128_or = scalar_or #I128 -let isize_or = scalar_or #Isize - -/// And -let u8_and = scalar_and #U8 -let u16_and = scalar_and #U16 -let u32_and = scalar_and #U32 -let u64_and = scalar_and #U64 -let u128_and = scalar_and #U128 -let usize_and = scalar_and #Usize -let i8_and = scalar_and #I8 -let i16_and = scalar_and #I16 -let i32_and = scalar_and #I32 -let i64_and = scalar_and #I64 -let i128_and = scalar_and #I128 -let isize_and = scalar_and #Isize - -/// Shift left -let u8_shl #ty = scalar_shl #U8 #ty -let u16_shl #ty = scalar_shl #U16 #ty -let u32_shl #ty = scalar_shl #U32 #ty -let u64_shl #ty = scalar_shl #U64 #ty -let u128_shl #ty = scalar_shl #U128 #ty -let usize_shl #ty = scalar_shl #Usize #ty -let i8_shl #ty = scalar_shl #I8 #ty -let i16_shl #ty = scalar_shl #I16 #ty -let i32_shl #ty = scalar_shl #I32 #ty -let i64_shl #ty = scalar_shl #I64 #ty -let i128_shl #ty = scalar_shl #I128 #ty -let isize_shl #ty = scalar_shl #Isize #ty - -/// Shift right -let u8_shr #ty = scalar_shr #U8 #ty -let u16_shr #ty = scalar_shr #U16 #ty -let u32_shr #ty = scalar_shr #U32 #ty -let u64_shr #ty = scalar_shr #U64 #ty -let u128_shr #ty = scalar_shr #U128 #ty -let usize_shr #ty = scalar_shr #Usize #ty -let i8_shr #ty = scalar_shr #I8 #ty -let i16_shr #ty = scalar_shr #I16 #ty -let i32_shr #ty = scalar_shr #I32 #ty -let i64_shr #ty = scalar_shr #I64 #ty -let i128_shr #ty = scalar_shr #I128 #ty -let isize_shr #ty = scalar_shr #Isize #ty - -(*** core *) - -/// Trait declaration: [core::clone::Clone] -noeq type core_clone_Clone (self : Type0) = { - clone : self → result self -} - -let core_clone_impls_CloneBool_clone (b : bool) : bool = b - -let core_clone_CloneBool : core_clone_Clone bool = { - clone = fun b -> Ok (core_clone_impls_CloneBool_clone b) -} - -let core_clone_impls_CloneUsize_clone (x : usize) : usize = x -let core_clone_impls_CloneU8_clone (x : u8) : u8 = x -let core_clone_impls_CloneU16_clone (x : u16) : u16 = x -let core_clone_impls_CloneU32_clone (x : u32) : u32 = x -let core_clone_impls_CloneU64_clone (x : u64) : u64 = x -let core_clone_impls_CloneU128_clone (x : u128) : u128 = x - -let core_clone_impls_CloneIsize_clone (x : isize) : isize = x -let core_clone_impls_CloneI8_clone (x : i8) : i8 = x -let core_clone_impls_CloneI16_clone (x : i16) : i16 = x -let core_clone_impls_CloneI32_clone (x : i32) : i32 = x -let core_clone_impls_CloneI64_clone (x : i64) : i64 = x -let core_clone_impls_CloneI128_clone (x : i128) : i128 = x - -let core_clone_CloneUsize : core_clone_Clone usize = { - clone = fun x -> Ok (core_clone_impls_CloneUsize_clone x) -} - -let core_clone_CloneU8 : core_clone_Clone u8 = { - clone = fun x -> Ok (core_clone_impls_CloneU8_clone x) -} - -let core_clone_CloneU16 : core_clone_Clone u16 = { - clone = fun x -> Ok (core_clone_impls_CloneU16_clone x) -} - -let core_clone_CloneU32 : core_clone_Clone u32 = { - clone = fun x -> Ok (core_clone_impls_CloneU32_clone x) -} - -let core_clone_CloneU64 : core_clone_Clone u64 = { - clone = fun x -> Ok (core_clone_impls_CloneU64_clone x) -} - -let core_clone_CloneU128 : core_clone_Clone u128 = { - clone = fun x -> Ok (core_clone_impls_CloneU128_clone x) -} - -let core_clone_CloneIsize : core_clone_Clone isize = { - clone = fun x -> Ok (core_clone_impls_CloneIsize_clone x) -} - -let core_clone_CloneI8 : core_clone_Clone i8 = { - clone = fun x -> Ok (core_clone_impls_CloneI8_clone x) -} - -let core_clone_CloneI16 : core_clone_Clone i16 = { - clone = fun x -> Ok (core_clone_impls_CloneI16_clone x) -} - -let core_clone_CloneI32 : core_clone_Clone i32 = { - clone = fun x -> Ok (core_clone_impls_CloneI32_clone x) -} - -let core_clone_CloneI64 : core_clone_Clone i64 = { - clone = fun x -> Ok (core_clone_impls_CloneI64_clone x) -} - -let core_clone_CloneI128 : core_clone_Clone i128 = { - clone = fun x -> Ok (core_clone_impls_CloneI128_clone x) -} - -(** [core::option::{core::option::Option}::unwrap] *) -let core_option_Option_unwrap (t : Type0) (x : option t) : result t = - match x with - | None -> Fail Failure - | Some x -> Ok x - -(*** core::ops *) - -// Trait declaration: [core::ops::index::Index] -noeq type core_ops_index_Index (self idx : Type0) = { - output : Type0; - index : self → idx → result output -} - -// Trait declaration: [core::ops::index::IndexMut] -noeq type core_ops_index_IndexMut (self idx : Type0) = { - indexInst : core_ops_index_Index self idx; - index_mut : self → idx → result (indexInst.output & (indexInst.output → result self)); -} - -// Trait declaration [core::ops::deref::Deref] -noeq type core_ops_deref_Deref (self : Type0) = { - target : Type0; - deref : self → result target; -} - -// Trait declaration [core::ops::deref::DerefMut] -noeq type core_ops_deref_DerefMut (self : Type0) = { - derefInst : core_ops_deref_Deref self; - deref_mut : self → result (derefInst.target & (derefInst.target → result self)); -} - -type core_ops_range_Range (a : Type0) = { - start : a; - end_ : a; -} - -(*** [alloc] *) - -let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Ok x -let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result (t & (t -> result t)) = - Ok (x, (fun x -> Ok x)) - -// Trait instance -let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = { - target = self; - deref = alloc_boxed_Box_deref self; -} - -// Trait instance -let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = { - derefInst = alloc_boxed_Box_coreopsDerefInst self; - deref_mut = alloc_boxed_Box_deref_mut self; -} - -(*** Array *) -type array (a : Type0) (n : usize) = s:list a{length s = n} - -// We tried putting the normalize_term condition as a refinement on the list -// but it didn't work. It works with the requires clause. -let mk_array (a : Type0) (n : usize) - (l : list a) : - Pure (array a n) - (requires (normalize_term(FStar.List.Tot.length l) = n)) - (ensures (fun _ -> True)) = - normalize_term_spec (FStar.List.Tot.length l); - l - -let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a = - if i < length x then Ok (index x i) - else Fail Failure - -let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : - result (array a n) = - if i < length x then Ok (list_update x i nx) - else Fail Failure - -let array_index_mut_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : - result (a & (a -> result (array a n))) = - match array_index_usize a n x i with - | Fail e -> Fail e - | Ok v -> - Ok (v, array_update_usize a n x i) - -(*** Slice *) -type slice (a : Type0) = s:list a{length s <= usize_max} - -let slice_len (a : Type0) (s : slice a) : usize = length s - -let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a = - if i < length x then Ok (index x i) - else Fail Failure - -let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) = - if i < length x then Ok (list_update x i nx) - else Fail Failure - -let slice_index_mut_usize (a : Type0) (s : slice a) (i : usize) : - result (a & (a -> result (slice a))) = - match slice_index_usize a s i with - | Fail e -> Fail e - | Ok x -> - Ok (x, slice_update_usize a s i) - -(*** Subslices *) - -let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Ok x -let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) = - if length s = n then Ok s - else Fail Failure - -let array_to_slice_mut (a : Type0) (n : usize) (x : array a n) : - result (slice a & (slice a -> result (array a n))) = - Ok (x, array_from_slice a n x) - -// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *) -let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) = - admit() - -let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) = - admit() - -let array_repeat (a : Type0) (n : usize) (x : a) : array a n = - admit() - -let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) = - admit() - -let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) = - admit() - -(*** Vector *) -type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max} - -let alloc_vec_Vec_new (a : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); [] -let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v - -// Helper -let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a = - if i < length v then Ok (index v i) else Fail Failure -// Helper -let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) = - if i < length v then Ok (list_update v i x) else Fail Failure - -let alloc_vec_Vec_index_mut_usize (#a : Type0) (v: alloc_vec_Vec a) (i: usize) : - result (a & (a → result (alloc_vec_Vec a))) = - match alloc_vec_Vec_index_usize v i with - | Ok x -> - Ok (x, alloc_vec_Vec_update_usize v i) - | Fail e -> Fail e - -let alloc_vec_Vec_push (a : Type0) (v : alloc_vec_Vec a) (x : a) : - Pure (result (alloc_vec_Vec a)) - (requires True) - (ensures (fun res -> - match res with - | Fail e -> e == Failure - | Ok v' -> length v' = length v + 1)) = - if length v < usize_max then begin - (**) assert_norm(length [x] == 1); - (**) append_length v [x]; - (**) assert(length (append v [x]) = length v + 1); - Ok (append v [x]) - end - else Fail Failure - -let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) = - if i < length v then Ok (list_update v i x) else Fail Failure - -// Trait declaration: [core::slice::index::private_slice_index::Sealed] -type core_slice_index_private_slice_index_Sealed (self : Type0) = unit - -// Trait declaration: [core::slice::index::SliceIndex] -noeq type core_slice_index_SliceIndex (self t : Type0) = { - sealedInst : core_slice_index_private_slice_index_Sealed self; - output : Type0; - get : self → t → result (option output); - get_mut : self → t → result (option output & (option output -> result t)); - get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output); - get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output); - index : self → t → result output; - index_mut : self → t → result (output & (output -> result t)); -} - -// [core::slice::index::[T]::index]: forward function -let core_slice_index_Slice_index - (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) - (s : slice t) (i : idx) : result inst.output = - let* x = inst.get i s in - match x with - | None -> Fail Failure - | Some x -> Ok x - -// [core::slice::index::Range:::get]: forward function -let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) : - result (option (slice t)) = - admit () // TODO - -// [core::slice::index::Range::get_mut]: forward function -let core_slice_index_RangeUsize_get_mut (t : Type0) : - core_ops_range_Range usize → slice t → result (option (slice t) & (option (slice t) -> result (slice t))) = - admit () // TODO - -// [core::slice::index::Range::get_unchecked]: forward function -let core_slice_index_RangeUsize_get_unchecked - (t : Type0) : - core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) = - // Don't know what the model should be - for now we always fail to make - // sure code which uses it fails - fun _ _ -> Fail Failure - -// [core::slice::index::Range::get_unchecked_mut]: forward function -let core_slice_index_RangeUsize_get_unchecked_mut - (t : Type0) : - core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) = - // Don't know what the model should be - for now we always fail to make - // sure code which uses it fails - fun _ _ -> Fail Failure - -// [core::slice::index::Range::index]: forward function -let core_slice_index_RangeUsize_index - (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) = - admit () // TODO - -// [core::slice::index::Range::index_mut]: forward function -let core_slice_index_RangeUsize_index_mut (t : Type0) : - core_ops_range_Range usize → slice t → result (slice t & (slice t -> result (slice t))) = - admit () // TODO - -// [core::slice::index::[T]::index_mut]: forward function -let core_slice_index_Slice_index_mut - (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) : - slice t → idx → result (inst.output & (inst.output -> result (slice t))) = - admit () // - -// [core::array::[T; N]::index]: forward function -let core_array_Array_index - (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx) - (a : array t n) (i : idx) : result inst.output = - admit () // TODO - -// [core::array::[T; N]::index_mut]: forward function -let core_array_Array_index_mut - (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx) - (a : array t n) (i : idx) : - result (inst.indexInst.output & (inst.indexInst.output -> result (array t n))) = - admit () // TODO - -// Trait implementation: [core::slice::index::private_slice_index::Range] -let core_slice_index_private_slice_index_SealedRangeUsizeInst - : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = () - -// Trait implementation: [core::slice::index::Range] -let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) : - core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = { - sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst; - output = slice t; - get = core_slice_index_RangeUsize_get t; - get_mut = core_slice_index_RangeUsize_get_mut t; - get_unchecked = core_slice_index_RangeUsize_get_unchecked t; - get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t; - index = core_slice_index_RangeUsize_index t; - index_mut = core_slice_index_RangeUsize_index_mut t; -} - -// Trait implementation: [core::slice::index::[T]] -let core_ops_index_IndexSliceTIInst (t idx : Type0) - (inst : core_slice_index_SliceIndex idx (slice t)) : - core_ops_index_Index (slice t) idx = { - output = inst.output; - index = core_slice_index_Slice_index t idx inst; -} - -// Trait implementation: [core::slice::index::[T]] -let core_ops_index_IndexMutSliceTIInst (t idx : Type0) - (inst : core_slice_index_SliceIndex idx (slice t)) : - core_ops_index_IndexMut (slice t) idx = { - indexInst = core_ops_index_IndexSliceTIInst t idx inst; - index_mut = core_slice_index_Slice_index_mut t idx inst; -} - -// Trait implementation: [core::array::[T; N]] -let core_ops_index_IndexArrayInst (t idx : Type0) (n : usize) - (inst : core_ops_index_Index (slice t) idx) : - core_ops_index_Index (array t n) idx = { - output = inst.output; - index = core_array_Array_index t idx n inst; -} - -// Trait implementation: [core::array::[T; N]] -let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize) - (inst : core_ops_index_IndexMut (slice t) idx) : - core_ops_index_IndexMut (array t n) idx = { - indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst; - index_mut = core_array_Array_index_mut t idx n inst; -} - -// [core::slice::index::usize::get]: forward function -let core_slice_index_usize_get - (t : Type0) : usize → slice t → result (option t) = - admit () // TODO - -// [core::slice::index::usize::get_mut]: forward function -let core_slice_index_usize_get_mut (t : Type0) : - usize → slice t → result (option t & (option t -> result (slice t))) = - admit () // TODO - -// [core::slice::index::usize::get_unchecked]: forward function -let core_slice_index_usize_get_unchecked - (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) = - admit () // TODO - -// [core::slice::index::usize::get_unchecked_mut]: forward function -let core_slice_index_usize_get_unchecked_mut - (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) = - admit () // TODO - -// [core::slice::index::usize::index]: forward function -let core_slice_index_usize_index (t : Type0) : usize → slice t → result t = - admit () // TODO - -// [core::slice::index::usize::index_mut]: forward function -let core_slice_index_usize_index_mut (t : Type0) : - usize → slice t → result (t & (t -> result (slice t))) = - admit () // TODO - -// Trait implementation: [core::slice::index::private_slice_index::usize] -let core_slice_index_private_slice_index_SealedUsizeInst - : core_slice_index_private_slice_index_Sealed usize = () - -// Trait implementation: [core::slice::index::usize] -let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) : - core_slice_index_SliceIndex usize (slice t) = { - sealedInst = core_slice_index_private_slice_index_SealedUsizeInst; - output = t; - get = core_slice_index_usize_get t; - get_mut = core_slice_index_usize_get_mut t; - get_unchecked = core_slice_index_usize_get_unchecked t; - get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t; - index = core_slice_index_usize_index t; - index_mut = core_slice_index_usize_index_mut t; -} - -// [alloc::vec::Vec::index]: forward function -let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) - (self : alloc_vec_Vec t) (i : idx) : result inst.output = - admit () // TODO - -// [alloc::vec::Vec::index_mut]: forward function -let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) - (self : alloc_vec_Vec t) (i : idx) : - result (inst.output & (inst.output -> result (alloc_vec_Vec t))) = - admit () // TODO - -// Trait implementation: [alloc::vec::Vec] -let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0) - (inst : core_slice_index_SliceIndex idx (slice t)) : - core_ops_index_Index (alloc_vec_Vec t) idx = { - output = inst.output; - index = alloc_vec_Vec_index t idx inst; -} - -// Trait implementation: [alloc::vec::Vec] -let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0) - (inst : core_slice_index_SliceIndex idx (slice t)) : - core_ops_index_IndexMut (alloc_vec_Vec t) idx = { - indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst; - index_mut = alloc_vec_Vec_index_mut t idx inst; -} - -(*** Theorems *) - -let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : - Lemma ( - alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i == - alloc_vec_Vec_index_usize v i) - [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)] - = - admit() - -let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : - Lemma ( - alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i == - alloc_vec_Vec_index_mut_usize v i) - [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)] - = - admit() diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean index 4f05fbc8..e76912cc 100644 --- a/tests/lean/Hashmap/Funs.lean +++ b/tests/lean/Hashmap/Funs.lean @@ -2,17 +2,18 @@ -- [hashmap]: function definitions import Base import Hashmap.Types +import Hashmap.FunsExternal open Primitives namespace hashmap /- [hashmap::hash_key]: - Source: 'tests/src/hashmap.rs', lines 35:0-35:32 -/ + Source: 'tests/src/hashmap.rs', lines 37:0-37:32 -/ def hash_key (k : Usize) : Result Usize := Result.ok k /- [hashmap::{hashmap::HashMap}::allocate_slots]: loop 0: - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 -/ + Source: 'tests/src/hashmap.rs', lines 60:4-66:5 -/ divergent def HashMap.allocate_slots_loop (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) : Result (alloc.vec.Vec (List T)) @@ -26,7 +27,7 @@ divergent def HashMap.allocate_slots_loop else Result.ok slots /- [hashmap::{hashmap::HashMap}::allocate_slots]: - Source: 'tests/src/hashmap.rs', lines 58:4-58:76 -/ + Source: 'tests/src/hashmap.rs', lines 60:4-60:76 -/ def HashMap.allocate_slots (T : Type) (slots : alloc.vec.Vec (List T)) (n : Usize) : Result (alloc.vec.Vec (List T)) @@ -34,7 +35,7 @@ def HashMap.allocate_slots HashMap.allocate_slots_loop T slots n /- [hashmap::{hashmap::HashMap}::new_with_capacity]: - Source: 'tests/src/hashmap.rs', lines 67:4-71:13 -/ + Source: 'tests/src/hashmap.rs', lines 69:4-73:13 -/ def HashMap.new_with_capacity (T : Type) (capacity : Usize) (max_load_dividend : Usize) (max_load_divisor : Usize) : @@ -53,12 +54,12 @@ def HashMap.new_with_capacity } /- [hashmap::{hashmap::HashMap}::new]: - Source: 'tests/src/hashmap.rs', lines 83:4-83:24 -/ + Source: 'tests/src/hashmap.rs', lines 85:4-85:24 -/ def HashMap.new (T : Type) : Result (HashMap T) := HashMap.new_with_capacity T 32#usize 4#usize 5#usize /- [hashmap::{hashmap::HashMap}::clear]: loop 0: - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 -/ + Source: 'tests/src/hashmap.rs', lines 90:4-98:5 -/ divergent def HashMap.clear_loop (T : Type) (slots : alloc.vec.Vec (List T)) (i : Usize) : Result (alloc.vec.Vec (List T)) @@ -76,19 +77,19 @@ divergent def HashMap.clear_loop else Result.ok slots /- [hashmap::{hashmap::HashMap}::clear]: - Source: 'tests/src/hashmap.rs', lines 88:4-88:27 -/ + Source: 'tests/src/hashmap.rs', lines 90:4-90:27 -/ def HashMap.clear (T : Type) (self : HashMap T) : Result (HashMap T) := do let hm ← HashMap.clear_loop T self.slots 0#usize Result.ok { self with num_entries := 0#usize, slots := hm } /- [hashmap::{hashmap::HashMap}::len]: - Source: 'tests/src/hashmap.rs', lines 98:4-98:30 -/ + Source: 'tests/src/hashmap.rs', lines 100:4-100:30 -/ def HashMap.len (T : Type) (self : HashMap T) : Result Usize := Result.ok self.num_entries /- [hashmap::{hashmap::HashMap}::insert_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 -/ + Source: 'tests/src/hashmap.rs', lines 107:4-124:5 -/ divergent def HashMap.insert_in_list_loop (T : Type) (key : Usize) (value : T) (ls : List T) : Result (Bool × (List T)) @@ -104,7 +105,7 @@ divergent def HashMap.insert_in_list_loop | List.Nil => Result.ok (true, List.Cons key value List.Nil) /- [hashmap::{hashmap::HashMap}::insert_in_list]: - Source: 'tests/src/hashmap.rs', lines 105:4-105:71 -/ + Source: 'tests/src/hashmap.rs', lines 107:4-107:71 -/ def HashMap.insert_in_list (T : Type) (key : Usize) (value : T) (ls : List T) : Result (Bool × (List T)) @@ -112,7 +113,7 @@ def HashMap.insert_in_list HashMap.insert_in_list_loop T key value ls /- [hashmap::{hashmap::HashMap}::insert_no_resize]: - Source: 'tests/src/hashmap.rs', lines 125:4-125:54 -/ + Source: 'tests/src/hashmap.rs', lines 127:4-127:54 -/ def HashMap.insert_no_resize (T : Type) (self : HashMap T) (key : Usize) (value : T) : Result (HashMap T) @@ -136,7 +137,7 @@ def HashMap.insert_no_resize Result.ok { self with slots := v } /- [hashmap::{hashmap::HashMap}::move_elements_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 -/ + Source: 'tests/src/hashmap.rs', lines 193:4-206:5 -/ divergent def HashMap.move_elements_from_list_loop (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) := match ls with @@ -147,13 +148,13 @@ divergent def HashMap.move_elements_from_list_loop | List.Nil => Result.ok ntable /- [hashmap::{hashmap::HashMap}::move_elements_from_list]: - Source: 'tests/src/hashmap.rs', lines 191:4-191:72 -/ + Source: 'tests/src/hashmap.rs', lines 193:4-193:72 -/ def HashMap.move_elements_from_list (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) := HashMap.move_elements_from_list_loop T ntable ls /- [hashmap::{hashmap::HashMap}::move_elements]: loop 0: - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 -/ + Source: 'tests/src/hashmap.rs', lines 181:4-190:5 -/ divergent def HashMap.move_elements_loop (T : Type) (ntable : HashMap T) (slots : alloc.vec.Vec (List T)) (i : Usize) : @@ -174,7 +175,7 @@ divergent def HashMap.move_elements_loop else Result.ok (ntable, slots) /- [hashmap::{hashmap::HashMap}::move_elements]: - Source: 'tests/src/hashmap.rs', lines 179:4-179:95 -/ + Source: 'tests/src/hashmap.rs', lines 181:4-181:95 -/ def HashMap.move_elements (T : Type) (ntable : HashMap T) (slots : alloc.vec.Vec (List T)) (i : Usize) : @@ -183,7 +184,7 @@ def HashMap.move_elements HashMap.move_elements_loop T ntable slots i /- [hashmap::{hashmap::HashMap}::try_resize]: - Source: 'tests/src/hashmap.rs', lines 148:4-148:28 -/ + Source: 'tests/src/hashmap.rs', lines 150:4-150:28 -/ def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) := do let max_usize ← Scalar.cast .Usize core_u32_max @@ -207,7 +208,7 @@ def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) := else Result.ok { self with max_load_factor := (i, i1) } /- [hashmap::{hashmap::HashMap}::insert]: - Source: 'tests/src/hashmap.rs', lines 137:4-137:48 -/ + Source: 'tests/src/hashmap.rs', lines 139:4-139:48 -/ def HashMap.insert (T : Type) (self : HashMap T) (key : Usize) (value : T) : Result (HashMap T) @@ -220,7 +221,7 @@ def HashMap.insert else Result.ok self1 /- [hashmap::{hashmap::HashMap}::contains_key_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 -/ + Source: 'tests/src/hashmap.rs', lines 216:4-229:5 -/ divergent def HashMap.contains_key_in_list_loop (T : Type) (key : Usize) (ls : List T) : Result Bool := match ls with @@ -231,13 +232,13 @@ divergent def HashMap.contains_key_in_list_loop | List.Nil => Result.ok false /- [hashmap::{hashmap::HashMap}::contains_key_in_list]: - Source: 'tests/src/hashmap.rs', lines 214:4-214:68 -/ + Source: 'tests/src/hashmap.rs', lines 216:4-216:68 -/ def HashMap.contains_key_in_list (T : Type) (key : Usize) (ls : List T) : Result Bool := HashMap.contains_key_in_list_loop T key ls /- [hashmap::{hashmap::HashMap}::contains_key]: - Source: 'tests/src/hashmap.rs', lines 207:4-207:49 -/ + Source: 'tests/src/hashmap.rs', lines 209:4-209:49 -/ def HashMap.contains_key (T : Type) (self : HashMap T) (key : Usize) : Result Bool := do @@ -250,7 +251,7 @@ def HashMap.contains_key HashMap.contains_key_in_list T key l /- [hashmap::{hashmap::HashMap}::get_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 -/ + Source: 'tests/src/hashmap.rs', lines 234:4-247:5 -/ divergent def HashMap.get_in_list_loop (T : Type) (key : Usize) (ls : List T) : Result T := match ls with @@ -261,12 +262,12 @@ divergent def HashMap.get_in_list_loop | List.Nil => Result.fail .panic /- [hashmap::{hashmap::HashMap}::get_in_list]: - Source: 'tests/src/hashmap.rs', lines 232:4-232:70 -/ + Source: 'tests/src/hashmap.rs', lines 234:4-234:70 -/ def HashMap.get_in_list (T : Type) (key : Usize) (ls : List T) : Result T := HashMap.get_in_list_loop T key ls /- [hashmap::{hashmap::HashMap}::get]: - Source: 'tests/src/hashmap.rs', lines 247:4-247:55 -/ + Source: 'tests/src/hashmap.rs', lines 249:4-249:55 -/ def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T := do let hash ← hash_key key @@ -278,7 +279,7 @@ def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T := HashMap.get_in_list T key l /- [hashmap::{hashmap::HashMap}::get_mut_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 -/ + Source: 'tests/src/hashmap.rs', lines 255:4-264:5 -/ divergent def HashMap.get_mut_in_list_loop (T : Type) (ls : List T) (key : Usize) : Result (T × (T → Result (List T))) @@ -301,7 +302,7 @@ divergent def HashMap.get_mut_in_list_loop | List.Nil => Result.fail .panic /- [hashmap::{hashmap::HashMap}::get_mut_in_list]: - Source: 'tests/src/hashmap.rs', lines 253:4-253:86 -/ + Source: 'tests/src/hashmap.rs', lines 255:4-255:86 -/ def HashMap.get_mut_in_list (T : Type) (ls : List T) (key : Usize) : Result (T × (T → Result (List T))) @@ -309,7 +310,7 @@ def HashMap.get_mut_in_list HashMap.get_mut_in_list_loop T ls key /- [hashmap::{hashmap::HashMap}::get_mut]: - Source: 'tests/src/hashmap.rs', lines 265:4-265:67 -/ + Source: 'tests/src/hashmap.rs', lines 267:4-267:67 -/ def HashMap.get_mut (T : Type) (self : HashMap T) (key : Usize) : Result (T × (T → Result (HashMap T))) @@ -331,7 +332,7 @@ def HashMap.get_mut Result.ok (t, back) /- [hashmap::{hashmap::HashMap}::remove_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 -/ + Source: 'tests/src/hashmap.rs', lines 275:4-301:5 -/ divergent def HashMap.remove_from_list_loop (T : Type) (key : Usize) (ls : List T) : Result ((Option T) × (List T)) := match ls with @@ -350,13 +351,13 @@ divergent def HashMap.remove_from_list_loop | List.Nil => Result.ok (none, List.Nil) /- [hashmap::{hashmap::HashMap}::remove_from_list]: - Source: 'tests/src/hashmap.rs', lines 273:4-273:69 -/ + Source: 'tests/src/hashmap.rs', lines 275:4-275:69 -/ def HashMap.remove_from_list (T : Type) (key : Usize) (ls : List T) : Result ((Option T) × (List T)) := HashMap.remove_from_list_loop T key ls /- [hashmap::{hashmap::HashMap}::remove]: - Source: 'tests/src/hashmap.rs', lines 302:4-302:52 -/ + Source: 'tests/src/hashmap.rs', lines 304:4-304:52 -/ def HashMap.remove (T : Type) (self : HashMap T) (key : Usize) : Result ((Option T) × (HashMap T)) @@ -380,8 +381,17 @@ def HashMap.remove let v ← index_mut_back l1 Result.ok (some x1, { self with num_entries := i1, slots := v }) +/- [hashmap::insert_on_disk]: + Source: 'tests/src/hashmap.rs', lines 335:0-335:43 -/ +def insert_on_disk + (key : Usize) (value : U64) (st : State) : Result (State × Unit) := + do + let (st1, hm) ← hashmap_utils.deserialize st + let hm1 ← HashMap.insert U64 hm key value + hashmap_utils.serialize hm1 st1 + /- [hashmap::test1]: - Source: 'tests/src/hashmap.rs', lines 323:0-323:10 -/ + Source: 'tests/src/hashmap.rs', lines 350:0-350:10 -/ def test1 : Result Unit := do let hm ← HashMap.new U64 diff --git a/tests/lean/Hashmap/FunsExternal.lean b/tests/lean/Hashmap/FunsExternal.lean new file mode 100644 index 00000000..7454696b --- /dev/null +++ b/tests/lean/Hashmap/FunsExternal.lean @@ -0,0 +1,19 @@ +-- [hashmap]: external functions. +import Base +import Hashmap.Types +open Primitives +open hashmap + +-- TODO: fill those bodies + +/- [hashmap::hashmap_utils::deserialize]: + Source: 'tests/src/hashmap.rs', lines 330:4-330:47 -/ +def hashmap_utils.deserialize + : State → Result (State × (HashMap U64)) := + fun _ => .fail .panic + +/- [hashmap::hashmap_utils::serialize]: + Source: 'tests/src/hashmap.rs', lines 325:4-325:46 -/ +def hashmap_utils.serialize + : HashMap U64 → State → Result (State × Unit) := + fun _ _ => .fail .panic diff --git a/tests/lean/Hashmap/FunsExternal_Template.lean b/tests/lean/Hashmap/FunsExternal_Template.lean new file mode 100644 index 00000000..16b4b6af --- /dev/null +++ b/tests/lean/Hashmap/FunsExternal_Template.lean @@ -0,0 +1,17 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [hashmap]: external functions. +-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. +import Base +import Hashmap.Types +open Primitives +open hashmap + +/- [hashmap::hashmap_utils::deserialize]: + Source: 'tests/src/hashmap.rs', lines 330:4-330:47 -/ +axiom hashmap_utils.deserialize : State → Result (State × (HashMap U64)) + +/- [hashmap::hashmap_utils::serialize]: + Source: 'tests/src/hashmap.rs', lines 325:4-325:46 -/ +axiom hashmap_utils.serialize + : HashMap U64 → State → Result (State × Unit) + diff --git a/tests/lean/Hashmap/Types.lean b/tests/lean/Hashmap/Types.lean index a98b972f..b4301106 100644 --- a/tests/lean/Hashmap/Types.lean +++ b/tests/lean/Hashmap/Types.lean @@ -1,18 +1,19 @@ -- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS -- [hashmap]: type definitions import Base +import Hashmap.TypesExternal open Primitives namespace hashmap /- [hashmap::List] - Source: 'tests/src/hashmap.rs', lines 27:0-27:16 -/ + Source: 'tests/src/hashmap.rs', lines 29:0-29:16 -/ inductive List (T : Type) := | Cons : Usize → T → List T → List T | Nil : List T /- [hashmap::HashMap] - Source: 'tests/src/hashmap.rs', lines 43:0-43:21 -/ + Source: 'tests/src/hashmap.rs', lines 45:0-45:21 -/ structure HashMap (T : Type) where num_entries : Usize max_load_factor : (Usize × Usize) diff --git a/tests/lean/Hashmap/TypesExternal.lean b/tests/lean/Hashmap/TypesExternal.lean new file mode 100644 index 00000000..b32c4c42 --- /dev/null +++ b/tests/lean/Hashmap/TypesExternal.lean @@ -0,0 +1,7 @@ +-- [hashmap]: external types. +import Base +open Primitives + +/- The state type used in the state-error monad -/ +axiom State : Type + diff --git a/tests/lean/Hashmap/TypesExternal_Template.lean b/tests/lean/Hashmap/TypesExternal_Template.lean new file mode 100644 index 00000000..03c3d157 --- /dev/null +++ b/tests/lean/Hashmap/TypesExternal_Template.lean @@ -0,0 +1,9 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [hashmap]: external types. +-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. +import Base +open Primitives + +/- The state type used in the state-error monad -/ +axiom State : Type + diff --git a/tests/lean/HashmapMain.lean b/tests/lean/HashmapMain.lean deleted file mode 100644 index 1a4e7f82..00000000 --- a/tests/lean/HashmapMain.lean +++ /dev/null @@ -1 +0,0 @@ -import HashmapMain.Funs diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean deleted file mode 100644 index 45d6b058..00000000 --- a/tests/lean/HashmapMain/Funs.lean +++ /dev/null @@ -1,463 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [hashmap_main]: function definitions -import Base -import HashmapMain.Types -import HashmapMain.FunsExternal -open Primitives - -namespace hashmap_main - -/- [hashmap_main::hashmap::hash_key]: - Source: 'tests/src/hashmap.rs', lines 35:0-35:32 -/ -def hashmap.hash_key (k : Usize) : Result Usize := - Result.ok k - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::allocate_slots]: loop 0: - Source: 'tests/src/hashmap.rs', lines 58:4-64:5 -/ -divergent def hashmap.HashMap.allocate_slots_loop - (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) : - Result (alloc.vec.Vec (hashmap.List T)) - := - if n > 0#usize - then - do - let slots1 ← alloc.vec.Vec.push (hashmap.List T) slots hashmap.List.Nil - let n1 ← n - 1#usize - hashmap.HashMap.allocate_slots_loop T slots1 n1 - else Result.ok slots - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::allocate_slots]: - Source: 'tests/src/hashmap.rs', lines 58:4-58:76 -/ -def hashmap.HashMap.allocate_slots - (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (n : Usize) : - Result (alloc.vec.Vec (hashmap.List T)) - := - hashmap.HashMap.allocate_slots_loop T slots n - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::new_with_capacity]: - Source: 'tests/src/hashmap.rs', lines 67:4-71:13 -/ -def hashmap.HashMap.new_with_capacity - (T : Type) (capacity : Usize) (max_load_dividend : Usize) - (max_load_divisor : Usize) : - Result (hashmap.HashMap T) - := - do - let slots ← - hashmap.HashMap.allocate_slots T (alloc.vec.Vec.new (hashmap.List T)) - capacity - let i ← capacity * max_load_dividend - let i1 ← i / max_load_divisor - Result.ok - { - num_entries := 0#usize, - max_load_factor := (max_load_dividend, max_load_divisor), - max_load := i1, - slots := slots - } - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::new]: - Source: 'tests/src/hashmap.rs', lines 83:4-83:24 -/ -def hashmap.HashMap.new (T : Type) : Result (hashmap.HashMap T) := - hashmap.HashMap.new_with_capacity T 32#usize 4#usize 5#usize - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::clear]: loop 0: - Source: 'tests/src/hashmap.rs', lines 88:4-96:5 -/ -divergent def hashmap.HashMap.clear_loop - (T : Type) (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) : - Result (alloc.vec.Vec (hashmap.List T)) - := - let i1 := alloc.vec.Vec.len (hashmap.List T) slots - if i < i1 - then - do - let (_, index_mut_back) ← - alloc.vec.Vec.index_mut (hashmap.List T) Usize - (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i - let i2 ← i + 1#usize - let slots1 ← index_mut_back hashmap.List.Nil - hashmap.HashMap.clear_loop T slots1 i2 - else Result.ok slots - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::clear]: - Source: 'tests/src/hashmap.rs', lines 88:4-88:27 -/ -def hashmap.HashMap.clear - (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) := - do - let hm ← hashmap.HashMap.clear_loop T self.slots 0#usize - Result.ok { self with num_entries := 0#usize, slots := hm } - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::len]: - Source: 'tests/src/hashmap.rs', lines 98:4-98:30 -/ -def hashmap.HashMap.len (T : Type) (self : hashmap.HashMap T) : Result Usize := - Result.ok self.num_entries - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 105:4-122:5 -/ -divergent def hashmap.HashMap.insert_in_list_loop - (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : - Result (Bool × (hashmap.List T)) - := - match ls with - | hashmap.List.Cons ckey cvalue tl => - if ckey = key - then Result.ok (false, hashmap.List.Cons ckey value tl) - else - do - let (b, tl1) ← hashmap.HashMap.insert_in_list_loop T key value tl - Result.ok (b, hashmap.List.Cons ckey cvalue tl1) - | hashmap.List.Nil => - Result.ok (true, hashmap.List.Cons key value hashmap.List.Nil) - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_in_list]: - Source: 'tests/src/hashmap.rs', lines 105:4-105:71 -/ -def hashmap.HashMap.insert_in_list - (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : - Result (Bool × (hashmap.List T)) - := - hashmap.HashMap.insert_in_list_loop T key value ls - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert_no_resize]: - Source: 'tests/src/hashmap.rs', lines 125:4-125:54 -/ -def hashmap.HashMap.insert_no_resize - (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) : - Result (hashmap.HashMap T) - := - do - let hash ← hashmap.hash_key key - let i := alloc.vec.Vec.len (hashmap.List T) self.slots - let hash_mod ← hash % i - let (l, index_mut_back) ← - alloc.vec.Vec.index_mut (hashmap.List T) Usize - (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots - hash_mod - let (inserted, l1) ← hashmap.HashMap.insert_in_list T key value l - if inserted - then - do - let i1 ← self.num_entries + 1#usize - let v ← index_mut_back l1 - Result.ok { self with num_entries := i1, slots := v } - else do - let v ← index_mut_back l1 - Result.ok { self with slots := v } - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 191:4-204:5 -/ -divergent def hashmap.HashMap.move_elements_from_list_loop - (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) : - Result (hashmap.HashMap T) - := - match ls with - | hashmap.List.Cons k v tl => - do - let ntable1 ← hashmap.HashMap.insert_no_resize T ntable k v - hashmap.HashMap.move_elements_from_list_loop T ntable1 tl - | hashmap.List.Nil => Result.ok ntable - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements_from_list]: - Source: 'tests/src/hashmap.rs', lines 191:4-191:72 -/ -def hashmap.HashMap.move_elements_from_list - (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) : - Result (hashmap.HashMap T) - := - hashmap.HashMap.move_elements_from_list_loop T ntable ls - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements]: loop 0: - Source: 'tests/src/hashmap.rs', lines 179:4-188:5 -/ -divergent def hashmap.HashMap.move_elements_loop - (T : Type) (ntable : hashmap.HashMap T) - (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) : - Result ((hashmap.HashMap T) × (alloc.vec.Vec (hashmap.List T))) - := - let i1 := alloc.vec.Vec.len (hashmap.List T) slots - if i < i1 - then - do - let (l, index_mut_back) ← - alloc.vec.Vec.index_mut (hashmap.List T) Usize - (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) slots i - let (ls, l1) := core.mem.replace (hashmap.List T) l hashmap.List.Nil - let ntable1 ← hashmap.HashMap.move_elements_from_list T ntable ls - let i2 ← i + 1#usize - let slots1 ← index_mut_back l1 - hashmap.HashMap.move_elements_loop T ntable1 slots1 i2 - else Result.ok (ntable, slots) - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::move_elements]: - Source: 'tests/src/hashmap.rs', lines 179:4-179:95 -/ -def hashmap.HashMap.move_elements - (T : Type) (ntable : hashmap.HashMap T) - (slots : alloc.vec.Vec (hashmap.List T)) (i : Usize) : - Result ((hashmap.HashMap T) × (alloc.vec.Vec (hashmap.List T))) - := - hashmap.HashMap.move_elements_loop T ntable slots i - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::try_resize]: - Source: 'tests/src/hashmap.rs', lines 148:4-148:28 -/ -def hashmap.HashMap.try_resize - (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) := - do - let max_usize ← Scalar.cast .Usize core_u32_max - let capacity := alloc.vec.Vec.len (hashmap.List T) self.slots - let n1 ← max_usize / 2#usize - let (i, i1) := self.max_load_factor - let i2 ← n1 / i - if capacity <= i2 - then - do - let i3 ← capacity * 2#usize - let ntable ← hashmap.HashMap.new_with_capacity T i3 i i1 - let p ← hashmap.HashMap.move_elements T ntable self.slots 0#usize - let (ntable1, _) := p - Result.ok - { - ntable1 - with - num_entries := self.num_entries, max_load_factor := (i, i1) - } - else Result.ok { self with max_load_factor := (i, i1) } - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::insert]: - Source: 'tests/src/hashmap.rs', lines 137:4-137:48 -/ -def hashmap.HashMap.insert - (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) : - Result (hashmap.HashMap T) - := - do - let self1 ← hashmap.HashMap.insert_no_resize T self key value - let i ← hashmap.HashMap.len T self1 - if i > self1.max_load - then hashmap.HashMap.try_resize T self1 - else Result.ok self1 - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 214:4-227:5 -/ -divergent def hashmap.HashMap.contains_key_in_list_loop - (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool := - match ls with - | hashmap.List.Cons ckey _ tl => - if ckey = key - then Result.ok true - else hashmap.HashMap.contains_key_in_list_loop T key tl - | hashmap.List.Nil => Result.ok false - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key_in_list]: - Source: 'tests/src/hashmap.rs', lines 214:4-214:68 -/ -def hashmap.HashMap.contains_key_in_list - (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool := - hashmap.HashMap.contains_key_in_list_loop T key ls - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::contains_key]: - Source: 'tests/src/hashmap.rs', lines 207:4-207:49 -/ -def hashmap.HashMap.contains_key - (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result Bool := - do - let hash ← hashmap.hash_key key - let i := alloc.vec.Vec.len (hashmap.List T) self.slots - let hash_mod ← hash % i - let l ← - alloc.vec.Vec.index (hashmap.List T) Usize - (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots - hash_mod - hashmap.HashMap.contains_key_in_list T key l - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 232:4-245:5 -/ -divergent def hashmap.HashMap.get_in_list_loop - (T : Type) (key : Usize) (ls : hashmap.List T) : Result T := - match ls with - | hashmap.List.Cons ckey cvalue tl => - if ckey = key - then Result.ok cvalue - else hashmap.HashMap.get_in_list_loop T key tl - | hashmap.List.Nil => Result.fail .panic - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_in_list]: - Source: 'tests/src/hashmap.rs', lines 232:4-232:70 -/ -def hashmap.HashMap.get_in_list - (T : Type) (key : Usize) (ls : hashmap.List T) : Result T := - hashmap.HashMap.get_in_list_loop T key ls - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get]: - Source: 'tests/src/hashmap.rs', lines 247:4-247:55 -/ -def hashmap.HashMap.get - (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T := - do - let hash ← hashmap.hash_key key - let i := alloc.vec.Vec.len (hashmap.List T) self.slots - let hash_mod ← hash % i - let l ← - alloc.vec.Vec.index (hashmap.List T) Usize - (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots - hash_mod - hashmap.HashMap.get_in_list T key l - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut_in_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 253:4-262:5 -/ -divergent def hashmap.HashMap.get_mut_in_list_loop - (T : Type) (ls : hashmap.List T) (key : Usize) : - Result (T × (T → Result (hashmap.List T))) - := - match ls with - | hashmap.List.Cons ckey cvalue tl => - if ckey = key - then - let back := fun ret => Result.ok (hashmap.List.Cons ckey ret tl) - Result.ok (cvalue, back) - else - do - let (t, back) ← hashmap.HashMap.get_mut_in_list_loop T tl key - let back1 := - fun ret => - do - let tl1 ← back ret - Result.ok (hashmap.List.Cons ckey cvalue tl1) - Result.ok (t, back1) - | hashmap.List.Nil => Result.fail .panic - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut_in_list]: - Source: 'tests/src/hashmap.rs', lines 253:4-253:86 -/ -def hashmap.HashMap.get_mut_in_list - (T : Type) (ls : hashmap.List T) (key : Usize) : - Result (T × (T → Result (hashmap.List T))) - := - hashmap.HashMap.get_mut_in_list_loop T ls key - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::get_mut]: - Source: 'tests/src/hashmap.rs', lines 265:4-265:67 -/ -def hashmap.HashMap.get_mut - (T : Type) (self : hashmap.HashMap T) (key : Usize) : - Result (T × (T → Result (hashmap.HashMap T))) - := - do - let hash ← hashmap.hash_key key - let i := alloc.vec.Vec.len (hashmap.List T) self.slots - let hash_mod ← hash % i - let (l, index_mut_back) ← - alloc.vec.Vec.index_mut (hashmap.List T) Usize - (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots - hash_mod - let (t, get_mut_in_list_back) ← hashmap.HashMap.get_mut_in_list T l key - let back := - fun ret => - do - let l1 ← get_mut_in_list_back ret - let v ← index_mut_back l1 - Result.ok { self with slots := v } - Result.ok (t, back) - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove_from_list]: loop 0: - Source: 'tests/src/hashmap.rs', lines 273:4-299:5 -/ -divergent def hashmap.HashMap.remove_from_list_loop - (T : Type) (key : Usize) (ls : hashmap.List T) : - Result ((Option T) × (hashmap.List T)) - := - match ls with - | hashmap.List.Cons ckey t tl => - if ckey = key - then - let (mv_ls, _) := - core.mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl) - hashmap.List.Nil - match mv_ls with - | hashmap.List.Cons _ cvalue tl1 => Result.ok (some cvalue, tl1) - | hashmap.List.Nil => Result.fail .panic - else - do - let (o, tl1) ← hashmap.HashMap.remove_from_list_loop T key tl - Result.ok (o, hashmap.List.Cons ckey t tl1) - | hashmap.List.Nil => Result.ok (none, hashmap.List.Nil) - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove_from_list]: - Source: 'tests/src/hashmap.rs', lines 273:4-273:69 -/ -def hashmap.HashMap.remove_from_list - (T : Type) (key : Usize) (ls : hashmap.List T) : - Result ((Option T) × (hashmap.List T)) - := - hashmap.HashMap.remove_from_list_loop T key ls - -/- [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap}::remove]: - Source: 'tests/src/hashmap.rs', lines 302:4-302:52 -/ -def hashmap.HashMap.remove - (T : Type) (self : hashmap.HashMap T) (key : Usize) : - Result ((Option T) × (hashmap.HashMap T)) - := - do - let hash ← hashmap.hash_key key - let i := alloc.vec.Vec.len (hashmap.List T) self.slots - let hash_mod ← hash % i - let (l, index_mut_back) ← - alloc.vec.Vec.index_mut (hashmap.List T) Usize - (core.slice.index.SliceIndexUsizeSliceTInst (hashmap.List T)) self.slots - hash_mod - let (x, l1) ← hashmap.HashMap.remove_from_list T key l - match x with - | none => - do - let v ← index_mut_back l1 - Result.ok (none, { self with slots := v }) - | some x1 => - do - let i1 ← self.num_entries - 1#usize - let v ← index_mut_back l1 - Result.ok (some x1, { self with num_entries := i1, slots := v }) - -/- [hashmap_main::hashmap::test1]: - Source: 'tests/src/hashmap.rs', lines 323:0-323:10 -/ -def hashmap.test1 : Result Unit := - do - let hm ← hashmap.HashMap.new U64 - let hm1 ← hashmap.HashMap.insert U64 hm 0#usize 42#u64 - let hm2 ← hashmap.HashMap.insert U64 hm1 128#usize 18#u64 - let hm3 ← hashmap.HashMap.insert U64 hm2 1024#usize 138#u64 - let hm4 ← hashmap.HashMap.insert U64 hm3 1056#usize 256#u64 - let i ← hashmap.HashMap.get U64 hm4 128#usize - if ¬ (i = 18#u64) - then Result.fail .panic - else - do - let (_, get_mut_back) ← hashmap.HashMap.get_mut U64 hm4 1024#usize - let hm5 ← get_mut_back 56#u64 - let i1 ← hashmap.HashMap.get U64 hm5 1024#usize - if ¬ (i1 = 56#u64) - then Result.fail .panic - else - do - let (x, hm6) ← hashmap.HashMap.remove U64 hm5 1024#usize - match x with - | none => Result.fail .panic - | some x1 => - if ¬ (x1 = 56#u64) - then Result.fail .panic - else - do - let i2 ← hashmap.HashMap.get U64 hm6 0#usize - if ¬ (i2 = 42#u64) - then Result.fail .panic - else - do - let i3 ← hashmap.HashMap.get U64 hm6 128#usize - if ¬ (i3 = 18#u64) - then Result.fail .panic - else - do - let i4 ← hashmap.HashMap.get U64 hm6 1056#usize - if ¬ (i4 = 256#u64) - then Result.fail .panic - else Result.ok () - -/- [hashmap_main::insert_on_disk]: - Source: 'tests/src/hashmap_main.rs', lines 13:0-13:43 -/ -def insert_on_disk - (key : Usize) (value : U64) (st : State) : Result (State × Unit) := - do - let (st1, hm) ← hashmap_utils.deserialize st - let hm1 ← hashmap.HashMap.insert U64 hm key value - hashmap_utils.serialize hm1 st1 - -/- [hashmap_main::main]: - Source: 'tests/src/hashmap_main.rs', lines 22:0-22:13 -/ -def main : Result Unit := - Result.ok () - -end hashmap_main diff --git a/tests/lean/HashmapMain/FunsExternal.lean b/tests/lean/HashmapMain/FunsExternal.lean deleted file mode 100644 index b394b32b..00000000 --- a/tests/lean/HashmapMain/FunsExternal.lean +++ /dev/null @@ -1,17 +0,0 @@ --- [hashmap_main]: templates for the external functions. -import Base -import HashmapMain.Types -open Primitives -open hashmap_main - --- TODO: fill those bodies - -/- [hashmap_main::hashmap_utils::deserialize] -/ -def hashmap_utils.deserialize - : State → Result (State × (hashmap.HashMap U64)) := - fun _ => .fail .panic - -/- [hashmap_main::hashmap_utils::serialize] -/ -def hashmap_utils.serialize - : hashmap.HashMap U64 → State → Result (State × Unit) := - fun _ _ => .fail .panic diff --git a/tests/lean/HashmapMain/FunsExternal_Template.lean b/tests/lean/HashmapMain/FunsExternal_Template.lean deleted file mode 100644 index 1a6c40d5..00000000 --- a/tests/lean/HashmapMain/FunsExternal_Template.lean +++ /dev/null @@ -1,18 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [hashmap_main]: external functions. --- This is a template file: rename it to "FunsExternal.lean" and fill the holes. -import Base -import HashmapMain.Types -open Primitives -open hashmap_main - -/- [hashmap_main::hashmap_utils::deserialize]: - Source: 'tests/src/hashmap_utils.rs', lines 11:0-11:43 -/ -axiom hashmap_utils.deserialize - : State → Result (State × (hashmap.HashMap U64)) - -/- [hashmap_main::hashmap_utils::serialize]: - Source: 'tests/src/hashmap_utils.rs', lines 6:0-6:42 -/ -axiom hashmap_utils.serialize - : hashmap.HashMap U64 → State → Result (State × Unit) - diff --git a/tests/lean/HashmapMain/Opaque.lean b/tests/lean/HashmapMain/Opaque.lean deleted file mode 100644 index a410b253..00000000 --- a/tests/lean/HashmapMain/Opaque.lean +++ /dev/null @@ -1,18 +0,0 @@ --- [hashmap_main]: opaque function definitions -import Base -import HashmapMain.Types -open Primitives - -namespace hashmap_main - -structure OpaqueDefs where - - /- [hashmap_main::hashmap_utils::deserialize] -/ - hashmap_utils.deserialize_fwd - : State → Result (State × (hashmap_hash_map_t U64)) - - /- [hashmap_main::hashmap_utils::serialize] -/ - hashmap_utils.serialize_fwd - : hashmap_hash_map_t U64 → State → Result (State × Unit) - -end hashmap_main diff --git a/tests/lean/HashmapMain/Types.lean b/tests/lean/HashmapMain/Types.lean deleted file mode 100644 index 54f11e1e..00000000 --- a/tests/lean/HashmapMain/Types.lean +++ /dev/null @@ -1,23 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [hashmap_main]: type definitions -import Base -import HashmapMain.TypesExternal -open Primitives - -namespace hashmap_main - -/- [hashmap_main::hashmap::List] - Source: 'tests/src/hashmap.rs', lines 27:0-27:16 -/ -inductive hashmap.List (T : Type) := -| Cons : Usize → T → hashmap.List T → hashmap.List T -| Nil : hashmap.List T - -/- [hashmap_main::hashmap::HashMap] - Source: 'tests/src/hashmap.rs', lines 43:0-43:21 -/ -structure hashmap.HashMap (T : Type) where - num_entries : Usize - max_load_factor : (Usize × Usize) - max_load : Usize - slots : alloc.vec.Vec (hashmap.List T) - -end hashmap_main diff --git a/tests/lean/HashmapMain/TypesExternal.lean b/tests/lean/HashmapMain/TypesExternal.lean deleted file mode 100644 index 4e1cdbe9..00000000 --- a/tests/lean/HashmapMain/TypesExternal.lean +++ /dev/null @@ -1,7 +0,0 @@ --- [hashmap_main]: external types. -import Base -open Primitives - -/- The state type used in the state-error monad -/ -axiom State : Type - diff --git a/tests/lean/HashmapMain/TypesExternal_Template.lean b/tests/lean/HashmapMain/TypesExternal_Template.lean deleted file mode 100644 index cfa8bbb1..00000000 --- a/tests/lean/HashmapMain/TypesExternal_Template.lean +++ /dev/null @@ -1,9 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [hashmap_main]: external types. --- This is a template file: rename it to "TypesExternal.lean" and fill the holes. -import Base -open Primitives - -/- The state type used in the state-error monad -/ -axiom State : Type - diff --git a/tests/lean/lakefile.lean b/tests/lean/lakefile.lean index 3a777824..bb13ddf2 100644 --- a/tests/lean/lakefile.lean +++ b/tests/lean/lakefile.lean @@ -13,7 +13,6 @@ package «tests» {} @[default_target] lean_lib Constants @[default_target] lean_lib External @[default_target] lean_lib Hashmap -@[default_target] lean_lib HashmapMain @[default_target] lean_lib Loops @[default_target] lean_lib NoNestedBorrows @[default_target] lean_lib Paper diff --git a/tests/src/hashmap.rs b/tests/src/hashmap.rs index 4552e4f2..ccb96e1e 100644 --- a/tests/src/hashmap.rs +++ b/tests/src/hashmap.rs @@ -1,9 +1,11 @@ +//@ charon-args=--opaque=hashmap_utils +//@ aeneas-args=-state -split-files //@ [coq] aeneas-args=-use-fuel -//@ aeneas-args=-split-files //@ [fstar] aeneas-args=-decreases-clauses -template-clauses //@ [lean] aeneas-args=-no-gen-lib-entry // ^ the `-no-gen-lib-entry` is because we add a custom import in the Hashmap.lean file: we do not // want to overwrite it. +// Possible to add `--no-code-duplication` if we use the optimized MIR // TODO: reactivate -test-trans-units //! A hashmap implementation. @@ -314,6 +316,31 @@ impl HashMap { } } +// This is a module so we can tell charon to leave it opaque +mod hashmap_utils { + use crate::*; + + /// Serialize a hash map - we don't have traits, so we fix the type of the + /// values (this is not the interesting part anyway) + pub(crate) fn serialize(_hm: HashMap) { + unimplemented!(); + } + /// Deserialize a hash map - we don't have traits, so we fix the type of the + /// values (this is not the interesting part anyway) + pub(crate) fn deserialize() -> HashMap { + unimplemented!(); + } +} + +pub fn insert_on_disk(key: Key, value: u64) { + // Deserialize + let mut hm = hashmap_utils::deserialize(); + // Update + hm.insert(key, value); + // Serialize + hashmap_utils::serialize(hm); +} + /// I currently can't retrieve functions marked with the attribute #[test], /// while I want to extract the unit tests and use the normalize on them, /// so I have to define the test functions somewhere and call them from diff --git a/tests/src/hashmap_main.rs b/tests/src/hashmap_main.rs deleted file mode 100644 index 0c827844..00000000 --- a/tests/src/hashmap_main.rs +++ /dev/null @@ -1,22 +0,0 @@ -//@ charon-args=--opaque=hashmap_utils -//@ aeneas-args=-state -split-files -//@ [coq] aeneas-args=-use-fuel -//@ [fstar] aeneas-args=-decreases-clauses -template-clauses -// Possible to add `--no-code-duplication` if we use the optimized MIR -// TODO: reactivate -test-trans-units -mod hashmap; -mod hashmap_utils; - -use crate::hashmap::*; -use crate::hashmap_utils::*; - -pub fn insert_on_disk(key: Key, value: u64) { - // Deserialize - let mut hm = deserialize(); - // Update - hm.insert(key, value); - // Serialize - serialize(hm); -} - -pub fn main() {} diff --git a/tests/src/hashmap_utils.rs b/tests/src/hashmap_utils.rs deleted file mode 100644 index 33de49e1..00000000 --- a/tests/src/hashmap_utils.rs +++ /dev/null @@ -1,13 +0,0 @@ -//@ skip -use crate::hashmap::*; - -/// Serialize a hash map - we don't have traits, so we fix the type of the -/// values (this is not the interesting part anyway) -pub(crate) fn serialize(_hm: HashMap) { - unimplemented!(); -} -/// Deserialize a hash map - we don't have traits, so we fix the type of the -/// values (this is not the interesting part anyway) -pub(crate) fn deserialize() -> HashMap { - unimplemented!(); -} -- cgit v1.2.3 From f77e3f9cbe2ea7abeb4be815bdbf33d0c98076c2 Mon Sep 17 00:00:00 2001 From: Nadrieril Date: Mon, 27 May 2024 13:28:28 +0200 Subject: tests: Rename betree_main -> betree --- flake.nix | 4 +- tests/coq/betree/BetreeMain_Funs.v | 837 ---------- tests/coq/betree/BetreeMain_FunsExternal.v | 39 - .../coq/betree/BetreeMain_FunsExternal_Template.v | 40 - tests/coq/betree/BetreeMain_Types.v | 118 -- tests/coq/betree/BetreeMain_TypesExternal.v | 14 - .../coq/betree/BetreeMain_TypesExternal_Template.v | 15 - tests/coq/betree/Betree_Funs.v | 837 ++++++++++ tests/coq/betree/Betree_FunsExternal.v | 39 + tests/coq/betree/Betree_FunsExternal_Template.v | 40 + tests/coq/betree/Betree_Types.v | 118 ++ tests/coq/betree/Betree_TypesExternal.v | 14 + tests/coq/betree/Betree_TypesExternal_Template.v | 15 + tests/coq/betree/_CoqProject | 12 +- tests/fstar/betree/Betree.Clauses.Template.fst | 117 ++ tests/fstar/betree/Betree.Clauses.fst | 210 +++ tests/fstar/betree/Betree.Funs.fst | 676 ++++++++ tests/fstar/betree/Betree.FunsExternal.fsti | 30 + tests/fstar/betree/Betree.Types.fst | 61 + tests/fstar/betree/Betree.TypesExternal.fsti | 10 + tests/fstar/betree/BetreeMain.Clauses.Template.fst | 117 -- tests/fstar/betree/BetreeMain.Clauses.fst | 210 --- tests/fstar/betree/BetreeMain.Funs.fst | 676 -------- tests/fstar/betree/BetreeMain.FunsExternal.fsti | 30 - tests/fstar/betree/BetreeMain.Types.fst | 61 - tests/fstar/betree/BetreeMain.TypesExternal.fsti | 10 - tests/hol4/betree/betreeMain_FunsScript.sml | 1212 -------------- tests/hol4/betree/betreeMain_FunsTheory.sig | 1230 -------------- tests/hol4/betree/betreeMain_OpaqueScript.sml | 26 - tests/hol4/betree/betreeMain_OpaqueTheory.sig | 11 - tests/hol4/betree/betreeMain_TypesScript.sml | 76 - tests/hol4/betree/betreeMain_TypesTheory.sig | 1751 -------------------- tests/hol4/betree/betree_FunsScript.sml | 1212 ++++++++++++++ tests/hol4/betree/betree_FunsTheory.sig | 1230 ++++++++++++++ tests/hol4/betree/betree_OpaqueScript.sml | 26 + tests/hol4/betree/betree_OpaqueTheory.sig | 11 + tests/hol4/betree/betree_TypesScript.sml | 76 + tests/hol4/betree/betree_TypesTheory.sig | 1751 ++++++++++++++++++++ tests/lean/Betree/Funs.lean | 699 ++++++++ tests/lean/Betree/FunsExternal.lean | 30 + tests/lean/Betree/FunsExternal_Template.lean | 30 + tests/lean/Betree/Types.lean | 83 + tests/lean/Betree/TypesExternal.lean | 7 + tests/lean/Betree/TypesExternal_Template.lean | 9 + tests/lean/BetreeMain.lean | 1 - tests/lean/BetreeMain/Funs.lean | 699 -------- tests/lean/BetreeMain/FunsExternal.lean | 30 - tests/lean/BetreeMain/FunsExternal_Template.lean | 30 - tests/lean/BetreeMain/Types.lean | 83 - tests/lean/BetreeMain/TypesExternal.lean | 7 - tests/lean/BetreeMain/TypesExternal_Template.lean | 9 - tests/lean/lakefile.lean | 2 +- tests/test_runner/run_test.ml | 7 +- 53 files changed, 7342 insertions(+), 7346 deletions(-) delete mode 100644 tests/coq/betree/BetreeMain_Funs.v delete mode 100644 tests/coq/betree/BetreeMain_FunsExternal.v delete mode 100644 tests/coq/betree/BetreeMain_FunsExternal_Template.v delete mode 100644 tests/coq/betree/BetreeMain_Types.v delete mode 100644 tests/coq/betree/BetreeMain_TypesExternal.v delete mode 100644 tests/coq/betree/BetreeMain_TypesExternal_Template.v create mode 100644 tests/coq/betree/Betree_Funs.v create mode 100644 tests/coq/betree/Betree_FunsExternal.v create mode 100644 tests/coq/betree/Betree_FunsExternal_Template.v create mode 100644 tests/coq/betree/Betree_Types.v create mode 100644 tests/coq/betree/Betree_TypesExternal.v create mode 100644 tests/coq/betree/Betree_TypesExternal_Template.v create mode 100644 tests/fstar/betree/Betree.Clauses.Template.fst create mode 100644 tests/fstar/betree/Betree.Clauses.fst create mode 100644 tests/fstar/betree/Betree.Funs.fst create mode 100644 tests/fstar/betree/Betree.FunsExternal.fsti create mode 100644 tests/fstar/betree/Betree.Types.fst create mode 100644 tests/fstar/betree/Betree.TypesExternal.fsti delete mode 100644 tests/fstar/betree/BetreeMain.Clauses.Template.fst delete mode 100644 tests/fstar/betree/BetreeMain.Clauses.fst delete mode 100644 tests/fstar/betree/BetreeMain.Funs.fst delete mode 100644 tests/fstar/betree/BetreeMain.FunsExternal.fsti delete mode 100644 tests/fstar/betree/BetreeMain.Types.fst delete mode 100644 tests/fstar/betree/BetreeMain.TypesExternal.fsti delete mode 100644 tests/hol4/betree/betreeMain_FunsScript.sml delete mode 100644 tests/hol4/betree/betreeMain_FunsTheory.sig delete mode 100644 tests/hol4/betree/betreeMain_OpaqueScript.sml delete mode 100644 tests/hol4/betree/betreeMain_OpaqueTheory.sig delete mode 100644 tests/hol4/betree/betreeMain_TypesScript.sml delete mode 100644 tests/hol4/betree/betreeMain_TypesTheory.sig create mode 100644 tests/hol4/betree/betree_FunsScript.sml create mode 100644 tests/hol4/betree/betree_FunsTheory.sig create mode 100644 tests/hol4/betree/betree_OpaqueScript.sml create mode 100644 tests/hol4/betree/betree_OpaqueTheory.sig create mode 100644 tests/hol4/betree/betree_TypesScript.sml create mode 100644 tests/hol4/betree/betree_TypesTheory.sig create mode 100644 tests/lean/Betree/Funs.lean create mode 100644 tests/lean/Betree/FunsExternal.lean create mode 100644 tests/lean/Betree/FunsExternal_Template.lean create mode 100644 tests/lean/Betree/Types.lean create mode 100644 tests/lean/Betree/TypesExternal.lean create mode 100644 tests/lean/Betree/TypesExternal_Template.lean delete mode 100644 tests/lean/BetreeMain.lean delete mode 100644 tests/lean/BetreeMain/Funs.lean delete mode 100644 tests/lean/BetreeMain/FunsExternal.lean delete mode 100644 tests/lean/BetreeMain/FunsExternal_Template.lean delete mode 100644 tests/lean/BetreeMain/Types.lean delete mode 100644 tests/lean/BetreeMain/TypesExternal.lean delete mode 100644 tests/lean/BetreeMain/TypesExternal_Template.lean diff --git a/flake.nix b/flake.nix index f1a2258a..654c0006 100644 --- a/flake.nix +++ b/flake.nix @@ -90,7 +90,7 @@ betree-llbc = charon.extractCrateWithCharon.${system} { name = "betree"; src = ./tests/src/betree; - charonFlags = "--polonius --opaque=betree_utils --crate betree_main"; + charonFlags = "--polonius --opaque=betree_utils"; craneExtraArgs.checkPhaseCargoCommand = '' cargo rustc -- --test -Zpolonius ./target/debug/betree @@ -125,7 +125,7 @@ mkdir tests/llbc export LLBC_DIR=tests/llbc # Copy over the llbc file we can't generate ourselves. - cp ${betree-llbc}/llbc/betree_main.llbc $LLBC_DIR + cp ${betree-llbc}/llbc/betree.llbc $LLBC_DIR # Run the tests with extra sanity checks enabled IN_CI=1 make test-all -j $NIX_BUILD_CORES diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v deleted file mode 100644 index e0a1d8a2..00000000 --- a/tests/coq/betree/BetreeMain_Funs.v +++ /dev/null @@ -1,837 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: function definitions *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Import BetreeMain_Types. -Include BetreeMain_Types. -Require Import BetreeMain_FunsExternal. -Include BetreeMain_FunsExternal. -Module BetreeMain_Funs. - -(** [betree_main::betree::load_internal_node]: - Source: 'src/betree.rs', lines 36:0-36:52 *) -Definition betree_load_internal_node - (id : u64) (st : state) : - result (state * (betree_List_t (u64 * betree_Message_t))) - := - betree_utils_load_internal_node id st -. - -(** [betree_main::betree::store_internal_node]: - Source: 'src/betree.rs', lines 41:0-41:60 *) -Definition betree_store_internal_node - (id : u64) (content : betree_List_t (u64 * betree_Message_t)) (st : state) : - result (state * unit) - := - betree_utils_store_internal_node id content st -. - -(** [betree_main::betree::load_leaf_node]: - Source: 'src/betree.rs', lines 46:0-46:44 *) -Definition betree_load_leaf_node - (id : u64) (st : state) : result (state * (betree_List_t (u64 * u64))) := - betree_utils_load_leaf_node id st -. - -(** [betree_main::betree::store_leaf_node]: - Source: 'src/betree.rs', lines 51:0-51:52 *) -Definition betree_store_leaf_node - (id : u64) (content : betree_List_t (u64 * u64)) (st : state) : - result (state * unit) - := - betree_utils_store_leaf_node id content st -. - -(** [betree_main::betree::fresh_node_id]: - Source: 'src/betree.rs', lines 55:0-55:48 *) -Definition betree_fresh_node_id (counter : u64) : result (u64 * u64) := - counter1 <- u64_add counter 1%u64; Ok (counter, counter1) -. - -(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: - Source: 'src/betree.rs', lines 206:4-206:20 *) -Definition betree_NodeIdCounter_new : result betree_NodeIdCounter_t := - Ok {| betree_NodeIdCounter_next_node_id := 0%u64 |} -. - -(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: - Source: 'src/betree.rs', lines 210:4-210:36 *) -Definition betree_NodeIdCounter_fresh_id - (self : betree_NodeIdCounter_t) : result (u64 * betree_NodeIdCounter_t) := - i <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64; - Ok (self.(betree_NodeIdCounter_next_node_id), - {| betree_NodeIdCounter_next_node_id := i |}) -. - -(** [betree_main::betree::upsert_update]: - Source: 'src/betree.rs', lines 234:0-234:70 *) -Definition betree_upsert_update - (prev : option u64) (st : betree_UpsertFunState_t) : result u64 := - match prev with - | None => - match st with - | Betree_UpsertFunState_Add v => Ok v - | Betree_UpsertFunState_Sub _ => Ok 0%u64 - end - | Some prev1 => - match st with - | Betree_UpsertFunState_Add v => - margin <- u64_sub core_u64_max prev1; - if margin s>= v then u64_add prev1 v else Ok core_u64_max - | Betree_UpsertFunState_Sub v => - if prev1 s>= v then u64_sub prev1 v else Ok 0%u64 - end - end -. - -(** [betree_main::betree::{betree_main::betree::List#1}::len]: - Source: 'src/betree.rs', lines 276:4-276:24 *) -Fixpoint betree_List_len - (T : Type) (n : nat) (self : betree_List_t T) : result u64 := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match self with - | Betree_List_Cons _ tl => i <- betree_List_len T n1 tl; u64_add 1%u64 i - | Betree_List_Nil => Ok 0%u64 - end - end -. - -(** [betree_main::betree::{betree_main::betree::List#1}::split_at]: - Source: 'src/betree.rs', lines 284:4-284:51 *) -Fixpoint betree_List_split_at - (T : Type) (n : nat) (self : betree_List_t T) (n1 : u64) : - result ((betree_List_t T) * (betree_List_t T)) - := - match n with - | O => Fail_ OutOfFuel - | S n2 => - if n1 s= 0%u64 - then Ok (Betree_List_Nil, self) - else - match self with - | Betree_List_Cons hd tl => - i <- u64_sub n1 1%u64; - p <- betree_List_split_at T n2 tl i; - let (ls0, ls1) := p in - Ok (Betree_List_Cons hd ls0, ls1) - | Betree_List_Nil => Fail_ Failure - end - end -. - -(** [betree_main::betree::{betree_main::betree::List#1}::push_front]: - Source: 'src/betree.rs', lines 299:4-299:34 *) -Definition betree_List_push_front - (T : Type) (self : betree_List_t T) (x : T) : result (betree_List_t T) := - let (tl, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in - Ok (Betree_List_Cons x tl) -. - -(** [betree_main::betree::{betree_main::betree::List#1}::pop_front]: - Source: 'src/betree.rs', lines 306:4-306:32 *) -Definition betree_List_pop_front - (T : Type) (self : betree_List_t T) : result (T * (betree_List_t T)) := - let (ls, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in - match ls with - | Betree_List_Cons x tl => Ok (x, tl) - | Betree_List_Nil => Fail_ Failure - end -. - -(** [betree_main::betree::{betree_main::betree::List#1}::hd]: - Source: 'src/betree.rs', lines 318:4-318:22 *) -Definition betree_List_hd (T : Type) (self : betree_List_t T) : result T := - match self with - | Betree_List_Cons hd _ => Ok hd - | Betree_List_Nil => Fail_ Failure - end -. - -(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: - Source: 'src/betree.rs', lines 327:4-327:44 *) -Definition betree_ListPairU64T_head_has_key - (T : Type) (self : betree_List_t (u64 * T)) (key : u64) : result bool := - match self with - | Betree_List_Cons hd _ => let (i, _) := hd in Ok (i s= key) - | Betree_List_Nil => Ok false - end -. - -(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: - Source: 'src/betree.rs', lines 339:4-339:73 *) -Fixpoint betree_ListPairU64T_partition_at_pivot - (T : Type) (n : nat) (self : betree_List_t (u64 * T)) (pivot : u64) : - result ((betree_List_t (u64 * T)) * (betree_List_t (u64 * T))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match self with - | Betree_List_Cons hd tl => - let (i, t) := hd in - if i s>= pivot - then Ok (Betree_List_Nil, Betree_List_Cons (i, t) tl) - else ( - p <- betree_ListPairU64T_partition_at_pivot T n1 tl pivot; - let (ls0, ls1) := p in - Ok (Betree_List_Cons (i, t) ls0, ls1)) - | Betree_List_Nil => Ok (Betree_List_Nil, Betree_List_Nil) - end - end -. - -(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: - Source: 'src/betree.rs', lines 359:4-364:17 *) -Definition betree_Leaf_split - (n : nat) (self : betree_Leaf_t) (content : betree_List_t (u64 * u64)) - (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) - (st : state) : - result (state * (betree_Internal_t * betree_NodeIdCounter_t)) - := - p <- - betree_List_split_at (u64 * u64) n content - params.(betree_Params_split_size); - let (content0, content1) := p in - p1 <- betree_List_hd (u64 * u64) content1; - let (pivot, _) := p1 in - p2 <- betree_NodeIdCounter_fresh_id node_id_cnt; - let (id0, node_id_cnt1) := p2 in - p3 <- betree_NodeIdCounter_fresh_id node_id_cnt1; - let (id1, node_id_cnt2) := p3 in - p4 <- betree_store_leaf_node id0 content0 st; - let (st1, _) := p4 in - p5 <- betree_store_leaf_node id1 content1 st1; - let (st2, _) := p5 in - let n1 := Betree_Node_Leaf - {| - betree_Leaf_id := id0; - betree_Leaf_size := params.(betree_Params_split_size) - |} in - let n2 := Betree_Node_Leaf - {| - betree_Leaf_id := id1; - betree_Leaf_size := params.(betree_Params_split_size) - |} in - Ok (st2, (mkbetree_Internal_t self.(betree_Leaf_id) pivot n1 n2, - node_id_cnt2)) -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: - Source: 'src/betree.rs', lines 789:4-792:34 *) -Fixpoint betree_Node_lookup_first_message_for_key - (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) : - result ((betree_List_t (u64 * betree_Message_t)) * (betree_List_t (u64 * - betree_Message_t) -> result (betree_List_t (u64 * betree_Message_t)))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match msgs with - | Betree_List_Cons x next_msgs => - let (i, m) := x in - if i s>= key - then Ok (Betree_List_Cons (i, m) next_msgs, Ok) - else ( - p <- betree_Node_lookup_first_message_for_key n1 key next_msgs; - let (l, lookup_first_message_for_key_back) := p in - let back := - fun (ret : betree_List_t (u64 * betree_Message_t)) => - next_msgs1 <- lookup_first_message_for_key_back ret; - Ok (Betree_List_Cons (i, m) next_msgs1) in - Ok (l, back)) - | Betree_List_Nil => Ok (Betree_List_Nil, Ok) - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: - Source: 'src/betree.rs', lines 636:4-636:80 *) -Fixpoint betree_Node_lookup_in_bindings - (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) : - result (option u64) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match bindings with - | Betree_List_Cons hd tl => - let (i, i1) := hd in - if i s= key - then Ok (Some i1) - else - if i s> key then Ok None else betree_Node_lookup_in_bindings n1 key tl - | Betree_List_Nil => Ok None - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: - Source: 'src/betree.rs', lines 819:4-819:90 *) -Fixpoint betree_Node_apply_upserts - (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (prev : option u64) - (key : u64) : - result (u64 * (betree_List_t (u64 * betree_Message_t))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - b <- betree_ListPairU64T_head_has_key betree_Message_t msgs key; - if b - then ( - p <- betree_List_pop_front (u64 * betree_Message_t) msgs; - let (msg, msgs1) := p in - let (_, m) := msg in - match m with - | Betree_Message_Insert _ => Fail_ Failure - | Betree_Message_Delete => Fail_ Failure - | Betree_Message_Upsert s => - v <- betree_upsert_update prev s; - betree_Node_apply_upserts n1 msgs1 (Some v) key - end) - else ( - v <- core_option_Option_unwrap u64 prev; - msgs1 <- - betree_List_push_front (u64 * betree_Message_t) msgs (key, - Betree_Message_Insert v); - Ok (v, msgs1)) - end -. - -(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: - Source: 'src/betree.rs', lines 395:4-395:63 *) -Fixpoint betree_Internal_lookup_in_children - (n : nat) (self : betree_Internal_t) (key : u64) (st : state) : - result (state * ((option u64) * betree_Internal_t)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - if key s< self.(betree_Internal_pivot) - then ( - p <- betree_Node_lookup n1 self.(betree_Internal_left) key st; - let (st1, p1) := p in - let (o, n2) := p1 in - Ok (st1, (o, mkbetree_Internal_t self.(betree_Internal_id) - self.(betree_Internal_pivot) n2 self.(betree_Internal_right)))) - else ( - p <- betree_Node_lookup n1 self.(betree_Internal_right) key st; - let (st1, p1) := p in - let (o, n2) := p1 in - Ok (st1, (o, mkbetree_Internal_t self.(betree_Internal_id) - self.(betree_Internal_pivot) self.(betree_Internal_left) n2))) - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: - Source: 'src/betree.rs', lines 709:4-709:58 *) -with betree_Node_lookup - (n : nat) (self : betree_Node_t) (key : u64) (st : state) : - result (state * ((option u64) * betree_Node_t)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match self with - | Betree_Node_Internal node => - p <- betree_load_internal_node node.(betree_Internal_id) st; - let (st1, msgs) := p in - p1 <- betree_Node_lookup_first_message_for_key n1 key msgs; - let (pending, lookup_first_message_for_key_back) := p1 in - match pending with - | Betree_List_Cons p2 l => - let (k, msg) := p2 in - if k s<> key - then ( - p3 <- betree_Internal_lookup_in_children n1 node key st1; - let (st2, p4) := p3 in - let (o, node1) := p4 in - _ <- lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l); - Ok (st2, (o, Betree_Node_Internal node1))) - else - match msg with - | Betree_Message_Insert v => - _ <- - lookup_first_message_for_key_back (Betree_List_Cons (k, - Betree_Message_Insert v) l); - Ok (st1, (Some v, Betree_Node_Internal node)) - | Betree_Message_Delete => - _ <- - lookup_first_message_for_key_back (Betree_List_Cons (k, - Betree_Message_Delete) l); - Ok (st1, (None, Betree_Node_Internal node)) - | Betree_Message_Upsert ufs => - p3 <- betree_Internal_lookup_in_children n1 node key st1; - let (st2, p4) := p3 in - let (v, node1) := p4 in - p5 <- - betree_Node_apply_upserts n1 (Betree_List_Cons (k, - Betree_Message_Upsert ufs) l) v key; - let (v1, pending1) := p5 in - msgs1 <- lookup_first_message_for_key_back pending1; - p6 <- - betree_store_internal_node node1.(betree_Internal_id) msgs1 st2; - let (st3, _) := p6 in - Ok (st3, (Some v1, Betree_Node_Internal node1)) - end - | Betree_List_Nil => - p2 <- betree_Internal_lookup_in_children n1 node key st1; - let (st2, p3) := p2 in - let (o, node1) := p3 in - _ <- lookup_first_message_for_key_back Betree_List_Nil; - Ok (st2, (o, Betree_Node_Internal node1)) - end - | Betree_Node_Leaf node => - p <- betree_load_leaf_node node.(betree_Leaf_id) st; - let (st1, bindings) := p in - o <- betree_Node_lookup_in_bindings n1 key bindings; - Ok (st1, (o, Betree_Node_Leaf node)) - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: - Source: 'src/betree.rs', lines 674:4-674:77 *) -Fixpoint betree_Node_filter_messages_for_key - (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) : - result (betree_List_t (u64 * betree_Message_t)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match msgs with - | Betree_List_Cons p l => - let (k, m) := p in - if k s= key - then ( - p1 <- - betree_List_pop_front (u64 * betree_Message_t) (Betree_List_Cons (k, - m) l); - let (_, msgs1) := p1 in - betree_Node_filter_messages_for_key n1 key msgs1) - else Ok (Betree_List_Cons (k, m) l) - | Betree_List_Nil => Ok Betree_List_Nil - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: - Source: 'src/betree.rs', lines 689:4-692:34 *) -Fixpoint betree_Node_lookup_first_message_after_key - (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) : - result ((betree_List_t (u64 * betree_Message_t)) * (betree_List_t (u64 * - betree_Message_t) -> result (betree_List_t (u64 * betree_Message_t)))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match msgs with - | Betree_List_Cons p next_msgs => - let (k, m) := p in - if k s= key - then ( - p1 <- betree_Node_lookup_first_message_after_key n1 key next_msgs; - let (l, lookup_first_message_after_key_back) := p1 in - let back := - fun (ret : betree_List_t (u64 * betree_Message_t)) => - next_msgs1 <- lookup_first_message_after_key_back ret; - Ok (Betree_List_Cons (k, m) next_msgs1) in - Ok (l, back)) - else Ok (Betree_List_Cons (k, m) next_msgs, Ok) - | Betree_List_Nil => Ok (Betree_List_Nil, Ok) - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: - Source: 'src/betree.rs', lines 521:4-521:89 *) -Definition betree_Node_apply_to_internal - (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (key : u64) - (new_msg : betree_Message_t) : - result (betree_List_t (u64 * betree_Message_t)) - := - p <- betree_Node_lookup_first_message_for_key n key msgs; - let (msgs1, lookup_first_message_for_key_back) := p in - b <- betree_ListPairU64T_head_has_key betree_Message_t msgs1 key; - if b - then - match new_msg with - | Betree_Message_Insert i => - msgs2 <- betree_Node_filter_messages_for_key n key msgs1; - msgs3 <- - betree_List_push_front (u64 * betree_Message_t) msgs2 (key, - Betree_Message_Insert i); - lookup_first_message_for_key_back msgs3 - | Betree_Message_Delete => - msgs2 <- betree_Node_filter_messages_for_key n key msgs1; - msgs3 <- - betree_List_push_front (u64 * betree_Message_t) msgs2 (key, - Betree_Message_Delete); - lookup_first_message_for_key_back msgs3 - | Betree_Message_Upsert s => - p1 <- betree_List_hd (u64 * betree_Message_t) msgs1; - let (_, m) := p1 in - match m with - | Betree_Message_Insert prev => - v <- betree_upsert_update (Some prev) s; - p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1; - let (_, msgs2) := p2 in - msgs3 <- - betree_List_push_front (u64 * betree_Message_t) msgs2 (key, - Betree_Message_Insert v); - lookup_first_message_for_key_back msgs3 - | Betree_Message_Delete => - p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1; - let (_, msgs2) := p2 in - v <- betree_upsert_update None s; - msgs3 <- - betree_List_push_front (u64 * betree_Message_t) msgs2 (key, - Betree_Message_Insert v); - lookup_first_message_for_key_back msgs3 - | Betree_Message_Upsert _ => - p2 <- betree_Node_lookup_first_message_after_key n key msgs1; - let (msgs2, lookup_first_message_after_key_back) := p2 in - msgs3 <- - betree_List_push_front (u64 * betree_Message_t) msgs2 (key, - Betree_Message_Upsert s); - msgs4 <- lookup_first_message_after_key_back msgs3; - lookup_first_message_for_key_back msgs4 - end - end - else ( - msgs2 <- - betree_List_push_front (u64 * betree_Message_t) msgs1 (key, new_msg); - lookup_first_message_for_key_back msgs2) -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: - Source: 'src/betree.rs', lines 502:4-505:5 *) -Fixpoint betree_Node_apply_messages_to_internal - (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) - (new_msgs : betree_List_t (u64 * betree_Message_t)) : - result (betree_List_t (u64 * betree_Message_t)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match new_msgs with - | Betree_List_Cons new_msg new_msgs_tl => - let (i, m) := new_msg in - msgs1 <- betree_Node_apply_to_internal n1 msgs i m; - betree_Node_apply_messages_to_internal n1 msgs1 new_msgs_tl - | Betree_List_Nil => Ok msgs - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: - Source: 'src/betree.rs', lines 653:4-656:32 *) -Fixpoint betree_Node_lookup_mut_in_bindings - (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) : - result ((betree_List_t (u64 * u64)) * (betree_List_t (u64 * u64) -> result - (betree_List_t (u64 * u64)))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match bindings with - | Betree_List_Cons hd tl => - let (i, i1) := hd in - if i s>= key - then Ok (Betree_List_Cons (i, i1) tl, Ok) - else ( - p <- betree_Node_lookup_mut_in_bindings n1 key tl; - let (l, lookup_mut_in_bindings_back) := p in - let back := - fun (ret : betree_List_t (u64 * u64)) => - tl1 <- lookup_mut_in_bindings_back ret; - Ok (Betree_List_Cons (i, i1) tl1) in - Ok (l, back)) - | Betree_List_Nil => Ok (Betree_List_Nil, Ok) - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: - Source: 'src/betree.rs', lines 460:4-460:87 *) -Definition betree_Node_apply_to_leaf - (n : nat) (bindings : betree_List_t (u64 * u64)) (key : u64) - (new_msg : betree_Message_t) : - result (betree_List_t (u64 * u64)) - := - p <- betree_Node_lookup_mut_in_bindings n key bindings; - let (bindings1, lookup_mut_in_bindings_back) := p in - b <- betree_ListPairU64T_head_has_key u64 bindings1 key; - if b - then ( - p1 <- betree_List_pop_front (u64 * u64) bindings1; - let (hd, bindings2) := p1 in - match new_msg with - | Betree_Message_Insert v => - bindings3 <- betree_List_push_front (u64 * u64) bindings2 (key, v); - lookup_mut_in_bindings_back bindings3 - | Betree_Message_Delete => lookup_mut_in_bindings_back bindings2 - | Betree_Message_Upsert s => - let (_, i) := hd in - v <- betree_upsert_update (Some i) s; - bindings3 <- betree_List_push_front (u64 * u64) bindings2 (key, v); - lookup_mut_in_bindings_back bindings3 - end) - else - match new_msg with - | Betree_Message_Insert v => - bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v); - lookup_mut_in_bindings_back bindings2 - | Betree_Message_Delete => lookup_mut_in_bindings_back bindings1 - | Betree_Message_Upsert s => - v <- betree_upsert_update None s; - bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v); - lookup_mut_in_bindings_back bindings2 - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: - Source: 'src/betree.rs', lines 444:4-447:5 *) -Fixpoint betree_Node_apply_messages_to_leaf - (n : nat) (bindings : betree_List_t (u64 * u64)) - (new_msgs : betree_List_t (u64 * betree_Message_t)) : - result (betree_List_t (u64 * u64)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match new_msgs with - | Betree_List_Cons new_msg new_msgs_tl => - let (i, m) := new_msg in - bindings1 <- betree_Node_apply_to_leaf n1 bindings i m; - betree_Node_apply_messages_to_leaf n1 bindings1 new_msgs_tl - | Betree_List_Nil => Ok bindings - end - end -. - -(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: - Source: 'src/betree.rs', lines 410:4-415:26 *) -Fixpoint betree_Internal_flush - (n : nat) (self : betree_Internal_t) (params : betree_Params_t) - (node_id_cnt : betree_NodeIdCounter_t) - (content : betree_List_t (u64 * betree_Message_t)) (st : state) : - result (state * ((betree_List_t (u64 * betree_Message_t)) * - (betree_Internal_t * betree_NodeIdCounter_t))) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - p <- - betree_ListPairU64T_partition_at_pivot betree_Message_t n1 content - self.(betree_Internal_pivot); - let (msgs_left, msgs_right) := p in - len_left <- betree_List_len (u64 * betree_Message_t) n1 msgs_left; - if len_left s>= params.(betree_Params_min_flush_size) - then ( - p1 <- - betree_Node_apply_messages n1 self.(betree_Internal_left) params - node_id_cnt msgs_left st; - let (st1, p2) := p1 in - let (n2, node_id_cnt1) := p2 in - len_right <- betree_List_len (u64 * betree_Message_t) n1 msgs_right; - if len_right s>= params.(betree_Params_min_flush_size) - then ( - p3 <- - betree_Node_apply_messages n1 self.(betree_Internal_right) params - node_id_cnt1 msgs_right st1; - let (st2, p4) := p3 in - let (n3, node_id_cnt2) := p4 in - Ok (st2, (Betree_List_Nil, (mkbetree_Internal_t - self.(betree_Internal_id) self.(betree_Internal_pivot) n2 n3, - node_id_cnt2)))) - else - Ok (st1, (msgs_right, (mkbetree_Internal_t self.(betree_Internal_id) - self.(betree_Internal_pivot) n2 self.(betree_Internal_right), - node_id_cnt1)))) - else ( - p1 <- - betree_Node_apply_messages n1 self.(betree_Internal_right) params - node_id_cnt msgs_right st; - let (st1, p2) := p1 in - let (n2, node_id_cnt1) := p2 in - Ok (st1, (msgs_left, (mkbetree_Internal_t self.(betree_Internal_id) - self.(betree_Internal_pivot) self.(betree_Internal_left) n2, - node_id_cnt1)))) - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: - Source: 'src/betree.rs', lines 588:4-593:5 *) -with betree_Node_apply_messages - (n : nat) (self : betree_Node_t) (params : betree_Params_t) - (node_id_cnt : betree_NodeIdCounter_t) - (msgs : betree_List_t (u64 * betree_Message_t)) (st : state) : - result (state * (betree_Node_t * betree_NodeIdCounter_t)) - := - match n with - | O => Fail_ OutOfFuel - | S n1 => - match self with - | Betree_Node_Internal node => - p <- betree_load_internal_node node.(betree_Internal_id) st; - let (st1, content) := p in - content1 <- betree_Node_apply_messages_to_internal n1 content msgs; - num_msgs <- betree_List_len (u64 * betree_Message_t) n1 content1; - if num_msgs s>= params.(betree_Params_min_flush_size) - then ( - p1 <- betree_Internal_flush n1 node params node_id_cnt content1 st1; - let (st2, p2) := p1 in - let (content2, p3) := p2 in - let (node1, node_id_cnt1) := p3 in - p4 <- - betree_store_internal_node node1.(betree_Internal_id) content2 st2; - let (st3, _) := p4 in - Ok (st3, (Betree_Node_Internal node1, node_id_cnt1))) - else ( - p1 <- - betree_store_internal_node node.(betree_Internal_id) content1 st1; - let (st2, _) := p1 in - Ok (st2, (Betree_Node_Internal node, node_id_cnt))) - | Betree_Node_Leaf node => - p <- betree_load_leaf_node node.(betree_Leaf_id) st; - let (st1, content) := p in - content1 <- betree_Node_apply_messages_to_leaf n1 content msgs; - len <- betree_List_len (u64 * u64) n1 content1; - i <- u64_mul 2%u64 params.(betree_Params_split_size); - if len s>= i - then ( - p1 <- betree_Leaf_split n1 node content1 params node_id_cnt st1; - let (st2, p2) := p1 in - let (new_node, node_id_cnt1) := p2 in - p3 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st2; - let (st3, _) := p3 in - Ok (st3, (Betree_Node_Internal new_node, node_id_cnt1))) - else ( - p1 <- betree_store_leaf_node node.(betree_Leaf_id) content1 st1; - let (st2, _) := p1 in - Ok (st2, (Betree_Node_Leaf - {| betree_Leaf_id := node.(betree_Leaf_id); betree_Leaf_size := len - |}, node_id_cnt))) - end - end -. - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: - Source: 'src/betree.rs', lines 576:4-582:5 *) -Definition betree_Node_apply - (n : nat) (self : betree_Node_t) (params : betree_Params_t) - (node_id_cnt : betree_NodeIdCounter_t) (key : u64) - (new_msg : betree_Message_t) (st : state) : - result (state * (betree_Node_t * betree_NodeIdCounter_t)) - := - p <- - betree_Node_apply_messages n self params node_id_cnt (Betree_List_Cons - (key, new_msg) Betree_List_Nil) st; - let (st1, p1) := p in - let (self1, node_id_cnt1) := p1 in - Ok (st1, (self1, node_id_cnt1)) -. - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]: - Source: 'src/betree.rs', lines 849:4-849:60 *) -Definition betree_BeTree_new - (min_flush_size : u64) (split_size : u64) (st : state) : - result (state * betree_BeTree_t) - := - node_id_cnt <- betree_NodeIdCounter_new; - p <- betree_NodeIdCounter_fresh_id node_id_cnt; - let (id, node_id_cnt1) := p in - p1 <- betree_store_leaf_node id Betree_List_Nil st; - let (st1, _) := p1 in - Ok (st1, - {| - betree_BeTree_params := - {| - betree_Params_min_flush_size := min_flush_size; - betree_Params_split_size := split_size - |}; - betree_BeTree_node_id_cnt := node_id_cnt1; - betree_BeTree_root := - (Betree_Node_Leaf - {| betree_Leaf_id := id; betree_Leaf_size := 0%u64 |}) - |}) -. - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: - Source: 'src/betree.rs', lines 868:4-868:47 *) -Definition betree_BeTree_apply - (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) - (st : state) : - result (state * betree_BeTree_t) - := - p <- - betree_Node_apply n self.(betree_BeTree_root) self.(betree_BeTree_params) - self.(betree_BeTree_node_id_cnt) key msg st; - let (st1, p1) := p in - let (n1, nic) := p1 in - Ok (st1, - {| - betree_BeTree_params := self.(betree_BeTree_params); - betree_BeTree_node_id_cnt := nic; - betree_BeTree_root := n1 - |}) -. - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: - Source: 'src/betree.rs', lines 874:4-874:52 *) -Definition betree_BeTree_insert - (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) : - result (state * betree_BeTree_t) - := - betree_BeTree_apply n self key (Betree_Message_Insert value) st -. - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: - Source: 'src/betree.rs', lines 880:4-880:38 *) -Definition betree_BeTree_delete - (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) : - result (state * betree_BeTree_t) - := - betree_BeTree_apply n self key Betree_Message_Delete st -. - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: - Source: 'src/betree.rs', lines 886:4-886:59 *) -Definition betree_BeTree_upsert - (n : nat) (self : betree_BeTree_t) (key : u64) - (upd : betree_UpsertFunState_t) (st : state) : - result (state * betree_BeTree_t) - := - betree_BeTree_apply n self key (Betree_Message_Upsert upd) st -. - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: - Source: 'src/betree.rs', lines 895:4-895:62 *) -Definition betree_BeTree_lookup - (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) : - result (state * ((option u64) * betree_BeTree_t)) - := - p <- betree_Node_lookup n self.(betree_BeTree_root) key st; - let (st1, p1) := p in - let (o, n1) := p1 in - Ok (st1, (o, - {| - betree_BeTree_params := self.(betree_BeTree_params); - betree_BeTree_node_id_cnt := self.(betree_BeTree_node_id_cnt); - betree_BeTree_root := n1 - |})) -. - -(** [betree_main::main]: - Source: 'src/main.rs', lines 4:0-4:9 *) -Definition main : result unit := - Ok tt. - -(** Unit test for [betree_main::main] *) -Check (main )%return. - -End BetreeMain_Funs. diff --git a/tests/coq/betree/BetreeMain_FunsExternal.v b/tests/coq/betree/BetreeMain_FunsExternal.v deleted file mode 100644 index 099a2e8f..00000000 --- a/tests/coq/betree/BetreeMain_FunsExternal.v +++ /dev/null @@ -1,39 +0,0 @@ -(** [betree_main]: external functions. --- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Export BetreeMain_Types. -Import BetreeMain_Types. -Module BetreeMain_FunsExternal. - -(** [betree_main::betree_utils::load_internal_node]: forward function - Source: 'src/betree_utils.rs', lines 98:0-98:63 *) -Axiom betree_utils_load_internal_node - : u64 -> state -> result (state * (betree_List_t (u64 * betree_Message_t))) -. - -(** [betree_main::betree_utils::store_internal_node]: forward function - Source: 'src/betree_utils.rs', lines 115:0-115:71 *) -Axiom betree_utils_store_internal_node - : - u64 -> betree_List_t (u64 * betree_Message_t) -> state -> result (state * - unit) -. - -(** [betree_main::betree_utils::load_leaf_node]: forward function - Source: 'src/betree_utils.rs', lines 132:0-132:55 *) -Axiom betree_utils_load_leaf_node - : u64 -> state -> result (state * (betree_List_t (u64 * u64))) -. - -(** [betree_main::betree_utils::store_leaf_node]: forward function - Source: 'src/betree_utils.rs', lines 145:0-145:63 *) -Axiom betree_utils_store_leaf_node - : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit) -. - -End BetreeMain_FunsExternal. diff --git a/tests/coq/betree/BetreeMain_FunsExternal_Template.v b/tests/coq/betree/BetreeMain_FunsExternal_Template.v deleted file mode 100644 index 58be2733..00000000 --- a/tests/coq/betree/BetreeMain_FunsExternal_Template.v +++ /dev/null @@ -1,40 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: external functions. --- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Import BetreeMain_Types. -Include BetreeMain_Types. -Module BetreeMain_FunsExternal_Template. - -(** [betree_main::betree_utils::load_internal_node]: - Source: 'src/betree_utils.rs', lines 98:0-98:63 *) -Axiom betree_utils_load_internal_node - : u64 -> state -> result (state * (betree_List_t (u64 * betree_Message_t))) -. - -(** [betree_main::betree_utils::store_internal_node]: - Source: 'src/betree_utils.rs', lines 115:0-115:71 *) -Axiom betree_utils_store_internal_node - : - u64 -> betree_List_t (u64 * betree_Message_t) -> state -> result (state * - unit) -. - -(** [betree_main::betree_utils::load_leaf_node]: - Source: 'src/betree_utils.rs', lines 132:0-132:55 *) -Axiom betree_utils_load_leaf_node - : u64 -> state -> result (state * (betree_List_t (u64 * u64))) -. - -(** [betree_main::betree_utils::store_leaf_node]: - Source: 'src/betree_utils.rs', lines 145:0-145:63 *) -Axiom betree_utils_store_leaf_node - : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit) -. - -End BetreeMain_FunsExternal_Template. diff --git a/tests/coq/betree/BetreeMain_Types.v b/tests/coq/betree/BetreeMain_Types.v deleted file mode 100644 index acbc2085..00000000 --- a/tests/coq/betree/BetreeMain_Types.v +++ /dev/null @@ -1,118 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: type definitions *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Require Import BetreeMain_TypesExternal. -Include BetreeMain_TypesExternal. -Module BetreeMain_Types. - -(** [betree_main::betree::List] - Source: 'src/betree.rs', lines 17:0-17:23 *) -Inductive betree_List_t (T : Type) := -| Betree_List_Cons : T -> betree_List_t T -> betree_List_t T -| Betree_List_Nil : betree_List_t T -. - -Arguments Betree_List_Cons { _ }. -Arguments Betree_List_Nil { _ }. - -(** [betree_main::betree::UpsertFunState] - Source: 'src/betree.rs', lines 63:0-63:23 *) -Inductive betree_UpsertFunState_t := -| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t -| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t -. - -(** [betree_main::betree::Message] - Source: 'src/betree.rs', lines 69:0-69:23 *) -Inductive betree_Message_t := -| Betree_Message_Insert : u64 -> betree_Message_t -| Betree_Message_Delete : betree_Message_t -| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t -. - -(** [betree_main::betree::Leaf] - Source: 'src/betree.rs', lines 167:0-167:11 *) -Record betree_Leaf_t := -mkbetree_Leaf_t { - betree_Leaf_id : u64; betree_Leaf_size : u64; -} -. - -(** [betree_main::betree::Internal] - Source: 'src/betree.rs', lines 156:0-156:15 *) -Inductive betree_Internal_t := -| mkbetree_Internal_t : - u64 -> - u64 -> - betree_Node_t -> - betree_Node_t -> - betree_Internal_t - -(** [betree_main::betree::Node] - Source: 'src/betree.rs', lines 179:0-179:9 *) -with betree_Node_t := -| Betree_Node_Internal : betree_Internal_t -> betree_Node_t -| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t -. - -Definition betree_Internal_id (x : betree_Internal_t) := - match x with | mkbetree_Internal_t x1 _ _ _ => x1 end -. - -Notation "x2 .(betree_Internal_id)" := (betree_Internal_id x2) (at level 9). - -Definition betree_Internal_pivot (x : betree_Internal_t) := - match x with | mkbetree_Internal_t _ x1 _ _ => x1 end -. - -Notation "x2 .(betree_Internal_pivot)" := (betree_Internal_pivot x2) - (at level 9) -. - -Definition betree_Internal_left (x : betree_Internal_t) := - match x with | mkbetree_Internal_t _ _ x1 _ => x1 end -. - -Notation "x2 .(betree_Internal_left)" := (betree_Internal_left x2) (at level 9) -. - -Definition betree_Internal_right (x : betree_Internal_t) := - match x with | mkbetree_Internal_t _ _ _ x1 => x1 end -. - -Notation "x2 .(betree_Internal_right)" := (betree_Internal_right x2) - (at level 9) -. - -(** [betree_main::betree::Params] - Source: 'src/betree.rs', lines 187:0-187:13 *) -Record betree_Params_t := -mkbetree_Params_t { - betree_Params_min_flush_size : u64; betree_Params_split_size : u64; -} -. - -(** [betree_main::betree::NodeIdCounter] - Source: 'src/betree.rs', lines 201:0-201:20 *) -Record betree_NodeIdCounter_t := -mkbetree_NodeIdCounter_t { - betree_NodeIdCounter_next_node_id : u64; -} -. - -(** [betree_main::betree::BeTree] - Source: 'src/betree.rs', lines 218:0-218:17 *) -Record betree_BeTree_t := -mkbetree_BeTree_t { - betree_BeTree_params : betree_Params_t; - betree_BeTree_node_id_cnt : betree_NodeIdCounter_t; - betree_BeTree_root : betree_Node_t; -} -. - -End BetreeMain_Types. diff --git a/tests/coq/betree/BetreeMain_TypesExternal.v b/tests/coq/betree/BetreeMain_TypesExternal.v deleted file mode 100644 index 870d2601..00000000 --- a/tests/coq/betree/BetreeMain_TypesExternal.v +++ /dev/null @@ -1,14 +0,0 @@ -(** [betree_main]: external types. --- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Module BetreeMain_TypesExternal. - -(** The state type used in the state-error monad *) -Axiom state : Type. - -End BetreeMain_TypesExternal. diff --git a/tests/coq/betree/BetreeMain_TypesExternal_Template.v b/tests/coq/betree/BetreeMain_TypesExternal_Template.v deleted file mode 100644 index 651de2b7..00000000 --- a/tests/coq/betree/BetreeMain_TypesExternal_Template.v +++ /dev/null @@ -1,15 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: external types. --- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *) -Require Import Primitives. -Import Primitives. -Require Import Coq.ZArith.ZArith. -Require Import List. -Import ListNotations. -Local Open Scope Primitives_scope. -Module BetreeMain_TypesExternal_Template. - -(** The state type used in the state-error monad *) -Axiom state : Type. - -End BetreeMain_TypesExternal_Template. diff --git a/tests/coq/betree/Betree_Funs.v b/tests/coq/betree/Betree_Funs.v new file mode 100644 index 00000000..b965d423 --- /dev/null +++ b/tests/coq/betree/Betree_Funs.v @@ -0,0 +1,837 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: function definitions *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Require Import Betree_Types. +Include Betree_Types. +Require Import Betree_FunsExternal. +Include Betree_FunsExternal. +Module Betree_Funs. + +(** [betree::betree::load_internal_node]: + Source: 'src/betree.rs', lines 36:0-36:52 *) +Definition betree_load_internal_node + (id : u64) (st : state) : + result (state * (betree_List_t (u64 * betree_Message_t))) + := + betree_utils_load_internal_node id st +. + +(** [betree::betree::store_internal_node]: + Source: 'src/betree.rs', lines 41:0-41:60 *) +Definition betree_store_internal_node + (id : u64) (content : betree_List_t (u64 * betree_Message_t)) (st : state) : + result (state * unit) + := + betree_utils_store_internal_node id content st +. + +(** [betree::betree::load_leaf_node]: + Source: 'src/betree.rs', lines 46:0-46:44 *) +Definition betree_load_leaf_node + (id : u64) (st : state) : result (state * (betree_List_t (u64 * u64))) := + betree_utils_load_leaf_node id st +. + +(** [betree::betree::store_leaf_node]: + Source: 'src/betree.rs', lines 51:0-51:52 *) +Definition betree_store_leaf_node + (id : u64) (content : betree_List_t (u64 * u64)) (st : state) : + result (state * unit) + := + betree_utils_store_leaf_node id content st +. + +(** [betree::betree::fresh_node_id]: + Source: 'src/betree.rs', lines 55:0-55:48 *) +Definition betree_fresh_node_id (counter : u64) : result (u64 * u64) := + counter1 <- u64_add counter 1%u64; Ok (counter, counter1) +. + +(** [betree::betree::{betree::betree::NodeIdCounter}::new]: + Source: 'src/betree.rs', lines 206:4-206:20 *) +Definition betree_NodeIdCounter_new : result betree_NodeIdCounter_t := + Ok {| betree_NodeIdCounter_next_node_id := 0%u64 |} +. + +(** [betree::betree::{betree::betree::NodeIdCounter}::fresh_id]: + Source: 'src/betree.rs', lines 210:4-210:36 *) +Definition betree_NodeIdCounter_fresh_id + (self : betree_NodeIdCounter_t) : result (u64 * betree_NodeIdCounter_t) := + i <- u64_add self.(betree_NodeIdCounter_next_node_id) 1%u64; + Ok (self.(betree_NodeIdCounter_next_node_id), + {| betree_NodeIdCounter_next_node_id := i |}) +. + +(** [betree::betree::upsert_update]: + Source: 'src/betree.rs', lines 234:0-234:70 *) +Definition betree_upsert_update + (prev : option u64) (st : betree_UpsertFunState_t) : result u64 := + match prev with + | None => + match st with + | Betree_UpsertFunState_Add v => Ok v + | Betree_UpsertFunState_Sub _ => Ok 0%u64 + end + | Some prev1 => + match st with + | Betree_UpsertFunState_Add v => + margin <- u64_sub core_u64_max prev1; + if margin s>= v then u64_add prev1 v else Ok core_u64_max + | Betree_UpsertFunState_Sub v => + if prev1 s>= v then u64_sub prev1 v else Ok 0%u64 + end + end +. + +(** [betree::betree::{betree::betree::List#1}::len]: + Source: 'src/betree.rs', lines 276:4-276:24 *) +Fixpoint betree_List_len + (T : Type) (n : nat) (self : betree_List_t T) : result u64 := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match self with + | Betree_List_Cons _ tl => i <- betree_List_len T n1 tl; u64_add 1%u64 i + | Betree_List_Nil => Ok 0%u64 + end + end +. + +(** [betree::betree::{betree::betree::List#1}::split_at]: + Source: 'src/betree.rs', lines 284:4-284:51 *) +Fixpoint betree_List_split_at + (T : Type) (n : nat) (self : betree_List_t T) (n1 : u64) : + result ((betree_List_t T) * (betree_List_t T)) + := + match n with + | O => Fail_ OutOfFuel + | S n2 => + if n1 s= 0%u64 + then Ok (Betree_List_Nil, self) + else + match self with + | Betree_List_Cons hd tl => + i <- u64_sub n1 1%u64; + p <- betree_List_split_at T n2 tl i; + let (ls0, ls1) := p in + Ok (Betree_List_Cons hd ls0, ls1) + | Betree_List_Nil => Fail_ Failure + end + end +. + +(** [betree::betree::{betree::betree::List#1}::push_front]: + Source: 'src/betree.rs', lines 299:4-299:34 *) +Definition betree_List_push_front + (T : Type) (self : betree_List_t T) (x : T) : result (betree_List_t T) := + let (tl, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in + Ok (Betree_List_Cons x tl) +. + +(** [betree::betree::{betree::betree::List#1}::pop_front]: + Source: 'src/betree.rs', lines 306:4-306:32 *) +Definition betree_List_pop_front + (T : Type) (self : betree_List_t T) : result (T * (betree_List_t T)) := + let (ls, _) := core_mem_replace (betree_List_t T) self Betree_List_Nil in + match ls with + | Betree_List_Cons x tl => Ok (x, tl) + | Betree_List_Nil => Fail_ Failure + end +. + +(** [betree::betree::{betree::betree::List#1}::hd]: + Source: 'src/betree.rs', lines 318:4-318:22 *) +Definition betree_List_hd (T : Type) (self : betree_List_t T) : result T := + match self with + | Betree_List_Cons hd _ => Ok hd + | Betree_List_Nil => Fail_ Failure + end +. + +(** [betree::betree::{betree::betree::List<(u64, T)>#2}::head_has_key]: + Source: 'src/betree.rs', lines 327:4-327:44 *) +Definition betree_ListPairU64T_head_has_key + (T : Type) (self : betree_List_t (u64 * T)) (key : u64) : result bool := + match self with + | Betree_List_Cons hd _ => let (i, _) := hd in Ok (i s= key) + | Betree_List_Nil => Ok false + end +. + +(** [betree::betree::{betree::betree::List<(u64, T)>#2}::partition_at_pivot]: + Source: 'src/betree.rs', lines 339:4-339:73 *) +Fixpoint betree_ListPairU64T_partition_at_pivot + (T : Type) (n : nat) (self : betree_List_t (u64 * T)) (pivot : u64) : + result ((betree_List_t (u64 * T)) * (betree_List_t (u64 * T))) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match self with + | Betree_List_Cons hd tl => + let (i, t) := hd in + if i s>= pivot + then Ok (Betree_List_Nil, Betree_List_Cons (i, t) tl) + else ( + p <- betree_ListPairU64T_partition_at_pivot T n1 tl pivot; + let (ls0, ls1) := p in + Ok (Betree_List_Cons (i, t) ls0, ls1)) + | Betree_List_Nil => Ok (Betree_List_Nil, Betree_List_Nil) + end + end +. + +(** [betree::betree::{betree::betree::Leaf#3}::split]: + Source: 'src/betree.rs', lines 359:4-364:17 *) +Definition betree_Leaf_split + (n : nat) (self : betree_Leaf_t) (content : betree_List_t (u64 * u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (st : state) : + result (state * (betree_Internal_t * betree_NodeIdCounter_t)) + := + p <- + betree_List_split_at (u64 * u64) n content + params.(betree_Params_split_size); + let (content0, content1) := p in + p1 <- betree_List_hd (u64 * u64) content1; + let (pivot, _) := p1 in + p2 <- betree_NodeIdCounter_fresh_id node_id_cnt; + let (id0, node_id_cnt1) := p2 in + p3 <- betree_NodeIdCounter_fresh_id node_id_cnt1; + let (id1, node_id_cnt2) := p3 in + p4 <- betree_store_leaf_node id0 content0 st; + let (st1, _) := p4 in + p5 <- betree_store_leaf_node id1 content1 st1; + let (st2, _) := p5 in + let n1 := Betree_Node_Leaf + {| + betree_Leaf_id := id0; + betree_Leaf_size := params.(betree_Params_split_size) + |} in + let n2 := Betree_Node_Leaf + {| + betree_Leaf_id := id1; + betree_Leaf_size := params.(betree_Params_split_size) + |} in + Ok (st2, (mkbetree_Internal_t self.(betree_Leaf_id) pivot n1 n2, + node_id_cnt2)) +. + +(** [betree::betree::{betree::betree::Node#5}::lookup_first_message_for_key]: + Source: 'src/betree.rs', lines 789:4-792:34 *) +Fixpoint betree_Node_lookup_first_message_for_key + (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) : + result ((betree_List_t (u64 * betree_Message_t)) * (betree_List_t (u64 * + betree_Message_t) -> result (betree_List_t (u64 * betree_Message_t)))) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match msgs with + | Betree_List_Cons x next_msgs => + let (i, m) := x in + if i s>= key + then Ok (Betree_List_Cons (i, m) next_msgs, Ok) + else ( + p <- betree_Node_lookup_first_message_for_key n1 key next_msgs; + let (l, lookup_first_message_for_key_back) := p in + let back := + fun (ret : betree_List_t (u64 * betree_Message_t)) => + next_msgs1 <- lookup_first_message_for_key_back ret; + Ok (Betree_List_Cons (i, m) next_msgs1) in + Ok (l, back)) + | Betree_List_Nil => Ok (Betree_List_Nil, Ok) + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::lookup_in_bindings]: + Source: 'src/betree.rs', lines 636:4-636:80 *) +Fixpoint betree_Node_lookup_in_bindings + (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) : + result (option u64) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match bindings with + | Betree_List_Cons hd tl => + let (i, i1) := hd in + if i s= key + then Ok (Some i1) + else + if i s> key then Ok None else betree_Node_lookup_in_bindings n1 key tl + | Betree_List_Nil => Ok None + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::apply_upserts]: + Source: 'src/betree.rs', lines 819:4-819:90 *) +Fixpoint betree_Node_apply_upserts + (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (prev : option u64) + (key : u64) : + result (u64 * (betree_List_t (u64 * betree_Message_t))) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + b <- betree_ListPairU64T_head_has_key betree_Message_t msgs key; + if b + then ( + p <- betree_List_pop_front (u64 * betree_Message_t) msgs; + let (msg, msgs1) := p in + let (_, m) := msg in + match m with + | Betree_Message_Insert _ => Fail_ Failure + | Betree_Message_Delete => Fail_ Failure + | Betree_Message_Upsert s => + v <- betree_upsert_update prev s; + betree_Node_apply_upserts n1 msgs1 (Some v) key + end) + else ( + v <- core_option_Option_unwrap u64 prev; + msgs1 <- + betree_List_push_front (u64 * betree_Message_t) msgs (key, + Betree_Message_Insert v); + Ok (v, msgs1)) + end +. + +(** [betree::betree::{betree::betree::Internal#4}::lookup_in_children]: + Source: 'src/betree.rs', lines 395:4-395:63 *) +Fixpoint betree_Internal_lookup_in_children + (n : nat) (self : betree_Internal_t) (key : u64) (st : state) : + result (state * ((option u64) * betree_Internal_t)) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + if key s< self.(betree_Internal_pivot) + then ( + p <- betree_Node_lookup n1 self.(betree_Internal_left) key st; + let (st1, p1) := p in + let (o, n2) := p1 in + Ok (st1, (o, mkbetree_Internal_t self.(betree_Internal_id) + self.(betree_Internal_pivot) n2 self.(betree_Internal_right)))) + else ( + p <- betree_Node_lookup n1 self.(betree_Internal_right) key st; + let (st1, p1) := p in + let (o, n2) := p1 in + Ok (st1, (o, mkbetree_Internal_t self.(betree_Internal_id) + self.(betree_Internal_pivot) self.(betree_Internal_left) n2))) + end + +(** [betree::betree::{betree::betree::Node#5}::lookup]: + Source: 'src/betree.rs', lines 709:4-709:58 *) +with betree_Node_lookup + (n : nat) (self : betree_Node_t) (key : u64) (st : state) : + result (state * ((option u64) * betree_Node_t)) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match self with + | Betree_Node_Internal node => + p <- betree_load_internal_node node.(betree_Internal_id) st; + let (st1, msgs) := p in + p1 <- betree_Node_lookup_first_message_for_key n1 key msgs; + let (pending, lookup_first_message_for_key_back) := p1 in + match pending with + | Betree_List_Cons p2 l => + let (k, msg) := p2 in + if k s<> key + then ( + p3 <- betree_Internal_lookup_in_children n1 node key st1; + let (st2, p4) := p3 in + let (o, node1) := p4 in + _ <- lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l); + Ok (st2, (o, Betree_Node_Internal node1))) + else + match msg with + | Betree_Message_Insert v => + _ <- + lookup_first_message_for_key_back (Betree_List_Cons (k, + Betree_Message_Insert v) l); + Ok (st1, (Some v, Betree_Node_Internal node)) + | Betree_Message_Delete => + _ <- + lookup_first_message_for_key_back (Betree_List_Cons (k, + Betree_Message_Delete) l); + Ok (st1, (None, Betree_Node_Internal node)) + | Betree_Message_Upsert ufs => + p3 <- betree_Internal_lookup_in_children n1 node key st1; + let (st2, p4) := p3 in + let (v, node1) := p4 in + p5 <- + betree_Node_apply_upserts n1 (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key; + let (v1, pending1) := p5 in + msgs1 <- lookup_first_message_for_key_back pending1; + p6 <- + betree_store_internal_node node1.(betree_Internal_id) msgs1 st2; + let (st3, _) := p6 in + Ok (st3, (Some v1, Betree_Node_Internal node1)) + end + | Betree_List_Nil => + p2 <- betree_Internal_lookup_in_children n1 node key st1; + let (st2, p3) := p2 in + let (o, node1) := p3 in + _ <- lookup_first_message_for_key_back Betree_List_Nil; + Ok (st2, (o, Betree_Node_Internal node1)) + end + | Betree_Node_Leaf node => + p <- betree_load_leaf_node node.(betree_Leaf_id) st; + let (st1, bindings) := p in + o <- betree_Node_lookup_in_bindings n1 key bindings; + Ok (st1, (o, Betree_Node_Leaf node)) + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::filter_messages_for_key]: + Source: 'src/betree.rs', lines 674:4-674:77 *) +Fixpoint betree_Node_filter_messages_for_key + (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) : + result (betree_List_t (u64 * betree_Message_t)) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match msgs with + | Betree_List_Cons p l => + let (k, m) := p in + if k s= key + then ( + p1 <- + betree_List_pop_front (u64 * betree_Message_t) (Betree_List_Cons (k, + m) l); + let (_, msgs1) := p1 in + betree_Node_filter_messages_for_key n1 key msgs1) + else Ok (Betree_List_Cons (k, m) l) + | Betree_List_Nil => Ok Betree_List_Nil + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::lookup_first_message_after_key]: + Source: 'src/betree.rs', lines 689:4-692:34 *) +Fixpoint betree_Node_lookup_first_message_after_key + (n : nat) (key : u64) (msgs : betree_List_t (u64 * betree_Message_t)) : + result ((betree_List_t (u64 * betree_Message_t)) * (betree_List_t (u64 * + betree_Message_t) -> result (betree_List_t (u64 * betree_Message_t)))) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match msgs with + | Betree_List_Cons p next_msgs => + let (k, m) := p in + if k s= key + then ( + p1 <- betree_Node_lookup_first_message_after_key n1 key next_msgs; + let (l, lookup_first_message_after_key_back) := p1 in + let back := + fun (ret : betree_List_t (u64 * betree_Message_t)) => + next_msgs1 <- lookup_first_message_after_key_back ret; + Ok (Betree_List_Cons (k, m) next_msgs1) in + Ok (l, back)) + else Ok (Betree_List_Cons (k, m) next_msgs, Ok) + | Betree_List_Nil => Ok (Betree_List_Nil, Ok) + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::apply_to_internal]: + Source: 'src/betree.rs', lines 521:4-521:89 *) +Definition betree_Node_apply_to_internal + (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 * betree_Message_t)) + := + p <- betree_Node_lookup_first_message_for_key n key msgs; + let (msgs1, lookup_first_message_for_key_back) := p in + b <- betree_ListPairU64T_head_has_key betree_Message_t msgs1 key; + if b + then + match new_msg with + | Betree_Message_Insert i => + msgs2 <- betree_Node_filter_messages_for_key n key msgs1; + msgs3 <- + betree_List_push_front (u64 * betree_Message_t) msgs2 (key, + Betree_Message_Insert i); + lookup_first_message_for_key_back msgs3 + | Betree_Message_Delete => + msgs2 <- betree_Node_filter_messages_for_key n key msgs1; + msgs3 <- + betree_List_push_front (u64 * betree_Message_t) msgs2 (key, + Betree_Message_Delete); + lookup_first_message_for_key_back msgs3 + | Betree_Message_Upsert s => + p1 <- betree_List_hd (u64 * betree_Message_t) msgs1; + let (_, m) := p1 in + match m with + | Betree_Message_Insert prev => + v <- betree_upsert_update (Some prev) s; + p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1; + let (_, msgs2) := p2 in + msgs3 <- + betree_List_push_front (u64 * betree_Message_t) msgs2 (key, + Betree_Message_Insert v); + lookup_first_message_for_key_back msgs3 + | Betree_Message_Delete => + p2 <- betree_List_pop_front (u64 * betree_Message_t) msgs1; + let (_, msgs2) := p2 in + v <- betree_upsert_update None s; + msgs3 <- + betree_List_push_front (u64 * betree_Message_t) msgs2 (key, + Betree_Message_Insert v); + lookup_first_message_for_key_back msgs3 + | Betree_Message_Upsert _ => + p2 <- betree_Node_lookup_first_message_after_key n key msgs1; + let (msgs2, lookup_first_message_after_key_back) := p2 in + msgs3 <- + betree_List_push_front (u64 * betree_Message_t) msgs2 (key, + Betree_Message_Upsert s); + msgs4 <- lookup_first_message_after_key_back msgs3; + lookup_first_message_for_key_back msgs4 + end + end + else ( + msgs2 <- + betree_List_push_front (u64 * betree_Message_t) msgs1 (key, new_msg); + lookup_first_message_for_key_back msgs2) +. + +(** [betree::betree::{betree::betree::Node#5}::apply_messages_to_internal]: + Source: 'src/betree.rs', lines 502:4-505:5 *) +Fixpoint betree_Node_apply_messages_to_internal + (n : nat) (msgs : betree_List_t (u64 * betree_Message_t)) + (new_msgs : betree_List_t (u64 * betree_Message_t)) : + result (betree_List_t (u64 * betree_Message_t)) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match new_msgs with + | Betree_List_Cons new_msg new_msgs_tl => + let (i, m) := new_msg in + msgs1 <- betree_Node_apply_to_internal n1 msgs i m; + betree_Node_apply_messages_to_internal n1 msgs1 new_msgs_tl + | Betree_List_Nil => Ok msgs + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::lookup_mut_in_bindings]: + Source: 'src/betree.rs', lines 653:4-656:32 *) +Fixpoint betree_Node_lookup_mut_in_bindings + (n : nat) (key : u64) (bindings : betree_List_t (u64 * u64)) : + result ((betree_List_t (u64 * u64)) * (betree_List_t (u64 * u64) -> result + (betree_List_t (u64 * u64)))) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match bindings with + | Betree_List_Cons hd tl => + let (i, i1) := hd in + if i s>= key + then Ok (Betree_List_Cons (i, i1) tl, Ok) + else ( + p <- betree_Node_lookup_mut_in_bindings n1 key tl; + let (l, lookup_mut_in_bindings_back) := p in + let back := + fun (ret : betree_List_t (u64 * u64)) => + tl1 <- lookup_mut_in_bindings_back ret; + Ok (Betree_List_Cons (i, i1) tl1) in + Ok (l, back)) + | Betree_List_Nil => Ok (Betree_List_Nil, Ok) + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::apply_to_leaf]: + Source: 'src/betree.rs', lines 460:4-460:87 *) +Definition betree_Node_apply_to_leaf + (n : nat) (bindings : betree_List_t (u64 * u64)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 * u64)) + := + p <- betree_Node_lookup_mut_in_bindings n key bindings; + let (bindings1, lookup_mut_in_bindings_back) := p in + b <- betree_ListPairU64T_head_has_key u64 bindings1 key; + if b + then ( + p1 <- betree_List_pop_front (u64 * u64) bindings1; + let (hd, bindings2) := p1 in + match new_msg with + | Betree_Message_Insert v => + bindings3 <- betree_List_push_front (u64 * u64) bindings2 (key, v); + lookup_mut_in_bindings_back bindings3 + | Betree_Message_Delete => lookup_mut_in_bindings_back bindings2 + | Betree_Message_Upsert s => + let (_, i) := hd in + v <- betree_upsert_update (Some i) s; + bindings3 <- betree_List_push_front (u64 * u64) bindings2 (key, v); + lookup_mut_in_bindings_back bindings3 + end) + else + match new_msg with + | Betree_Message_Insert v => + bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v); + lookup_mut_in_bindings_back bindings2 + | Betree_Message_Delete => lookup_mut_in_bindings_back bindings1 + | Betree_Message_Upsert s => + v <- betree_upsert_update None s; + bindings2 <- betree_List_push_front (u64 * u64) bindings1 (key, v); + lookup_mut_in_bindings_back bindings2 + end +. + +(** [betree::betree::{betree::betree::Node#5}::apply_messages_to_leaf]: + Source: 'src/betree.rs', lines 444:4-447:5 *) +Fixpoint betree_Node_apply_messages_to_leaf + (n : nat) (bindings : betree_List_t (u64 * u64)) + (new_msgs : betree_List_t (u64 * betree_Message_t)) : + result (betree_List_t (u64 * u64)) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match new_msgs with + | Betree_List_Cons new_msg new_msgs_tl => + let (i, m) := new_msg in + bindings1 <- betree_Node_apply_to_leaf n1 bindings i m; + betree_Node_apply_messages_to_leaf n1 bindings1 new_msgs_tl + | Betree_List_Nil => Ok bindings + end + end +. + +(** [betree::betree::{betree::betree::Internal#4}::flush]: + Source: 'src/betree.rs', lines 410:4-415:26 *) +Fixpoint betree_Internal_flush + (n : nat) (self : betree_Internal_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 * betree_Message_t)) (st : state) : + result (state * ((betree_List_t (u64 * betree_Message_t)) * + (betree_Internal_t * betree_NodeIdCounter_t))) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + p <- + betree_ListPairU64T_partition_at_pivot betree_Message_t n1 content + self.(betree_Internal_pivot); + let (msgs_left, msgs_right) := p in + len_left <- betree_List_len (u64 * betree_Message_t) n1 msgs_left; + if len_left s>= params.(betree_Params_min_flush_size) + then ( + p1 <- + betree_Node_apply_messages n1 self.(betree_Internal_left) params + node_id_cnt msgs_left st; + let (st1, p2) := p1 in + let (n2, node_id_cnt1) := p2 in + len_right <- betree_List_len (u64 * betree_Message_t) n1 msgs_right; + if len_right s>= params.(betree_Params_min_flush_size) + then ( + p3 <- + betree_Node_apply_messages n1 self.(betree_Internal_right) params + node_id_cnt1 msgs_right st1; + let (st2, p4) := p3 in + let (n3, node_id_cnt2) := p4 in + Ok (st2, (Betree_List_Nil, (mkbetree_Internal_t + self.(betree_Internal_id) self.(betree_Internal_pivot) n2 n3, + node_id_cnt2)))) + else + Ok (st1, (msgs_right, (mkbetree_Internal_t self.(betree_Internal_id) + self.(betree_Internal_pivot) n2 self.(betree_Internal_right), + node_id_cnt1)))) + else ( + p1 <- + betree_Node_apply_messages n1 self.(betree_Internal_right) params + node_id_cnt msgs_right st; + let (st1, p2) := p1 in + let (n2, node_id_cnt1) := p2 in + Ok (st1, (msgs_left, (mkbetree_Internal_t self.(betree_Internal_id) + self.(betree_Internal_pivot) self.(betree_Internal_left) n2, + node_id_cnt1)))) + end + +(** [betree::betree::{betree::betree::Node#5}::apply_messages]: + Source: 'src/betree.rs', lines 588:4-593:5 *) +with betree_Node_apply_messages + (n : nat) (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 * betree_Message_t)) (st : state) : + result (state * (betree_Node_t * betree_NodeIdCounter_t)) + := + match n with + | O => Fail_ OutOfFuel + | S n1 => + match self with + | Betree_Node_Internal node => + p <- betree_load_internal_node node.(betree_Internal_id) st; + let (st1, content) := p in + content1 <- betree_Node_apply_messages_to_internal n1 content msgs; + num_msgs <- betree_List_len (u64 * betree_Message_t) n1 content1; + if num_msgs s>= params.(betree_Params_min_flush_size) + then ( + p1 <- betree_Internal_flush n1 node params node_id_cnt content1 st1; + let (st2, p2) := p1 in + let (content2, p3) := p2 in + let (node1, node_id_cnt1) := p3 in + p4 <- + betree_store_internal_node node1.(betree_Internal_id) content2 st2; + let (st3, _) := p4 in + Ok (st3, (Betree_Node_Internal node1, node_id_cnt1))) + else ( + p1 <- + betree_store_internal_node node.(betree_Internal_id) content1 st1; + let (st2, _) := p1 in + Ok (st2, (Betree_Node_Internal node, node_id_cnt))) + | Betree_Node_Leaf node => + p <- betree_load_leaf_node node.(betree_Leaf_id) st; + let (st1, content) := p in + content1 <- betree_Node_apply_messages_to_leaf n1 content msgs; + len <- betree_List_len (u64 * u64) n1 content1; + i <- u64_mul 2%u64 params.(betree_Params_split_size); + if len s>= i + then ( + p1 <- betree_Leaf_split n1 node content1 params node_id_cnt st1; + let (st2, p2) := p1 in + let (new_node, node_id_cnt1) := p2 in + p3 <- betree_store_leaf_node node.(betree_Leaf_id) Betree_List_Nil st2; + let (st3, _) := p3 in + Ok (st3, (Betree_Node_Internal new_node, node_id_cnt1))) + else ( + p1 <- betree_store_leaf_node node.(betree_Leaf_id) content1 st1; + let (st2, _) := p1 in + Ok (st2, (Betree_Node_Leaf + {| betree_Leaf_id := node.(betree_Leaf_id); betree_Leaf_size := len + |}, node_id_cnt))) + end + end +. + +(** [betree::betree::{betree::betree::Node#5}::apply]: + Source: 'src/betree.rs', lines 576:4-582:5 *) +Definition betree_Node_apply + (n : nat) (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) (key : u64) + (new_msg : betree_Message_t) (st : state) : + result (state * (betree_Node_t * betree_NodeIdCounter_t)) + := + p <- + betree_Node_apply_messages n self params node_id_cnt (Betree_List_Cons + (key, new_msg) Betree_List_Nil) st; + let (st1, p1) := p in + let (self1, node_id_cnt1) := p1 in + Ok (st1, (self1, node_id_cnt1)) +. + +(** [betree::betree::{betree::betree::BeTree#6}::new]: + Source: 'src/betree.rs', lines 849:4-849:60 *) +Definition betree_BeTree_new + (min_flush_size : u64) (split_size : u64) (st : state) : + result (state * betree_BeTree_t) + := + node_id_cnt <- betree_NodeIdCounter_new; + p <- betree_NodeIdCounter_fresh_id node_id_cnt; + let (id, node_id_cnt1) := p in + p1 <- betree_store_leaf_node id Betree_List_Nil st; + let (st1, _) := p1 in + Ok (st1, + {| + betree_BeTree_params := + {| + betree_Params_min_flush_size := min_flush_size; + betree_Params_split_size := split_size + |}; + betree_BeTree_node_id_cnt := node_id_cnt1; + betree_BeTree_root := + (Betree_Node_Leaf + {| betree_Leaf_id := id; betree_Leaf_size := 0%u64 |}) + |}) +. + +(** [betree::betree::{betree::betree::BeTree#6}::apply]: + Source: 'src/betree.rs', lines 868:4-868:47 *) +Definition betree_BeTree_apply + (n : nat) (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) + (st : state) : + result (state * betree_BeTree_t) + := + p <- + betree_Node_apply n self.(betree_BeTree_root) self.(betree_BeTree_params) + self.(betree_BeTree_node_id_cnt) key msg st; + let (st1, p1) := p in + let (n1, nic) := p1 in + Ok (st1, + {| + betree_BeTree_params := self.(betree_BeTree_params); + betree_BeTree_node_id_cnt := nic; + betree_BeTree_root := n1 + |}) +. + +(** [betree::betree::{betree::betree::BeTree#6}::insert]: + Source: 'src/betree.rs', lines 874:4-874:52 *) +Definition betree_BeTree_insert + (n : nat) (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) : + result (state * betree_BeTree_t) + := + betree_BeTree_apply n self key (Betree_Message_Insert value) st +. + +(** [betree::betree::{betree::betree::BeTree#6}::delete]: + Source: 'src/betree.rs', lines 880:4-880:38 *) +Definition betree_BeTree_delete + (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) : + result (state * betree_BeTree_t) + := + betree_BeTree_apply n self key Betree_Message_Delete st +. + +(** [betree::betree::{betree::betree::BeTree#6}::upsert]: + Source: 'src/betree.rs', lines 886:4-886:59 *) +Definition betree_BeTree_upsert + (n : nat) (self : betree_BeTree_t) (key : u64) + (upd : betree_UpsertFunState_t) (st : state) : + result (state * betree_BeTree_t) + := + betree_BeTree_apply n self key (Betree_Message_Upsert upd) st +. + +(** [betree::betree::{betree::betree::BeTree#6}::lookup]: + Source: 'src/betree.rs', lines 895:4-895:62 *) +Definition betree_BeTree_lookup + (n : nat) (self : betree_BeTree_t) (key : u64) (st : state) : + result (state * ((option u64) * betree_BeTree_t)) + := + p <- betree_Node_lookup n self.(betree_BeTree_root) key st; + let (st1, p1) := p in + let (o, n1) := p1 in + Ok (st1, (o, + {| + betree_BeTree_params := self.(betree_BeTree_params); + betree_BeTree_node_id_cnt := self.(betree_BeTree_node_id_cnt); + betree_BeTree_root := n1 + |})) +. + +(** [betree::main]: + Source: 'src/main.rs', lines 4:0-4:9 *) +Definition main : result unit := + Ok tt. + +(** Unit test for [betree::main] *) +Check (main )%return. + +End Betree_Funs. diff --git a/tests/coq/betree/Betree_FunsExternal.v b/tests/coq/betree/Betree_FunsExternal.v new file mode 100644 index 00000000..0263c272 --- /dev/null +++ b/tests/coq/betree/Betree_FunsExternal.v @@ -0,0 +1,39 @@ +(** [betree_main]: external functions. +-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Require Export Betree_Types. +Import Betree_Types. +Module Betree_FunsExternal. + +(** [betree_main::betree_utils::load_internal_node]: forward function + Source: 'src/betree_utils.rs', lines 98:0-98:63 *) +Axiom betree_utils_load_internal_node + : u64 -> state -> result (state * (betree_List_t (u64 * betree_Message_t))) +. + +(** [betree_main::betree_utils::store_internal_node]: forward function + Source: 'src/betree_utils.rs', lines 115:0-115:71 *) +Axiom betree_utils_store_internal_node + : + u64 -> betree_List_t (u64 * betree_Message_t) -> state -> result (state * + unit) +. + +(** [betree_main::betree_utils::load_leaf_node]: forward function + Source: 'src/betree_utils.rs', lines 132:0-132:55 *) +Axiom betree_utils_load_leaf_node + : u64 -> state -> result (state * (betree_List_t (u64 * u64))) +. + +(** [betree_main::betree_utils::store_leaf_node]: forward function + Source: 'src/betree_utils.rs', lines 145:0-145:63 *) +Axiom betree_utils_store_leaf_node + : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit) +. + +End Betree_FunsExternal. diff --git a/tests/coq/betree/Betree_FunsExternal_Template.v b/tests/coq/betree/Betree_FunsExternal_Template.v new file mode 100644 index 00000000..2a2fddfc --- /dev/null +++ b/tests/coq/betree/Betree_FunsExternal_Template.v @@ -0,0 +1,40 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: external functions. +-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Require Import Betree_Types. +Include Betree_Types. +Module Betree_FunsExternal_Template. + +(** [betree::betree_utils::load_internal_node]: + Source: 'src/betree_utils.rs', lines 98:0-98:63 *) +Axiom betree_utils_load_internal_node + : u64 -> state -> result (state * (betree_List_t (u64 * betree_Message_t))) +. + +(** [betree::betree_utils::store_internal_node]: + Source: 'src/betree_utils.rs', lines 115:0-115:71 *) +Axiom betree_utils_store_internal_node + : + u64 -> betree_List_t (u64 * betree_Message_t) -> state -> result (state * + unit) +. + +(** [betree::betree_utils::load_leaf_node]: + Source: 'src/betree_utils.rs', lines 132:0-132:55 *) +Axiom betree_utils_load_leaf_node + : u64 -> state -> result (state * (betree_List_t (u64 * u64))) +. + +(** [betree::betree_utils::store_leaf_node]: + Source: 'src/betree_utils.rs', lines 145:0-145:63 *) +Axiom betree_utils_store_leaf_node + : u64 -> betree_List_t (u64 * u64) -> state -> result (state * unit) +. + +End Betree_FunsExternal_Template. diff --git a/tests/coq/betree/Betree_Types.v b/tests/coq/betree/Betree_Types.v new file mode 100644 index 00000000..aa39d8e4 --- /dev/null +++ b/tests/coq/betree/Betree_Types.v @@ -0,0 +1,118 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: type definitions *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Require Import Betree_TypesExternal. +Include Betree_TypesExternal. +Module Betree_Types. + +(** [betree::betree::List] + Source: 'src/betree.rs', lines 17:0-17:23 *) +Inductive betree_List_t (T : Type) := +| Betree_List_Cons : T -> betree_List_t T -> betree_List_t T +| Betree_List_Nil : betree_List_t T +. + +Arguments Betree_List_Cons { _ }. +Arguments Betree_List_Nil { _ }. + +(** [betree::betree::UpsertFunState] + Source: 'src/betree.rs', lines 63:0-63:23 *) +Inductive betree_UpsertFunState_t := +| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t +| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t +. + +(** [betree::betree::Message] + Source: 'src/betree.rs', lines 69:0-69:23 *) +Inductive betree_Message_t := +| Betree_Message_Insert : u64 -> betree_Message_t +| Betree_Message_Delete : betree_Message_t +| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t +. + +(** [betree::betree::Leaf] + Source: 'src/betree.rs', lines 167:0-167:11 *) +Record betree_Leaf_t := +mkbetree_Leaf_t { + betree_Leaf_id : u64; betree_Leaf_size : u64; +} +. + +(** [betree::betree::Internal] + Source: 'src/betree.rs', lines 156:0-156:15 *) +Inductive betree_Internal_t := +| mkbetree_Internal_t : + u64 -> + u64 -> + betree_Node_t -> + betree_Node_t -> + betree_Internal_t + +(** [betree::betree::Node] + Source: 'src/betree.rs', lines 179:0-179:9 *) +with betree_Node_t := +| Betree_Node_Internal : betree_Internal_t -> betree_Node_t +| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t +. + +Definition betree_Internal_id (x : betree_Internal_t) := + match x with | mkbetree_Internal_t x1 _ _ _ => x1 end +. + +Notation "x2 .(betree_Internal_id)" := (betree_Internal_id x2) (at level 9). + +Definition betree_Internal_pivot (x : betree_Internal_t) := + match x with | mkbetree_Internal_t _ x1 _ _ => x1 end +. + +Notation "x2 .(betree_Internal_pivot)" := (betree_Internal_pivot x2) + (at level 9) +. + +Definition betree_Internal_left (x : betree_Internal_t) := + match x with | mkbetree_Internal_t _ _ x1 _ => x1 end +. + +Notation "x2 .(betree_Internal_left)" := (betree_Internal_left x2) (at level 9) +. + +Definition betree_Internal_right (x : betree_Internal_t) := + match x with | mkbetree_Internal_t _ _ _ x1 => x1 end +. + +Notation "x2 .(betree_Internal_right)" := (betree_Internal_right x2) + (at level 9) +. + +(** [betree::betree::Params] + Source: 'src/betree.rs', lines 187:0-187:13 *) +Record betree_Params_t := +mkbetree_Params_t { + betree_Params_min_flush_size : u64; betree_Params_split_size : u64; +} +. + +(** [betree::betree::NodeIdCounter] + Source: 'src/betree.rs', lines 201:0-201:20 *) +Record betree_NodeIdCounter_t := +mkbetree_NodeIdCounter_t { + betree_NodeIdCounter_next_node_id : u64; +} +. + +(** [betree::betree::BeTree] + Source: 'src/betree.rs', lines 218:0-218:17 *) +Record betree_BeTree_t := +mkbetree_BeTree_t { + betree_BeTree_params : betree_Params_t; + betree_BeTree_node_id_cnt : betree_NodeIdCounter_t; + betree_BeTree_root : betree_Node_t; +} +. + +End Betree_Types. diff --git a/tests/coq/betree/Betree_TypesExternal.v b/tests/coq/betree/Betree_TypesExternal.v new file mode 100644 index 00000000..37487d6d --- /dev/null +++ b/tests/coq/betree/Betree_TypesExternal.v @@ -0,0 +1,14 @@ +(** [betree_main]: external types. +-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Module Betree_TypesExternal. + +(** The state type used in the state-error monad *) +Axiom state : Type. + +End Betree_TypesExternal. diff --git a/tests/coq/betree/Betree_TypesExternal_Template.v b/tests/coq/betree/Betree_TypesExternal_Template.v new file mode 100644 index 00000000..a40811cb --- /dev/null +++ b/tests/coq/betree/Betree_TypesExternal_Template.v @@ -0,0 +1,15 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: external types. +-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Module Betree_TypesExternal_Template. + +(** The state type used in the state-error monad *) +Axiom state : Type. + +End Betree_TypesExternal_Template. diff --git a/tests/coq/betree/_CoqProject b/tests/coq/betree/_CoqProject index b14bed66..9fb7fe64 100644 --- a/tests/coq/betree/_CoqProject +++ b/tests/coq/betree/_CoqProject @@ -3,10 +3,10 @@ -arg -w -arg all -BetreeMain_TypesExternal_Template.v -BetreeMain_Types.v +Betree_TypesExternal_Template.v +Betree_Types.v Primitives.v -BetreeMain_FunsExternal_Template.v -BetreeMain_Funs.v -BetreeMain_TypesExternal.v -BetreeMain_FunsExternal.v +Betree_FunsExternal_Template.v +Betree_Funs.v +Betree_TypesExternal.v +Betree_FunsExternal.v diff --git a/tests/fstar/betree/Betree.Clauses.Template.fst b/tests/fstar/betree/Betree.Clauses.Template.fst new file mode 100644 index 00000000..fad8c5ba --- /dev/null +++ b/tests/fstar/betree/Betree.Clauses.Template.fst @@ -0,0 +1,117 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: templates for the decreases clauses *) +module Betree.Clauses.Template +open Primitives +open Betree.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [betree::betree::{betree::betree::List#1}::len]: decreases clause + Source: 'src/betree.rs', lines 276:4-276:24 *) +unfold +let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat = + admit () + +(** [betree::betree::{betree::betree::List#1}::split_at]: decreases clause + Source: 'src/betree.rs', lines 284:4-284:51 *) +unfold +let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) + (n : u64) : nat = + admit () + +(** [betree::betree::{betree::betree::List<(u64, T)>#2}::partition_at_pivot]: decreases clause + Source: 'src/betree.rs', lines 339:4-339:73 *) +unfold +let betree_ListPairU64T_partition_at_pivot_decreases (t : Type0) + (self : betree_List_t (u64 & t)) (pivot : u64) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::lookup_first_message_for_key]: decreases clause + Source: 'src/betree.rs', lines 789:4-792:34 *) +unfold +let betree_Node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::lookup_in_bindings]: decreases clause + Source: 'src/betree.rs', lines 636:4-636:80 *) +unfold +let betree_Node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::apply_upserts]: decreases clause + Source: 'src/betree.rs', lines 819:4-819:90 *) +unfold +let betree_Node_apply_upserts_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) + (key : u64) : nat = + admit () + +(** [betree::betree::{betree::betree::Internal#4}::lookup_in_children]: decreases clause + Source: 'src/betree.rs', lines 395:4-395:63 *) +unfold +let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) + (key : u64) (st : state) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::lookup]: decreases clause + Source: 'src/betree.rs', lines 709:4-709:58 *) +unfold +let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) + (st : state) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::filter_messages_for_key]: decreases clause + Source: 'src/betree.rs', lines 674:4-674:77 *) +unfold +let betree_Node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::lookup_first_message_after_key]: decreases clause + Source: 'src/betree.rs', lines 689:4-692:34 *) +unfold +let betree_Node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::apply_messages_to_internal]: decreases clause + Source: 'src/betree.rs', lines 502:4-505:5 *) +unfold +let betree_Node_apply_messages_to_internal_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::lookup_mut_in_bindings]: decreases clause + Source: 'src/betree.rs', lines 653:4-656:32 *) +unfold +let betree_Node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::apply_messages_to_leaf]: decreases clause + Source: 'src/betree.rs', lines 444:4-447:5 *) +unfold +let betree_Node_apply_messages_to_leaf_decreases + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = + admit () + +(** [betree::betree::{betree::betree::Internal#4}::flush]: decreases clause + Source: 'src/betree.rs', lines 410:4-415:26 *) +unfold +let betree_Internal_flush_decreases (self : betree_Internal_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = + admit () + +(** [betree::betree::{betree::betree::Node#5}::apply_messages]: decreases clause + Source: 'src/betree.rs', lines 588:4-593:5 *) +unfold +let betree_Node_apply_messages_decreases (self : betree_Node_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = + admit () + diff --git a/tests/fstar/betree/Betree.Clauses.fst b/tests/fstar/betree/Betree.Clauses.fst new file mode 100644 index 00000000..ae201cee --- /dev/null +++ b/tests/fstar/betree/Betree.Clauses.fst @@ -0,0 +1,210 @@ +(** [betree_main]: templates for the decreases clauses *) +module Betree.Clauses +open Primitives +open Betree.Types + +#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" + +(*** Well-founded relations *) + +(* We had a few issues when proving termination of the mutually recursive functions: + * - betree_Internal_flush + * - betree_Node_apply_messages + * + * The quantity which effectively decreases is: + * (betree_size, messages_length) + * where messages_length is 0 when there are no messages + * (and where we use the lexicographic ordering, of course) + * + * However, the `%[...]` and `{:well-founded ...} notations are not available outside + * of `decrease` clauses. + * + * We thus resorted to writing and proving correct a well-founded relation over + * pairs of natural numbers. The trick is that `<<` can be used outside of decrease + * clauses, and can be used to trigger SMT patterns. + * + * What follows is adapted from: + * https://www.fstar-lang.org/tutorial/book/part2/part2_well_founded.html + * + * Also, the following PR might make things easier: + * https://github.com/FStarLang/FStar/pull/2561 + *) + +module P = FStar.Preorder +module W = FStar.WellFounded +module L = FStar.LexicographicOrdering + +let lt_nat (x y:nat) : Type = x < y == true +let rec wf_lt_nat (x:nat) + : W.acc lt_nat x + = W.AccIntro (fun y _ -> wf_lt_nat y) + +// A type abbreviation for a pair of nats +let nat_pair = (x:nat & nat) + +// Making a lexicographic ordering from a pair of nat ordering +let lex_order_nat_pair : P.relation nat_pair = + L.lex_t lt_nat (fun _ -> lt_nat) + +// The lex order on nat pairs is well-founded, using our general proof +// of lexicographic composition of well-founded orders +let lex_order_nat_pair_wf : W.well_founded lex_order_nat_pair = + L.lex_t_wf wf_lt_nat (fun _ -> wf_lt_nat) + +// A utility to introduce lt_nat +let mk_lt_nat (x:nat) (y:nat { x < y }) : lt_nat x y = + let _ : equals (x < y) true = Refl in + () + +// A utility to make a lex ordering of nat pairs +let mk_lex_order_nat_pair (xy0:nat_pair) + (xy1:nat_pair { + let (|x0, y0|) = xy0 in + let (|x1, y1|) = xy1 in + x0 < x1 \/ (x0 == x1 /\ y0 < y1) + }) : lex_order_nat_pair xy0 xy1 = + let (|x0, y0|) = xy0 in + let (|x1, y1|) = xy1 in + if x0 < x1 then L.Left_lex x0 x1 y0 y1 (mk_lt_nat x0 x1) + else L.Right_lex x0 y0 y1 (mk_lt_nat y0 y1) + +let rec coerce #a #r #x (p:W.acc #a r x) : Tot (W.acc r x) (decreases p) = + W.AccIntro (fun y r -> coerce (p.access_smaller y r)) + +let coerce_wf #a #r (p: (x:a -> W.acc r x)) : x:a -> W.acc r x = + fun x -> coerce (p x) + +(* We need this axiom, which comes from the following discussion: + * https://github.com/FStarLang/FStar/issues/1916 + * An issue here is that the `{well-founded ... }` notation + *) +assume +val axiom_well_founded (a : Type) (rel : a -> a -> Type0) + (rwf : W.well_founded #a rel) (x y : a) : + Lemma (requires (rel x y)) (ensures (x << y)) + +(* This lemma has a pattern (which makes it work) *) +let wf_nat_pair_lem (p0 p1 : nat_pair) : + Lemma + (requires ( + let (|x0, y0|) = p0 in + let (|x1, y1|) = p1 in + x0 < x1 || (x0 = x1 && y0 < y1))) + (ensures (p0 << p1)) + [SMTPat (p0 << p1)] = + let rel = lex_order_nat_pair in + let rel_wf = lex_order_nat_pair_wf in + let _ = mk_lex_order_nat_pair p0 p1 in + assert(rel p0 p1); + axiom_well_founded nat_pair rel rel_wf p0 p1 + +(*** Decrease clauses *) +/// "Standard" decrease clauses + +(** [betree_main::betree::List::{1}::len]: decreases clause *) +unfold +let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : betree_List_t t = + self + +(** [betree_main::betree::List::{1}::split_at]: decreases clause *) +unfold +let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) + (n : u64) : nat = + n + +(** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) +unfold +let betree_ListPairU64T_partition_at_pivot_decreases (t : Type0) + (self : betree_List_t (u64 & t)) (pivot : u64) : betree_List_t (u64 & t) = + self + +(** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) +unfold +let betree_Node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = + bindings + +(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) +unfold +let betree_Node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = + msgs + +(** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) +unfold +let betree_Node_apply_upserts_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) + (key : u64) : betree_List_t (u64 & betree_Message_t) = + msgs + +(** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) +unfold +let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) + (key : u64) (st : state) : betree_Internal_t = + self + +(** [betree_main::betree::Node::{5}::lookup]: decreases clause *) +unfold +let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) + (st : state) : betree_Node_t = + self + +(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) +unfold +let betree_Node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = + bindings + +unfold +let betree_Node_apply_messages_to_leaf_decreases + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = + new_msgs + +(** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) +unfold +let betree_Node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = + msgs + +(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) +unfold +let betree_Node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = + msgs + +let betree_Node_apply_messages_to_internal_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = + new_msgs + +(*** Decrease clauses - nat_pair *) +/// The following decrease clauses use the [nat_pair] definition and the well-founded +/// relation proven above. + +let rec betree_size (bt : betree_Node_t) : nat = + match bt with + | Betree_Node_Internal node -> 1 + betree_Internal_size node + | Betree_Node_Leaf _ -> 1 + +and betree_Internal_size (node : betree_Internal_t) : nat = + 1 + betree_size node.left + betree_size node.right + +let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat = + match ls with + | Betree_List_Cons _ tl -> 1 + betree_List_len tl + | Betree_List_Nil -> 0 + +(** [betree_main::betree::Internal::{4}::flush]: decreases clause *) +unfold +let betree_Internal_flush_decreases (self : betree_Internal_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = + (|betree_Internal_size self, 0|) + +(** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) +unfold +let betree_Node_apply_messages_decreases (self : betree_Node_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = + (|betree_size self, betree_List_len msgs|) diff --git a/tests/fstar/betree/Betree.Funs.fst b/tests/fstar/betree/Betree.Funs.fst new file mode 100644 index 00000000..07f561f5 --- /dev/null +++ b/tests/fstar/betree/Betree.Funs.fst @@ -0,0 +1,676 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: function definitions *) +module Betree.Funs +open Primitives +include Betree.Types +include Betree.FunsExternal +include Betree.Clauses + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [betree::betree::load_internal_node]: + Source: 'src/betree.rs', lines 36:0-36:52 *) +let betree_load_internal_node + (id : u64) (st : state) : + result (state & (betree_List_t (u64 & betree_Message_t))) + = + betree_utils_load_internal_node id st + +(** [betree::betree::store_internal_node]: + Source: 'src/betree.rs', lines 41:0-41:60 *) +let betree_store_internal_node + (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) : + result (state & unit) + = + betree_utils_store_internal_node id content st + +(** [betree::betree::load_leaf_node]: + Source: 'src/betree.rs', lines 46:0-46:44 *) +let betree_load_leaf_node + (id : u64) (st : state) : result (state & (betree_List_t (u64 & u64))) = + betree_utils_load_leaf_node id st + +(** [betree::betree::store_leaf_node]: + Source: 'src/betree.rs', lines 51:0-51:52 *) +let betree_store_leaf_node + (id : u64) (content : betree_List_t (u64 & u64)) (st : state) : + result (state & unit) + = + betree_utils_store_leaf_node id content st + +(** [betree::betree::fresh_node_id]: + Source: 'src/betree.rs', lines 55:0-55:48 *) +let betree_fresh_node_id (counter : u64) : result (u64 & u64) = + let* counter1 = u64_add counter 1 in Ok (counter, counter1) + +(** [betree::betree::{betree::betree::NodeIdCounter}::new]: + Source: 'src/betree.rs', lines 206:4-206:20 *) +let betree_NodeIdCounter_new : result betree_NodeIdCounter_t = + Ok { next_node_id = 0 } + +(** [betree::betree::{betree::betree::NodeIdCounter}::fresh_id]: + Source: 'src/betree.rs', lines 210:4-210:36 *) +let betree_NodeIdCounter_fresh_id + (self : betree_NodeIdCounter_t) : result (u64 & betree_NodeIdCounter_t) = + let* i = u64_add self.next_node_id 1 in + Ok (self.next_node_id, { next_node_id = i }) + +(** [betree::betree::upsert_update]: + Source: 'src/betree.rs', lines 234:0-234:70 *) +let betree_upsert_update + (prev : option u64) (st : betree_UpsertFunState_t) : result u64 = + begin match prev with + | None -> + begin match st with + | Betree_UpsertFunState_Add v -> Ok v + | Betree_UpsertFunState_Sub _ -> Ok 0 + end + | Some prev1 -> + begin match st with + | Betree_UpsertFunState_Add v -> + let* margin = u64_sub core_u64_max prev1 in + if margin >= v then u64_add prev1 v else Ok core_u64_max + | Betree_UpsertFunState_Sub v -> + if prev1 >= v then u64_sub prev1 v else Ok 0 + end + end + +(** [betree::betree::{betree::betree::List#1}::len]: + Source: 'src/betree.rs', lines 276:4-276:24 *) +let rec betree_List_len + (t : Type0) (self : betree_List_t t) : + Tot (result u64) (decreases (betree_List_len_decreases t self)) + = + begin match self with + | Betree_List_Cons _ tl -> let* i = betree_List_len t tl in u64_add 1 i + | Betree_List_Nil -> Ok 0 + end + +(** [betree::betree::{betree::betree::List#1}::split_at]: + Source: 'src/betree.rs', lines 284:4-284:51 *) +let rec betree_List_split_at + (t : Type0) (self : betree_List_t t) (n : u64) : + Tot (result ((betree_List_t t) & (betree_List_t t))) + (decreases (betree_List_split_at_decreases t self n)) + = + if n = 0 + then Ok (Betree_List_Nil, self) + else + begin match self with + | Betree_List_Cons hd tl -> + let* i = u64_sub n 1 in + let* p = betree_List_split_at t tl i in + let (ls0, ls1) = p in + Ok (Betree_List_Cons hd ls0, ls1) + | Betree_List_Nil -> Fail Failure + end + +(** [betree::betree::{betree::betree::List#1}::push_front]: + Source: 'src/betree.rs', lines 299:4-299:34 *) +let betree_List_push_front + (t : Type0) (self : betree_List_t t) (x : t) : result (betree_List_t t) = + let (tl, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in + Ok (Betree_List_Cons x tl) + +(** [betree::betree::{betree::betree::List#1}::pop_front]: + Source: 'src/betree.rs', lines 306:4-306:32 *) +let betree_List_pop_front + (t : Type0) (self : betree_List_t t) : result (t & (betree_List_t t)) = + let (ls, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in + begin match ls with + | Betree_List_Cons x tl -> Ok (x, tl) + | Betree_List_Nil -> Fail Failure + end + +(** [betree::betree::{betree::betree::List#1}::hd]: + Source: 'src/betree.rs', lines 318:4-318:22 *) +let betree_List_hd (t : Type0) (self : betree_List_t t) : result t = + begin match self with + | Betree_List_Cons hd _ -> Ok hd + | Betree_List_Nil -> Fail Failure + end + +(** [betree::betree::{betree::betree::List<(u64, T)>#2}::head_has_key]: + Source: 'src/betree.rs', lines 327:4-327:44 *) +let betree_ListPairU64T_head_has_key + (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool = + begin match self with + | Betree_List_Cons hd _ -> let (i, _) = hd in Ok (i = key) + | Betree_List_Nil -> Ok false + end + +(** [betree::betree::{betree::betree::List<(u64, T)>#2}::partition_at_pivot]: + Source: 'src/betree.rs', lines 339:4-339:73 *) +let rec betree_ListPairU64T_partition_at_pivot + (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) : + Tot (result ((betree_List_t (u64 & t)) & (betree_List_t (u64 & t)))) + (decreases (betree_ListPairU64T_partition_at_pivot_decreases t self pivot)) + = + begin match self with + | Betree_List_Cons hd tl -> + let (i, x) = hd in + if i >= pivot + then Ok (Betree_List_Nil, Betree_List_Cons (i, x) tl) + else + let* p = betree_ListPairU64T_partition_at_pivot t tl pivot in + let (ls0, ls1) = p in + Ok (Betree_List_Cons (i, x) ls0, ls1) + | Betree_List_Nil -> Ok (Betree_List_Nil, Betree_List_Nil) + end + +(** [betree::betree::{betree::betree::Leaf#3}::split]: + Source: 'src/betree.rs', lines 359:4-364:17 *) +let betree_Leaf_split + (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (st : state) : + result (state & (betree_Internal_t & betree_NodeIdCounter_t)) + = + let* p = betree_List_split_at (u64 & u64) content params.split_size in + let (content0, content1) = p in + let* p1 = betree_List_hd (u64 & u64) content1 in + let (pivot, _) = p1 in + let* (id0, node_id_cnt1) = betree_NodeIdCounter_fresh_id node_id_cnt in + let* (id1, node_id_cnt2) = betree_NodeIdCounter_fresh_id node_id_cnt1 in + let* (st1, _) = betree_store_leaf_node id0 content0 st in + let* (st2, _) = betree_store_leaf_node id1 content1 st1 in + let n = Betree_Node_Leaf { id = id0; size = params.split_size } in + let n1 = Betree_Node_Leaf { id = id1; size = params.split_size } in + Ok (st2, ({ id = self.id; pivot = pivot; left = n; right = n1 }, + node_id_cnt2)) + +(** [betree::betree::{betree::betree::Node#5}::lookup_first_message_for_key]: + Source: 'src/betree.rs', lines 789:4-792:34 *) +let rec betree_Node_lookup_first_message_for_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 & + betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t))))) + (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs)) + = + begin match msgs with + | Betree_List_Cons x next_msgs -> + let (i, m) = x in + if i >= key + then Ok (Betree_List_Cons (i, m) next_msgs, Ok) + else + let* (l, lookup_first_message_for_key_back) = + betree_Node_lookup_first_message_for_key key next_msgs in + let back = + fun ret -> + let* next_msgs1 = lookup_first_message_for_key_back ret in + Ok (Betree_List_Cons (i, m) next_msgs1) in + Ok (l, back) + | Betree_List_Nil -> Ok (Betree_List_Nil, Ok) + end + +(** [betree::betree::{betree::betree::Node#5}::lookup_in_bindings]: + Source: 'src/betree.rs', lines 636:4-636:80 *) +let rec betree_Node_lookup_in_bindings + (key : u64) (bindings : betree_List_t (u64 & u64)) : + Tot (result (option u64)) + (decreases (betree_Node_lookup_in_bindings_decreases key bindings)) + = + begin match bindings with + | Betree_List_Cons hd tl -> + let (i, i1) = hd in + if i = key + then Ok (Some i1) + else if i > key then Ok None else betree_Node_lookup_in_bindings key tl + | Betree_List_Nil -> Ok None + end + +(** [betree::betree::{betree::betree::Node#5}::apply_upserts]: + Source: 'src/betree.rs', lines 819:4-819:90 *) +let rec betree_Node_apply_upserts + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) + (key : u64) : + Tot (result (u64 & (betree_List_t (u64 & betree_Message_t)))) + (decreases (betree_Node_apply_upserts_decreases msgs prev key)) + = + let* b = betree_ListPairU64T_head_has_key betree_Message_t msgs key in + if b + then + let* (msg, msgs1) = betree_List_pop_front (u64 & betree_Message_t) msgs in + let (_, m) = msg in + begin match m with + | Betree_Message_Insert _ -> Fail Failure + | Betree_Message_Delete -> Fail Failure + | Betree_Message_Upsert s -> + let* v = betree_upsert_update prev s in + betree_Node_apply_upserts msgs1 (Some v) key + end + else + let* v = core_option_Option_unwrap u64 prev in + let* msgs1 = + betree_List_push_front (u64 & betree_Message_t) msgs (key, + Betree_Message_Insert v) in + Ok (v, msgs1) + +(** [betree::betree::{betree::betree::Internal#4}::lookup_in_children]: + Source: 'src/betree.rs', lines 395:4-395:63 *) +let rec betree_Internal_lookup_in_children + (self : betree_Internal_t) (key : u64) (st : state) : + Tot (result (state & ((option u64) & betree_Internal_t))) + (decreases (betree_Internal_lookup_in_children_decreases self key st)) + = + if key < self.pivot + then + let* (st1, (o, n)) = betree_Node_lookup self.left key st in + Ok (st1, (o, { self with left = n })) + else + let* (st1, (o, n)) = betree_Node_lookup self.right key st in + Ok (st1, (o, { self with right = n })) + +(** [betree::betree::{betree::betree::Node#5}::lookup]: + Source: 'src/betree.rs', lines 709:4-709:58 *) +and betree_Node_lookup + (self : betree_Node_t) (key : u64) (st : state) : + Tot (result (state & ((option u64) & betree_Node_t))) + (decreases (betree_Node_lookup_decreases self key st)) + = + begin match self with + | Betree_Node_Internal node -> + let* (st1, msgs) = betree_load_internal_node node.id st in + let* (pending, lookup_first_message_for_key_back) = + betree_Node_lookup_first_message_for_key key msgs in + begin match pending with + | Betree_List_Cons p l -> + let (k, msg) = p in + if k <> key + then + let* (st2, (o, node1)) = + betree_Internal_lookup_in_children node key st1 in + let* _ = + lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l) in + Ok (st2, (o, Betree_Node_Internal node1)) + else + begin match msg with + | Betree_Message_Insert v -> + let* _ = + lookup_first_message_for_key_back (Betree_List_Cons (k, + Betree_Message_Insert v) l) in + Ok (st1, (Some v, Betree_Node_Internal node)) + | Betree_Message_Delete -> + let* _ = + lookup_first_message_for_key_back (Betree_List_Cons (k, + Betree_Message_Delete) l) in + Ok (st1, (None, Betree_Node_Internal node)) + | Betree_Message_Upsert ufs -> + let* (st2, (v, node1)) = + betree_Internal_lookup_in_children node key st1 in + let* (v1, pending1) = + betree_Node_apply_upserts (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key in + let* msgs1 = lookup_first_message_for_key_back pending1 in + let* (st3, _) = betree_store_internal_node node1.id msgs1 st2 in + Ok (st3, (Some v1, Betree_Node_Internal node1)) + end + | Betree_List_Nil -> + let* (st2, (o, node1)) = betree_Internal_lookup_in_children node key st1 + in + let* _ = lookup_first_message_for_key_back Betree_List_Nil in + Ok (st2, (o, Betree_Node_Internal node1)) + end + | Betree_Node_Leaf node -> + let* (st1, bindings) = betree_load_leaf_node node.id st in + let* o = betree_Node_lookup_in_bindings key bindings in + Ok (st1, (o, Betree_Node_Leaf node)) + end + +(** [betree::betree::{betree::betree::Node#5}::filter_messages_for_key]: + Source: 'src/betree.rs', lines 674:4-674:77 *) +let rec betree_Node_filter_messages_for_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_filter_messages_for_key_decreases key msgs)) + = + begin match msgs with + | Betree_List_Cons p l -> + let (k, m) = p in + if k = key + then + let* (_, msgs1) = + betree_List_pop_front (u64 & betree_Message_t) (Betree_List_Cons (k, m) + l) in + betree_Node_filter_messages_for_key key msgs1 + else Ok (Betree_List_Cons (k, m) l) + | Betree_List_Nil -> Ok Betree_List_Nil + end + +(** [betree::betree::{betree::betree::Node#5}::lookup_first_message_after_key]: + Source: 'src/betree.rs', lines 689:4-692:34 *) +let rec betree_Node_lookup_first_message_after_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 & + betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t))))) + (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs)) + = + begin match msgs with + | Betree_List_Cons p next_msgs -> + let (k, m) = p in + if k = key + then + let* (l, lookup_first_message_after_key_back) = + betree_Node_lookup_first_message_after_key key next_msgs in + let back = + fun ret -> + let* next_msgs1 = lookup_first_message_after_key_back ret in + Ok (Betree_List_Cons (k, m) next_msgs1) in + Ok (l, back) + else Ok (Betree_List_Cons (k, m) next_msgs, Ok) + | Betree_List_Nil -> Ok (Betree_List_Nil, Ok) + end + +(** [betree::betree::{betree::betree::Node#5}::apply_to_internal]: + Source: 'src/betree.rs', lines 521:4-521:89 *) +let betree_Node_apply_to_internal + (msgs : betree_List_t (u64 & betree_Message_t)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 & betree_Message_t)) + = + let* (msgs1, lookup_first_message_for_key_back) = + betree_Node_lookup_first_message_for_key key msgs in + let* b = betree_ListPairU64T_head_has_key betree_Message_t msgs1 key in + if b + then + begin match new_msg with + | Betree_Message_Insert i -> + let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in + let* msgs3 = + betree_List_push_front (u64 & betree_Message_t) msgs2 (key, + Betree_Message_Insert i) in + lookup_first_message_for_key_back msgs3 + | Betree_Message_Delete -> + let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in + let* msgs3 = + betree_List_push_front (u64 & betree_Message_t) msgs2 (key, + Betree_Message_Delete) in + lookup_first_message_for_key_back msgs3 + | Betree_Message_Upsert s -> + let* p = betree_List_hd (u64 & betree_Message_t) msgs1 in + let (_, m) = p in + begin match m with + | Betree_Message_Insert prev -> + let* v = betree_upsert_update (Some prev) s in + let* (_, msgs2) = betree_List_pop_front (u64 & betree_Message_t) msgs1 + in + let* msgs3 = + betree_List_push_front (u64 & betree_Message_t) msgs2 (key, + Betree_Message_Insert v) in + lookup_first_message_for_key_back msgs3 + | Betree_Message_Delete -> + let* (_, msgs2) = betree_List_pop_front (u64 & betree_Message_t) msgs1 + in + let* v = betree_upsert_update None s in + let* msgs3 = + betree_List_push_front (u64 & betree_Message_t) msgs2 (key, + Betree_Message_Insert v) in + lookup_first_message_for_key_back msgs3 + | Betree_Message_Upsert _ -> + let* (msgs2, lookup_first_message_after_key_back) = + betree_Node_lookup_first_message_after_key key msgs1 in + let* msgs3 = + betree_List_push_front (u64 & betree_Message_t) msgs2 (key, + Betree_Message_Upsert s) in + let* msgs4 = lookup_first_message_after_key_back msgs3 in + lookup_first_message_for_key_back msgs4 + end + end + else + let* msgs2 = + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, new_msg) in + lookup_first_message_for_key_back msgs2 + +(** [betree::betree::{betree::betree::Node#5}::apply_messages_to_internal]: + Source: 'src/betree.rs', lines 502:4-505:5 *) +let rec betree_Node_apply_messages_to_internal + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_apply_messages_to_internal_decreases msgs new_msgs)) + = + begin match new_msgs with + | Betree_List_Cons new_msg new_msgs_tl -> + let (i, m) = new_msg in + let* msgs1 = betree_Node_apply_to_internal msgs i m in + betree_Node_apply_messages_to_internal msgs1 new_msgs_tl + | Betree_List_Nil -> Ok msgs + end + +(** [betree::betree::{betree::betree::Node#5}::lookup_mut_in_bindings]: + Source: 'src/betree.rs', lines 653:4-656:32 *) +let rec betree_Node_lookup_mut_in_bindings + (key : u64) (bindings : betree_List_t (u64 & u64)) : + Tot (result ((betree_List_t (u64 & u64)) & (betree_List_t (u64 & u64) -> + result (betree_List_t (u64 & u64))))) + (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings)) + = + begin match bindings with + | Betree_List_Cons hd tl -> + let (i, i1) = hd in + if i >= key + then Ok (Betree_List_Cons (i, i1) tl, Ok) + else + let* (l, lookup_mut_in_bindings_back) = + betree_Node_lookup_mut_in_bindings key tl in + let back = + fun ret -> + let* tl1 = lookup_mut_in_bindings_back ret in + Ok (Betree_List_Cons (i, i1) tl1) in + Ok (l, back) + | Betree_List_Nil -> Ok (Betree_List_Nil, Ok) + end + +(** [betree::betree::{betree::betree::Node#5}::apply_to_leaf]: + Source: 'src/betree.rs', lines 460:4-460:87 *) +let betree_Node_apply_to_leaf + (bindings : betree_List_t (u64 & u64)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 & u64)) + = + let* (bindings1, lookup_mut_in_bindings_back) = + betree_Node_lookup_mut_in_bindings key bindings in + let* b = betree_ListPairU64T_head_has_key u64 bindings1 key in + if b + then + let* (hd, bindings2) = betree_List_pop_front (u64 & u64) bindings1 in + begin match new_msg with + | Betree_Message_Insert v -> + let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in + lookup_mut_in_bindings_back bindings3 + | Betree_Message_Delete -> lookup_mut_in_bindings_back bindings2 + | Betree_Message_Upsert s -> + let (_, i) = hd in + let* v = betree_upsert_update (Some i) s in + let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in + lookup_mut_in_bindings_back bindings3 + end + else + begin match new_msg with + | Betree_Message_Insert v -> + let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in + lookup_mut_in_bindings_back bindings2 + | Betree_Message_Delete -> lookup_mut_in_bindings_back bindings1 + | Betree_Message_Upsert s -> + let* v = betree_upsert_update None s in + let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in + lookup_mut_in_bindings_back bindings2 + end + +(** [betree::betree::{betree::betree::Node#5}::apply_messages_to_leaf]: + Source: 'src/betree.rs', lines 444:4-447:5 *) +let rec betree_Node_apply_messages_to_leaf + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & u64))) + (decreases (betree_Node_apply_messages_to_leaf_decreases bindings new_msgs)) + = + begin match new_msgs with + | Betree_List_Cons new_msg new_msgs_tl -> + let (i, m) = new_msg in + let* bindings1 = betree_Node_apply_to_leaf bindings i m in + betree_Node_apply_messages_to_leaf bindings1 new_msgs_tl + | Betree_List_Nil -> Ok bindings + end + +(** [betree::betree::{betree::betree::Internal#4}::flush]: + Source: 'src/betree.rs', lines 410:4-415:26 *) +let rec betree_Internal_flush + (self : betree_Internal_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : + Tot (result (state & ((betree_List_t (u64 & betree_Message_t)) & + (betree_Internal_t & betree_NodeIdCounter_t)))) + (decreases ( + betree_Internal_flush_decreases self params node_id_cnt content st)) + = + let* p = + betree_ListPairU64T_partition_at_pivot betree_Message_t content self.pivot + in + let (msgs_left, msgs_right) = p in + let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in + if len_left >= params.min_flush_size + then + let* (st1, p1) = + betree_Node_apply_messages self.left params node_id_cnt msgs_left st in + let (n, node_id_cnt1) = p1 in + let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in + if len_right >= params.min_flush_size + then + let* (st2, p2) = + betree_Node_apply_messages self.right params node_id_cnt1 msgs_right + st1 in + let (n1, node_id_cnt2) = p2 in + Ok (st2, (Betree_List_Nil, ({ self with left = n; right = n1 }, + node_id_cnt2))) + else Ok (st1, (msgs_right, ({ self with left = n }, node_id_cnt1))) + else + let* (st1, p1) = + betree_Node_apply_messages self.right params node_id_cnt msgs_right st in + let (n, node_id_cnt1) = p1 in + Ok (st1, (msgs_left, ({ self with right = n }, node_id_cnt1))) + +(** [betree::betree::{betree::betree::Node#5}::apply_messages]: + Source: 'src/betree.rs', lines 588:4-593:5 *) +and betree_Node_apply_messages + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : + Tot (result (state & (betree_Node_t & betree_NodeIdCounter_t))) + (decreases ( + betree_Node_apply_messages_decreases self params node_id_cnt msgs st)) + = + begin match self with + | Betree_Node_Internal node -> + let* (st1, content) = betree_load_internal_node node.id st in + let* content1 = betree_Node_apply_messages_to_internal content msgs in + let* num_msgs = betree_List_len (u64 & betree_Message_t) content1 in + if num_msgs >= params.min_flush_size + then + let* (st2, (content2, p)) = + betree_Internal_flush node params node_id_cnt content1 st1 in + let (node1, node_id_cnt1) = p in + let* (st3, _) = betree_store_internal_node node1.id content2 st2 in + Ok (st3, (Betree_Node_Internal node1, node_id_cnt1)) + else + let* (st2, _) = betree_store_internal_node node.id content1 st1 in + Ok (st2, (Betree_Node_Internal node, node_id_cnt)) + | Betree_Node_Leaf node -> + let* (st1, content) = betree_load_leaf_node node.id st in + let* content1 = betree_Node_apply_messages_to_leaf content msgs in + let* len = betree_List_len (u64 & u64) content1 in + let* i = u64_mul 2 params.split_size in + if len >= i + then + let* (st2, (new_node, node_id_cnt1)) = + betree_Leaf_split node content1 params node_id_cnt st1 in + let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in + Ok (st3, (Betree_Node_Internal new_node, node_id_cnt1)) + else + let* (st2, _) = betree_store_leaf_node node.id content1 st1 in + Ok (st2, (Betree_Node_Leaf { node with size = len }, node_id_cnt)) + end + +(** [betree::betree::{betree::betree::Node#5}::apply]: + Source: 'src/betree.rs', lines 576:4-582:5 *) +let betree_Node_apply + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) (key : u64) + (new_msg : betree_Message_t) (st : state) : + result (state & (betree_Node_t & betree_NodeIdCounter_t)) + = + let* (st1, p) = + betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key, + new_msg) Betree_List_Nil) st in + let (self1, node_id_cnt1) = p in + Ok (st1, (self1, node_id_cnt1)) + +(** [betree::betree::{betree::betree::BeTree#6}::new]: + Source: 'src/betree.rs', lines 849:4-849:60 *) +let betree_BeTree_new + (min_flush_size : u64) (split_size : u64) (st : state) : + result (state & betree_BeTree_t) + = + let* node_id_cnt = betree_NodeIdCounter_new in + let* (id, node_id_cnt1) = betree_NodeIdCounter_fresh_id node_id_cnt in + let* (st1, _) = betree_store_leaf_node id Betree_List_Nil st in + Ok (st1, + { + params = { min_flush_size = min_flush_size; split_size = split_size }; + node_id_cnt = node_id_cnt1; + root = (Betree_Node_Leaf { id = id; size = 0 }) + }) + +(** [betree::betree::{betree::betree::BeTree#6}::apply]: + Source: 'src/betree.rs', lines 868:4-868:47 *) +let betree_BeTree_apply + (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) : + result (state & betree_BeTree_t) + = + let* (st1, p) = + betree_Node_apply self.root self.params self.node_id_cnt key msg st in + let (n, nic) = p in + Ok (st1, { self with node_id_cnt = nic; root = n }) + +(** [betree::betree::{betree::betree::BeTree#6}::insert]: + Source: 'src/betree.rs', lines 874:4-874:52 *) +let betree_BeTree_insert + (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) : + result (state & betree_BeTree_t) + = + betree_BeTree_apply self key (Betree_Message_Insert value) st + +(** [betree::betree::{betree::betree::BeTree#6}::delete]: + Source: 'src/betree.rs', lines 880:4-880:38 *) +let betree_BeTree_delete + (self : betree_BeTree_t) (key : u64) (st : state) : + result (state & betree_BeTree_t) + = + betree_BeTree_apply self key Betree_Message_Delete st + +(** [betree::betree::{betree::betree::BeTree#6}::upsert]: + Source: 'src/betree.rs', lines 886:4-886:59 *) +let betree_BeTree_upsert + (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t) + (st : state) : + result (state & betree_BeTree_t) + = + betree_BeTree_apply self key (Betree_Message_Upsert upd) st + +(** [betree::betree::{betree::betree::BeTree#6}::lookup]: + Source: 'src/betree.rs', lines 895:4-895:62 *) +let betree_BeTree_lookup + (self : betree_BeTree_t) (key : u64) (st : state) : + result (state & ((option u64) & betree_BeTree_t)) + = + let* (st1, (o, n)) = betree_Node_lookup self.root key st in + Ok (st1, (o, { self with root = n })) + +(** [betree::main]: + Source: 'src/main.rs', lines 4:0-4:9 *) +let main : result unit = + Ok () + +(** Unit test for [betree::main] *) +let _ = assert_norm (main = Ok ()) + diff --git a/tests/fstar/betree/Betree.FunsExternal.fsti b/tests/fstar/betree/Betree.FunsExternal.fsti new file mode 100644 index 00000000..db96eead --- /dev/null +++ b/tests/fstar/betree/Betree.FunsExternal.fsti @@ -0,0 +1,30 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: external function declarations *) +module Betree.FunsExternal +open Primitives +include Betree.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [betree::betree_utils::load_internal_node]: + Source: 'src/betree_utils.rs', lines 98:0-98:63 *) +val betree_utils_load_internal_node + : u64 -> state -> result (state & (betree_List_t (u64 & betree_Message_t))) + +(** [betree::betree_utils::store_internal_node]: + Source: 'src/betree_utils.rs', lines 115:0-115:71 *) +val betree_utils_store_internal_node + : + u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state & + unit) + +(** [betree::betree_utils::load_leaf_node]: + Source: 'src/betree_utils.rs', lines 132:0-132:55 *) +val betree_utils_load_leaf_node + : u64 -> state -> result (state & (betree_List_t (u64 & u64))) + +(** [betree::betree_utils::store_leaf_node]: + Source: 'src/betree_utils.rs', lines 145:0-145:63 *) +val betree_utils_store_leaf_node + : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit) + diff --git a/tests/fstar/betree/Betree.Types.fst b/tests/fstar/betree/Betree.Types.fst new file mode 100644 index 00000000..6b8e063b --- /dev/null +++ b/tests/fstar/betree/Betree.Types.fst @@ -0,0 +1,61 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: type definitions *) +module Betree.Types +open Primitives +include Betree.TypesExternal + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [betree::betree::List] + Source: 'src/betree.rs', lines 17:0-17:23 *) +type betree_List_t (t : Type0) = +| Betree_List_Cons : t -> betree_List_t t -> betree_List_t t +| Betree_List_Nil : betree_List_t t + +(** [betree::betree::UpsertFunState] + Source: 'src/betree.rs', lines 63:0-63:23 *) +type betree_UpsertFunState_t = +| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t +| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t + +(** [betree::betree::Message] + Source: 'src/betree.rs', lines 69:0-69:23 *) +type betree_Message_t = +| Betree_Message_Insert : u64 -> betree_Message_t +| Betree_Message_Delete : betree_Message_t +| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t + +(** [betree::betree::Leaf] + Source: 'src/betree.rs', lines 167:0-167:11 *) +type betree_Leaf_t = { id : u64; size : u64; } + +(** [betree::betree::Internal] + Source: 'src/betree.rs', lines 156:0-156:15 *) +type betree_Internal_t = +{ + id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t; +} + +(** [betree::betree::Node] + Source: 'src/betree.rs', lines 179:0-179:9 *) +and betree_Node_t = +| Betree_Node_Internal : betree_Internal_t -> betree_Node_t +| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t + +(** [betree::betree::Params] + Source: 'src/betree.rs', lines 187:0-187:13 *) +type betree_Params_t = { min_flush_size : u64; split_size : u64; } + +(** [betree::betree::NodeIdCounter] + Source: 'src/betree.rs', lines 201:0-201:20 *) +type betree_NodeIdCounter_t = { next_node_id : u64; } + +(** [betree::betree::BeTree] + Source: 'src/betree.rs', lines 218:0-218:17 *) +type betree_BeTree_t = +{ + params : betree_Params_t; + node_id_cnt : betree_NodeIdCounter_t; + root : betree_Node_t; +} + diff --git a/tests/fstar/betree/Betree.TypesExternal.fsti b/tests/fstar/betree/Betree.TypesExternal.fsti new file mode 100644 index 00000000..39e53ec9 --- /dev/null +++ b/tests/fstar/betree/Betree.TypesExternal.fsti @@ -0,0 +1,10 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: external type declarations *) +module Betree.TypesExternal +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** The state type used in the state-error monad *) +val state : Type0 + diff --git a/tests/fstar/betree/BetreeMain.Clauses.Template.fst b/tests/fstar/betree/BetreeMain.Clauses.Template.fst deleted file mode 100644 index b317dca4..00000000 --- a/tests/fstar/betree/BetreeMain.Clauses.Template.fst +++ /dev/null @@ -1,117 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: templates for the decreases clauses *) -module BetreeMain.Clauses.Template -open Primitives -open BetreeMain.Types - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [betree_main::betree::{betree_main::betree::List#1}::len]: decreases clause - Source: 'src/betree.rs', lines 276:4-276:24 *) -unfold -let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::List#1}::split_at]: decreases clause - Source: 'src/betree.rs', lines 284:4-284:51 *) -unfold -let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) - (n : u64) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: decreases clause - Source: 'src/betree.rs', lines 339:4-339:73 *) -unfold -let betree_ListPairU64T_partition_at_pivot_decreases (t : Type0) - (self : betree_List_t (u64 & t)) (pivot : u64) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: decreases clause - Source: 'src/betree.rs', lines 789:4-792:34 *) -unfold -let betree_Node_lookup_first_message_for_key_decreases (key : u64) - (msgs : betree_List_t (u64 & betree_Message_t)) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: decreases clause - Source: 'src/betree.rs', lines 636:4-636:80 *) -unfold -let betree_Node_lookup_in_bindings_decreases (key : u64) - (bindings : betree_List_t (u64 & u64)) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: decreases clause - Source: 'src/betree.rs', lines 819:4-819:90 *) -unfold -let betree_Node_apply_upserts_decreases - (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) - (key : u64) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: decreases clause - Source: 'src/betree.rs', lines 395:4-395:63 *) -unfold -let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) - (key : u64) (st : state) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: decreases clause - Source: 'src/betree.rs', lines 709:4-709:58 *) -unfold -let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) - (st : state) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: decreases clause - Source: 'src/betree.rs', lines 674:4-674:77 *) -unfold -let betree_Node_filter_messages_for_key_decreases (key : u64) - (msgs : betree_List_t (u64 & betree_Message_t)) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: decreases clause - Source: 'src/betree.rs', lines 689:4-692:34 *) -unfold -let betree_Node_lookup_first_message_after_key_decreases (key : u64) - (msgs : betree_List_t (u64 & betree_Message_t)) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: decreases clause - Source: 'src/betree.rs', lines 502:4-505:5 *) -unfold -let betree_Node_apply_messages_to_internal_decreases - (msgs : betree_List_t (u64 & betree_Message_t)) - (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: decreases clause - Source: 'src/betree.rs', lines 653:4-656:32 *) -unfold -let betree_Node_lookup_mut_in_bindings_decreases (key : u64) - (bindings : betree_List_t (u64 & u64)) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: decreases clause - Source: 'src/betree.rs', lines 444:4-447:5 *) -unfold -let betree_Node_apply_messages_to_leaf_decreases - (bindings : betree_List_t (u64 & u64)) - (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: decreases clause - Source: 'src/betree.rs', lines 410:4-415:26 *) -unfold -let betree_Internal_flush_decreases (self : betree_Internal_t) - (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) - (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = - admit () - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: decreases clause - Source: 'src/betree.rs', lines 588:4-593:5 *) -unfold -let betree_Node_apply_messages_decreases (self : betree_Node_t) - (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) - (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = - admit () - diff --git a/tests/fstar/betree/BetreeMain.Clauses.fst b/tests/fstar/betree/BetreeMain.Clauses.fst deleted file mode 100644 index b95d4c7e..00000000 --- a/tests/fstar/betree/BetreeMain.Clauses.fst +++ /dev/null @@ -1,210 +0,0 @@ -(** [betree_main]: templates for the decreases clauses *) -module BetreeMain.Clauses -open Primitives -open BetreeMain.Types - -#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" - -(*** Well-founded relations *) - -(* We had a few issues when proving termination of the mutually recursive functions: - * - betree_Internal_flush - * - betree_Node_apply_messages - * - * The quantity which effectively decreases is: - * (betree_size, messages_length) - * where messages_length is 0 when there are no messages - * (and where we use the lexicographic ordering, of course) - * - * However, the `%[...]` and `{:well-founded ...} notations are not available outside - * of `decrease` clauses. - * - * We thus resorted to writing and proving correct a well-founded relation over - * pairs of natural numbers. The trick is that `<<` can be used outside of decrease - * clauses, and can be used to trigger SMT patterns. - * - * What follows is adapted from: - * https://www.fstar-lang.org/tutorial/book/part2/part2_well_founded.html - * - * Also, the following PR might make things easier: - * https://github.com/FStarLang/FStar/pull/2561 - *) - -module P = FStar.Preorder -module W = FStar.WellFounded -module L = FStar.LexicographicOrdering - -let lt_nat (x y:nat) : Type = x < y == true -let rec wf_lt_nat (x:nat) - : W.acc lt_nat x - = W.AccIntro (fun y _ -> wf_lt_nat y) - -// A type abbreviation for a pair of nats -let nat_pair = (x:nat & nat) - -// Making a lexicographic ordering from a pair of nat ordering -let lex_order_nat_pair : P.relation nat_pair = - L.lex_t lt_nat (fun _ -> lt_nat) - -// The lex order on nat pairs is well-founded, using our general proof -// of lexicographic composition of well-founded orders -let lex_order_nat_pair_wf : W.well_founded lex_order_nat_pair = - L.lex_t_wf wf_lt_nat (fun _ -> wf_lt_nat) - -// A utility to introduce lt_nat -let mk_lt_nat (x:nat) (y:nat { x < y }) : lt_nat x y = - let _ : equals (x < y) true = Refl in - () - -// A utility to make a lex ordering of nat pairs -let mk_lex_order_nat_pair (xy0:nat_pair) - (xy1:nat_pair { - let (|x0, y0|) = xy0 in - let (|x1, y1|) = xy1 in - x0 < x1 \/ (x0 == x1 /\ y0 < y1) - }) : lex_order_nat_pair xy0 xy1 = - let (|x0, y0|) = xy0 in - let (|x1, y1|) = xy1 in - if x0 < x1 then L.Left_lex x0 x1 y0 y1 (mk_lt_nat x0 x1) - else L.Right_lex x0 y0 y1 (mk_lt_nat y0 y1) - -let rec coerce #a #r #x (p:W.acc #a r x) : Tot (W.acc r x) (decreases p) = - W.AccIntro (fun y r -> coerce (p.access_smaller y r)) - -let coerce_wf #a #r (p: (x:a -> W.acc r x)) : x:a -> W.acc r x = - fun x -> coerce (p x) - -(* We need this axiom, which comes from the following discussion: - * https://github.com/FStarLang/FStar/issues/1916 - * An issue here is that the `{well-founded ... }` notation - *) -assume -val axiom_well_founded (a : Type) (rel : a -> a -> Type0) - (rwf : W.well_founded #a rel) (x y : a) : - Lemma (requires (rel x y)) (ensures (x << y)) - -(* This lemma has a pattern (which makes it work) *) -let wf_nat_pair_lem (p0 p1 : nat_pair) : - Lemma - (requires ( - let (|x0, y0|) = p0 in - let (|x1, y1|) = p1 in - x0 < x1 || (x0 = x1 && y0 < y1))) - (ensures (p0 << p1)) - [SMTPat (p0 << p1)] = - let rel = lex_order_nat_pair in - let rel_wf = lex_order_nat_pair_wf in - let _ = mk_lex_order_nat_pair p0 p1 in - assert(rel p0 p1); - axiom_well_founded nat_pair rel rel_wf p0 p1 - -(*** Decrease clauses *) -/// "Standard" decrease clauses - -(** [betree_main::betree::List::{1}::len]: decreases clause *) -unfold -let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : betree_List_t t = - self - -(** [betree_main::betree::List::{1}::split_at]: decreases clause *) -unfold -let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) - (n : u64) : nat = - n - -(** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) -unfold -let betree_ListPairU64T_partition_at_pivot_decreases (t : Type0) - (self : betree_List_t (u64 & t)) (pivot : u64) : betree_List_t (u64 & t) = - self - -(** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) -unfold -let betree_Node_lookup_in_bindings_decreases (key : u64) - (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = - bindings - -(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) -unfold -let betree_Node_lookup_first_message_for_key_decreases (key : u64) - (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = - msgs - -(** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) -unfold -let betree_Node_apply_upserts_decreases - (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) - (key : u64) : betree_List_t (u64 & betree_Message_t) = - msgs - -(** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) -unfold -let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) - (key : u64) (st : state) : betree_Internal_t = - self - -(** [betree_main::betree::Node::{5}::lookup]: decreases clause *) -unfold -let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) - (st : state) : betree_Node_t = - self - -(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) -unfold -let betree_Node_lookup_mut_in_bindings_decreases (key : u64) - (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = - bindings - -unfold -let betree_Node_apply_messages_to_leaf_decreases - (bindings : betree_List_t (u64 & u64)) - (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = - new_msgs - -(** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) -unfold -let betree_Node_filter_messages_for_key_decreases (key : u64) - (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = - msgs - -(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) -unfold -let betree_Node_lookup_first_message_after_key_decreases (key : u64) - (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = - msgs - -let betree_Node_apply_messages_to_internal_decreases - (msgs : betree_List_t (u64 & betree_Message_t)) - (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = - new_msgs - -(*** Decrease clauses - nat_pair *) -/// The following decrease clauses use the [nat_pair] definition and the well-founded -/// relation proven above. - -let rec betree_size (bt : betree_Node_t) : nat = - match bt with - | Betree_Node_Internal node -> 1 + betree_Internal_size node - | Betree_Node_Leaf _ -> 1 - -and betree_Internal_size (node : betree_Internal_t) : nat = - 1 + betree_size node.left + betree_size node.right - -let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat = - match ls with - | Betree_List_Cons _ tl -> 1 + betree_List_len tl - | Betree_List_Nil -> 0 - -(** [betree_main::betree::Internal::{4}::flush]: decreases clause *) -unfold -let betree_Internal_flush_decreases (self : betree_Internal_t) - (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) - (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = - (|betree_Internal_size self, 0|) - -(** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) -unfold -let betree_Node_apply_messages_decreases (self : betree_Node_t) - (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) - (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = - (|betree_size self, betree_List_len msgs|) diff --git a/tests/fstar/betree/BetreeMain.Funs.fst b/tests/fstar/betree/BetreeMain.Funs.fst deleted file mode 100644 index 9942ef68..00000000 --- a/tests/fstar/betree/BetreeMain.Funs.fst +++ /dev/null @@ -1,676 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: function definitions *) -module BetreeMain.Funs -open Primitives -include BetreeMain.Types -include BetreeMain.FunsExternal -include BetreeMain.Clauses - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [betree_main::betree::load_internal_node]: - Source: 'src/betree.rs', lines 36:0-36:52 *) -let betree_load_internal_node - (id : u64) (st : state) : - result (state & (betree_List_t (u64 & betree_Message_t))) - = - betree_utils_load_internal_node id st - -(** [betree_main::betree::store_internal_node]: - Source: 'src/betree.rs', lines 41:0-41:60 *) -let betree_store_internal_node - (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) : - result (state & unit) - = - betree_utils_store_internal_node id content st - -(** [betree_main::betree::load_leaf_node]: - Source: 'src/betree.rs', lines 46:0-46:44 *) -let betree_load_leaf_node - (id : u64) (st : state) : result (state & (betree_List_t (u64 & u64))) = - betree_utils_load_leaf_node id st - -(** [betree_main::betree::store_leaf_node]: - Source: 'src/betree.rs', lines 51:0-51:52 *) -let betree_store_leaf_node - (id : u64) (content : betree_List_t (u64 & u64)) (st : state) : - result (state & unit) - = - betree_utils_store_leaf_node id content st - -(** [betree_main::betree::fresh_node_id]: - Source: 'src/betree.rs', lines 55:0-55:48 *) -let betree_fresh_node_id (counter : u64) : result (u64 & u64) = - let* counter1 = u64_add counter 1 in Ok (counter, counter1) - -(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: - Source: 'src/betree.rs', lines 206:4-206:20 *) -let betree_NodeIdCounter_new : result betree_NodeIdCounter_t = - Ok { next_node_id = 0 } - -(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: - Source: 'src/betree.rs', lines 210:4-210:36 *) -let betree_NodeIdCounter_fresh_id - (self : betree_NodeIdCounter_t) : result (u64 & betree_NodeIdCounter_t) = - let* i = u64_add self.next_node_id 1 in - Ok (self.next_node_id, { next_node_id = i }) - -(** [betree_main::betree::upsert_update]: - Source: 'src/betree.rs', lines 234:0-234:70 *) -let betree_upsert_update - (prev : option u64) (st : betree_UpsertFunState_t) : result u64 = - begin match prev with - | None -> - begin match st with - | Betree_UpsertFunState_Add v -> Ok v - | Betree_UpsertFunState_Sub _ -> Ok 0 - end - | Some prev1 -> - begin match st with - | Betree_UpsertFunState_Add v -> - let* margin = u64_sub core_u64_max prev1 in - if margin >= v then u64_add prev1 v else Ok core_u64_max - | Betree_UpsertFunState_Sub v -> - if prev1 >= v then u64_sub prev1 v else Ok 0 - end - end - -(** [betree_main::betree::{betree_main::betree::List#1}::len]: - Source: 'src/betree.rs', lines 276:4-276:24 *) -let rec betree_List_len - (t : Type0) (self : betree_List_t t) : - Tot (result u64) (decreases (betree_List_len_decreases t self)) - = - begin match self with - | Betree_List_Cons _ tl -> let* i = betree_List_len t tl in u64_add 1 i - | Betree_List_Nil -> Ok 0 - end - -(** [betree_main::betree::{betree_main::betree::List#1}::split_at]: - Source: 'src/betree.rs', lines 284:4-284:51 *) -let rec betree_List_split_at - (t : Type0) (self : betree_List_t t) (n : u64) : - Tot (result ((betree_List_t t) & (betree_List_t t))) - (decreases (betree_List_split_at_decreases t self n)) - = - if n = 0 - then Ok (Betree_List_Nil, self) - else - begin match self with - | Betree_List_Cons hd tl -> - let* i = u64_sub n 1 in - let* p = betree_List_split_at t tl i in - let (ls0, ls1) = p in - Ok (Betree_List_Cons hd ls0, ls1) - | Betree_List_Nil -> Fail Failure - end - -(** [betree_main::betree::{betree_main::betree::List#1}::push_front]: - Source: 'src/betree.rs', lines 299:4-299:34 *) -let betree_List_push_front - (t : Type0) (self : betree_List_t t) (x : t) : result (betree_List_t t) = - let (tl, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in - Ok (Betree_List_Cons x tl) - -(** [betree_main::betree::{betree_main::betree::List#1}::pop_front]: - Source: 'src/betree.rs', lines 306:4-306:32 *) -let betree_List_pop_front - (t : Type0) (self : betree_List_t t) : result (t & (betree_List_t t)) = - let (ls, _) = core_mem_replace (betree_List_t t) self Betree_List_Nil in - begin match ls with - | Betree_List_Cons x tl -> Ok (x, tl) - | Betree_List_Nil -> Fail Failure - end - -(** [betree_main::betree::{betree_main::betree::List#1}::hd]: - Source: 'src/betree.rs', lines 318:4-318:22 *) -let betree_List_hd (t : Type0) (self : betree_List_t t) : result t = - begin match self with - | Betree_List_Cons hd _ -> Ok hd - | Betree_List_Nil -> Fail Failure - end - -(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: - Source: 'src/betree.rs', lines 327:4-327:44 *) -let betree_ListPairU64T_head_has_key - (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool = - begin match self with - | Betree_List_Cons hd _ -> let (i, _) = hd in Ok (i = key) - | Betree_List_Nil -> Ok false - end - -(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: - Source: 'src/betree.rs', lines 339:4-339:73 *) -let rec betree_ListPairU64T_partition_at_pivot - (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) : - Tot (result ((betree_List_t (u64 & t)) & (betree_List_t (u64 & t)))) - (decreases (betree_ListPairU64T_partition_at_pivot_decreases t self pivot)) - = - begin match self with - | Betree_List_Cons hd tl -> - let (i, x) = hd in - if i >= pivot - then Ok (Betree_List_Nil, Betree_List_Cons (i, x) tl) - else - let* p = betree_ListPairU64T_partition_at_pivot t tl pivot in - let (ls0, ls1) = p in - Ok (Betree_List_Cons (i, x) ls0, ls1) - | Betree_List_Nil -> Ok (Betree_List_Nil, Betree_List_Nil) - end - -(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: - Source: 'src/betree.rs', lines 359:4-364:17 *) -let betree_Leaf_split - (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) - (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) - (st : state) : - result (state & (betree_Internal_t & betree_NodeIdCounter_t)) - = - let* p = betree_List_split_at (u64 & u64) content params.split_size in - let (content0, content1) = p in - let* p1 = betree_List_hd (u64 & u64) content1 in - let (pivot, _) = p1 in - let* (id0, node_id_cnt1) = betree_NodeIdCounter_fresh_id node_id_cnt in - let* (id1, node_id_cnt2) = betree_NodeIdCounter_fresh_id node_id_cnt1 in - let* (st1, _) = betree_store_leaf_node id0 content0 st in - let* (st2, _) = betree_store_leaf_node id1 content1 st1 in - let n = Betree_Node_Leaf { id = id0; size = params.split_size } in - let n1 = Betree_Node_Leaf { id = id1; size = params.split_size } in - Ok (st2, ({ id = self.id; pivot = pivot; left = n; right = n1 }, - node_id_cnt2)) - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: - Source: 'src/betree.rs', lines 789:4-792:34 *) -let rec betree_Node_lookup_first_message_for_key - (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : - Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 & - betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t))))) - (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs)) - = - begin match msgs with - | Betree_List_Cons x next_msgs -> - let (i, m) = x in - if i >= key - then Ok (Betree_List_Cons (i, m) next_msgs, Ok) - else - let* (l, lookup_first_message_for_key_back) = - betree_Node_lookup_first_message_for_key key next_msgs in - let back = - fun ret -> - let* next_msgs1 = lookup_first_message_for_key_back ret in - Ok (Betree_List_Cons (i, m) next_msgs1) in - Ok (l, back) - | Betree_List_Nil -> Ok (Betree_List_Nil, Ok) - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: - Source: 'src/betree.rs', lines 636:4-636:80 *) -let rec betree_Node_lookup_in_bindings - (key : u64) (bindings : betree_List_t (u64 & u64)) : - Tot (result (option u64)) - (decreases (betree_Node_lookup_in_bindings_decreases key bindings)) - = - begin match bindings with - | Betree_List_Cons hd tl -> - let (i, i1) = hd in - if i = key - then Ok (Some i1) - else if i > key then Ok None else betree_Node_lookup_in_bindings key tl - | Betree_List_Nil -> Ok None - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: - Source: 'src/betree.rs', lines 819:4-819:90 *) -let rec betree_Node_apply_upserts - (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) - (key : u64) : - Tot (result (u64 & (betree_List_t (u64 & betree_Message_t)))) - (decreases (betree_Node_apply_upserts_decreases msgs prev key)) - = - let* b = betree_ListPairU64T_head_has_key betree_Message_t msgs key in - if b - then - let* (msg, msgs1) = betree_List_pop_front (u64 & betree_Message_t) msgs in - let (_, m) = msg in - begin match m with - | Betree_Message_Insert _ -> Fail Failure - | Betree_Message_Delete -> Fail Failure - | Betree_Message_Upsert s -> - let* v = betree_upsert_update prev s in - betree_Node_apply_upserts msgs1 (Some v) key - end - else - let* v = core_option_Option_unwrap u64 prev in - let* msgs1 = - betree_List_push_front (u64 & betree_Message_t) msgs (key, - Betree_Message_Insert v) in - Ok (v, msgs1) - -(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: - Source: 'src/betree.rs', lines 395:4-395:63 *) -let rec betree_Internal_lookup_in_children - (self : betree_Internal_t) (key : u64) (st : state) : - Tot (result (state & ((option u64) & betree_Internal_t))) - (decreases (betree_Internal_lookup_in_children_decreases self key st)) - = - if key < self.pivot - then - let* (st1, (o, n)) = betree_Node_lookup self.left key st in - Ok (st1, (o, { self with left = n })) - else - let* (st1, (o, n)) = betree_Node_lookup self.right key st in - Ok (st1, (o, { self with right = n })) - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: - Source: 'src/betree.rs', lines 709:4-709:58 *) -and betree_Node_lookup - (self : betree_Node_t) (key : u64) (st : state) : - Tot (result (state & ((option u64) & betree_Node_t))) - (decreases (betree_Node_lookup_decreases self key st)) - = - begin match self with - | Betree_Node_Internal node -> - let* (st1, msgs) = betree_load_internal_node node.id st in - let* (pending, lookup_first_message_for_key_back) = - betree_Node_lookup_first_message_for_key key msgs in - begin match pending with - | Betree_List_Cons p l -> - let (k, msg) = p in - if k <> key - then - let* (st2, (o, node1)) = - betree_Internal_lookup_in_children node key st1 in - let* _ = - lookup_first_message_for_key_back (Betree_List_Cons (k, msg) l) in - Ok (st2, (o, Betree_Node_Internal node1)) - else - begin match msg with - | Betree_Message_Insert v -> - let* _ = - lookup_first_message_for_key_back (Betree_List_Cons (k, - Betree_Message_Insert v) l) in - Ok (st1, (Some v, Betree_Node_Internal node)) - | Betree_Message_Delete -> - let* _ = - lookup_first_message_for_key_back (Betree_List_Cons (k, - Betree_Message_Delete) l) in - Ok (st1, (None, Betree_Node_Internal node)) - | Betree_Message_Upsert ufs -> - let* (st2, (v, node1)) = - betree_Internal_lookup_in_children node key st1 in - let* (v1, pending1) = - betree_Node_apply_upserts (Betree_List_Cons (k, - Betree_Message_Upsert ufs) l) v key in - let* msgs1 = lookup_first_message_for_key_back pending1 in - let* (st3, _) = betree_store_internal_node node1.id msgs1 st2 in - Ok (st3, (Some v1, Betree_Node_Internal node1)) - end - | Betree_List_Nil -> - let* (st2, (o, node1)) = betree_Internal_lookup_in_children node key st1 - in - let* _ = lookup_first_message_for_key_back Betree_List_Nil in - Ok (st2, (o, Betree_Node_Internal node1)) - end - | Betree_Node_Leaf node -> - let* (st1, bindings) = betree_load_leaf_node node.id st in - let* o = betree_Node_lookup_in_bindings key bindings in - Ok (st1, (o, Betree_Node_Leaf node)) - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: - Source: 'src/betree.rs', lines 674:4-674:77 *) -let rec betree_Node_filter_messages_for_key - (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : - Tot (result (betree_List_t (u64 & betree_Message_t))) - (decreases (betree_Node_filter_messages_for_key_decreases key msgs)) - = - begin match msgs with - | Betree_List_Cons p l -> - let (k, m) = p in - if k = key - then - let* (_, msgs1) = - betree_List_pop_front (u64 & betree_Message_t) (Betree_List_Cons (k, m) - l) in - betree_Node_filter_messages_for_key key msgs1 - else Ok (Betree_List_Cons (k, m) l) - | Betree_List_Nil -> Ok Betree_List_Nil - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: - Source: 'src/betree.rs', lines 689:4-692:34 *) -let rec betree_Node_lookup_first_message_after_key - (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : - Tot (result ((betree_List_t (u64 & betree_Message_t)) & (betree_List_t (u64 & - betree_Message_t) -> result (betree_List_t (u64 & betree_Message_t))))) - (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs)) - = - begin match msgs with - | Betree_List_Cons p next_msgs -> - let (k, m) = p in - if k = key - then - let* (l, lookup_first_message_after_key_back) = - betree_Node_lookup_first_message_after_key key next_msgs in - let back = - fun ret -> - let* next_msgs1 = lookup_first_message_after_key_back ret in - Ok (Betree_List_Cons (k, m) next_msgs1) in - Ok (l, back) - else Ok (Betree_List_Cons (k, m) next_msgs, Ok) - | Betree_List_Nil -> Ok (Betree_List_Nil, Ok) - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: - Source: 'src/betree.rs', lines 521:4-521:89 *) -let betree_Node_apply_to_internal - (msgs : betree_List_t (u64 & betree_Message_t)) (key : u64) - (new_msg : betree_Message_t) : - result (betree_List_t (u64 & betree_Message_t)) - = - let* (msgs1, lookup_first_message_for_key_back) = - betree_Node_lookup_first_message_for_key key msgs in - let* b = betree_ListPairU64T_head_has_key betree_Message_t msgs1 key in - if b - then - begin match new_msg with - | Betree_Message_Insert i -> - let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in - let* msgs3 = - betree_List_push_front (u64 & betree_Message_t) msgs2 (key, - Betree_Message_Insert i) in - lookup_first_message_for_key_back msgs3 - | Betree_Message_Delete -> - let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in - let* msgs3 = - betree_List_push_front (u64 & betree_Message_t) msgs2 (key, - Betree_Message_Delete) in - lookup_first_message_for_key_back msgs3 - | Betree_Message_Upsert s -> - let* p = betree_List_hd (u64 & betree_Message_t) msgs1 in - let (_, m) = p in - begin match m with - | Betree_Message_Insert prev -> - let* v = betree_upsert_update (Some prev) s in - let* (_, msgs2) = betree_List_pop_front (u64 & betree_Message_t) msgs1 - in - let* msgs3 = - betree_List_push_front (u64 & betree_Message_t) msgs2 (key, - Betree_Message_Insert v) in - lookup_first_message_for_key_back msgs3 - | Betree_Message_Delete -> - let* (_, msgs2) = betree_List_pop_front (u64 & betree_Message_t) msgs1 - in - let* v = betree_upsert_update None s in - let* msgs3 = - betree_List_push_front (u64 & betree_Message_t) msgs2 (key, - Betree_Message_Insert v) in - lookup_first_message_for_key_back msgs3 - | Betree_Message_Upsert _ -> - let* (msgs2, lookup_first_message_after_key_back) = - betree_Node_lookup_first_message_after_key key msgs1 in - let* msgs3 = - betree_List_push_front (u64 & betree_Message_t) msgs2 (key, - Betree_Message_Upsert s) in - let* msgs4 = lookup_first_message_after_key_back msgs3 in - lookup_first_message_for_key_back msgs4 - end - end - else - let* msgs2 = - betree_List_push_front (u64 & betree_Message_t) msgs1 (key, new_msg) in - lookup_first_message_for_key_back msgs2 - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: - Source: 'src/betree.rs', lines 502:4-505:5 *) -let rec betree_Node_apply_messages_to_internal - (msgs : betree_List_t (u64 & betree_Message_t)) - (new_msgs : betree_List_t (u64 & betree_Message_t)) : - Tot (result (betree_List_t (u64 & betree_Message_t))) - (decreases (betree_Node_apply_messages_to_internal_decreases msgs new_msgs)) - = - begin match new_msgs with - | Betree_List_Cons new_msg new_msgs_tl -> - let (i, m) = new_msg in - let* msgs1 = betree_Node_apply_to_internal msgs i m in - betree_Node_apply_messages_to_internal msgs1 new_msgs_tl - | Betree_List_Nil -> Ok msgs - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: - Source: 'src/betree.rs', lines 653:4-656:32 *) -let rec betree_Node_lookup_mut_in_bindings - (key : u64) (bindings : betree_List_t (u64 & u64)) : - Tot (result ((betree_List_t (u64 & u64)) & (betree_List_t (u64 & u64) -> - result (betree_List_t (u64 & u64))))) - (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings)) - = - begin match bindings with - | Betree_List_Cons hd tl -> - let (i, i1) = hd in - if i >= key - then Ok (Betree_List_Cons (i, i1) tl, Ok) - else - let* (l, lookup_mut_in_bindings_back) = - betree_Node_lookup_mut_in_bindings key tl in - let back = - fun ret -> - let* tl1 = lookup_mut_in_bindings_back ret in - Ok (Betree_List_Cons (i, i1) tl1) in - Ok (l, back) - | Betree_List_Nil -> Ok (Betree_List_Nil, Ok) - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: - Source: 'src/betree.rs', lines 460:4-460:87 *) -let betree_Node_apply_to_leaf - (bindings : betree_List_t (u64 & u64)) (key : u64) - (new_msg : betree_Message_t) : - result (betree_List_t (u64 & u64)) - = - let* (bindings1, lookup_mut_in_bindings_back) = - betree_Node_lookup_mut_in_bindings key bindings in - let* b = betree_ListPairU64T_head_has_key u64 bindings1 key in - if b - then - let* (hd, bindings2) = betree_List_pop_front (u64 & u64) bindings1 in - begin match new_msg with - | Betree_Message_Insert v -> - let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in - lookup_mut_in_bindings_back bindings3 - | Betree_Message_Delete -> lookup_mut_in_bindings_back bindings2 - | Betree_Message_Upsert s -> - let (_, i) = hd in - let* v = betree_upsert_update (Some i) s in - let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in - lookup_mut_in_bindings_back bindings3 - end - else - begin match new_msg with - | Betree_Message_Insert v -> - let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in - lookup_mut_in_bindings_back bindings2 - | Betree_Message_Delete -> lookup_mut_in_bindings_back bindings1 - | Betree_Message_Upsert s -> - let* v = betree_upsert_update None s in - let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in - lookup_mut_in_bindings_back bindings2 - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: - Source: 'src/betree.rs', lines 444:4-447:5 *) -let rec betree_Node_apply_messages_to_leaf - (bindings : betree_List_t (u64 & u64)) - (new_msgs : betree_List_t (u64 & betree_Message_t)) : - Tot (result (betree_List_t (u64 & u64))) - (decreases (betree_Node_apply_messages_to_leaf_decreases bindings new_msgs)) - = - begin match new_msgs with - | Betree_List_Cons new_msg new_msgs_tl -> - let (i, m) = new_msg in - let* bindings1 = betree_Node_apply_to_leaf bindings i m in - betree_Node_apply_messages_to_leaf bindings1 new_msgs_tl - | Betree_List_Nil -> Ok bindings - end - -(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: - Source: 'src/betree.rs', lines 410:4-415:26 *) -let rec betree_Internal_flush - (self : betree_Internal_t) (params : betree_Params_t) - (node_id_cnt : betree_NodeIdCounter_t) - (content : betree_List_t (u64 & betree_Message_t)) (st : state) : - Tot (result (state & ((betree_List_t (u64 & betree_Message_t)) & - (betree_Internal_t & betree_NodeIdCounter_t)))) - (decreases ( - betree_Internal_flush_decreases self params node_id_cnt content st)) - = - let* p = - betree_ListPairU64T_partition_at_pivot betree_Message_t content self.pivot - in - let (msgs_left, msgs_right) = p in - let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in - if len_left >= params.min_flush_size - then - let* (st1, p1) = - betree_Node_apply_messages self.left params node_id_cnt msgs_left st in - let (n, node_id_cnt1) = p1 in - let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in - if len_right >= params.min_flush_size - then - let* (st2, p2) = - betree_Node_apply_messages self.right params node_id_cnt1 msgs_right - st1 in - let (n1, node_id_cnt2) = p2 in - Ok (st2, (Betree_List_Nil, ({ self with left = n; right = n1 }, - node_id_cnt2))) - else Ok (st1, (msgs_right, ({ self with left = n }, node_id_cnt1))) - else - let* (st1, p1) = - betree_Node_apply_messages self.right params node_id_cnt msgs_right st in - let (n, node_id_cnt1) = p1 in - Ok (st1, (msgs_left, ({ self with right = n }, node_id_cnt1))) - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: - Source: 'src/betree.rs', lines 588:4-593:5 *) -and betree_Node_apply_messages - (self : betree_Node_t) (params : betree_Params_t) - (node_id_cnt : betree_NodeIdCounter_t) - (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : - Tot (result (state & (betree_Node_t & betree_NodeIdCounter_t))) - (decreases ( - betree_Node_apply_messages_decreases self params node_id_cnt msgs st)) - = - begin match self with - | Betree_Node_Internal node -> - let* (st1, content) = betree_load_internal_node node.id st in - let* content1 = betree_Node_apply_messages_to_internal content msgs in - let* num_msgs = betree_List_len (u64 & betree_Message_t) content1 in - if num_msgs >= params.min_flush_size - then - let* (st2, (content2, p)) = - betree_Internal_flush node params node_id_cnt content1 st1 in - let (node1, node_id_cnt1) = p in - let* (st3, _) = betree_store_internal_node node1.id content2 st2 in - Ok (st3, (Betree_Node_Internal node1, node_id_cnt1)) - else - let* (st2, _) = betree_store_internal_node node.id content1 st1 in - Ok (st2, (Betree_Node_Internal node, node_id_cnt)) - | Betree_Node_Leaf node -> - let* (st1, content) = betree_load_leaf_node node.id st in - let* content1 = betree_Node_apply_messages_to_leaf content msgs in - let* len = betree_List_len (u64 & u64) content1 in - let* i = u64_mul 2 params.split_size in - if len >= i - then - let* (st2, (new_node, node_id_cnt1)) = - betree_Leaf_split node content1 params node_id_cnt st1 in - let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in - Ok (st3, (Betree_Node_Internal new_node, node_id_cnt1)) - else - let* (st2, _) = betree_store_leaf_node node.id content1 st1 in - Ok (st2, (Betree_Node_Leaf { node with size = len }, node_id_cnt)) - end - -(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: - Source: 'src/betree.rs', lines 576:4-582:5 *) -let betree_Node_apply - (self : betree_Node_t) (params : betree_Params_t) - (node_id_cnt : betree_NodeIdCounter_t) (key : u64) - (new_msg : betree_Message_t) (st : state) : - result (state & (betree_Node_t & betree_NodeIdCounter_t)) - = - let* (st1, p) = - betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key, - new_msg) Betree_List_Nil) st in - let (self1, node_id_cnt1) = p in - Ok (st1, (self1, node_id_cnt1)) - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]: - Source: 'src/betree.rs', lines 849:4-849:60 *) -let betree_BeTree_new - (min_flush_size : u64) (split_size : u64) (st : state) : - result (state & betree_BeTree_t) - = - let* node_id_cnt = betree_NodeIdCounter_new in - let* (id, node_id_cnt1) = betree_NodeIdCounter_fresh_id node_id_cnt in - let* (st1, _) = betree_store_leaf_node id Betree_List_Nil st in - Ok (st1, - { - params = { min_flush_size = min_flush_size; split_size = split_size }; - node_id_cnt = node_id_cnt1; - root = (Betree_Node_Leaf { id = id; size = 0 }) - }) - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: - Source: 'src/betree.rs', lines 868:4-868:47 *) -let betree_BeTree_apply - (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) : - result (state & betree_BeTree_t) - = - let* (st1, p) = - betree_Node_apply self.root self.params self.node_id_cnt key msg st in - let (n, nic) = p in - Ok (st1, { self with node_id_cnt = nic; root = n }) - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: - Source: 'src/betree.rs', lines 874:4-874:52 *) -let betree_BeTree_insert - (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) : - result (state & betree_BeTree_t) - = - betree_BeTree_apply self key (Betree_Message_Insert value) st - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: - Source: 'src/betree.rs', lines 880:4-880:38 *) -let betree_BeTree_delete - (self : betree_BeTree_t) (key : u64) (st : state) : - result (state & betree_BeTree_t) - = - betree_BeTree_apply self key Betree_Message_Delete st - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: - Source: 'src/betree.rs', lines 886:4-886:59 *) -let betree_BeTree_upsert - (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t) - (st : state) : - result (state & betree_BeTree_t) - = - betree_BeTree_apply self key (Betree_Message_Upsert upd) st - -(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: - Source: 'src/betree.rs', lines 895:4-895:62 *) -let betree_BeTree_lookup - (self : betree_BeTree_t) (key : u64) (st : state) : - result (state & ((option u64) & betree_BeTree_t)) - = - let* (st1, (o, n)) = betree_Node_lookup self.root key st in - Ok (st1, (o, { self with root = n })) - -(** [betree_main::main]: - Source: 'src/main.rs', lines 4:0-4:9 *) -let main : result unit = - Ok () - -(** Unit test for [betree_main::main] *) -let _ = assert_norm (main = Ok ()) - diff --git a/tests/fstar/betree/BetreeMain.FunsExternal.fsti b/tests/fstar/betree/BetreeMain.FunsExternal.fsti deleted file mode 100644 index 8be98acf..00000000 --- a/tests/fstar/betree/BetreeMain.FunsExternal.fsti +++ /dev/null @@ -1,30 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: external function declarations *) -module BetreeMain.FunsExternal -open Primitives -include BetreeMain.Types - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [betree_main::betree_utils::load_internal_node]: - Source: 'src/betree_utils.rs', lines 98:0-98:63 *) -val betree_utils_load_internal_node - : u64 -> state -> result (state & (betree_List_t (u64 & betree_Message_t))) - -(** [betree_main::betree_utils::store_internal_node]: - Source: 'src/betree_utils.rs', lines 115:0-115:71 *) -val betree_utils_store_internal_node - : - u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state & - unit) - -(** [betree_main::betree_utils::load_leaf_node]: - Source: 'src/betree_utils.rs', lines 132:0-132:55 *) -val betree_utils_load_leaf_node - : u64 -> state -> result (state & (betree_List_t (u64 & u64))) - -(** [betree_main::betree_utils::store_leaf_node]: - Source: 'src/betree_utils.rs', lines 145:0-145:63 *) -val betree_utils_store_leaf_node - : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit) - diff --git a/tests/fstar/betree/BetreeMain.Types.fst b/tests/fstar/betree/BetreeMain.Types.fst deleted file mode 100644 index b87219b2..00000000 --- a/tests/fstar/betree/BetreeMain.Types.fst +++ /dev/null @@ -1,61 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: type definitions *) -module BetreeMain.Types -open Primitives -include BetreeMain.TypesExternal - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [betree_main::betree::List] - Source: 'src/betree.rs', lines 17:0-17:23 *) -type betree_List_t (t : Type0) = -| Betree_List_Cons : t -> betree_List_t t -> betree_List_t t -| Betree_List_Nil : betree_List_t t - -(** [betree_main::betree::UpsertFunState] - Source: 'src/betree.rs', lines 63:0-63:23 *) -type betree_UpsertFunState_t = -| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t -| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t - -(** [betree_main::betree::Message] - Source: 'src/betree.rs', lines 69:0-69:23 *) -type betree_Message_t = -| Betree_Message_Insert : u64 -> betree_Message_t -| Betree_Message_Delete : betree_Message_t -| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t - -(** [betree_main::betree::Leaf] - Source: 'src/betree.rs', lines 167:0-167:11 *) -type betree_Leaf_t = { id : u64; size : u64; } - -(** [betree_main::betree::Internal] - Source: 'src/betree.rs', lines 156:0-156:15 *) -type betree_Internal_t = -{ - id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t; -} - -(** [betree_main::betree::Node] - Source: 'src/betree.rs', lines 179:0-179:9 *) -and betree_Node_t = -| Betree_Node_Internal : betree_Internal_t -> betree_Node_t -| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t - -(** [betree_main::betree::Params] - Source: 'src/betree.rs', lines 187:0-187:13 *) -type betree_Params_t = { min_flush_size : u64; split_size : u64; } - -(** [betree_main::betree::NodeIdCounter] - Source: 'src/betree.rs', lines 201:0-201:20 *) -type betree_NodeIdCounter_t = { next_node_id : u64; } - -(** [betree_main::betree::BeTree] - Source: 'src/betree.rs', lines 218:0-218:17 *) -type betree_BeTree_t = -{ - params : betree_Params_t; - node_id_cnt : betree_NodeIdCounter_t; - root : betree_Node_t; -} - diff --git a/tests/fstar/betree/BetreeMain.TypesExternal.fsti b/tests/fstar/betree/BetreeMain.TypesExternal.fsti deleted file mode 100644 index 1b2c53a6..00000000 --- a/tests/fstar/betree/BetreeMain.TypesExternal.fsti +++ /dev/null @@ -1,10 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: external type declarations *) -module BetreeMain.TypesExternal -open Primitives - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** The state type used in the state-error monad *) -val state : Type0 - diff --git a/tests/hol4/betree/betreeMain_FunsScript.sml b/tests/hol4/betree/betreeMain_FunsScript.sml deleted file mode 100644 index bd16c16c..00000000 --- a/tests/hol4/betree/betreeMain_FunsScript.sml +++ /dev/null @@ -1,1212 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: function definitions *) -open primitivesLib divDefLib -open betreeMain_TypesTheory betreeMain_OpaqueTheory - -val _ = new_theory "betreeMain_Funs" - - -val betree_load_internal_node_fwd_def = Define ‘ - (** [betree_main::betree::load_internal_node]: forward function *) - betree_load_internal_node_fwd - (id : u64) (st : state) : - (state # (u64 # betree_message_t) betree_list_t) result - = - betree_utils_load_internal_node_fwd id st -’ - -val betree_store_internal_node_fwd_def = Define ‘ - (** [betree_main::betree::store_internal_node]: forward function *) - betree_store_internal_node_fwd - (id : u64) (content : (u64 # betree_message_t) betree_list_t) (st : state) - : - (state # unit) result - = - do - (st0, _) <- betree_utils_store_internal_node_fwd id content st; - Return (st0, ()) - od -’ - -val betree_load_leaf_node_fwd_def = Define ‘ - (** [betree_main::betree::load_leaf_node]: forward function *) - betree_load_leaf_node_fwd - (id : u64) (st : state) : (state # (u64 # u64) betree_list_t) result = - betree_utils_load_leaf_node_fwd id st -’ - -val betree_store_leaf_node_fwd_def = Define ‘ - (** [betree_main::betree::store_leaf_node]: forward function *) - betree_store_leaf_node_fwd - (id : u64) (content : (u64 # u64) betree_list_t) (st : state) : - (state # unit) result - = - do - (st0, _) <- betree_utils_store_leaf_node_fwd id content st; - Return (st0, ()) - od -’ - -val betree_fresh_node_id_fwd_def = Define ‘ - (** [betree_main::betree::fresh_node_id]: forward function *) - betree_fresh_node_id_fwd (counter : u64) : u64 result = - do - _ <- u64_add counter (int_to_u64 1); - Return counter - od -’ - -val betree_fresh_node_id_back_def = Define ‘ - (** [betree_main::betree::fresh_node_id]: backward function 0 *) - betree_fresh_node_id_back (counter : u64) : u64 result = - u64_add counter (int_to_u64 1) -’ - -val betree_node_id_counter_new_fwd_def = Define ‘ - (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *) - betree_node_id_counter_new_fwd : betree_node_id_counter_t result = - Return (<| betree_node_id_counter_next_node_id := (int_to_u64 0) |>) -’ - -val betree_node_id_counter_fresh_id_fwd_def = Define ‘ - (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *) - betree_node_id_counter_fresh_id_fwd - (self : betree_node_id_counter_t) : u64 result = - do - _ <- u64_add self.betree_node_id_counter_next_node_id (int_to_u64 1); - Return self.betree_node_id_counter_next_node_id - od -’ - -val betree_node_id_counter_fresh_id_back_def = Define ‘ - (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *) - betree_node_id_counter_fresh_id_back - (self : betree_node_id_counter_t) : betree_node_id_counter_t result = - do - i <- u64_add self.betree_node_id_counter_next_node_id (int_to_u64 1); - Return (<| betree_node_id_counter_next_node_id := i |>) - od -’ - -val betree_upsert_update_fwd_def = Define ‘ - (** [betree_main::betree::upsert_update]: forward function *) - betree_upsert_update_fwd - (prev : u64 option) (st : betree_upsert_fun_state_t) : u64 result = - (case prev of - | NONE => - (case st of - | BetreeUpsertFunStateAdd v => Return v - | BetreeUpsertFunStateSub i => Return (int_to_u64 0)) - | SOME prev0 => - (case st of - | BetreeUpsertFunStateAdd v => - do - margin <- u64_sub core_u64_max prev0; - if u64_ge margin v then u64_add prev0 v else Return core_u64_max - od - | BetreeUpsertFunStateSub v => - if u64_ge prev0 v then u64_sub prev0 v else Return (int_to_u64 0))) -’ - -val [betree_list_len_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::List::{1}::len]: forward function *) - betree_list_len_fwd (self : 't betree_list_t) : u64 result = - (case self of - | BetreeListCons t tl => - do - i <- betree_list_len_fwd tl; - u64_add (int_to_u64 1) i - od - | BetreeListNil => Return (int_to_u64 0)) -’ - -val [betree_list_split_at_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::List::{1}::split_at]: forward function *) - betree_list_split_at_fwd - (self : 't betree_list_t) (n : u64) : - ('t betree_list_t # 't betree_list_t) result - = - if n = int_to_u64 0 - then Return (BetreeListNil, self) - else - (case self of - | BetreeListCons hd tl => - do - i <- u64_sub n (int_to_u64 1); - p <- betree_list_split_at_fwd tl i; - let (ls0, ls1) = p in let l = ls0 in Return (BetreeListCons hd l, ls1) - od - | BetreeListNil => Fail Failure) -’ - -val betree_list_push_front_fwd_back_def = Define ‘ - (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function - (there is a single backward function, and the forward function returns ()) *) - betree_list_push_front_fwd_back - (self : 't betree_list_t) (x : 't) : 't betree_list_t result = - let tl = mem_replace_fwd self BetreeListNil in - let l = tl in - Return (BetreeListCons x l) -’ - -val betree_list_pop_front_fwd_def = Define ‘ - (** [betree_main::betree::List::{1}::pop_front]: forward function *) - betree_list_pop_front_fwd (self : 't betree_list_t) : 't result = - let ls = mem_replace_fwd self BetreeListNil in - (case ls of - | BetreeListCons x tl => Return x - | BetreeListNil => Fail Failure) -’ - -val betree_list_pop_front_back_def = Define ‘ - (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *) - betree_list_pop_front_back - (self : 't betree_list_t) : 't betree_list_t result = - let ls = mem_replace_fwd self BetreeListNil in - (case ls of - | BetreeListCons x tl => Return tl - | BetreeListNil => Fail Failure) -’ - -val betree_list_hd_fwd_def = Define ‘ - (** [betree_main::betree::List::{1}::hd]: forward function *) - betree_list_hd_fwd (self : 't betree_list_t) : 't result = - (case self of - | BetreeListCons hd l => Return hd - | BetreeListNil => Fail Failure) -’ - -val betree_list_head_has_key_fwd_def = Define ‘ - (** [betree_main::betree::List::{2}::head_has_key]: forward function *) - betree_list_head_has_key_fwd - (self : (u64 # 't) betree_list_t) (key : u64) : bool result = - (case self of - | BetreeListCons hd l => let (i, _) = hd in Return (i = key) - | BetreeListNil => Return F) -’ - -val [betree_list_partition_at_pivot_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *) - betree_list_partition_at_pivot_fwd - (self : (u64 # 't) betree_list_t) (pivot : u64) : - ((u64 # 't) betree_list_t # (u64 # 't) betree_list_t) result - = - (case self of - | BetreeListCons hd tl => - let (i, t) = hd in - if u64_ge i pivot - then Return (BetreeListNil, BetreeListCons (i, t) tl) - else ( - do - p <- betree_list_partition_at_pivot_fwd tl pivot; - let (ls0, ls1) = p in - let l = ls0 in - Return (BetreeListCons (i, t) l, ls1) - od) - | BetreeListNil => Return (BetreeListNil, BetreeListNil)) -’ - -val betree_leaf_split_fwd_def = Define ‘ - (** [betree_main::betree::Leaf::{3}::split]: forward function *) - betree_leaf_split_fwd - (self : betree_leaf_t) (content : (u64 # u64) betree_list_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : state) : - (state # betree_internal_t) result - = - do - p <- betree_list_split_at_fwd content params.betree_params_split_size; - let (content0, content1) = p in - do - p0 <- betree_list_hd_fwd content1; - let (pivot, _) = p0 in - do - id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; - node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt; - id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; - (st0, _) <- betree_store_leaf_node_fwd id0 content0 st; - (st1, _) <- betree_store_leaf_node_fwd id1 content1 st0; - let n = BetreeNodeLeaf - (<| - betree_leaf_id := id0; - betree_leaf_size := params.betree_params_split_size - |>) in - let n0 = BetreeNodeLeaf - (<| - betree_leaf_id := id1; - betree_leaf_size := params.betree_params_split_size - |>) in - Return (st1, - <| - betree_internal_id := self.betree_leaf_id; - betree_internal_pivot := pivot; - betree_internal_left := n; - betree_internal_right := n0 - |>) - od - od - od -’ - -val betree_leaf_split_back_def = Define ‘ - (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *) - betree_leaf_split_back - (self : betree_leaf_t) (content : (u64 # u64) betree_list_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : state) : - betree_node_id_counter_t result - = - do - p <- betree_list_split_at_fwd content params.betree_params_split_size; - let (content0, content1) = p in - do - _ <- betree_list_hd_fwd content1; - id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; - node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt; - id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; - (st0, _) <- betree_store_leaf_node_fwd id0 content0 st; - _ <- betree_store_leaf_node_fwd id1 content1 st0; - betree_node_id_counter_fresh_id_back node_id_cnt0 - od - od -’ - -val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *) - betree_node_lookup_first_message_for_key_fwd - (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) : - (u64 # betree_message_t) betree_list_t result - = - (case msgs of - | BetreeListCons x next_msgs => - let (i, m) = x in - if u64_ge i key - then Return (BetreeListCons (i, m) next_msgs) - else betree_node_lookup_first_message_for_key_fwd key next_msgs - | BetreeListNil => Return BetreeListNil) -’ - -val [betree_node_lookup_first_message_for_key_back_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *) - betree_node_lookup_first_message_for_key_back - (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) - (ret : (u64 # betree_message_t) betree_list_t) : - (u64 # betree_message_t) betree_list_t result - = - (case msgs of - | BetreeListCons x next_msgs => - let (i, m) = x in - if u64_ge i key - then Return ret - else ( - do - next_msgs0 <- - betree_node_lookup_first_message_for_key_back key next_msgs ret; - Return (BetreeListCons (i, m) next_msgs0) - od) - | BetreeListNil => Return ret) -’ - -val [betree_node_apply_upserts_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *) - betree_node_apply_upserts_fwd - (msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option) - (key : u64) (st : state) : - (state # u64) result - = - do - b <- betree_list_head_has_key_fwd msgs key; - if b - then ( - do - msg <- betree_list_pop_front_fwd msgs; - let (_, m) = msg in - (case m of - | BetreeMessageInsert i => Fail Failure - | BetreeMessageDelete => Fail Failure - | BetreeMessageUpsert s => - do - v <- betree_upsert_update_fwd prev s; - msgs0 <- betree_list_pop_front_back msgs; - betree_node_apply_upserts_fwd msgs0 (SOME v) key st - od) - od) - else ( - do - (st0, v) <- core_option_option_unwrap_fwd prev st; - _ <- betree_list_push_front_fwd_back msgs (key, BetreeMessageInsert v); - Return (st0, v) - od) - od -’ - -val [betree_node_apply_upserts_back_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *) - betree_node_apply_upserts_back - (msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option) - (key : u64) (st : state) : - (u64 # betree_message_t) betree_list_t result - = - do - b <- betree_list_head_has_key_fwd msgs key; - if b - then ( - do - msg <- betree_list_pop_front_fwd msgs; - let (_, m) = msg in - (case m of - | BetreeMessageInsert i => Fail Failure - | BetreeMessageDelete => Fail Failure - | BetreeMessageUpsert s => - do - v <- betree_upsert_update_fwd prev s; - msgs0 <- betree_list_pop_front_back msgs; - betree_node_apply_upserts_back msgs0 (SOME v) key st - od) - od) - else ( - do - (_, v) <- core_option_option_unwrap_fwd prev st; - betree_list_push_front_fwd_back msgs (key, BetreeMessageInsert v) - od) - od -’ - -val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *) - betree_node_lookup_in_bindings_fwd - (key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result = - (case bindings of - | BetreeListCons hd tl => - let (i, i0) = hd in - if i = key - then Return (SOME i0) - else - if u64_gt i key - then Return NONE - else betree_node_lookup_in_bindings_fwd key tl - | BetreeListNil => Return NONE) -’ - -val [betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def, betree_node_lookup_fwd_def, betree_node_lookup_back_def] = DefineDiv ‘ - (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *) - (betree_internal_lookup_in_children_fwd - (self : betree_internal_t) (key : u64) (st : state) : - (state # u64 option) result - = - if u64_lt key self.betree_internal_pivot - then betree_node_lookup_fwd self.betree_internal_left key st - else betree_node_lookup_fwd self.betree_internal_right key st) - /\ - - (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *) - (betree_internal_lookup_in_children_back - (self : betree_internal_t) (key : u64) (st : state) : - betree_internal_t result - = - if u64_lt key self.betree_internal_pivot - then ( - do - n <- betree_node_lookup_back self.betree_internal_left key st; - Return (self with <| betree_internal_left := n |>) - od) - else ( - do - n <- betree_node_lookup_back self.betree_internal_right key st; - Return (self with <| betree_internal_right := n |>) - od)) - /\ - - (** [betree_main::betree::Node::{5}::lookup]: forward function *) - (betree_node_lookup_fwd - (self : betree_node_t) (key : u64) (st : state) : - (state # u64 option) result - = - (case self of - | BetreeNodeInternal node => - do - (st0, msgs) <- betree_load_internal_node_fwd node.betree_internal_id st; - pending <- betree_node_lookup_first_message_for_key_fwd key msgs; - (case pending of - | BetreeListCons p l => - let (k, msg) = p in - if k <> key - then ( - do - (st1, opt) <- betree_internal_lookup_in_children_fwd node key st0; - _ <- - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l); - Return (st1, opt) - od) - else - (case msg of - | BetreeMessageInsert v => - do - _ <- - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l); - Return (st0, SOME v) - od - | BetreeMessageDelete => - do - _ <- - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l); - Return (st0, NONE) - od - | BetreeMessageUpsert ufs => - do - (st1, v) <- betree_internal_lookup_in_children_fwd node key st0; - (st2, v0) <- - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1; - node0 <- betree_internal_lookup_in_children_back node key st0; - pending0 <- - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1; - msgs0 <- - betree_node_lookup_first_message_for_key_back key msgs pending0; - (st3, _) <- - betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2; - Return (st3, SOME v0) - od) - | BetreeListNil => - do - (st1, opt) <- betree_internal_lookup_in_children_fwd node key st0; - _ <- - betree_node_lookup_first_message_for_key_back key msgs BetreeListNil; - Return (st1, opt) - od) - od - | BetreeNodeLeaf node => - do - (st0, bindings) <- betree_load_leaf_node_fwd node.betree_leaf_id st; - opt <- betree_node_lookup_in_bindings_fwd key bindings; - Return (st0, opt) - od)) - /\ - - (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *) - betree_node_lookup_back - (self : betree_node_t) (key : u64) (st : state) : betree_node_t result = - (case self of - | BetreeNodeInternal node => - do - (st0, msgs) <- betree_load_internal_node_fwd node.betree_internal_id st; - pending <- betree_node_lookup_first_message_for_key_fwd key msgs; - (case pending of - | BetreeListCons p l => - let (k, msg) = p in - if k <> key - then ( - do - _ <- - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l); - node0 <- betree_internal_lookup_in_children_back node key st0; - Return (BetreeNodeInternal node0) - od) - else - (case msg of - | BetreeMessageInsert v => - do - _ <- - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l); - Return (BetreeNodeInternal node) - od - | BetreeMessageDelete => - do - _ <- - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l); - Return (BetreeNodeInternal node) - od - | BetreeMessageUpsert ufs => - do - (st1, v) <- betree_internal_lookup_in_children_fwd node key st0; - (st2, _) <- - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1; - node0 <- betree_internal_lookup_in_children_back node key st0; - pending0 <- - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1; - msgs0 <- - betree_node_lookup_first_message_for_key_back key msgs pending0; - _ <- - betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2; - Return (BetreeNodeInternal node0) - od) - | BetreeListNil => - do - _ <- - betree_node_lookup_first_message_for_key_back key msgs BetreeListNil; - node0 <- betree_internal_lookup_in_children_back node key st0; - Return (BetreeNodeInternal node0) - od) - od - | BetreeNodeLeaf node => - do - (_, bindings) <- betree_load_leaf_node_fwd node.betree_leaf_id st; - _ <- betree_node_lookup_in_bindings_fwd key bindings; - Return (BetreeNodeLeaf node) - od) -’ - -val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function - (there is a single backward function, and the forward function returns ()) *) - betree_node_filter_messages_for_key_fwd_back - (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) : - (u64 # betree_message_t) betree_list_t result - = - (case msgs of - | BetreeListCons p l => - let (k, m) = p in - if k = key - then ( - do - msgs0 <- betree_list_pop_front_back (BetreeListCons (k, m) l); - betree_node_filter_messages_for_key_fwd_back key msgs0 - od) - else Return (BetreeListCons (k, m) l) - | BetreeListNil => Return BetreeListNil) -’ - -val [betree_node_lookup_first_message_after_key_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *) - betree_node_lookup_first_message_after_key_fwd - (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) : - (u64 # betree_message_t) betree_list_t result - = - (case msgs of - | BetreeListCons p next_msgs => - let (k, m) = p in - if k = key - then betree_node_lookup_first_message_after_key_fwd key next_msgs - else Return (BetreeListCons (k, m) next_msgs) - | BetreeListNil => Return BetreeListNil) -’ - -val [betree_node_lookup_first_message_after_key_back_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *) - betree_node_lookup_first_message_after_key_back - (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) - (ret : (u64 # betree_message_t) betree_list_t) : - (u64 # betree_message_t) betree_list_t result - = - (case msgs of - | BetreeListCons p next_msgs => - let (k, m) = p in - if k = key - then ( - do - next_msgs0 <- - betree_node_lookup_first_message_after_key_back key next_msgs ret; - Return (BetreeListCons (k, m) next_msgs0) - od) - else Return ret - | BetreeListNil => Return ret) -’ - -val betree_node_apply_to_internal_fwd_back_def = Define ‘ - (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function - (there is a single backward function, and the forward function returns ()) *) - betree_node_apply_to_internal_fwd_back - (msgs : (u64 # betree_message_t) betree_list_t) (key : u64) - (new_msg : betree_message_t) : - (u64 # betree_message_t) betree_list_t result - = - do - msgs0 <- betree_node_lookup_first_message_for_key_fwd key msgs; - b <- betree_list_head_has_key_fwd msgs0 key; - if b - then - (case new_msg of - | BetreeMessageInsert i => - do - msgs1 <- betree_node_filter_messages_for_key_fwd_back key msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 (key, BetreeMessageInsert i); - betree_node_lookup_first_message_for_key_back key msgs msgs2 - od - | BetreeMessageDelete => - do - msgs1 <- betree_node_filter_messages_for_key_fwd_back key msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 (key, BetreeMessageDelete); - betree_node_lookup_first_message_for_key_back key msgs msgs2 - od - | BetreeMessageUpsert s => - do - p <- betree_list_hd_fwd msgs0; - let (_, m) = p in - (case m of - | BetreeMessageInsert prev => - do - v <- betree_upsert_update_fwd (SOME prev) s; - msgs1 <- betree_list_pop_front_back msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 (key, BetreeMessageInsert v); - betree_node_lookup_first_message_for_key_back key msgs msgs2 - od - | BetreeMessageDelete => - do - v <- betree_upsert_update_fwd NONE s; - msgs1 <- betree_list_pop_front_back msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 (key, BetreeMessageInsert v); - betree_node_lookup_first_message_for_key_back key msgs msgs2 - od - | BetreeMessageUpsert ufs => - do - msgs1 <- betree_node_lookup_first_message_after_key_fwd key msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 (key, BetreeMessageUpsert s); - msgs3 <- - betree_node_lookup_first_message_after_key_back key msgs0 msgs2; - betree_node_lookup_first_message_for_key_back key msgs msgs3 - od) - od) - else ( - do - msgs1 <- betree_list_push_front_fwd_back msgs0 (key, new_msg); - betree_node_lookup_first_message_for_key_back key msgs msgs1 - od) - od -’ - -val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function - (there is a single backward function, and the forward function returns ()) *) - betree_node_apply_messages_to_internal_fwd_back - (msgs : (u64 # betree_message_t) betree_list_t) - (new_msgs : (u64 # betree_message_t) betree_list_t) : - (u64 # betree_message_t) betree_list_t result - = - (case new_msgs of - | BetreeListCons new_msg new_msgs_tl => - let (i, m) = new_msg in - do - msgs0 <- betree_node_apply_to_internal_fwd_back msgs i m; - betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl - od - | BetreeListNil => Return msgs) -’ - -val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *) - betree_node_lookup_mut_in_bindings_fwd - (key : u64) (bindings : (u64 # u64) betree_list_t) : - (u64 # u64) betree_list_t result - = - (case bindings of - | BetreeListCons hd tl => - let (i, i0) = hd in - if u64_ge i key - then Return (BetreeListCons (i, i0) tl) - else betree_node_lookup_mut_in_bindings_fwd key tl - | BetreeListNil => Return BetreeListNil) -’ - -val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *) - betree_node_lookup_mut_in_bindings_back - (key : u64) (bindings : (u64 # u64) betree_list_t) - (ret : (u64 # u64) betree_list_t) : - (u64 # u64) betree_list_t result - = - (case bindings of - | BetreeListCons hd tl => - let (i, i0) = hd in - if u64_ge i key - then Return ret - else ( - do - tl0 <- betree_node_lookup_mut_in_bindings_back key tl ret; - Return (BetreeListCons (i, i0) tl0) - od) - | BetreeListNil => Return ret) -’ - -val betree_node_apply_to_leaf_fwd_back_def = Define ‘ - (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function - (there is a single backward function, and the forward function returns ()) *) - betree_node_apply_to_leaf_fwd_back - (bindings : (u64 # u64) betree_list_t) (key : u64) - (new_msg : betree_message_t) : - (u64 # u64) betree_list_t result - = - do - bindings0 <- betree_node_lookup_mut_in_bindings_fwd key bindings; - b <- betree_list_head_has_key_fwd bindings0 key; - if b - then ( - do - hd <- betree_list_pop_front_fwd bindings0; - (case new_msg of - | BetreeMessageInsert v => - do - bindings1 <- betree_list_pop_front_back bindings0; - bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v); - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - od - | BetreeMessageDelete => - do - bindings1 <- betree_list_pop_front_back bindings0; - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - od - | BetreeMessageUpsert s => - let (_, i) = hd in - do - v <- betree_upsert_update_fwd (SOME i) s; - bindings1 <- betree_list_pop_front_back bindings0; - bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v); - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - od) - od) - else - (case new_msg of - | BetreeMessageInsert v => - do - bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v); - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - od - | BetreeMessageDelete => - betree_node_lookup_mut_in_bindings_back key bindings bindings0 - | BetreeMessageUpsert s => - do - v <- betree_upsert_update_fwd NONE s; - bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v); - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - od) - od -’ - -val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘ - (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function - (there is a single backward function, and the forward function returns ()) *) - betree_node_apply_messages_to_leaf_fwd_back - (bindings : (u64 # u64) betree_list_t) - (new_msgs : (u64 # betree_message_t) betree_list_t) : - (u64 # u64) betree_list_t result - = - (case new_msgs of - | BetreeListCons new_msg new_msgs_tl => - let (i, m) = new_msg in - do - bindings0 <- betree_node_apply_to_leaf_fwd_back bindings i m; - betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl - od - | BetreeListNil => Return bindings) -’ - -val [betree_internal_flush_fwd_def, betree_internal_flush_back_def, betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def] = DefineDiv ‘ - (** [betree_main::betree::Internal::{4}::flush]: forward function *) - (betree_internal_flush_fwd - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : (u64 # betree_message_t) betree_list_t) (st : state) : - (state # (u64 # betree_message_t) betree_list_t) result - = - do - p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot; - let (msgs_left, msgs_right) = p in - do - len_left <- betree_list_len_fwd msgs_left; - if u64_ge len_left params.betree_params_min_flush_size - then ( - do - (st0, _) <- - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st; - (_, node_id_cnt0) <- - betree_node_apply_messages_back self.betree_internal_left params - node_id_cnt msgs_left st; - len_right <- betree_list_len_fwd msgs_right; - if u64_ge len_right params.betree_params_min_flush_size - then ( - do - (st1, _) <- - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt0 msgs_right st0; - _ <- - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt0 msgs_right st0; - Return (st1, BetreeListNil) - od) - else Return (st0, msgs_right) - od) - else ( - do - (st0, _) <- - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt msgs_right st; - _ <- - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt msgs_right st; - Return (st0, msgs_left) - od) - od - od) - /\ - - (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *) - (betree_internal_flush_back - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : (u64 # betree_message_t) betree_list_t) (st : state) : - (betree_internal_t # betree_node_id_counter_t) result - = - do - p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot; - let (msgs_left, msgs_right) = p in - do - len_left <- betree_list_len_fwd msgs_left; - if u64_ge len_left params.betree_params_min_flush_size - then ( - do - (st0, _) <- - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st; - (n, node_id_cnt0) <- - betree_node_apply_messages_back self.betree_internal_left params - node_id_cnt msgs_left st; - len_right <- betree_list_len_fwd msgs_right; - if u64_ge len_right params.betree_params_min_flush_size - then ( - do - (n0, node_id_cnt1) <- - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt0 msgs_right st0; - Return - (self - with - <| - betree_internal_left := n; betree_internal_right := n0 - |>, node_id_cnt1) - od) - else Return (self with <| betree_internal_left := n |>, node_id_cnt0) - od) - else ( - do - (n, node_id_cnt0) <- - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt msgs_right st; - Return (self with <| betree_internal_right := n |>, node_id_cnt0) - od) - od - od) - /\ - - (** [betree_main::betree::Node::{5}::apply_messages]: forward function *) - (betree_node_apply_messages_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : (u64 # betree_message_t) betree_list_t) (st : state) : - (state # unit) result - = - (case self of - | BetreeNodeInternal node => - do - (st0, content) <- - betree_load_internal_node_fwd node.betree_internal_id st; - content0 <- betree_node_apply_messages_to_internal_fwd_back content msgs; - num_msgs <- betree_list_len_fwd content0; - if u64_ge num_msgs params.betree_params_min_flush_size - then ( - do - (st1, content1) <- - betree_internal_flush_fwd node params node_id_cnt content0 st0; - (node0, _) <- - betree_internal_flush_back node params node_id_cnt content0 st0; - (st2, _) <- - betree_store_internal_node_fwd node0.betree_internal_id content1 st1; - Return (st2, ()) - od) - else ( - do - (st1, _) <- - betree_store_internal_node_fwd node.betree_internal_id content0 st0; - Return (st1, ()) - od) - od - | BetreeNodeLeaf node => - do - (st0, content) <- betree_load_leaf_node_fwd node.betree_leaf_id st; - content0 <- betree_node_apply_messages_to_leaf_fwd_back content msgs; - len <- betree_list_len_fwd content0; - i <- u64_mul (int_to_u64 2) params.betree_params_split_size; - if u64_ge len i - then ( - do - (st1, _) <- betree_leaf_split_fwd node content0 params node_id_cnt st0; - (st2, _) <- - betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1; - Return (st2, ()) - od) - else ( - do - (st1, _) <- - betree_store_leaf_node_fwd node.betree_leaf_id content0 st0; - Return (st1, ()) - od) - od)) - /\ - - (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *) - betree_node_apply_messages_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : (u64 # betree_message_t) betree_list_t) (st : state) : - (betree_node_t # betree_node_id_counter_t) result - = - (case self of - | BetreeNodeInternal node => - do - (st0, content) <- - betree_load_internal_node_fwd node.betree_internal_id st; - content0 <- betree_node_apply_messages_to_internal_fwd_back content msgs; - num_msgs <- betree_list_len_fwd content0; - if u64_ge num_msgs params.betree_params_min_flush_size - then ( - do - (st1, content1) <- - betree_internal_flush_fwd node params node_id_cnt content0 st0; - (node0, node_id_cnt0) <- - betree_internal_flush_back node params node_id_cnt content0 st0; - _ <- - betree_store_internal_node_fwd node0.betree_internal_id content1 st1; - Return (BetreeNodeInternal node0, node_id_cnt0) - od) - else ( - do - _ <- - betree_store_internal_node_fwd node.betree_internal_id content0 st0; - Return (BetreeNodeInternal node, node_id_cnt) - od) - od - | BetreeNodeLeaf node => - do - (st0, content) <- betree_load_leaf_node_fwd node.betree_leaf_id st; - content0 <- betree_node_apply_messages_to_leaf_fwd_back content msgs; - len <- betree_list_len_fwd content0; - i <- u64_mul (int_to_u64 2) params.betree_params_split_size; - if u64_ge len i - then ( - do - (st1, new_node) <- - betree_leaf_split_fwd node content0 params node_id_cnt st0; - _ <- betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1; - node_id_cnt0 <- - betree_leaf_split_back node content0 params node_id_cnt st0; - Return (BetreeNodeInternal new_node, node_id_cnt0) - od) - else ( - do - _ <- betree_store_leaf_node_fwd node.betree_leaf_id content0 st0; - Return (BetreeNodeLeaf (node with <| betree_leaf_size := len |>), - node_id_cnt) - od) - od) -’ - -val betree_node_apply_fwd_def = Define ‘ - (** [betree_main::betree::Node::{5}::apply]: forward function *) - betree_node_apply_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : u64) - (new_msg : betree_message_t) (st : state) : - (state # unit) result - = - let l = BetreeListNil in - do - (st0, _) <- - betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons - (key, new_msg) l) st; - _ <- - betree_node_apply_messages_back self params node_id_cnt (BetreeListCons - (key, new_msg) l) st; - Return (st0, ()) - od -’ - -val betree_node_apply_back_def = Define ‘ - (** [betree_main::betree::Node::{5}::apply]: backward function 0 *) - betree_node_apply_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : u64) - (new_msg : betree_message_t) (st : state) : - (betree_node_t # betree_node_id_counter_t) result - = - let l = BetreeListNil in - betree_node_apply_messages_back self params node_id_cnt (BetreeListCons - (key, new_msg) l) st -’ - -val betree_be_tree_new_fwd_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::new]: forward function *) - betree_be_tree_new_fwd - (min_flush_size : u64) (split_size : u64) (st : state) : - (state # betree_be_tree_t) result - = - do - node_id_cnt <- betree_node_id_counter_new_fwd; - id <- betree_node_id_counter_fresh_id_fwd node_id_cnt; - (st0, _) <- betree_store_leaf_node_fwd id BetreeListNil st; - node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt; - Return (st0, - <| - betree_be_tree_params := - (<| - betree_params_min_flush_size := min_flush_size; - betree_params_split_size := split_size - |>); - betree_be_tree_node_id_cnt := node_id_cnt0; - betree_be_tree_root := - (BetreeNodeLeaf - (<| betree_leaf_id := id; betree_leaf_size := (int_to_u64 0) |>)) - |>) - od -’ - -val betree_be_tree_apply_fwd_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::apply]: forward function *) - betree_be_tree_apply_fwd - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) - : - (state # unit) result - = - do - (st0, _) <- - betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st; - _ <- - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st; - Return (st0, ()) - od -’ - -val betree_be_tree_apply_back_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *) - betree_be_tree_apply_back - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) - : - betree_be_tree_t result - = - do - (n, nic) <- - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st; - Return - (self - with - <| - betree_be_tree_node_id_cnt := nic; betree_be_tree_root := n - |>) - od -’ - -val betree_be_tree_insert_fwd_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::insert]: forward function *) - betree_be_tree_insert_fwd - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : - (state # unit) result - = - do - (st0, _) <- - betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st; - _ <- betree_be_tree_apply_back self key (BetreeMessageInsert value) st; - Return (st0, ()) - od -’ - -val betree_be_tree_insert_back_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *) - betree_be_tree_insert_back - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : - betree_be_tree_t result - = - betree_be_tree_apply_back self key (BetreeMessageInsert value) st -’ - -val betree_be_tree_delete_fwd_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::delete]: forward function *) - betree_be_tree_delete_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : - (state # unit) result - = - do - (st0, _) <- betree_be_tree_apply_fwd self key BetreeMessageDelete st; - _ <- betree_be_tree_apply_back self key BetreeMessageDelete st; - Return (st0, ()) - od -’ - -val betree_be_tree_delete_back_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *) - betree_be_tree_delete_back - (self : betree_be_tree_t) (key : u64) (st : state) : - betree_be_tree_t result - = - betree_be_tree_apply_back self key BetreeMessageDelete st -’ - -val betree_be_tree_upsert_fwd_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::upsert]: forward function *) - betree_be_tree_upsert_fwd - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) - (st : state) : - (state # unit) result - = - do - (st0, _) <- betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st; - _ <- betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st; - Return (st0, ()) - od -’ - -val betree_be_tree_upsert_back_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *) - betree_be_tree_upsert_back - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) - (st : state) : - betree_be_tree_t result - = - betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st -’ - -val betree_be_tree_lookup_fwd_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::lookup]: forward function *) - betree_be_tree_lookup_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : - (state # u64 option) result - = - betree_node_lookup_fwd self.betree_be_tree_root key st -’ - -val betree_be_tree_lookup_back_def = Define ‘ - (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *) - betree_be_tree_lookup_back - (self : betree_be_tree_t) (key : u64) (st : state) : - betree_be_tree_t result - = - do - n <- betree_node_lookup_back self.betree_be_tree_root key st; - Return (self with <| betree_be_tree_root := n |>) - od -’ - -val main_fwd_def = Define ‘ - (** [betree_main::main]: forward function *) - main_fwd : unit result = - Return () -’ - -(** Unit test for [betree_main::main] *) -val _ = assert_return (“main_fwd”) - -val _ = export_theory () diff --git a/tests/hol4/betree/betreeMain_FunsTheory.sig b/tests/hol4/betree/betreeMain_FunsTheory.sig deleted file mode 100644 index c922ca9f..00000000 --- a/tests/hol4/betree/betreeMain_FunsTheory.sig +++ /dev/null @@ -1,1230 +0,0 @@ -signature betreeMain_FunsTheory = -sig - type thm = Thm.thm - - (* Definitions *) - val betree_be_tree_apply_back_def : thm - val betree_be_tree_apply_fwd_def : thm - val betree_be_tree_delete_back_def : thm - val betree_be_tree_delete_fwd_def : thm - val betree_be_tree_insert_back_def : thm - val betree_be_tree_insert_fwd_def : thm - val betree_be_tree_lookup_back_def : thm - val betree_be_tree_lookup_fwd_def : thm - val betree_be_tree_new_fwd_def : thm - val betree_be_tree_upsert_back_def : thm - val betree_be_tree_upsert_fwd_def : thm - val betree_fresh_node_id_back_def : thm - val betree_fresh_node_id_fwd_def : thm - val betree_internal_flush_back_def : thm - val betree_internal_flush_fwd_def : thm - val betree_internal_lookup_in_children_back_def : thm - val betree_internal_lookup_in_children_fwd_def : thm - val betree_leaf_split_back_def : thm - val betree_leaf_split_fwd_def : thm - val betree_list_hd_fwd_def : thm - val betree_list_head_has_key_fwd_def : thm - val betree_list_len_fwd_def : thm - val betree_list_partition_at_pivot_fwd_def : thm - val betree_list_pop_front_back_def : thm - val betree_list_pop_front_fwd_def : thm - val betree_list_push_front_fwd_back_def : thm - val betree_list_split_at_fwd_def : thm - val betree_load_internal_node_fwd_def : thm - val betree_load_leaf_node_fwd_def : thm - val betree_node_apply_back_def : thm - val betree_node_apply_fwd_def : thm - val betree_node_apply_messages_back_def : thm - val betree_node_apply_messages_fwd_def : thm - val betree_node_apply_messages_to_internal_fwd_back_def : thm - val betree_node_apply_messages_to_leaf_fwd_back_def : thm - val betree_node_apply_to_internal_fwd_back_def : thm - val betree_node_apply_to_leaf_fwd_back_def : thm - val betree_node_apply_upserts_back_def : thm - val betree_node_apply_upserts_fwd_def : thm - val betree_node_filter_messages_for_key_fwd_back_def : thm - val betree_node_id_counter_fresh_id_back_def : thm - val betree_node_id_counter_fresh_id_fwd_def : thm - val betree_node_id_counter_new_fwd_def : thm - val betree_node_lookup_back_def : thm - val betree_node_lookup_first_message_after_key_back_def : thm - val betree_node_lookup_first_message_after_key_fwd_def : thm - val betree_node_lookup_first_message_for_key_back_def : thm - val betree_node_lookup_first_message_for_key_fwd_def : thm - val betree_node_lookup_fwd_def : thm - val betree_node_lookup_in_bindings_fwd_def : thm - val betree_node_lookup_mut_in_bindings_back_def : thm - val betree_node_lookup_mut_in_bindings_fwd_def : thm - val betree_store_internal_node_fwd_def : thm - val betree_store_leaf_node_fwd_def : thm - val betree_upsert_update_fwd_def : thm - val main_fwd_def : thm - - val betreeMain_Funs_grammars : type_grammar.grammar * term_grammar.grammar -(* - [betreeMain_Opaque] Parent theory of "betreeMain_Funs" - - [betree_be_tree_apply_back_def] Definition - - ⊢ ∀self key msg st. - betree_be_tree_apply_back self key msg st = - do - (n,nic) <- - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt - key msg st; - Return - (self with - <|betree_be_tree_node_id_cnt := nic; - betree_be_tree_root := n|>) - od - - [betree_be_tree_apply_fwd_def] Definition - - ⊢ ∀self key msg st. - betree_be_tree_apply_fwd self key msg st = - do - (st0,_) <- - betree_node_apply_fwd self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt - key msg st; - monad_ignore_bind - (betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt - key msg st) (Return (st0,())) - od - - [betree_be_tree_delete_back_def] Definition - - ⊢ ∀self key st. - betree_be_tree_delete_back self key st = - betree_be_tree_apply_back self key BetreeMessageDelete st - - [betree_be_tree_delete_fwd_def] Definition - - ⊢ ∀self key st. - betree_be_tree_delete_fwd self key st = - do - (st0,_) <- - betree_be_tree_apply_fwd self key BetreeMessageDelete st; - monad_ignore_bind - (betree_be_tree_apply_back self key BetreeMessageDelete st) - (Return (st0,())) - od - - [betree_be_tree_insert_back_def] Definition - - ⊢ ∀self key value st. - betree_be_tree_insert_back self key value st = - betree_be_tree_apply_back self key (BetreeMessageInsert value) st - - [betree_be_tree_insert_fwd_def] Definition - - ⊢ ∀self key value st. - betree_be_tree_insert_fwd self key value st = - do - (st0,_) <- - betree_be_tree_apply_fwd self key (BetreeMessageInsert value) - st; - monad_ignore_bind - (betree_be_tree_apply_back self key - (BetreeMessageInsert value) st) (Return (st0,())) - od - - [betree_be_tree_lookup_back_def] Definition - - ⊢ ∀self key st. - betree_be_tree_lookup_back self key st = - do - n <- betree_node_lookup_back self.betree_be_tree_root key st; - Return (self with betree_be_tree_root := n) - od - - [betree_be_tree_lookup_fwd_def] Definition - - ⊢ ∀self key st. - betree_be_tree_lookup_fwd self key st = - betree_node_lookup_fwd self.betree_be_tree_root key st - - [betree_be_tree_new_fwd_def] Definition - - ⊢ ∀min_flush_size split_size st. - betree_be_tree_new_fwd min_flush_size split_size st = - do - node_id_cnt <- betree_node_id_counter_new_fwd; - id <- betree_node_id_counter_fresh_id_fwd node_id_cnt; - (st0,_) <- betree_store_leaf_node_fwd id BetreeListNil st; - node_id_cnt0 <- - betree_node_id_counter_fresh_id_back node_id_cnt; - Return - (st0, - <|betree_be_tree_params := - <|betree_params_min_flush_size := min_flush_size; - betree_params_split_size := split_size|>; - betree_be_tree_node_id_cnt := node_id_cnt0; - betree_be_tree_root := - BetreeNodeLeaf - <|betree_leaf_id := id; - betree_leaf_size := int_to_u64 0|> |>) - od - - [betree_be_tree_upsert_back_def] Definition - - ⊢ ∀self key upd st. - betree_be_tree_upsert_back self key upd st = - betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st - - [betree_be_tree_upsert_fwd_def] Definition - - ⊢ ∀self key upd st. - betree_be_tree_upsert_fwd self key upd st = - do - (st0,_) <- - betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) - st; - monad_ignore_bind - (betree_be_tree_apply_back self key (BetreeMessageUpsert upd) - st) (Return (st0,())) - od - - [betree_fresh_node_id_back_def] Definition - - ⊢ ∀counter. - betree_fresh_node_id_back counter = - u64_add counter (int_to_u64 1) - - [betree_fresh_node_id_fwd_def] Definition - - ⊢ ∀counter. - betree_fresh_node_id_fwd counter = - monad_ignore_bind (u64_add counter (int_to_u64 1)) - (Return counter) - - [betree_internal_flush_back_def] Definition - - ⊢ ∀self params node_id_cnt content st. - betree_internal_flush_back self params node_id_cnt content st = - do - p <- - betree_list_partition_at_pivot_fwd content - self.betree_internal_pivot; - (msgs_left,msgs_right) <<- p; - len_left <- betree_list_len_fwd msgs_left; - if u64_ge len_left params.betree_params_min_flush_size then - do - (st0,_) <- - betree_node_apply_messages_fwd self.betree_internal_left - params node_id_cnt msgs_left st; - (n,node_id_cnt0) <- - betree_node_apply_messages_back self.betree_internal_left - params node_id_cnt msgs_left st; - len_right <- betree_list_len_fwd msgs_right; - if - u64_ge len_right params.betree_params_min_flush_size - then - do - (n0,node_id_cnt1) <- - betree_node_apply_messages_back - self.betree_internal_right params node_id_cnt0 - msgs_right st0; - Return - (self with - <|betree_internal_left := n; - betree_internal_right := n0|>,node_id_cnt1) - od - else - Return (self with betree_internal_left := n,node_id_cnt0) - od - else - do - (n,node_id_cnt0) <- - betree_node_apply_messages_back - self.betree_internal_right params node_id_cnt - msgs_right st; - Return (self with betree_internal_right := n,node_id_cnt0) - od - od - - [betree_internal_flush_fwd_def] Definition - - ⊢ ∀self params node_id_cnt content st. - betree_internal_flush_fwd self params node_id_cnt content st = - do - p <- - betree_list_partition_at_pivot_fwd content - self.betree_internal_pivot; - (msgs_left,msgs_right) <<- p; - len_left <- betree_list_len_fwd msgs_left; - if u64_ge len_left params.betree_params_min_flush_size then - do - (st0,_) <- - betree_node_apply_messages_fwd self.betree_internal_left - params node_id_cnt msgs_left st; - (_,node_id_cnt0) <- - betree_node_apply_messages_back self.betree_internal_left - params node_id_cnt msgs_left st; - len_right <- betree_list_len_fwd msgs_right; - if - u64_ge len_right params.betree_params_min_flush_size - then - do - (st1,_) <- - betree_node_apply_messages_fwd - self.betree_internal_right params node_id_cnt0 - msgs_right st0; - monad_ignore_bind - (betree_node_apply_messages_back - self.betree_internal_right params node_id_cnt0 - msgs_right st0) (Return (st1,BetreeListNil)) - od - else Return (st0,msgs_right) - od - else - do - (st0,_) <- - betree_node_apply_messages_fwd self.betree_internal_right - params node_id_cnt msgs_right st; - monad_ignore_bind - (betree_node_apply_messages_back - self.betree_internal_right params node_id_cnt - msgs_right st) (Return (st0,msgs_left)) - od - od - - [betree_internal_lookup_in_children_back_def] Definition - - ⊢ ∀self key st. - betree_internal_lookup_in_children_back self key st = - if u64_lt key self.betree_internal_pivot then - do - n <- betree_node_lookup_back self.betree_internal_left key st; - Return (self with betree_internal_left := n) - od - else - do - n <- - betree_node_lookup_back self.betree_internal_right key st; - Return (self with betree_internal_right := n) - od - - [betree_internal_lookup_in_children_fwd_def] Definition - - ⊢ ∀self key st. - betree_internal_lookup_in_children_fwd self key st = - if u64_lt key self.betree_internal_pivot then - betree_node_lookup_fwd self.betree_internal_left key st - else betree_node_lookup_fwd self.betree_internal_right key st - - [betree_leaf_split_back_def] Definition - - ⊢ ∀self content params node_id_cnt st. - betree_leaf_split_back self content params node_id_cnt st = - do - p <- - betree_list_split_at_fwd content - params.betree_params_split_size; - (content0,content1) <<- p; - monad_ignore_bind (betree_list_hd_fwd content1) - do - id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; - node_id_cnt0 <- - betree_node_id_counter_fresh_id_back node_id_cnt; - id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; - (st0,_) <- betree_store_leaf_node_fwd id0 content0 st; - monad_ignore_bind - (betree_store_leaf_node_fwd id1 content1 st0) - (betree_node_id_counter_fresh_id_back node_id_cnt0) - od - od - - [betree_leaf_split_fwd_def] Definition - - ⊢ ∀self content params node_id_cnt st. - betree_leaf_split_fwd self content params node_id_cnt st = - do - p <- - betree_list_split_at_fwd content - params.betree_params_split_size; - (content0,content1) <<- p; - p0 <- betree_list_hd_fwd content1; - (pivot,_) <<- p0; - id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; - node_id_cnt0 <- - betree_node_id_counter_fresh_id_back node_id_cnt; - id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; - (st0,_) <- betree_store_leaf_node_fwd id0 content0 st; - (st1,_) <- betree_store_leaf_node_fwd id1 content1 st0; - n <<- - BetreeNodeLeaf - <|betree_leaf_id := id0; - betree_leaf_size := params.betree_params_split_size|>; - n0 <<- - BetreeNodeLeaf - <|betree_leaf_id := id1; - betree_leaf_size := params.betree_params_split_size|>; - Return - (st1, - <|betree_internal_id := self.betree_leaf_id; - betree_internal_pivot := pivot; betree_internal_left := n; - betree_internal_right := n0|>) - od - - [betree_list_hd_fwd_def] Definition - - ⊢ ∀self. - betree_list_hd_fwd self = - case self of - BetreeListCons hd l => Return hd - | BetreeListNil => Fail Failure - - [betree_list_head_has_key_fwd_def] Definition - - ⊢ ∀self key. - betree_list_head_has_key_fwd self key = - case self of - BetreeListCons hd l => (let (i,_) = hd in Return (i = key)) - | BetreeListNil => Return F - - [betree_list_len_fwd_def] Definition - - ⊢ ∀self. - betree_list_len_fwd self = - case self of - BetreeListCons t tl => - do i <- betree_list_len_fwd tl; u64_add (int_to_u64 1) i od - | BetreeListNil => Return (int_to_u64 0) - - [betree_list_partition_at_pivot_fwd_def] Definition - - ⊢ ∀self pivot. - betree_list_partition_at_pivot_fwd self pivot = - case self of - BetreeListCons hd tl => - (let - (i,t) = hd - in - if u64_ge i pivot then - Return (BetreeListNil,BetreeListCons (i,t) tl) - else - do - p <- betree_list_partition_at_pivot_fwd tl pivot; - (ls0,ls1) <<- p; - l <<- ls0; - Return (BetreeListCons (i,t) l,ls1) - od) - | BetreeListNil => Return (BetreeListNil,BetreeListNil) - - [betree_list_pop_front_back_def] Definition - - ⊢ ∀self. - betree_list_pop_front_back self = - (let - ls = mem_replace_fwd self BetreeListNil - in - case ls of - BetreeListCons x tl => Return tl - | BetreeListNil => Fail Failure) - - [betree_list_pop_front_fwd_def] Definition - - ⊢ ∀self. - betree_list_pop_front_fwd self = - (let - ls = mem_replace_fwd self BetreeListNil - in - case ls of - BetreeListCons x tl => Return x - | BetreeListNil => Fail Failure) - - [betree_list_push_front_fwd_back_def] Definition - - ⊢ ∀self x. - betree_list_push_front_fwd_back self x = - (let - tl = mem_replace_fwd self BetreeListNil; - l = tl - in - Return (BetreeListCons x l)) - - [betree_list_split_at_fwd_def] Definition - - ⊢ ∀self n. - betree_list_split_at_fwd self n = - if n = int_to_u64 0 then Return (BetreeListNil,self) - else - case self of - BetreeListCons hd tl => - do - i <- u64_sub n (int_to_u64 1); - p <- betree_list_split_at_fwd tl i; - (ls0,ls1) <<- p; - l <<- ls0; - Return (BetreeListCons hd l,ls1) - od - | BetreeListNil => Fail Failure - - [betree_load_internal_node_fwd_def] Definition - - ⊢ ∀id st. - betree_load_internal_node_fwd id st = - betree_utils_load_internal_node_fwd id st - - [betree_load_leaf_node_fwd_def] Definition - - ⊢ ∀id st. - betree_load_leaf_node_fwd id st = - betree_utils_load_leaf_node_fwd id st - - [betree_node_apply_back_def] Definition - - ⊢ ∀self params node_id_cnt key new_msg st. - betree_node_apply_back self params node_id_cnt key new_msg st = - (let - l = BetreeListNil - in - betree_node_apply_messages_back self params node_id_cnt - (BetreeListCons (key,new_msg) l) st) - - [betree_node_apply_fwd_def] Definition - - ⊢ ∀self params node_id_cnt key new_msg st. - betree_node_apply_fwd self params node_id_cnt key new_msg st = - (let - l = BetreeListNil - in - do - (st0,_) <- - betree_node_apply_messages_fwd self params node_id_cnt - (BetreeListCons (key,new_msg) l) st; - monad_ignore_bind - (betree_node_apply_messages_back self params node_id_cnt - (BetreeListCons (key,new_msg) l) st) (Return (st0,())) - od) - - [betree_node_apply_messages_back_def] Definition - - ⊢ ∀self params node_id_cnt msgs st. - betree_node_apply_messages_back self params node_id_cnt msgs st = - case self of - BetreeNodeInternal node => - do - (st0,content) <- - betree_load_internal_node_fwd node.betree_internal_id st; - content0 <- - betree_node_apply_messages_to_internal_fwd_back content - msgs; - num_msgs <- betree_list_len_fwd content0; - if u64_ge num_msgs params.betree_params_min_flush_size then - do - (st1,content1) <- - betree_internal_flush_fwd node params node_id_cnt - content0 st0; - (node0,node_id_cnt0) <- - betree_internal_flush_back node params node_id_cnt - content0 st0; - monad_ignore_bind - (betree_store_internal_node_fwd - node0.betree_internal_id content1 st1) - (Return (BetreeNodeInternal node0,node_id_cnt0)) - od - else - monad_ignore_bind - (betree_store_internal_node_fwd node.betree_internal_id - content0 st0) - (Return (BetreeNodeInternal node,node_id_cnt)) - od - | BetreeNodeLeaf node' => - do - (st0,content) <- - betree_load_leaf_node_fwd node'.betree_leaf_id st; - content0 <- - betree_node_apply_messages_to_leaf_fwd_back content msgs; - len <- betree_list_len_fwd content0; - i <- u64_mul (int_to_u64 2) params.betree_params_split_size; - if u64_ge len i then - do - (st1,new_node) <- - betree_leaf_split_fwd node' content0 params node_id_cnt - st0; - monad_ignore_bind - (betree_store_leaf_node_fwd node'.betree_leaf_id - BetreeListNil st1) - do - node_id_cnt0 <- - betree_leaf_split_back node' content0 params - node_id_cnt st0; - Return (BetreeNodeInternal new_node,node_id_cnt0) - od - od - else - monad_ignore_bind - (betree_store_leaf_node_fwd node'.betree_leaf_id content0 - st0) - (Return - (BetreeNodeLeaf (node' with betree_leaf_size := len), - node_id_cnt)) - od - - [betree_node_apply_messages_fwd_def] Definition - - ⊢ ∀self params node_id_cnt msgs st. - betree_node_apply_messages_fwd self params node_id_cnt msgs st = - case self of - BetreeNodeInternal node => - do - (st0,content) <- - betree_load_internal_node_fwd node.betree_internal_id st; - content0 <- - betree_node_apply_messages_to_internal_fwd_back content - msgs; - num_msgs <- betree_list_len_fwd content0; - if u64_ge num_msgs params.betree_params_min_flush_size then - do - (st1,content1) <- - betree_internal_flush_fwd node params node_id_cnt - content0 st0; - (node0,_) <- - betree_internal_flush_back node params node_id_cnt - content0 st0; - (st2,_) <- - betree_store_internal_node_fwd - node0.betree_internal_id content1 st1; - Return (st2,()) - od - else - do - (st1,_) <- - betree_store_internal_node_fwd - node.betree_internal_id content0 st0; - Return (st1,()) - od - od - | BetreeNodeLeaf node' => - do - (st0,content) <- - betree_load_leaf_node_fwd node'.betree_leaf_id st; - content0 <- - betree_node_apply_messages_to_leaf_fwd_back content msgs; - len <- betree_list_len_fwd content0; - i <- u64_mul (int_to_u64 2) params.betree_params_split_size; - if u64_ge len i then - do - (st1,_) <- - betree_leaf_split_fwd node' content0 params node_id_cnt - st0; - (st2,_) <- - betree_store_leaf_node_fwd node'.betree_leaf_id - BetreeListNil st1; - Return (st2,()) - od - else - do - (st1,_) <- - betree_store_leaf_node_fwd node'.betree_leaf_id - content0 st0; - Return (st1,()) - od - od - - [betree_node_apply_messages_to_internal_fwd_back_def] Definition - - ⊢ ∀msgs new_msgs. - betree_node_apply_messages_to_internal_fwd_back msgs new_msgs = - case new_msgs of - BetreeListCons new_msg new_msgs_tl => - (let - (i,m) = new_msg - in - do - msgs0 <- betree_node_apply_to_internal_fwd_back msgs i m; - betree_node_apply_messages_to_internal_fwd_back msgs0 - new_msgs_tl - od) - | BetreeListNil => Return msgs - - [betree_node_apply_messages_to_leaf_fwd_back_def] Definition - - ⊢ ∀bindings new_msgs. - betree_node_apply_messages_to_leaf_fwd_back bindings new_msgs = - case new_msgs of - BetreeListCons new_msg new_msgs_tl => - (let - (i,m) = new_msg - in - do - bindings0 <- - betree_node_apply_to_leaf_fwd_back bindings i m; - betree_node_apply_messages_to_leaf_fwd_back bindings0 - new_msgs_tl - od) - | BetreeListNil => Return bindings - - [betree_node_apply_to_internal_fwd_back_def] Definition - - ⊢ ∀msgs key new_msg. - betree_node_apply_to_internal_fwd_back msgs key new_msg = - do - msgs0 <- betree_node_lookup_first_message_for_key_fwd key msgs; - b <- betree_list_head_has_key_fwd msgs0 key; - if b then - case new_msg of - BetreeMessageInsert i => - do - msgs1 <- - betree_node_filter_messages_for_key_fwd_back key - msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 - (key,BetreeMessageInsert i); - betree_node_lookup_first_message_for_key_back key msgs - msgs2 - od - | BetreeMessageDelete => - do - msgs1 <- - betree_node_filter_messages_for_key_fwd_back key msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 - (key,BetreeMessageDelete); - betree_node_lookup_first_message_for_key_back key msgs - msgs2 - od - | BetreeMessageUpsert s => - do - p <- betree_list_hd_fwd msgs0; - (_,m) <<- p; - case m of - BetreeMessageInsert prev => - do - v <- betree_upsert_update_fwd (SOME prev) s; - msgs1 <- betree_list_pop_front_back msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 - (key,BetreeMessageInsert v); - betree_node_lookup_first_message_for_key_back key - msgs msgs2 - od - | BetreeMessageDelete => - do - v <- betree_upsert_update_fwd NONE s; - msgs1 <- betree_list_pop_front_back msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 - (key,BetreeMessageInsert v); - betree_node_lookup_first_message_for_key_back key - msgs msgs2 - od - | BetreeMessageUpsert ufs => - do - msgs1 <- - betree_node_lookup_first_message_after_key_fwd key - msgs0; - msgs2 <- - betree_list_push_front_fwd_back msgs1 - (key,BetreeMessageUpsert s); - msgs3 <- - betree_node_lookup_first_message_after_key_back key - msgs0 msgs2; - betree_node_lookup_first_message_for_key_back key - msgs msgs3 - od - od - else - do - msgs1 <- - betree_list_push_front_fwd_back msgs0 (key,new_msg); - betree_node_lookup_first_message_for_key_back key msgs - msgs1 - od - od - - [betree_node_apply_to_leaf_fwd_back_def] Definition - - ⊢ ∀bindings key new_msg. - betree_node_apply_to_leaf_fwd_back bindings key new_msg = - do - bindings0 <- - betree_node_lookup_mut_in_bindings_fwd key bindings; - b <- betree_list_head_has_key_fwd bindings0 key; - if b then - do - hd <- betree_list_pop_front_fwd bindings0; - case new_msg of - BetreeMessageInsert v => - do - bindings1 <- betree_list_pop_front_back bindings0; - bindings2 <- - betree_list_push_front_fwd_back bindings1 (key,v); - betree_node_lookup_mut_in_bindings_back key bindings - bindings2 - od - | BetreeMessageDelete => - do - bindings1 <- betree_list_pop_front_back bindings0; - betree_node_lookup_mut_in_bindings_back key bindings - bindings1 - od - | BetreeMessageUpsert s => - (let - (_,i) = hd - in - do - v <- betree_upsert_update_fwd (SOME i) s; - bindings1 <- betree_list_pop_front_back bindings0; - bindings2 <- - betree_list_push_front_fwd_back bindings1 (key,v); - betree_node_lookup_mut_in_bindings_back key bindings - bindings2 - od) - od - else - case new_msg of - BetreeMessageInsert v => - do - bindings1 <- - betree_list_push_front_fwd_back bindings0 (key,v); - betree_node_lookup_mut_in_bindings_back key bindings - bindings1 - od - | BetreeMessageDelete => - betree_node_lookup_mut_in_bindings_back key bindings - bindings0 - | BetreeMessageUpsert s => - do - v <- betree_upsert_update_fwd NONE s; - bindings1 <- - betree_list_push_front_fwd_back bindings0 (key,v); - betree_node_lookup_mut_in_bindings_back key bindings - bindings1 - od - od - - [betree_node_apply_upserts_back_def] Definition - - ⊢ ∀msgs prev key st. - betree_node_apply_upserts_back msgs prev key st = - do - b <- betree_list_head_has_key_fwd msgs key; - if b then - do - msg <- betree_list_pop_front_fwd msgs; - (_,m) <<- msg; - case m of - BetreeMessageInsert i => Fail Failure - | BetreeMessageDelete => Fail Failure - | BetreeMessageUpsert s => - do - v <- betree_upsert_update_fwd prev s; - msgs0 <- betree_list_pop_front_back msgs; - betree_node_apply_upserts_back msgs0 (SOME v) key st - od - od - else - do - (_,v) <- core_option_option_unwrap_fwd prev st; - betree_list_push_front_fwd_back msgs - (key,BetreeMessageInsert v) - od - od - - [betree_node_apply_upserts_fwd_def] Definition - - ⊢ ∀msgs prev key st. - betree_node_apply_upserts_fwd msgs prev key st = - do - b <- betree_list_head_has_key_fwd msgs key; - if b then - do - msg <- betree_list_pop_front_fwd msgs; - (_,m) <<- msg; - case m of - BetreeMessageInsert i => Fail Failure - | BetreeMessageDelete => Fail Failure - | BetreeMessageUpsert s => - do - v <- betree_upsert_update_fwd prev s; - msgs0 <- betree_list_pop_front_back msgs; - betree_node_apply_upserts_fwd msgs0 (SOME v) key st - od - od - else - do - (st0,v) <- core_option_option_unwrap_fwd prev st; - monad_ignore_bind - (betree_list_push_front_fwd_back msgs - (key,BetreeMessageInsert v)) (Return (st0,v)) - od - od - - [betree_node_filter_messages_for_key_fwd_back_def] Definition - - ⊢ ∀key msgs. - betree_node_filter_messages_for_key_fwd_back key msgs = - case msgs of - BetreeListCons p l => - (let - (k,m) = p - in - if k = key then - do - msgs0 <- - betree_list_pop_front_back (BetreeListCons (k,m) l); - betree_node_filter_messages_for_key_fwd_back key msgs0 - od - else Return (BetreeListCons (k,m) l)) - | BetreeListNil => Return BetreeListNil - - [betree_node_id_counter_fresh_id_back_def] Definition - - ⊢ ∀self. - betree_node_id_counter_fresh_id_back self = - do - i <- - u64_add self.betree_node_id_counter_next_node_id - (int_to_u64 1); - Return <|betree_node_id_counter_next_node_id := i|> - od - - [betree_node_id_counter_fresh_id_fwd_def] Definition - - ⊢ ∀self. - betree_node_id_counter_fresh_id_fwd self = - monad_ignore_bind - (u64_add self.betree_node_id_counter_next_node_id - (int_to_u64 1)) - (Return self.betree_node_id_counter_next_node_id) - - [betree_node_id_counter_new_fwd_def] Definition - - ⊢ betree_node_id_counter_new_fwd = - Return <|betree_node_id_counter_next_node_id := int_to_u64 0|> - - [betree_node_lookup_back_def] Definition - - ⊢ ∀self key st. - betree_node_lookup_back self key st = - case self of - BetreeNodeInternal node => - do - (st0,msgs) <- - betree_load_internal_node_fwd node.betree_internal_id st; - pending <- - betree_node_lookup_first_message_for_key_fwd key msgs; - case pending of - BetreeListCons p l => - (let - (k,msg) = p - in - if k ≠ key then - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back - key msgs (BetreeListCons (k,msg) l)) - do - node0 <- - betree_internal_lookup_in_children_back node - key st0; - Return (BetreeNodeInternal node0) - od - else - case msg of - BetreeMessageInsert v => - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back - key msgs - (BetreeListCons (k,BetreeMessageInsert v) - l)) (Return (BetreeNodeInternal node)) - | BetreeMessageDelete => - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back - key msgs - (BetreeListCons (k,BetreeMessageDelete) l)) - (Return (BetreeNodeInternal node)) - | BetreeMessageUpsert ufs => - do - (st1,v) <- - betree_internal_lookup_in_children_fwd node - key st0; - (st2,_) <- - betree_node_apply_upserts_fwd - (BetreeListCons - (k,BetreeMessageUpsert ufs) l) v key - st1; - node0 <- - betree_internal_lookup_in_children_back node - key st0; - pending0 <- - betree_node_apply_upserts_back - (BetreeListCons - (k,BetreeMessageUpsert ufs) l) v key - st1; - msgs0 <- - betree_node_lookup_first_message_for_key_back - key msgs pending0; - monad_ignore_bind - (betree_store_internal_node_fwd - node0.betree_internal_id msgs0 st2) - (Return (BetreeNodeInternal node0)) - od) - | BetreeListNil => - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back key msgs - BetreeListNil) - do - node0 <- - betree_internal_lookup_in_children_back node key - st0; - Return (BetreeNodeInternal node0) - od - od - | BetreeNodeLeaf node' => - do - (_,bindings) <- - betree_load_leaf_node_fwd node'.betree_leaf_id st; - monad_ignore_bind - (betree_node_lookup_in_bindings_fwd key bindings) - (Return (BetreeNodeLeaf node')) - od - - [betree_node_lookup_first_message_after_key_back_def] Definition - - ⊢ ∀key msgs ret. - betree_node_lookup_first_message_after_key_back key msgs ret = - case msgs of - BetreeListCons p next_msgs => - (let - (k,m) = p - in - if k = key then - do - next_msgs0 <- - betree_node_lookup_first_message_after_key_back key - next_msgs ret; - Return (BetreeListCons (k,m) next_msgs0) - od - else Return ret) - | BetreeListNil => Return ret - - [betree_node_lookup_first_message_after_key_fwd_def] Definition - - ⊢ ∀key msgs. - betree_node_lookup_first_message_after_key_fwd key msgs = - case msgs of - BetreeListCons p next_msgs => - (let - (k,m) = p - in - if k = key then - betree_node_lookup_first_message_after_key_fwd key - next_msgs - else Return (BetreeListCons (k,m) next_msgs)) - | BetreeListNil => Return BetreeListNil - - [betree_node_lookup_first_message_for_key_back_def] Definition - - ⊢ ∀key msgs ret. - betree_node_lookup_first_message_for_key_back key msgs ret = - case msgs of - BetreeListCons x next_msgs => - (let - (i,m) = x - in - if u64_ge i key then Return ret - else - do - next_msgs0 <- - betree_node_lookup_first_message_for_key_back key - next_msgs ret; - Return (BetreeListCons (i,m) next_msgs0) - od) - | BetreeListNil => Return ret - - [betree_node_lookup_first_message_for_key_fwd_def] Definition - - ⊢ ∀key msgs. - betree_node_lookup_first_message_for_key_fwd key msgs = - case msgs of - BetreeListCons x next_msgs => - (let - (i,m) = x - in - if u64_ge i key then - Return (BetreeListCons (i,m) next_msgs) - else - betree_node_lookup_first_message_for_key_fwd key - next_msgs) - | BetreeListNil => Return BetreeListNil - - [betree_node_lookup_fwd_def] Definition - - ⊢ ∀self key st. - betree_node_lookup_fwd self key st = - case self of - BetreeNodeInternal node => - do - (st0,msgs) <- - betree_load_internal_node_fwd node.betree_internal_id st; - pending <- - betree_node_lookup_first_message_for_key_fwd key msgs; - case pending of - BetreeListCons p l => - (let - (k,msg) = p - in - if k ≠ key then - do - (st1,opt) <- - betree_internal_lookup_in_children_fwd node - key st0; - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back - key msgs (BetreeListCons (k,msg) l)) - (Return (st1,opt)) - od - else - case msg of - BetreeMessageInsert v => - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back - key msgs - (BetreeListCons (k,BetreeMessageInsert v) - l)) (Return (st0,SOME v)) - | BetreeMessageDelete => - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back - key msgs - (BetreeListCons (k,BetreeMessageDelete) l)) - (Return (st0,NONE)) - | BetreeMessageUpsert ufs => - do - (st1,v) <- - betree_internal_lookup_in_children_fwd node - key st0; - (st2,v0) <- - betree_node_apply_upserts_fwd - (BetreeListCons - (k,BetreeMessageUpsert ufs) l) v key - st1; - node0 <- - betree_internal_lookup_in_children_back node - key st0; - pending0 <- - betree_node_apply_upserts_back - (BetreeListCons - (k,BetreeMessageUpsert ufs) l) v key - st1; - msgs0 <- - betree_node_lookup_first_message_for_key_back - key msgs pending0; - (st3,_) <- - betree_store_internal_node_fwd - node0.betree_internal_id msgs0 st2; - Return (st3,SOME v0) - od) - | BetreeListNil => - do - (st1,opt) <- - betree_internal_lookup_in_children_fwd node key st0; - monad_ignore_bind - (betree_node_lookup_first_message_for_key_back key - msgs BetreeListNil) (Return (st1,opt)) - od - od - | BetreeNodeLeaf node' => - do - (st0,bindings) <- - betree_load_leaf_node_fwd node'.betree_leaf_id st; - opt <- betree_node_lookup_in_bindings_fwd key bindings; - Return (st0,opt) - od - - [betree_node_lookup_in_bindings_fwd_def] Definition - - ⊢ ∀key bindings. - betree_node_lookup_in_bindings_fwd key bindings = - case bindings of - BetreeListCons hd tl => - (let - (i,i0) = hd - in - if i = key then Return (SOME i0) - else if u64_gt i key then Return NONE - else betree_node_lookup_in_bindings_fwd key tl) - | BetreeListNil => Return NONE - - [betree_node_lookup_mut_in_bindings_back_def] Definition - - ⊢ ∀key bindings ret. - betree_node_lookup_mut_in_bindings_back key bindings ret = - case bindings of - BetreeListCons hd tl => - (let - (i,i0) = hd - in - if u64_ge i key then Return ret - else - do - tl0 <- - betree_node_lookup_mut_in_bindings_back key tl ret; - Return (BetreeListCons (i,i0) tl0) - od) - | BetreeListNil => Return ret - - [betree_node_lookup_mut_in_bindings_fwd_def] Definition - - ⊢ ∀key bindings. - betree_node_lookup_mut_in_bindings_fwd key bindings = - case bindings of - BetreeListCons hd tl => - (let - (i,i0) = hd - in - if u64_ge i key then Return (BetreeListCons (i,i0) tl) - else betree_node_lookup_mut_in_bindings_fwd key tl) - | BetreeListNil => Return BetreeListNil - - [betree_store_internal_node_fwd_def] Definition - - ⊢ ∀id content st. - betree_store_internal_node_fwd id content st = - do - (st0,_) <- betree_utils_store_internal_node_fwd id content st; - Return (st0,()) - od - - [betree_store_leaf_node_fwd_def] Definition - - ⊢ ∀id content st. - betree_store_leaf_node_fwd id content st = - do - (st0,_) <- betree_utils_store_leaf_node_fwd id content st; - Return (st0,()) - od - - [betree_upsert_update_fwd_def] Definition - - ⊢ ∀prev st. - betree_upsert_update_fwd prev st = - case prev of - NONE => - (case st of - BetreeUpsertFunStateAdd v => Return v - | BetreeUpsertFunStateSub i => Return (int_to_u64 0)) - | SOME prev0 => - case st of - BetreeUpsertFunStateAdd v => - do - margin <- u64_sub core_u64_max prev0; - if u64_ge margin v then u64_add prev0 v - else Return core_u64_max - od - | BetreeUpsertFunStateSub v' => - if u64_ge prev0 v' then u64_sub prev0 v' - else Return (int_to_u64 0) - - [main_fwd_def] Definition - - ⊢ main_fwd = Return () - - -*) -end diff --git a/tests/hol4/betree/betreeMain_OpaqueScript.sml b/tests/hol4/betree/betreeMain_OpaqueScript.sml deleted file mode 100644 index 1d16db4c..00000000 --- a/tests/hol4/betree/betreeMain_OpaqueScript.sml +++ /dev/null @@ -1,26 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: external function declarations *) -open primitivesLib divDefLib -open betreeMain_TypesTheory - -val _ = new_theory "betreeMain_Opaque" - - -(** [betree_main::betree_utils::load_internal_node]: forward function *)val _ = new_constant ("betree_utils_load_internal_node_fwd", - “:u64 -> state -> (state # (u64 # betree_message_t) betree_list_t) - result”) - -(** [betree_main::betree_utils::store_internal_node]: forward function *)val _ = new_constant ("betree_utils_store_internal_node_fwd", - “:u64 -> (u64 # betree_message_t) betree_list_t -> state -> (state # unit) - result”) - -(** [betree_main::betree_utils::load_leaf_node]: forward function *)val _ = new_constant ("betree_utils_load_leaf_node_fwd", - “:u64 -> state -> (state # (u64 # u64) betree_list_t) result”) - -(** [betree_main::betree_utils::store_leaf_node]: forward function *)val _ = new_constant ("betree_utils_store_leaf_node_fwd", - “:u64 -> (u64 # u64) betree_list_t -> state -> (state # unit) result”) - -(** [core::option::Option::{0}::unwrap]: forward function *)val _ = new_constant ("core_option_option_unwrap_fwd", - “:'t option -> state -> (state # 't) result”) - -val _ = export_theory () diff --git a/tests/hol4/betree/betreeMain_OpaqueTheory.sig b/tests/hol4/betree/betreeMain_OpaqueTheory.sig deleted file mode 100644 index da7559a0..00000000 --- a/tests/hol4/betree/betreeMain_OpaqueTheory.sig +++ /dev/null @@ -1,11 +0,0 @@ -signature betreeMain_OpaqueTheory = -sig - type thm = Thm.thm - - val betreeMain_Opaque_grammars : type_grammar.grammar * term_grammar.grammar -(* - [betreeMain_Types] Parent theory of "betreeMain_Opaque" - - -*) -end diff --git a/tests/hol4/betree/betreeMain_TypesScript.sml b/tests/hol4/betree/betreeMain_TypesScript.sml deleted file mode 100644 index 779f6abb..00000000 --- a/tests/hol4/betree/betreeMain_TypesScript.sml +++ /dev/null @@ -1,76 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: type definitions *) -open primitivesLib divDefLib - -val _ = new_theory "betreeMain_Types" - - -Datatype: - (** [betree_main::betree::List] *) - betree_list_t = | BetreeListCons 't betree_list_t | BetreeListNil -End - -Datatype: - (** [betree_main::betree::UpsertFunState] *) - betree_upsert_fun_state_t = - | BetreeUpsertFunStateAdd u64 - | BetreeUpsertFunStateSub u64 -End - -Datatype: - (** [betree_main::betree::Message] *) - betree_message_t = - | BetreeMessageInsert u64 - | BetreeMessageDelete - | BetreeMessageUpsert betree_upsert_fun_state_t -End - -Datatype: - (** [betree_main::betree::Leaf] *) - betree_leaf_t = <| betree_leaf_id : u64; betree_leaf_size : u64; |> -End - -Datatype: - (** [betree_main::betree::Internal] *) - betree_internal_t = - <| - betree_internal_id : u64; - betree_internal_pivot : u64; - betree_internal_left : betree_node_t; - betree_internal_right : betree_node_t; - |> - ; - - (** [betree_main::betree::Node] *) - betree_node_t = - | BetreeNodeInternal betree_internal_t - | BetreeNodeLeaf betree_leaf_t -End - -Datatype: - (** [betree_main::betree::Params] *) - betree_params_t = - <| - betree_params_min_flush_size : u64; betree_params_split_size : u64; - |> -End - -Datatype: - (** [betree_main::betree::NodeIdCounter] *) - betree_node_id_counter_t = <| betree_node_id_counter_next_node_id : u64; |> -End - -Datatype: - (** [betree_main::betree::BeTree] *) - betree_be_tree_t = - <| - betree_be_tree_params : betree_params_t; - betree_be_tree_node_id_cnt : betree_node_id_counter_t; - betree_be_tree_root : betree_node_t; - |> -End - -(** The state type used in the state-error monad *) -val _ = new_type ("state", 0) - -val _ = export_theory () diff --git a/tests/hol4/betree/betreeMain_TypesTheory.sig b/tests/hol4/betree/betreeMain_TypesTheory.sig deleted file mode 100644 index cffe6afb..00000000 --- a/tests/hol4/betree/betreeMain_TypesTheory.sig +++ /dev/null @@ -1,1751 +0,0 @@ -signature betreeMain_TypesTheory = -sig - type thm = Thm.thm - - (* Definitions *) - val betree_be_tree_t_TY_DEF : thm - val betree_be_tree_t_betree_be_tree_node_id_cnt : thm - val betree_be_tree_t_betree_be_tree_node_id_cnt_fupd : thm - val betree_be_tree_t_betree_be_tree_params : thm - val betree_be_tree_t_betree_be_tree_params_fupd : thm - val betree_be_tree_t_betree_be_tree_root : thm - val betree_be_tree_t_betree_be_tree_root_fupd : thm - val betree_be_tree_t_case_def : thm - val betree_be_tree_t_size_def : thm - val betree_internal_t_TY_DEF : thm - val betree_internal_t_betree_internal_id : thm - val betree_internal_t_betree_internal_id_fupd : thm - val betree_internal_t_betree_internal_left : thm - val betree_internal_t_betree_internal_left_fupd : thm - val betree_internal_t_betree_internal_pivot : thm - val betree_internal_t_betree_internal_pivot_fupd : thm - val betree_internal_t_betree_internal_right : thm - val betree_internal_t_betree_internal_right_fupd : thm - val betree_internal_t_case_def : thm - val betree_internal_t_size_def : thm - val betree_leaf_t_TY_DEF : thm - val betree_leaf_t_betree_leaf_id : thm - val betree_leaf_t_betree_leaf_id_fupd : thm - val betree_leaf_t_betree_leaf_size : thm - val betree_leaf_t_betree_leaf_size_fupd : thm - val betree_leaf_t_case_def : thm - val betree_leaf_t_size_def : thm - val betree_list_t_TY_DEF : thm - val betree_list_t_case_def : thm - val betree_list_t_size_def : thm - val betree_message_t_TY_DEF : thm - val betree_message_t_case_def : thm - val betree_message_t_size_def : thm - val betree_node_id_counter_t_TY_DEF : thm - val betree_node_id_counter_t_betree_node_id_counter_next_node_id : thm - val betree_node_id_counter_t_betree_node_id_counter_next_node_id_fupd : thm - val betree_node_id_counter_t_case_def : thm - val betree_node_id_counter_t_size_def : thm - val betree_node_t_TY_DEF : thm - val betree_node_t_case_def : thm - val betree_params_t_TY_DEF : thm - val betree_params_t_betree_params_min_flush_size : thm - val betree_params_t_betree_params_min_flush_size_fupd : thm - val betree_params_t_betree_params_split_size : thm - val betree_params_t_betree_params_split_size_fupd : thm - val betree_params_t_case_def : thm - val betree_params_t_size_def : thm - val betree_upsert_fun_state_t_TY_DEF : thm - val betree_upsert_fun_state_t_case_def : thm - val betree_upsert_fun_state_t_size_def : thm - - (* Theorems *) - val EXISTS_betree_be_tree_t : thm - val EXISTS_betree_internal_t : thm - val EXISTS_betree_leaf_t : thm - val EXISTS_betree_node_id_counter_t : thm - val EXISTS_betree_params_t : thm - val FORALL_betree_be_tree_t : thm - val FORALL_betree_internal_t : thm - val FORALL_betree_leaf_t : thm - val FORALL_betree_node_id_counter_t : thm - val FORALL_betree_params_t : thm - val betree_be_tree_t_11 : thm - val betree_be_tree_t_Axiom : thm - val betree_be_tree_t_accessors : thm - val betree_be_tree_t_accfupds : thm - val betree_be_tree_t_case_cong : thm - val betree_be_tree_t_case_eq : thm - val betree_be_tree_t_component_equality : thm - val betree_be_tree_t_fn_updates : thm - val betree_be_tree_t_fupdcanon : thm - val betree_be_tree_t_fupdcanon_comp : thm - val betree_be_tree_t_fupdfupds : thm - val betree_be_tree_t_fupdfupds_comp : thm - val betree_be_tree_t_induction : thm - val betree_be_tree_t_literal_11 : thm - val betree_be_tree_t_literal_nchotomy : thm - val betree_be_tree_t_nchotomy : thm - val betree_be_tree_t_updates_eq_literal : thm - val betree_internal_t_11 : thm - val betree_internal_t_Axiom : thm - val betree_internal_t_accessors : thm - val betree_internal_t_accfupds : thm - val betree_internal_t_case_cong : thm - val betree_internal_t_case_eq : thm - val betree_internal_t_component_equality : thm - val betree_internal_t_fn_updates : thm - val betree_internal_t_fupdcanon : thm - val betree_internal_t_fupdcanon_comp : thm - val betree_internal_t_fupdfupds : thm - val betree_internal_t_fupdfupds_comp : thm - val betree_internal_t_induction : thm - val betree_internal_t_literal_11 : thm - val betree_internal_t_literal_nchotomy : thm - val betree_internal_t_nchotomy : thm - val betree_internal_t_updates_eq_literal : thm - val betree_leaf_t_11 : thm - val betree_leaf_t_Axiom : thm - val betree_leaf_t_accessors : thm - val betree_leaf_t_accfupds : thm - val betree_leaf_t_case_cong : thm - val betree_leaf_t_case_eq : thm - val betree_leaf_t_component_equality : thm - val betree_leaf_t_fn_updates : thm - val betree_leaf_t_fupdcanon : thm - val betree_leaf_t_fupdcanon_comp : thm - val betree_leaf_t_fupdfupds : thm - val betree_leaf_t_fupdfupds_comp : thm - val betree_leaf_t_induction : thm - val betree_leaf_t_literal_11 : thm - val betree_leaf_t_literal_nchotomy : thm - val betree_leaf_t_nchotomy : thm - val betree_leaf_t_updates_eq_literal : thm - val betree_list_t_11 : thm - val betree_list_t_Axiom : thm - val betree_list_t_case_cong : thm - val betree_list_t_case_eq : thm - val betree_list_t_distinct : thm - val betree_list_t_induction : thm - val betree_list_t_nchotomy : thm - val betree_message_t_11 : thm - val betree_message_t_Axiom : thm - val betree_message_t_case_cong : thm - val betree_message_t_case_eq : thm - val betree_message_t_distinct : thm - val betree_message_t_induction : thm - val betree_message_t_nchotomy : thm - val betree_node_id_counter_t_11 : thm - val betree_node_id_counter_t_Axiom : thm - val betree_node_id_counter_t_accessors : thm - val betree_node_id_counter_t_accfupds : thm - val betree_node_id_counter_t_case_cong : thm - val betree_node_id_counter_t_case_eq : thm - val betree_node_id_counter_t_component_equality : thm - val betree_node_id_counter_t_fn_updates : thm - val betree_node_id_counter_t_fupdfupds : thm - val betree_node_id_counter_t_fupdfupds_comp : thm - val betree_node_id_counter_t_induction : thm - val betree_node_id_counter_t_literal_11 : thm - val betree_node_id_counter_t_literal_nchotomy : thm - val betree_node_id_counter_t_nchotomy : thm - val betree_node_id_counter_t_updates_eq_literal : thm - val betree_node_t_11 : thm - val betree_node_t_Axiom : thm - val betree_node_t_case_cong : thm - val betree_node_t_case_eq : thm - val betree_node_t_distinct : thm - val betree_node_t_induction : thm - val betree_node_t_nchotomy : thm - val betree_params_t_11 : thm - val betree_params_t_Axiom : thm - val betree_params_t_accessors : thm - val betree_params_t_accfupds : thm - val betree_params_t_case_cong : thm - val betree_params_t_case_eq : thm - val betree_params_t_component_equality : thm - val betree_params_t_fn_updates : thm - val betree_params_t_fupdcanon : thm - val betree_params_t_fupdcanon_comp : thm - val betree_params_t_fupdfupds : thm - val betree_params_t_fupdfupds_comp : thm - val betree_params_t_induction : thm - val betree_params_t_literal_11 : thm - val betree_params_t_literal_nchotomy : thm - val betree_params_t_nchotomy : thm - val betree_params_t_updates_eq_literal : thm - val betree_upsert_fun_state_t_11 : thm - val betree_upsert_fun_state_t_Axiom : thm - val betree_upsert_fun_state_t_case_cong : thm - val betree_upsert_fun_state_t_case_eq : thm - val betree_upsert_fun_state_t_distinct : thm - val betree_upsert_fun_state_t_induction : thm - val betree_upsert_fun_state_t_nchotomy : thm - val datatype_betree_be_tree_t : thm - val datatype_betree_internal_t : thm - val datatype_betree_leaf_t : thm - val datatype_betree_list_t : thm - val datatype_betree_message_t : thm - val datatype_betree_node_id_counter_t : thm - val datatype_betree_params_t : thm - val datatype_betree_upsert_fun_state_t : thm - - val betreeMain_Types_grammars : type_grammar.grammar * term_grammar.grammar -(* - [divDef] Parent theory of "betreeMain_Types" - - [betree_be_tree_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0'. - ∀ $var$('betree_be_tree_t'). - (∀a0'. - (∃a0 a1 a2. - a0' = - (λa0 a1 a2. - ind_type$CONSTR 0 (a0,a1,a2) - (λn. ind_type$BOTTOM)) a0 a1 a2) ⇒ - $var$('betree_be_tree_t') a0') ⇒ - $var$('betree_be_tree_t') a0') rep - - [betree_be_tree_t_betree_be_tree_node_id_cnt] Definition - - ⊢ ∀b b0 b1. - (betree_be_tree_t b b0 b1).betree_be_tree_node_id_cnt = b0 - - [betree_be_tree_t_betree_be_tree_node_id_cnt_fupd] Definition - - ⊢ ∀f b b0 b1. - betree_be_tree_t b b0 b1 with - betree_be_tree_node_id_cnt updated_by f = - betree_be_tree_t b (f b0) b1 - - [betree_be_tree_t_betree_be_tree_params] Definition - - ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_params = b - - [betree_be_tree_t_betree_be_tree_params_fupd] Definition - - ⊢ ∀f b b0 b1. - betree_be_tree_t b b0 b1 with betree_be_tree_params updated_by f = - betree_be_tree_t (f b) b0 b1 - - [betree_be_tree_t_betree_be_tree_root] Definition - - ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_root = b1 - - [betree_be_tree_t_betree_be_tree_root_fupd] Definition - - ⊢ ∀f b b0 b1. - betree_be_tree_t b b0 b1 with betree_be_tree_root updated_by f = - betree_be_tree_t b b0 (f b1) - - [betree_be_tree_t_case_def] Definition - - ⊢ ∀a0 a1 a2 f. - betree_be_tree_t_CASE (betree_be_tree_t a0 a1 a2) f = f a0 a1 a2 - - [betree_be_tree_t_size_def] Definition - - ⊢ ∀a0 a1 a2. - betree_be_tree_t_size (betree_be_tree_t a0 a1 a2) = - 1 + - (betree_params_t_size a0 + - (betree_node_id_counter_t_size a1 + betree_node_t_size a2)) - - [betree_internal_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0'. - ∀ $var$('betree_internal_t') $var$('betree_node_t'). - (∀a0'. - (∃a0 a1 a2 a3. - a0' = - (λa0 a1 a2 a3. - ind_type$CONSTR 0 (a0,a1,ARB) - (ind_type$FCONS a2 - (ind_type$FCONS a3 (λn. ind_type$BOTTOM)))) - a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧ - $var$('betree_node_t') a3) ⇒ - $var$('betree_internal_t') a0') ∧ - (∀a1'. - (∃a. a1' = - (λa. - ind_type$CONSTR (SUC 0) (ARB,ARB,ARB) - (ind_type$FCONS a (λn. ind_type$BOTTOM))) - a ∧ $var$('betree_internal_t') a) ∨ - (∃a. a1' = - (λa. - ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a) - (λn. ind_type$BOTTOM)) a) ⇒ - $var$('betree_node_t') a1') ⇒ - $var$('betree_internal_t') a0') rep - - [betree_internal_t_betree_internal_id] Definition - - ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_id = u - - [betree_internal_t_betree_internal_id_fupd] Definition - - ⊢ ∀f u u0 b b0. - betree_internal_t u u0 b b0 with betree_internal_id updated_by f = - betree_internal_t (f u) u0 b b0 - - [betree_internal_t_betree_internal_left] Definition - - ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_left = b - - [betree_internal_t_betree_internal_left_fupd] Definition - - ⊢ ∀f u u0 b b0. - betree_internal_t u u0 b b0 with - betree_internal_left updated_by f = - betree_internal_t u u0 (f b) b0 - - [betree_internal_t_betree_internal_pivot] Definition - - ⊢ ∀u u0 b b0. - (betree_internal_t u u0 b b0).betree_internal_pivot = u0 - - [betree_internal_t_betree_internal_pivot_fupd] Definition - - ⊢ ∀f u u0 b b0. - betree_internal_t u u0 b b0 with - betree_internal_pivot updated_by f = - betree_internal_t u (f u0) b b0 - - [betree_internal_t_betree_internal_right] Definition - - ⊢ ∀u u0 b b0. - (betree_internal_t u u0 b b0).betree_internal_right = b0 - - [betree_internal_t_betree_internal_right_fupd] Definition - - ⊢ ∀f u u0 b b0. - betree_internal_t u u0 b b0 with - betree_internal_right updated_by f = - betree_internal_t u u0 b (f b0) - - [betree_internal_t_case_def] Definition - - ⊢ ∀a0 a1 a2 a3 f. - betree_internal_t_CASE (betree_internal_t a0 a1 a2 a3) f = - f a0 a1 a2 a3 - - [betree_internal_t_size_def] Definition - - ⊢ (∀a0 a1 a2 a3. - betree_internal_t_size (betree_internal_t a0 a1 a2 a3) = - 1 + (betree_node_t_size a2 + betree_node_t_size a3)) ∧ - (∀a. betree_node_t_size (BetreeNodeInternal a) = - 1 + betree_internal_t_size a) ∧ - ∀a. betree_node_t_size (BetreeNodeLeaf a) = - 1 + betree_leaf_t_size a - - [betree_leaf_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0'. - ∀ $var$('betree_leaf_t'). - (∀a0'. - (∃a0 a1. - a0' = - (λa0 a1. - ind_type$CONSTR 0 (a0,a1) - (λn. ind_type$BOTTOM)) a0 a1) ⇒ - $var$('betree_leaf_t') a0') ⇒ - $var$('betree_leaf_t') a0') rep - - [betree_leaf_t_betree_leaf_id] Definition - - ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_id = u - - [betree_leaf_t_betree_leaf_id_fupd] Definition - - ⊢ ∀f u u0. - betree_leaf_t u u0 with betree_leaf_id updated_by f = - betree_leaf_t (f u) u0 - - [betree_leaf_t_betree_leaf_size] Definition - - ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_size = u0 - - [betree_leaf_t_betree_leaf_size_fupd] Definition - - ⊢ ∀f u u0. - betree_leaf_t u u0 with betree_leaf_size updated_by f = - betree_leaf_t u (f u0) - - [betree_leaf_t_case_def] Definition - - ⊢ ∀a0 a1 f. betree_leaf_t_CASE (betree_leaf_t a0 a1) f = f a0 a1 - - [betree_leaf_t_size_def] Definition - - ⊢ ∀a0 a1. betree_leaf_t_size (betree_leaf_t a0 a1) = 1 - - [betree_list_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0'. - ∀ $var$('betree_list_t'). - (∀a0'. - (∃a0 a1. - a0' = - (λa0 a1. - ind_type$CONSTR 0 a0 - (ind_type$FCONS a1 (λn. ind_type$BOTTOM))) - a0 a1 ∧ $var$('betree_list_t') a1) ∨ - a0' = - ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ - $var$('betree_list_t') a0') ⇒ - $var$('betree_list_t') a0') rep - - [betree_list_t_case_def] Definition - - ⊢ (∀a0 a1 f v. - betree_list_t_CASE (BetreeListCons a0 a1) f v = f a0 a1) ∧ - ∀f v. betree_list_t_CASE BetreeListNil f v = v - - [betree_list_t_size_def] Definition - - ⊢ (∀f a0 a1. - betree_list_t_size f (BetreeListCons a0 a1) = - 1 + (f a0 + betree_list_t_size f a1)) ∧ - ∀f. betree_list_t_size f BetreeListNil = 0 - - [betree_message_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0. - ∀ $var$('betree_message_t'). - (∀a0. - (∃a. a0 = - (λa. - ind_type$CONSTR 0 (a,ARB) - (λn. ind_type$BOTTOM)) a) ∨ - a0 = - ind_type$CONSTR (SUC 0) (ARB,ARB) - (λn. ind_type$BOTTOM) ∨ - (∃a. a0 = - (λa. - ind_type$CONSTR (SUC (SUC 0)) (ARB,a) - (λn. ind_type$BOTTOM)) a) ⇒ - $var$('betree_message_t') a0) ⇒ - $var$('betree_message_t') a0) rep - - [betree_message_t_case_def] Definition - - ⊢ (∀a f v f1. - betree_message_t_CASE (BetreeMessageInsert a) f v f1 = f a) ∧ - (∀f v f1. betree_message_t_CASE BetreeMessageDelete f v f1 = v) ∧ - ∀a f v f1. - betree_message_t_CASE (BetreeMessageUpsert a) f v f1 = f1 a - - [betree_message_t_size_def] Definition - - ⊢ (∀a. betree_message_t_size (BetreeMessageInsert a) = 1) ∧ - betree_message_t_size BetreeMessageDelete = 0 ∧ - ∀a. betree_message_t_size (BetreeMessageUpsert a) = - 1 + betree_upsert_fun_state_t_size a - - [betree_node_id_counter_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0. - ∀ $var$('betree_node_id_counter_t'). - (∀a0. - (∃a. a0 = - (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) - a) ⇒ - $var$('betree_node_id_counter_t') a0) ⇒ - $var$('betree_node_id_counter_t') a0) rep - - [betree_node_id_counter_t_betree_node_id_counter_next_node_id] Definition - - ⊢ ∀u. (betree_node_id_counter_t u). - betree_node_id_counter_next_node_id = - u - - [betree_node_id_counter_t_betree_node_id_counter_next_node_id_fupd] Definition - - ⊢ ∀f u. - betree_node_id_counter_t u with - betree_node_id_counter_next_node_id updated_by f = - betree_node_id_counter_t (f u) - - [betree_node_id_counter_t_case_def] Definition - - ⊢ ∀a f. - betree_node_id_counter_t_CASE (betree_node_id_counter_t a) f = - f a - - [betree_node_id_counter_t_size_def] Definition - - ⊢ ∀a. betree_node_id_counter_t_size (betree_node_id_counter_t a) = 1 - - [betree_node_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa1'. - ∀ $var$('betree_internal_t') $var$('betree_node_t'). - (∀a0'. - (∃a0 a1 a2 a3. - a0' = - (λa0 a1 a2 a3. - ind_type$CONSTR 0 (a0,a1,ARB) - (ind_type$FCONS a2 - (ind_type$FCONS a3 (λn. ind_type$BOTTOM)))) - a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧ - $var$('betree_node_t') a3) ⇒ - $var$('betree_internal_t') a0') ∧ - (∀a1'. - (∃a. a1' = - (λa. - ind_type$CONSTR (SUC 0) (ARB,ARB,ARB) - (ind_type$FCONS a (λn. ind_type$BOTTOM))) - a ∧ $var$('betree_internal_t') a) ∨ - (∃a. a1' = - (λa. - ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a) - (λn. ind_type$BOTTOM)) a) ⇒ - $var$('betree_node_t') a1') ⇒ - $var$('betree_node_t') a1') rep - - [betree_node_t_case_def] Definition - - ⊢ (∀a f f1. betree_node_t_CASE (BetreeNodeInternal a) f f1 = f a) ∧ - ∀a f f1. betree_node_t_CASE (BetreeNodeLeaf a) f f1 = f1 a - - [betree_params_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0'. - ∀ $var$('betree_params_t'). - (∀a0'. - (∃a0 a1. - a0' = - (λa0 a1. - ind_type$CONSTR 0 (a0,a1) - (λn. ind_type$BOTTOM)) a0 a1) ⇒ - $var$('betree_params_t') a0') ⇒ - $var$('betree_params_t') a0') rep - - [betree_params_t_betree_params_min_flush_size] Definition - - ⊢ ∀u u0. (betree_params_t u u0).betree_params_min_flush_size = u - - [betree_params_t_betree_params_min_flush_size_fupd] Definition - - ⊢ ∀f u u0. - betree_params_t u u0 with - betree_params_min_flush_size updated_by f = - betree_params_t (f u) u0 - - [betree_params_t_betree_params_split_size] Definition - - ⊢ ∀u u0. (betree_params_t u u0).betree_params_split_size = u0 - - [betree_params_t_betree_params_split_size_fupd] Definition - - ⊢ ∀f u u0. - betree_params_t u u0 with betree_params_split_size updated_by f = - betree_params_t u (f u0) - - [betree_params_t_case_def] Definition - - ⊢ ∀a0 a1 f. betree_params_t_CASE (betree_params_t a0 a1) f = f a0 a1 - - [betree_params_t_size_def] Definition - - ⊢ ∀a0 a1. betree_params_t_size (betree_params_t a0 a1) = 1 - - [betree_upsert_fun_state_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0. - ∀ $var$('betree_upsert_fun_state_t'). - (∀a0. - (∃a. a0 = - (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) - a) ∨ - (∃a. a0 = - (λa. - ind_type$CONSTR (SUC 0) a - (λn. ind_type$BOTTOM)) a) ⇒ - $var$('betree_upsert_fun_state_t') a0) ⇒ - $var$('betree_upsert_fun_state_t') a0) rep - - [betree_upsert_fun_state_t_case_def] Definition - - ⊢ (∀a f f1. - betree_upsert_fun_state_t_CASE (BetreeUpsertFunStateAdd a) f f1 = - f a) ∧ - ∀a f f1. - betree_upsert_fun_state_t_CASE (BetreeUpsertFunStateSub a) f f1 = - f1 a - - [betree_upsert_fun_state_t_size_def] Definition - - ⊢ (∀a. betree_upsert_fun_state_t_size (BetreeUpsertFunStateAdd a) = 1) ∧ - ∀a. betree_upsert_fun_state_t_size (BetreeUpsertFunStateSub a) = 1 - - [EXISTS_betree_be_tree_t] Theorem - - ⊢ ∀P. (∃b. P b) ⇔ - ∃b2 b1 b0. - P - <|betree_be_tree_params := b2; - betree_be_tree_node_id_cnt := b1; - betree_be_tree_root := b0|> - - [EXISTS_betree_internal_t] Theorem - - ⊢ ∀P. (∃b. P b) ⇔ - ∃u0 u b1 b0. - P - <|betree_internal_id := u0; betree_internal_pivot := u; - betree_internal_left := b1; betree_internal_right := b0|> - - [EXISTS_betree_leaf_t] Theorem - - ⊢ ∀P. (∃b. P b) ⇔ - ∃u0 u. P <|betree_leaf_id := u0; betree_leaf_size := u|> - - [EXISTS_betree_node_id_counter_t] Theorem - - ⊢ ∀P. (∃b. P b) ⇔ ∃u. P <|betree_node_id_counter_next_node_id := u|> - - [EXISTS_betree_params_t] Theorem - - ⊢ ∀P. (∃b. P b) ⇔ - ∃u0 u. - P - <|betree_params_min_flush_size := u0; - betree_params_split_size := u|> - - [FORALL_betree_be_tree_t] Theorem - - ⊢ ∀P. (∀b. P b) ⇔ - ∀b2 b1 b0. - P - <|betree_be_tree_params := b2; - betree_be_tree_node_id_cnt := b1; - betree_be_tree_root := b0|> - - [FORALL_betree_internal_t] Theorem - - ⊢ ∀P. (∀b. P b) ⇔ - ∀u0 u b1 b0. - P - <|betree_internal_id := u0; betree_internal_pivot := u; - betree_internal_left := b1; betree_internal_right := b0|> - - [FORALL_betree_leaf_t] Theorem - - ⊢ ∀P. (∀b. P b) ⇔ - ∀u0 u. P <|betree_leaf_id := u0; betree_leaf_size := u|> - - [FORALL_betree_node_id_counter_t] Theorem - - ⊢ ∀P. (∀b. P b) ⇔ ∀u. P <|betree_node_id_counter_next_node_id := u|> - - [FORALL_betree_params_t] Theorem - - ⊢ ∀P. (∀b. P b) ⇔ - ∀u0 u. - P - <|betree_params_min_flush_size := u0; - betree_params_split_size := u|> - - [betree_be_tree_t_11] Theorem - - ⊢ ∀a0 a1 a2 a0' a1' a2'. - betree_be_tree_t a0 a1 a2 = betree_be_tree_t a0' a1' a2' ⇔ - a0 = a0' ∧ a1 = a1' ∧ a2 = a2' - - [betree_be_tree_t_Axiom] Theorem - - ⊢ ∀f. ∃fn. ∀a0 a1 a2. fn (betree_be_tree_t a0 a1 a2) = f a0 a1 a2 - - [betree_be_tree_t_accessors] Theorem - - ⊢ (∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_params = b) ∧ - (∀b b0 b1. - (betree_be_tree_t b b0 b1).betree_be_tree_node_id_cnt = b0) ∧ - ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_root = b1 - - [betree_be_tree_t_accfupds] Theorem - - ⊢ (∀f b. - (b with betree_be_tree_node_id_cnt updated_by f). - betree_be_tree_params = - b.betree_be_tree_params) ∧ - (∀f b. - (b with betree_be_tree_root updated_by f).betree_be_tree_params = - b.betree_be_tree_params) ∧ - (∀f b. - (b with betree_be_tree_params updated_by f). - betree_be_tree_node_id_cnt = - b.betree_be_tree_node_id_cnt) ∧ - (∀f b. - (b with betree_be_tree_root updated_by f). - betree_be_tree_node_id_cnt = - b.betree_be_tree_node_id_cnt) ∧ - (∀f b. - (b with betree_be_tree_params updated_by f).betree_be_tree_root = - b.betree_be_tree_root) ∧ - (∀f b. - (b with betree_be_tree_node_id_cnt updated_by f). - betree_be_tree_root = - b.betree_be_tree_root) ∧ - (∀f b. - (b with betree_be_tree_params updated_by f). - betree_be_tree_params = - f b.betree_be_tree_params) ∧ - (∀f b. - (b with betree_be_tree_node_id_cnt updated_by f). - betree_be_tree_node_id_cnt = - f b.betree_be_tree_node_id_cnt) ∧ - ∀f b. - (b with betree_be_tree_root updated_by f).betree_be_tree_root = - f b.betree_be_tree_root - - [betree_be_tree_t_case_cong] Theorem - - ⊢ ∀M M' f. - M = M' ∧ - (∀a0 a1 a2. - M' = betree_be_tree_t a0 a1 a2 ⇒ f a0 a1 a2 = f' a0 a1 a2) ⇒ - betree_be_tree_t_CASE M f = betree_be_tree_t_CASE M' f' - - [betree_be_tree_t_case_eq] Theorem - - ⊢ betree_be_tree_t_CASE x f = v ⇔ - ∃b b0 b1. x = betree_be_tree_t b b0 b1 ∧ f b b0 b1 = v - - [betree_be_tree_t_component_equality] Theorem - - ⊢ ∀b1 b2. - b1 = b2 ⇔ - b1.betree_be_tree_params = b2.betree_be_tree_params ∧ - b1.betree_be_tree_node_id_cnt = b2.betree_be_tree_node_id_cnt ∧ - b1.betree_be_tree_root = b2.betree_be_tree_root - - [betree_be_tree_t_fn_updates] Theorem - - ⊢ (∀f b b0 b1. - betree_be_tree_t b b0 b1 with betree_be_tree_params updated_by f = - betree_be_tree_t (f b) b0 b1) ∧ - (∀f b b0 b1. - betree_be_tree_t b b0 b1 with - betree_be_tree_node_id_cnt updated_by f = - betree_be_tree_t b (f b0) b1) ∧ - ∀f b b0 b1. - betree_be_tree_t b b0 b1 with betree_be_tree_root updated_by f = - betree_be_tree_t b b0 (f b1) - - [betree_be_tree_t_fupdcanon] Theorem - - ⊢ (∀g f b. - b with - <|betree_be_tree_node_id_cnt updated_by f; - betree_be_tree_params updated_by g|> = - b with - <|betree_be_tree_params updated_by g; - betree_be_tree_node_id_cnt updated_by f|>) ∧ - (∀g f b. - b with - <|betree_be_tree_root updated_by f; - betree_be_tree_params updated_by g|> = - b with - <|betree_be_tree_params updated_by g; - betree_be_tree_root updated_by f|>) ∧ - ∀g f b. - b with - <|betree_be_tree_root updated_by f; - betree_be_tree_node_id_cnt updated_by g|> = - b with - <|betree_be_tree_node_id_cnt updated_by g; - betree_be_tree_root updated_by f|> - - [betree_be_tree_t_fupdcanon_comp] Theorem - - ⊢ ((∀g f. - betree_be_tree_node_id_cnt_fupd f ∘ - betree_be_tree_params_fupd g = - betree_be_tree_params_fupd g ∘ - betree_be_tree_node_id_cnt_fupd f) ∧ - ∀h g f. - betree_be_tree_node_id_cnt_fupd f ∘ - betree_be_tree_params_fupd g ∘ h = - betree_be_tree_params_fupd g ∘ - betree_be_tree_node_id_cnt_fupd f ∘ h) ∧ - ((∀g f. - betree_be_tree_root_fupd f ∘ betree_be_tree_params_fupd g = - betree_be_tree_params_fupd g ∘ betree_be_tree_root_fupd f) ∧ - ∀h g f. - betree_be_tree_root_fupd f ∘ betree_be_tree_params_fupd g ∘ h = - betree_be_tree_params_fupd g ∘ betree_be_tree_root_fupd f ∘ h) ∧ - (∀g f. - betree_be_tree_root_fupd f ∘ betree_be_tree_node_id_cnt_fupd g = - betree_be_tree_node_id_cnt_fupd g ∘ betree_be_tree_root_fupd f) ∧ - ∀h g f. - betree_be_tree_root_fupd f ∘ betree_be_tree_node_id_cnt_fupd g ∘ - h = - betree_be_tree_node_id_cnt_fupd g ∘ betree_be_tree_root_fupd f ∘ - h - - [betree_be_tree_t_fupdfupds] Theorem - - ⊢ (∀g f b. - b with - <|betree_be_tree_params updated_by f; - betree_be_tree_params updated_by g|> = - b with betree_be_tree_params updated_by f ∘ g) ∧ - (∀g f b. - b with - <|betree_be_tree_node_id_cnt updated_by f; - betree_be_tree_node_id_cnt updated_by g|> = - b with betree_be_tree_node_id_cnt updated_by f ∘ g) ∧ - ∀g f b. - b with - <|betree_be_tree_root updated_by f; - betree_be_tree_root updated_by g|> = - b with betree_be_tree_root updated_by f ∘ g - - [betree_be_tree_t_fupdfupds_comp] Theorem - - ⊢ ((∀g f. - betree_be_tree_params_fupd f ∘ betree_be_tree_params_fupd g = - betree_be_tree_params_fupd (f ∘ g)) ∧ - ∀h g f. - betree_be_tree_params_fupd f ∘ betree_be_tree_params_fupd g ∘ h = - betree_be_tree_params_fupd (f ∘ g) ∘ h) ∧ - ((∀g f. - betree_be_tree_node_id_cnt_fupd f ∘ - betree_be_tree_node_id_cnt_fupd g = - betree_be_tree_node_id_cnt_fupd (f ∘ g)) ∧ - ∀h g f. - betree_be_tree_node_id_cnt_fupd f ∘ - betree_be_tree_node_id_cnt_fupd g ∘ h = - betree_be_tree_node_id_cnt_fupd (f ∘ g) ∘ h) ∧ - (∀g f. - betree_be_tree_root_fupd f ∘ betree_be_tree_root_fupd g = - betree_be_tree_root_fupd (f ∘ g)) ∧ - ∀h g f. - betree_be_tree_root_fupd f ∘ betree_be_tree_root_fupd g ∘ h = - betree_be_tree_root_fupd (f ∘ g) ∘ h - - [betree_be_tree_t_induction] Theorem - - ⊢ ∀P. (∀b b0 b1. P (betree_be_tree_t b b0 b1)) ⇒ ∀b. P b - - [betree_be_tree_t_literal_11] Theorem - - ⊢ ∀b21 b11 b01 b22 b12 b02. - <|betree_be_tree_params := b21; - betree_be_tree_node_id_cnt := b11; betree_be_tree_root := b01|> = - <|betree_be_tree_params := b22; - betree_be_tree_node_id_cnt := b12; betree_be_tree_root := b02|> ⇔ - b21 = b22 ∧ b11 = b12 ∧ b01 = b02 - - [betree_be_tree_t_literal_nchotomy] Theorem - - ⊢ ∀b. ∃b2 b1 b0. - b = - <|betree_be_tree_params := b2; betree_be_tree_node_id_cnt := b1; - betree_be_tree_root := b0|> - - [betree_be_tree_t_nchotomy] Theorem - - ⊢ ∀bb. ∃b b0 b1. bb = betree_be_tree_t b b0 b1 - - [betree_be_tree_t_updates_eq_literal] Theorem - - ⊢ ∀b b2 b1 b0. - b with - <|betree_be_tree_params := b2; betree_be_tree_node_id_cnt := b1; - betree_be_tree_root := b0|> = - <|betree_be_tree_params := b2; betree_be_tree_node_id_cnt := b1; - betree_be_tree_root := b0|> - - [betree_internal_t_11] Theorem - - ⊢ ∀a0 a1 a2 a3 a0' a1' a2' a3'. - betree_internal_t a0 a1 a2 a3 = betree_internal_t a0' a1' a2' a3' ⇔ - a0 = a0' ∧ a1 = a1' ∧ a2 = a2' ∧ a3 = a3' - - [betree_internal_t_Axiom] Theorem - - ⊢ ∀f0 f1 f2. ∃fn0 fn1. - (∀a0 a1 a2 a3. - fn0 (betree_internal_t a0 a1 a2 a3) = - f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧ - (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧ - ∀a. fn1 (BetreeNodeLeaf a) = f2 a - - [betree_internal_t_accessors] Theorem - - ⊢ (∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_id = u) ∧ - (∀u u0 b b0. - (betree_internal_t u u0 b b0).betree_internal_pivot = u0) ∧ - (∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_left = b) ∧ - ∀u u0 b b0. - (betree_internal_t u u0 b b0).betree_internal_right = b0 - - [betree_internal_t_accfupds] Theorem - - ⊢ (∀f b. - (b with betree_internal_pivot updated_by f).betree_internal_id = - b.betree_internal_id) ∧ - (∀f b. - (b with betree_internal_left updated_by f).betree_internal_id = - b.betree_internal_id) ∧ - (∀f b. - (b with betree_internal_right updated_by f).betree_internal_id = - b.betree_internal_id) ∧ - (∀f b. - (b with betree_internal_id updated_by f).betree_internal_pivot = - b.betree_internal_pivot) ∧ - (∀f b. - (b with betree_internal_left updated_by f).betree_internal_pivot = - b.betree_internal_pivot) ∧ - (∀f b. - (b with betree_internal_right updated_by f). - betree_internal_pivot = - b.betree_internal_pivot) ∧ - (∀f b. - (b with betree_internal_id updated_by f).betree_internal_left = - b.betree_internal_left) ∧ - (∀f b. - (b with betree_internal_pivot updated_by f).betree_internal_left = - b.betree_internal_left) ∧ - (∀f b. - (b with betree_internal_right updated_by f).betree_internal_left = - b.betree_internal_left) ∧ - (∀f b. - (b with betree_internal_id updated_by f).betree_internal_right = - b.betree_internal_right) ∧ - (∀f b. - (b with betree_internal_pivot updated_by f). - betree_internal_right = - b.betree_internal_right) ∧ - (∀f b. - (b with betree_internal_left updated_by f).betree_internal_right = - b.betree_internal_right) ∧ - (∀f b. - (b with betree_internal_id updated_by f).betree_internal_id = - f b.betree_internal_id) ∧ - (∀f b. - (b with betree_internal_pivot updated_by f). - betree_internal_pivot = - f b.betree_internal_pivot) ∧ - (∀f b. - (b with betree_internal_left updated_by f).betree_internal_left = - f b.betree_internal_left) ∧ - ∀f b. - (b with betree_internal_right updated_by f).betree_internal_right = - f b.betree_internal_right - - [betree_internal_t_case_cong] Theorem - - ⊢ ∀M M' f. - M = M' ∧ - (∀a0 a1 a2 a3. - M' = betree_internal_t a0 a1 a2 a3 ⇒ - f a0 a1 a2 a3 = f' a0 a1 a2 a3) ⇒ - betree_internal_t_CASE M f = betree_internal_t_CASE M' f' - - [betree_internal_t_case_eq] Theorem - - ⊢ betree_internal_t_CASE x f = v ⇔ - ∃u0 u b b0. x = betree_internal_t u0 u b b0 ∧ f u0 u b b0 = v - - [betree_internal_t_component_equality] Theorem - - ⊢ ∀b1 b2. - b1 = b2 ⇔ - b1.betree_internal_id = b2.betree_internal_id ∧ - b1.betree_internal_pivot = b2.betree_internal_pivot ∧ - b1.betree_internal_left = b2.betree_internal_left ∧ - b1.betree_internal_right = b2.betree_internal_right - - [betree_internal_t_fn_updates] Theorem - - ⊢ (∀f u u0 b b0. - betree_internal_t u u0 b b0 with betree_internal_id updated_by f = - betree_internal_t (f u) u0 b b0) ∧ - (∀f u u0 b b0. - betree_internal_t u u0 b b0 with - betree_internal_pivot updated_by f = - betree_internal_t u (f u0) b b0) ∧ - (∀f u u0 b b0. - betree_internal_t u u0 b b0 with - betree_internal_left updated_by f = - betree_internal_t u u0 (f b) b0) ∧ - ∀f u u0 b b0. - betree_internal_t u u0 b b0 with - betree_internal_right updated_by f = - betree_internal_t u u0 b (f b0) - - [betree_internal_t_fupdcanon] Theorem - - ⊢ (∀g f b. - b with - <|betree_internal_pivot updated_by f; - betree_internal_id updated_by g|> = - b with - <|betree_internal_id updated_by g; - betree_internal_pivot updated_by f|>) ∧ - (∀g f b. - b with - <|betree_internal_left updated_by f; - betree_internal_id updated_by g|> = - b with - <|betree_internal_id updated_by g; - betree_internal_left updated_by f|>) ∧ - (∀g f b. - b with - <|betree_internal_left updated_by f; - betree_internal_pivot updated_by g|> = - b with - <|betree_internal_pivot updated_by g; - betree_internal_left updated_by f|>) ∧ - (∀g f b. - b with - <|betree_internal_right updated_by f; - betree_internal_id updated_by g|> = - b with - <|betree_internal_id updated_by g; - betree_internal_right updated_by f|>) ∧ - (∀g f b. - b with - <|betree_internal_right updated_by f; - betree_internal_pivot updated_by g|> = - b with - <|betree_internal_pivot updated_by g; - betree_internal_right updated_by f|>) ∧ - ∀g f b. - b with - <|betree_internal_right updated_by f; - betree_internal_left updated_by g|> = - b with - <|betree_internal_left updated_by g; - betree_internal_right updated_by f|> - - [betree_internal_t_fupdcanon_comp] Theorem - - ⊢ ((∀g f. - betree_internal_pivot_fupd f ∘ betree_internal_id_fupd g = - betree_internal_id_fupd g ∘ betree_internal_pivot_fupd f) ∧ - ∀h g f. - betree_internal_pivot_fupd f ∘ betree_internal_id_fupd g ∘ h = - betree_internal_id_fupd g ∘ betree_internal_pivot_fupd f ∘ h) ∧ - ((∀g f. - betree_internal_left_fupd f ∘ betree_internal_id_fupd g = - betree_internal_id_fupd g ∘ betree_internal_left_fupd f) ∧ - ∀h g f. - betree_internal_left_fupd f ∘ betree_internal_id_fupd g ∘ h = - betree_internal_id_fupd g ∘ betree_internal_left_fupd f ∘ h) ∧ - ((∀g f. - betree_internal_left_fupd f ∘ betree_internal_pivot_fupd g = - betree_internal_pivot_fupd g ∘ betree_internal_left_fupd f) ∧ - ∀h g f. - betree_internal_left_fupd f ∘ betree_internal_pivot_fupd g ∘ h = - betree_internal_pivot_fupd g ∘ betree_internal_left_fupd f ∘ h) ∧ - ((∀g f. - betree_internal_right_fupd f ∘ betree_internal_id_fupd g = - betree_internal_id_fupd g ∘ betree_internal_right_fupd f) ∧ - ∀h g f. - betree_internal_right_fupd f ∘ betree_internal_id_fupd g ∘ h = - betree_internal_id_fupd g ∘ betree_internal_right_fupd f ∘ h) ∧ - ((∀g f. - betree_internal_right_fupd f ∘ betree_internal_pivot_fupd g = - betree_internal_pivot_fupd g ∘ betree_internal_right_fupd f) ∧ - ∀h g f. - betree_internal_right_fupd f ∘ betree_internal_pivot_fupd g ∘ h = - betree_internal_pivot_fupd g ∘ betree_internal_right_fupd f ∘ h) ∧ - (∀g f. - betree_internal_right_fupd f ∘ betree_internal_left_fupd g = - betree_internal_left_fupd g ∘ betree_internal_right_fupd f) ∧ - ∀h g f. - betree_internal_right_fupd f ∘ betree_internal_left_fupd g ∘ h = - betree_internal_left_fupd g ∘ betree_internal_right_fupd f ∘ h - - [betree_internal_t_fupdfupds] Theorem - - ⊢ (∀g f b. - b with - <|betree_internal_id updated_by f; - betree_internal_id updated_by g|> = - b with betree_internal_id updated_by f ∘ g) ∧ - (∀g f b. - b with - <|betree_internal_pivot updated_by f; - betree_internal_pivot updated_by g|> = - b with betree_internal_pivot updated_by f ∘ g) ∧ - (∀g f b. - b with - <|betree_internal_left updated_by f; - betree_internal_left updated_by g|> = - b with betree_internal_left updated_by f ∘ g) ∧ - ∀g f b. - b with - <|betree_internal_right updated_by f; - betree_internal_right updated_by g|> = - b with betree_internal_right updated_by f ∘ g - - [betree_internal_t_fupdfupds_comp] Theorem - - ⊢ ((∀g f. - betree_internal_id_fupd f ∘ betree_internal_id_fupd g = - betree_internal_id_fupd (f ∘ g)) ∧ - ∀h g f. - betree_internal_id_fupd f ∘ betree_internal_id_fupd g ∘ h = - betree_internal_id_fupd (f ∘ g) ∘ h) ∧ - ((∀g f. - betree_internal_pivot_fupd f ∘ betree_internal_pivot_fupd g = - betree_internal_pivot_fupd (f ∘ g)) ∧ - ∀h g f. - betree_internal_pivot_fupd f ∘ betree_internal_pivot_fupd g ∘ h = - betree_internal_pivot_fupd (f ∘ g) ∘ h) ∧ - ((∀g f. - betree_internal_left_fupd f ∘ betree_internal_left_fupd g = - betree_internal_left_fupd (f ∘ g)) ∧ - ∀h g f. - betree_internal_left_fupd f ∘ betree_internal_left_fupd g ∘ h = - betree_internal_left_fupd (f ∘ g) ∘ h) ∧ - (∀g f. - betree_internal_right_fupd f ∘ betree_internal_right_fupd g = - betree_internal_right_fupd (f ∘ g)) ∧ - ∀h g f. - betree_internal_right_fupd f ∘ betree_internal_right_fupd g ∘ h = - betree_internal_right_fupd (f ∘ g) ∘ h - - [betree_internal_t_induction] Theorem - - ⊢ ∀P0 P1. - (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧ - (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧ - (∀b. P1 (BetreeNodeLeaf b)) ⇒ - (∀b. P0 b) ∧ ∀b. P1 b - - [betree_internal_t_literal_11] Theorem - - ⊢ ∀u01 u1 b11 b01 u02 u2 b12 b02. - <|betree_internal_id := u01; betree_internal_pivot := u1; - betree_internal_left := b11; betree_internal_right := b01|> = - <|betree_internal_id := u02; betree_internal_pivot := u2; - betree_internal_left := b12; betree_internal_right := b02|> ⇔ - u01 = u02 ∧ u1 = u2 ∧ b11 = b12 ∧ b01 = b02 - - [betree_internal_t_literal_nchotomy] Theorem - - ⊢ ∀b. ∃u0 u b1 b0. - b = - <|betree_internal_id := u0; betree_internal_pivot := u; - betree_internal_left := b1; betree_internal_right := b0|> - - [betree_internal_t_nchotomy] Theorem - - ⊢ ∀bb. ∃u0 u b b0. bb = betree_internal_t u0 u b b0 - - [betree_internal_t_updates_eq_literal] Theorem - - ⊢ ∀b u0 u b1 b0. - b with - <|betree_internal_id := u0; betree_internal_pivot := u; - betree_internal_left := b1; betree_internal_right := b0|> = - <|betree_internal_id := u0; betree_internal_pivot := u; - betree_internal_left := b1; betree_internal_right := b0|> - - [betree_leaf_t_11] Theorem - - ⊢ ∀a0 a1 a0' a1'. - betree_leaf_t a0 a1 = betree_leaf_t a0' a1' ⇔ a0 = a0' ∧ a1 = a1' - - [betree_leaf_t_Axiom] Theorem - - ⊢ ∀f. ∃fn. ∀a0 a1. fn (betree_leaf_t a0 a1) = f a0 a1 - - [betree_leaf_t_accessors] Theorem - - ⊢ (∀u u0. (betree_leaf_t u u0).betree_leaf_id = u) ∧ - ∀u u0. (betree_leaf_t u u0).betree_leaf_size = u0 - - [betree_leaf_t_accfupds] Theorem - - ⊢ (∀f b. - (b with betree_leaf_size updated_by f).betree_leaf_id = - b.betree_leaf_id) ∧ - (∀f b. - (b with betree_leaf_id updated_by f).betree_leaf_size = - b.betree_leaf_size) ∧ - (∀f b. - (b with betree_leaf_id updated_by f).betree_leaf_id = - f b.betree_leaf_id) ∧ - ∀f b. - (b with betree_leaf_size updated_by f).betree_leaf_size = - f b.betree_leaf_size - - [betree_leaf_t_case_cong] Theorem - - ⊢ ∀M M' f. - M = M' ∧ (∀a0 a1. M' = betree_leaf_t a0 a1 ⇒ f a0 a1 = f' a0 a1) ⇒ - betree_leaf_t_CASE M f = betree_leaf_t_CASE M' f' - - [betree_leaf_t_case_eq] Theorem - - ⊢ betree_leaf_t_CASE x f = v ⇔ - ∃u u0. x = betree_leaf_t u u0 ∧ f u u0 = v - - [betree_leaf_t_component_equality] Theorem - - ⊢ ∀b1 b2. - b1 = b2 ⇔ - b1.betree_leaf_id = b2.betree_leaf_id ∧ - b1.betree_leaf_size = b2.betree_leaf_size - - [betree_leaf_t_fn_updates] Theorem - - ⊢ (∀f u u0. - betree_leaf_t u u0 with betree_leaf_id updated_by f = - betree_leaf_t (f u) u0) ∧ - ∀f u u0. - betree_leaf_t u u0 with betree_leaf_size updated_by f = - betree_leaf_t u (f u0) - - [betree_leaf_t_fupdcanon] Theorem - - ⊢ ∀g f b. - b with - <|betree_leaf_size updated_by f; betree_leaf_id updated_by g|> = - b with - <|betree_leaf_id updated_by g; betree_leaf_size updated_by f|> - - [betree_leaf_t_fupdcanon_comp] Theorem - - ⊢ (∀g f. - betree_leaf_size_fupd f ∘ betree_leaf_id_fupd g = - betree_leaf_id_fupd g ∘ betree_leaf_size_fupd f) ∧ - ∀h g f. - betree_leaf_size_fupd f ∘ betree_leaf_id_fupd g ∘ h = - betree_leaf_id_fupd g ∘ betree_leaf_size_fupd f ∘ h - - [betree_leaf_t_fupdfupds] Theorem - - ⊢ (∀g f b. - b with - <|betree_leaf_id updated_by f; betree_leaf_id updated_by g|> = - b with betree_leaf_id updated_by f ∘ g) ∧ - ∀g f b. - b with - <|betree_leaf_size updated_by f; betree_leaf_size updated_by g|> = - b with betree_leaf_size updated_by f ∘ g - - [betree_leaf_t_fupdfupds_comp] Theorem - - ⊢ ((∀g f. - betree_leaf_id_fupd f ∘ betree_leaf_id_fupd g = - betree_leaf_id_fupd (f ∘ g)) ∧ - ∀h g f. - betree_leaf_id_fupd f ∘ betree_leaf_id_fupd g ∘ h = - betree_leaf_id_fupd (f ∘ g) ∘ h) ∧ - (∀g f. - betree_leaf_size_fupd f ∘ betree_leaf_size_fupd g = - betree_leaf_size_fupd (f ∘ g)) ∧ - ∀h g f. - betree_leaf_size_fupd f ∘ betree_leaf_size_fupd g ∘ h = - betree_leaf_size_fupd (f ∘ g) ∘ h - - [betree_leaf_t_induction] Theorem - - ⊢ ∀P. (∀u u0. P (betree_leaf_t u u0)) ⇒ ∀b. P b - - [betree_leaf_t_literal_11] Theorem - - ⊢ ∀u01 u1 u02 u2. - <|betree_leaf_id := u01; betree_leaf_size := u1|> = - <|betree_leaf_id := u02; betree_leaf_size := u2|> ⇔ - u01 = u02 ∧ u1 = u2 - - [betree_leaf_t_literal_nchotomy] Theorem - - ⊢ ∀b. ∃u0 u. b = <|betree_leaf_id := u0; betree_leaf_size := u|> - - [betree_leaf_t_nchotomy] Theorem - - ⊢ ∀bb. ∃u u0. bb = betree_leaf_t u u0 - - [betree_leaf_t_updates_eq_literal] Theorem - - ⊢ ∀b u0 u. - b with <|betree_leaf_id := u0; betree_leaf_size := u|> = - <|betree_leaf_id := u0; betree_leaf_size := u|> - - [betree_list_t_11] Theorem - - ⊢ ∀a0 a1 a0' a1'. - BetreeListCons a0 a1 = BetreeListCons a0' a1' ⇔ - a0 = a0' ∧ a1 = a1' - - [betree_list_t_Axiom] Theorem - - ⊢ ∀f0 f1. ∃fn. - (∀a0 a1. fn (BetreeListCons a0 a1) = f0 a0 a1 (fn a1)) ∧ - fn BetreeListNil = f1 - - [betree_list_t_case_cong] Theorem - - ⊢ ∀M M' f v. - M = M' ∧ - (∀a0 a1. M' = BetreeListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ - (M' = BetreeListNil ⇒ v = v') ⇒ - betree_list_t_CASE M f v = betree_list_t_CASE M' f' v' - - [betree_list_t_case_eq] Theorem - - ⊢ betree_list_t_CASE x f v = v' ⇔ - (∃t b. x = BetreeListCons t b ∧ f t b = v') ∨ - x = BetreeListNil ∧ v = v' - - [betree_list_t_distinct] Theorem - - ⊢ ∀a1 a0. BetreeListCons a0 a1 ≠ BetreeListNil - - [betree_list_t_induction] Theorem - - ⊢ ∀P. (∀b. P b ⇒ ∀t. P (BetreeListCons t b)) ∧ P BetreeListNil ⇒ - ∀b. P b - - [betree_list_t_nchotomy] Theorem - - ⊢ ∀bb. (∃t b. bb = BetreeListCons t b) ∨ bb = BetreeListNil - - [betree_message_t_11] Theorem - - ⊢ (∀a a'. BetreeMessageInsert a = BetreeMessageInsert a' ⇔ a = a') ∧ - ∀a a'. BetreeMessageUpsert a = BetreeMessageUpsert a' ⇔ a = a' - - [betree_message_t_Axiom] Theorem - - ⊢ ∀f0 f1 f2. ∃fn. - (∀a. fn (BetreeMessageInsert a) = f0 a) ∧ - fn BetreeMessageDelete = f1 ∧ - ∀a. fn (BetreeMessageUpsert a) = f2 a - - [betree_message_t_case_cong] Theorem - - ⊢ ∀M M' f v f1. - M = M' ∧ (∀a. M' = BetreeMessageInsert a ⇒ f a = f' a) ∧ - (M' = BetreeMessageDelete ⇒ v = v') ∧ - (∀a. M' = BetreeMessageUpsert a ⇒ f1 a = f1' a) ⇒ - betree_message_t_CASE M f v f1 = - betree_message_t_CASE M' f' v' f1' - - [betree_message_t_case_eq] Theorem - - ⊢ betree_message_t_CASE x f v f1 = v' ⇔ - (∃u. x = BetreeMessageInsert u ∧ f u = v') ∨ - x = BetreeMessageDelete ∧ v = v' ∨ - ∃b. x = BetreeMessageUpsert b ∧ f1 b = v' - - [betree_message_t_distinct] Theorem - - ⊢ (∀a. BetreeMessageInsert a ≠ BetreeMessageDelete) ∧ - (∀a' a. BetreeMessageInsert a ≠ BetreeMessageUpsert a') ∧ - ∀a. BetreeMessageDelete ≠ BetreeMessageUpsert a - - [betree_message_t_induction] Theorem - - ⊢ ∀P. (∀u. P (BetreeMessageInsert u)) ∧ P BetreeMessageDelete ∧ - (∀b. P (BetreeMessageUpsert b)) ⇒ - ∀b. P b - - [betree_message_t_nchotomy] Theorem - - ⊢ ∀bb. - (∃u. bb = BetreeMessageInsert u) ∨ bb = BetreeMessageDelete ∨ - ∃b. bb = BetreeMessageUpsert b - - [betree_node_id_counter_t_11] Theorem - - ⊢ ∀a a'. - betree_node_id_counter_t a = betree_node_id_counter_t a' ⇔ a = a' - - [betree_node_id_counter_t_Axiom] Theorem - - ⊢ ∀f. ∃fn. ∀a. fn (betree_node_id_counter_t a) = f a - - [betree_node_id_counter_t_accessors] Theorem - - ⊢ ∀u. (betree_node_id_counter_t u). - betree_node_id_counter_next_node_id = - u - - [betree_node_id_counter_t_accfupds] Theorem - - ⊢ ∀f b. - (b with betree_node_id_counter_next_node_id updated_by f). - betree_node_id_counter_next_node_id = - f b.betree_node_id_counter_next_node_id - - [betree_node_id_counter_t_case_cong] Theorem - - ⊢ ∀M M' f. - M = M' ∧ (∀a. M' = betree_node_id_counter_t a ⇒ f a = f' a) ⇒ - betree_node_id_counter_t_CASE M f = - betree_node_id_counter_t_CASE M' f' - - [betree_node_id_counter_t_case_eq] Theorem - - ⊢ betree_node_id_counter_t_CASE x f = v ⇔ - ∃u. x = betree_node_id_counter_t u ∧ f u = v - - [betree_node_id_counter_t_component_equality] Theorem - - ⊢ ∀b1 b2. - b1 = b2 ⇔ - b1.betree_node_id_counter_next_node_id = - b2.betree_node_id_counter_next_node_id - - [betree_node_id_counter_t_fn_updates] Theorem - - ⊢ ∀f u. - betree_node_id_counter_t u with - betree_node_id_counter_next_node_id updated_by f = - betree_node_id_counter_t (f u) - - [betree_node_id_counter_t_fupdfupds] Theorem - - ⊢ ∀g f b. - b with - <|betree_node_id_counter_next_node_id updated_by f; - betree_node_id_counter_next_node_id updated_by g|> = - b with betree_node_id_counter_next_node_id updated_by f ∘ g - - [betree_node_id_counter_t_fupdfupds_comp] Theorem - - ⊢ (∀g f. - betree_node_id_counter_next_node_id_fupd f ∘ - betree_node_id_counter_next_node_id_fupd g = - betree_node_id_counter_next_node_id_fupd (f ∘ g)) ∧ - ∀h g f. - betree_node_id_counter_next_node_id_fupd f ∘ - betree_node_id_counter_next_node_id_fupd g ∘ h = - betree_node_id_counter_next_node_id_fupd (f ∘ g) ∘ h - - [betree_node_id_counter_t_induction] Theorem - - ⊢ ∀P. (∀u. P (betree_node_id_counter_t u)) ⇒ ∀b. P b - - [betree_node_id_counter_t_literal_11] Theorem - - ⊢ ∀u1 u2. - <|betree_node_id_counter_next_node_id := u1|> = - <|betree_node_id_counter_next_node_id := u2|> ⇔ u1 = u2 - - [betree_node_id_counter_t_literal_nchotomy] Theorem - - ⊢ ∀b. ∃u. b = <|betree_node_id_counter_next_node_id := u|> - - [betree_node_id_counter_t_nchotomy] Theorem - - ⊢ ∀bb. ∃u. bb = betree_node_id_counter_t u - - [betree_node_id_counter_t_updates_eq_literal] Theorem - - ⊢ ∀b u. - b with betree_node_id_counter_next_node_id := u = - <|betree_node_id_counter_next_node_id := u|> - - [betree_node_t_11] Theorem - - ⊢ (∀a a'. BetreeNodeInternal a = BetreeNodeInternal a' ⇔ a = a') ∧ - ∀a a'. BetreeNodeLeaf a = BetreeNodeLeaf a' ⇔ a = a' - - [betree_node_t_Axiom] Theorem - - ⊢ ∀f0 f1 f2. ∃fn0 fn1. - (∀a0 a1 a2 a3. - fn0 (betree_internal_t a0 a1 a2 a3) = - f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧ - (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧ - ∀a. fn1 (BetreeNodeLeaf a) = f2 a - - [betree_node_t_case_cong] Theorem - - ⊢ ∀M M' f f1. - M = M' ∧ (∀a. M' = BetreeNodeInternal a ⇒ f a = f' a) ∧ - (∀a. M' = BetreeNodeLeaf a ⇒ f1 a = f1' a) ⇒ - betree_node_t_CASE M f f1 = betree_node_t_CASE M' f' f1' - - [betree_node_t_case_eq] Theorem - - ⊢ betree_node_t_CASE x f f1 = v ⇔ - (∃b. x = BetreeNodeInternal b ∧ f b = v) ∨ - ∃b. x = BetreeNodeLeaf b ∧ f1 b = v - - [betree_node_t_distinct] Theorem - - ⊢ ∀a' a. BetreeNodeInternal a ≠ BetreeNodeLeaf a' - - [betree_node_t_induction] Theorem - - ⊢ ∀P0 P1. - (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧ - (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧ - (∀b. P1 (BetreeNodeLeaf b)) ⇒ - (∀b. P0 b) ∧ ∀b. P1 b - - [betree_node_t_nchotomy] Theorem - - ⊢ ∀bb. (∃b. bb = BetreeNodeInternal b) ∨ ∃b. bb = BetreeNodeLeaf b - - [betree_params_t_11] Theorem - - ⊢ ∀a0 a1 a0' a1'. - betree_params_t a0 a1 = betree_params_t a0' a1' ⇔ - a0 = a0' ∧ a1 = a1' - - [betree_params_t_Axiom] Theorem - - ⊢ ∀f. ∃fn. ∀a0 a1. fn (betree_params_t a0 a1) = f a0 a1 - - [betree_params_t_accessors] Theorem - - ⊢ (∀u u0. (betree_params_t u u0).betree_params_min_flush_size = u) ∧ - ∀u u0. (betree_params_t u u0).betree_params_split_size = u0 - - [betree_params_t_accfupds] Theorem - - ⊢ (∀f b. - (b with betree_params_split_size updated_by f). - betree_params_min_flush_size = - b.betree_params_min_flush_size) ∧ - (∀f b. - (b with betree_params_min_flush_size updated_by f). - betree_params_split_size = - b.betree_params_split_size) ∧ - (∀f b. - (b with betree_params_min_flush_size updated_by f). - betree_params_min_flush_size = - f b.betree_params_min_flush_size) ∧ - ∀f b. - (b with betree_params_split_size updated_by f). - betree_params_split_size = - f b.betree_params_split_size - - [betree_params_t_case_cong] Theorem - - ⊢ ∀M M' f. - M = M' ∧ - (∀a0 a1. M' = betree_params_t a0 a1 ⇒ f a0 a1 = f' a0 a1) ⇒ - betree_params_t_CASE M f = betree_params_t_CASE M' f' - - [betree_params_t_case_eq] Theorem - - ⊢ betree_params_t_CASE x f = v ⇔ - ∃u u0. x = betree_params_t u u0 ∧ f u u0 = v - - [betree_params_t_component_equality] Theorem - - ⊢ ∀b1 b2. - b1 = b2 ⇔ - b1.betree_params_min_flush_size = b2.betree_params_min_flush_size ∧ - b1.betree_params_split_size = b2.betree_params_split_size - - [betree_params_t_fn_updates] Theorem - - ⊢ (∀f u u0. - betree_params_t u u0 with - betree_params_min_flush_size updated_by f = - betree_params_t (f u) u0) ∧ - ∀f u u0. - betree_params_t u u0 with betree_params_split_size updated_by f = - betree_params_t u (f u0) - - [betree_params_t_fupdcanon] Theorem - - ⊢ ∀g f b. - b with - <|betree_params_split_size updated_by f; - betree_params_min_flush_size updated_by g|> = - b with - <|betree_params_min_flush_size updated_by g; - betree_params_split_size updated_by f|> - - [betree_params_t_fupdcanon_comp] Theorem - - ⊢ (∀g f. - betree_params_split_size_fupd f ∘ - betree_params_min_flush_size_fupd g = - betree_params_min_flush_size_fupd g ∘ - betree_params_split_size_fupd f) ∧ - ∀h g f. - betree_params_split_size_fupd f ∘ - betree_params_min_flush_size_fupd g ∘ h = - betree_params_min_flush_size_fupd g ∘ - betree_params_split_size_fupd f ∘ h - - [betree_params_t_fupdfupds] Theorem - - ⊢ (∀g f b. - b with - <|betree_params_min_flush_size updated_by f; - betree_params_min_flush_size updated_by g|> = - b with betree_params_min_flush_size updated_by f ∘ g) ∧ - ∀g f b. - b with - <|betree_params_split_size updated_by f; - betree_params_split_size updated_by g|> = - b with betree_params_split_size updated_by f ∘ g - - [betree_params_t_fupdfupds_comp] Theorem - - ⊢ ((∀g f. - betree_params_min_flush_size_fupd f ∘ - betree_params_min_flush_size_fupd g = - betree_params_min_flush_size_fupd (f ∘ g)) ∧ - ∀h g f. - betree_params_min_flush_size_fupd f ∘ - betree_params_min_flush_size_fupd g ∘ h = - betree_params_min_flush_size_fupd (f ∘ g) ∘ h) ∧ - (∀g f. - betree_params_split_size_fupd f ∘ - betree_params_split_size_fupd g = - betree_params_split_size_fupd (f ∘ g)) ∧ - ∀h g f. - betree_params_split_size_fupd f ∘ - betree_params_split_size_fupd g ∘ h = - betree_params_split_size_fupd (f ∘ g) ∘ h - - [betree_params_t_induction] Theorem - - ⊢ ∀P. (∀u u0. P (betree_params_t u u0)) ⇒ ∀b. P b - - [betree_params_t_literal_11] Theorem - - ⊢ ∀u01 u1 u02 u2. - <|betree_params_min_flush_size := u01; - betree_params_split_size := u1|> = - <|betree_params_min_flush_size := u02; - betree_params_split_size := u2|> ⇔ u01 = u02 ∧ u1 = u2 - - [betree_params_t_literal_nchotomy] Theorem - - ⊢ ∀b. ∃u0 u. - b = - <|betree_params_min_flush_size := u0; - betree_params_split_size := u|> - - [betree_params_t_nchotomy] Theorem - - ⊢ ∀bb. ∃u u0. bb = betree_params_t u u0 - - [betree_params_t_updates_eq_literal] Theorem - - ⊢ ∀b u0 u. - b with - <|betree_params_min_flush_size := u0; - betree_params_split_size := u|> = - <|betree_params_min_flush_size := u0; - betree_params_split_size := u|> - - [betree_upsert_fun_state_t_11] Theorem - - ⊢ (∀a a'. - BetreeUpsertFunStateAdd a = BetreeUpsertFunStateAdd a' ⇔ a = a') ∧ - ∀a a'. - BetreeUpsertFunStateSub a = BetreeUpsertFunStateSub a' ⇔ a = a' - - [betree_upsert_fun_state_t_Axiom] Theorem - - ⊢ ∀f0 f1. ∃fn. - (∀a. fn (BetreeUpsertFunStateAdd a) = f0 a) ∧ - ∀a. fn (BetreeUpsertFunStateSub a) = f1 a - - [betree_upsert_fun_state_t_case_cong] Theorem - - ⊢ ∀M M' f f1. - M = M' ∧ (∀a. M' = BetreeUpsertFunStateAdd a ⇒ f a = f' a) ∧ - (∀a. M' = BetreeUpsertFunStateSub a ⇒ f1 a = f1' a) ⇒ - betree_upsert_fun_state_t_CASE M f f1 = - betree_upsert_fun_state_t_CASE M' f' f1' - - [betree_upsert_fun_state_t_case_eq] Theorem - - ⊢ betree_upsert_fun_state_t_CASE x f f1 = v ⇔ - (∃u. x = BetreeUpsertFunStateAdd u ∧ f u = v) ∨ - ∃u. x = BetreeUpsertFunStateSub u ∧ f1 u = v - - [betree_upsert_fun_state_t_distinct] Theorem - - ⊢ ∀a' a. BetreeUpsertFunStateAdd a ≠ BetreeUpsertFunStateSub a' - - [betree_upsert_fun_state_t_induction] Theorem - - ⊢ ∀P. (∀u. P (BetreeUpsertFunStateAdd u)) ∧ - (∀u. P (BetreeUpsertFunStateSub u)) ⇒ - ∀b. P b - - [betree_upsert_fun_state_t_nchotomy] Theorem - - ⊢ ∀bb. - (∃u. bb = BetreeUpsertFunStateAdd u) ∨ - ∃u. bb = BetreeUpsertFunStateSub u - - [datatype_betree_be_tree_t] Theorem - - ⊢ DATATYPE - (record betree_be_tree_t betree_be_tree_params - betree_be_tree_node_id_cnt betree_be_tree_root) - - [datatype_betree_internal_t] Theorem - - ⊢ DATATYPE - (record betree_internal_t betree_internal_id - betree_internal_pivot betree_internal_left - betree_internal_right ∧ - betree_node_t BetreeNodeInternal BetreeNodeLeaf) - - [datatype_betree_leaf_t] Theorem - - ⊢ DATATYPE (record betree_leaf_t betree_leaf_id betree_leaf_size) - - [datatype_betree_list_t] Theorem - - ⊢ DATATYPE (betree_list_t BetreeListCons BetreeListNil) - - [datatype_betree_message_t] Theorem - - ⊢ DATATYPE - (betree_message_t BetreeMessageInsert BetreeMessageDelete - BetreeMessageUpsert) - - [datatype_betree_node_id_counter_t] Theorem - - ⊢ DATATYPE - (record betree_node_id_counter_t - betree_node_id_counter_next_node_id) - - [datatype_betree_params_t] Theorem - - ⊢ DATATYPE - (record betree_params_t betree_params_min_flush_size - betree_params_split_size) - - [datatype_betree_upsert_fun_state_t] Theorem - - ⊢ DATATYPE - (betree_upsert_fun_state_t BetreeUpsertFunStateAdd - BetreeUpsertFunStateSub) - - -*) -end diff --git a/tests/hol4/betree/betree_FunsScript.sml b/tests/hol4/betree/betree_FunsScript.sml new file mode 100644 index 00000000..49bcb446 --- /dev/null +++ b/tests/hol4/betree/betree_FunsScript.sml @@ -0,0 +1,1212 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: function definitions *) +open primitivesLib divDefLib +open betree_TypesTheory betree_OpaqueTheory + +val _ = new_theory "betree_Funs" + + +val betree_load_internal_node_fwd_def = Define ‘ + (** [betree::betree::load_internal_node]: forward function *) + betree_load_internal_node_fwd + (id : u64) (st : state) : + (state # (u64 # betree_message_t) betree_list_t) result + = + betree_utils_load_internal_node_fwd id st +’ + +val betree_store_internal_node_fwd_def = Define ‘ + (** [betree::betree::store_internal_node]: forward function *) + betree_store_internal_node_fwd + (id : u64) (content : (u64 # betree_message_t) betree_list_t) (st : state) + : + (state # unit) result + = + do + (st0, _) <- betree_utils_store_internal_node_fwd id content st; + Return (st0, ()) + od +’ + +val betree_load_leaf_node_fwd_def = Define ‘ + (** [betree::betree::load_leaf_node]: forward function *) + betree_load_leaf_node_fwd + (id : u64) (st : state) : (state # (u64 # u64) betree_list_t) result = + betree_utils_load_leaf_node_fwd id st +’ + +val betree_store_leaf_node_fwd_def = Define ‘ + (** [betree::betree::store_leaf_node]: forward function *) + betree_store_leaf_node_fwd + (id : u64) (content : (u64 # u64) betree_list_t) (st : state) : + (state # unit) result + = + do + (st0, _) <- betree_utils_store_leaf_node_fwd id content st; + Return (st0, ()) + od +’ + +val betree_fresh_node_id_fwd_def = Define ‘ + (** [betree::betree::fresh_node_id]: forward function *) + betree_fresh_node_id_fwd (counter : u64) : u64 result = + do + _ <- u64_add counter (int_to_u64 1); + Return counter + od +’ + +val betree_fresh_node_id_back_def = Define ‘ + (** [betree::betree::fresh_node_id]: backward function 0 *) + betree_fresh_node_id_back (counter : u64) : u64 result = + u64_add counter (int_to_u64 1) +’ + +val betree_node_id_counter_new_fwd_def = Define ‘ + (** [betree::betree::NodeIdCounter::{0}::new]: forward function *) + betree_node_id_counter_new_fwd : betree_node_id_counter_t result = + Return (<| betree_node_id_counter_next_node_id := (int_to_u64 0) |>) +’ + +val betree_node_id_counter_fresh_id_fwd_def = Define ‘ + (** [betree::betree::NodeIdCounter::{0}::fresh_id]: forward function *) + betree_node_id_counter_fresh_id_fwd + (self : betree_node_id_counter_t) : u64 result = + do + _ <- u64_add self.betree_node_id_counter_next_node_id (int_to_u64 1); + Return self.betree_node_id_counter_next_node_id + od +’ + +val betree_node_id_counter_fresh_id_back_def = Define ‘ + (** [betree::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *) + betree_node_id_counter_fresh_id_back + (self : betree_node_id_counter_t) : betree_node_id_counter_t result = + do + i <- u64_add self.betree_node_id_counter_next_node_id (int_to_u64 1); + Return (<| betree_node_id_counter_next_node_id := i |>) + od +’ + +val betree_upsert_update_fwd_def = Define ‘ + (** [betree::betree::upsert_update]: forward function *) + betree_upsert_update_fwd + (prev : u64 option) (st : betree_upsert_fun_state_t) : u64 result = + (case prev of + | NONE => + (case st of + | BetreeUpsertFunStateAdd v => Return v + | BetreeUpsertFunStateSub i => Return (int_to_u64 0)) + | SOME prev0 => + (case st of + | BetreeUpsertFunStateAdd v => + do + margin <- u64_sub core_u64_max prev0; + if u64_ge margin v then u64_add prev0 v else Return core_u64_max + od + | BetreeUpsertFunStateSub v => + if u64_ge prev0 v then u64_sub prev0 v else Return (int_to_u64 0))) +’ + +val [betree_list_len_fwd_def] = DefineDiv ‘ + (** [betree::betree::List::{1}::len]: forward function *) + betree_list_len_fwd (self : 't betree_list_t) : u64 result = + (case self of + | BetreeListCons t tl => + do + i <- betree_list_len_fwd tl; + u64_add (int_to_u64 1) i + od + | BetreeListNil => Return (int_to_u64 0)) +’ + +val [betree_list_split_at_fwd_def] = DefineDiv ‘ + (** [betree::betree::List::{1}::split_at]: forward function *) + betree_list_split_at_fwd + (self : 't betree_list_t) (n : u64) : + ('t betree_list_t # 't betree_list_t) result + = + if n = int_to_u64 0 + then Return (BetreeListNil, self) + else + (case self of + | BetreeListCons hd tl => + do + i <- u64_sub n (int_to_u64 1); + p <- betree_list_split_at_fwd tl i; + let (ls0, ls1) = p in let l = ls0 in Return (BetreeListCons hd l, ls1) + od + | BetreeListNil => Fail Failure) +’ + +val betree_list_push_front_fwd_back_def = Define ‘ + (** [betree::betree::List::{1}::push_front]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) + betree_list_push_front_fwd_back + (self : 't betree_list_t) (x : 't) : 't betree_list_t result = + let tl = mem_replace_fwd self BetreeListNil in + let l = tl in + Return (BetreeListCons x l) +’ + +val betree_list_pop_front_fwd_def = Define ‘ + (** [betree::betree::List::{1}::pop_front]: forward function *) + betree_list_pop_front_fwd (self : 't betree_list_t) : 't result = + let ls = mem_replace_fwd self BetreeListNil in + (case ls of + | BetreeListCons x tl => Return x + | BetreeListNil => Fail Failure) +’ + +val betree_list_pop_front_back_def = Define ‘ + (** [betree::betree::List::{1}::pop_front]: backward function 0 *) + betree_list_pop_front_back + (self : 't betree_list_t) : 't betree_list_t result = + let ls = mem_replace_fwd self BetreeListNil in + (case ls of + | BetreeListCons x tl => Return tl + | BetreeListNil => Fail Failure) +’ + +val betree_list_hd_fwd_def = Define ‘ + (** [betree::betree::List::{1}::hd]: forward function *) + betree_list_hd_fwd (self : 't betree_list_t) : 't result = + (case self of + | BetreeListCons hd l => Return hd + | BetreeListNil => Fail Failure) +’ + +val betree_list_head_has_key_fwd_def = Define ‘ + (** [betree::betree::List::{2}::head_has_key]: forward function *) + betree_list_head_has_key_fwd + (self : (u64 # 't) betree_list_t) (key : u64) : bool result = + (case self of + | BetreeListCons hd l => let (i, _) = hd in Return (i = key) + | BetreeListNil => Return F) +’ + +val [betree_list_partition_at_pivot_fwd_def] = DefineDiv ‘ + (** [betree::betree::List::{2}::partition_at_pivot]: forward function *) + betree_list_partition_at_pivot_fwd + (self : (u64 # 't) betree_list_t) (pivot : u64) : + ((u64 # 't) betree_list_t # (u64 # 't) betree_list_t) result + = + (case self of + | BetreeListCons hd tl => + let (i, t) = hd in + if u64_ge i pivot + then Return (BetreeListNil, BetreeListCons (i, t) tl) + else ( + do + p <- betree_list_partition_at_pivot_fwd tl pivot; + let (ls0, ls1) = p in + let l = ls0 in + Return (BetreeListCons (i, t) l, ls1) + od) + | BetreeListNil => Return (BetreeListNil, BetreeListNil)) +’ + +val betree_leaf_split_fwd_def = Define ‘ + (** [betree::betree::Leaf::{3}::split]: forward function *) + betree_leaf_split_fwd + (self : betree_leaf_t) (content : (u64 # u64) betree_list_t) + (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) + (st : state) : + (state # betree_internal_t) result + = + do + p <- betree_list_split_at_fwd content params.betree_params_split_size; + let (content0, content1) = p in + do + p0 <- betree_list_hd_fwd content1; + let (pivot, _) = p0 in + do + id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; + node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt; + id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; + (st0, _) <- betree_store_leaf_node_fwd id0 content0 st; + (st1, _) <- betree_store_leaf_node_fwd id1 content1 st0; + let n = BetreeNodeLeaf + (<| + betree_leaf_id := id0; + betree_leaf_size := params.betree_params_split_size + |>) in + let n0 = BetreeNodeLeaf + (<| + betree_leaf_id := id1; + betree_leaf_size := params.betree_params_split_size + |>) in + Return (st1, + <| + betree_internal_id := self.betree_leaf_id; + betree_internal_pivot := pivot; + betree_internal_left := n; + betree_internal_right := n0 + |>) + od + od + od +’ + +val betree_leaf_split_back_def = Define ‘ + (** [betree::betree::Leaf::{3}::split]: backward function 2 *) + betree_leaf_split_back + (self : betree_leaf_t) (content : (u64 # u64) betree_list_t) + (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) + (st : state) : + betree_node_id_counter_t result + = + do + p <- betree_list_split_at_fwd content params.betree_params_split_size; + let (content0, content1) = p in + do + _ <- betree_list_hd_fwd content1; + id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; + node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt; + id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; + (st0, _) <- betree_store_leaf_node_fwd id0 content0 st; + _ <- betree_store_leaf_node_fwd id1 content1 st0; + betree_node_id_counter_fresh_id_back node_id_cnt0 + od + od +’ + +val [betree_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::lookup_first_message_for_key]: forward function *) + betree_node_lookup_first_message_for_key_fwd + (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) : + (u64 # betree_message_t) betree_list_t result + = + (case msgs of + | BetreeListCons x next_msgs => + let (i, m) = x in + if u64_ge i key + then Return (BetreeListCons (i, m) next_msgs) + else betree_node_lookup_first_message_for_key_fwd key next_msgs + | BetreeListNil => Return BetreeListNil) +’ + +val [betree_node_lookup_first_message_for_key_back_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *) + betree_node_lookup_first_message_for_key_back + (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) + (ret : (u64 # betree_message_t) betree_list_t) : + (u64 # betree_message_t) betree_list_t result + = + (case msgs of + | BetreeListCons x next_msgs => + let (i, m) = x in + if u64_ge i key + then Return ret + else ( + do + next_msgs0 <- + betree_node_lookup_first_message_for_key_back key next_msgs ret; + Return (BetreeListCons (i, m) next_msgs0) + od) + | BetreeListNil => Return ret) +’ + +val [betree_node_apply_upserts_fwd_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::apply_upserts]: forward function *) + betree_node_apply_upserts_fwd + (msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option) + (key : u64) (st : state) : + (state # u64) result + = + do + b <- betree_list_head_has_key_fwd msgs key; + if b + then ( + do + msg <- betree_list_pop_front_fwd msgs; + let (_, m) = msg in + (case m of + | BetreeMessageInsert i => Fail Failure + | BetreeMessageDelete => Fail Failure + | BetreeMessageUpsert s => + do + v <- betree_upsert_update_fwd prev s; + msgs0 <- betree_list_pop_front_back msgs; + betree_node_apply_upserts_fwd msgs0 (SOME v) key st + od) + od) + else ( + do + (st0, v) <- core_option_option_unwrap_fwd prev st; + _ <- betree_list_push_front_fwd_back msgs (key, BetreeMessageInsert v); + Return (st0, v) + od) + od +’ + +val [betree_node_apply_upserts_back_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::apply_upserts]: backward function 0 *) + betree_node_apply_upserts_back + (msgs : (u64 # betree_message_t) betree_list_t) (prev : u64 option) + (key : u64) (st : state) : + (u64 # betree_message_t) betree_list_t result + = + do + b <- betree_list_head_has_key_fwd msgs key; + if b + then ( + do + msg <- betree_list_pop_front_fwd msgs; + let (_, m) = msg in + (case m of + | BetreeMessageInsert i => Fail Failure + | BetreeMessageDelete => Fail Failure + | BetreeMessageUpsert s => + do + v <- betree_upsert_update_fwd prev s; + msgs0 <- betree_list_pop_front_back msgs; + betree_node_apply_upserts_back msgs0 (SOME v) key st + od) + od) + else ( + do + (_, v) <- core_option_option_unwrap_fwd prev st; + betree_list_push_front_fwd_back msgs (key, BetreeMessageInsert v) + od) + od +’ + +val [betree_node_lookup_in_bindings_fwd_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::lookup_in_bindings]: forward function *) + betree_node_lookup_in_bindings_fwd + (key : u64) (bindings : (u64 # u64) betree_list_t) : u64 option result = + (case bindings of + | BetreeListCons hd tl => + let (i, i0) = hd in + if i = key + then Return (SOME i0) + else + if u64_gt i key + then Return NONE + else betree_node_lookup_in_bindings_fwd key tl + | BetreeListNil => Return NONE) +’ + +val [betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def, betree_node_lookup_fwd_def, betree_node_lookup_back_def] = DefineDiv ‘ + (** [betree::betree::Internal::{4}::lookup_in_children]: forward function *) + (betree_internal_lookup_in_children_fwd + (self : betree_internal_t) (key : u64) (st : state) : + (state # u64 option) result + = + if u64_lt key self.betree_internal_pivot + then betree_node_lookup_fwd self.betree_internal_left key st + else betree_node_lookup_fwd self.betree_internal_right key st) + /\ + + (** [betree::betree::Internal::{4}::lookup_in_children]: backward function 0 *) + (betree_internal_lookup_in_children_back + (self : betree_internal_t) (key : u64) (st : state) : + betree_internal_t result + = + if u64_lt key self.betree_internal_pivot + then ( + do + n <- betree_node_lookup_back self.betree_internal_left key st; + Return (self with <| betree_internal_left := n |>) + od) + else ( + do + n <- betree_node_lookup_back self.betree_internal_right key st; + Return (self with <| betree_internal_right := n |>) + od)) + /\ + + (** [betree::betree::Node::{5}::lookup]: forward function *) + (betree_node_lookup_fwd + (self : betree_node_t) (key : u64) (st : state) : + (state # u64 option) result + = + (case self of + | BetreeNodeInternal node => + do + (st0, msgs) <- betree_load_internal_node_fwd node.betree_internal_id st; + pending <- betree_node_lookup_first_message_for_key_fwd key msgs; + (case pending of + | BetreeListCons p l => + let (k, msg) = p in + if k <> key + then ( + do + (st1, opt) <- betree_internal_lookup_in_children_fwd node key st0; + _ <- + betree_node_lookup_first_message_for_key_back key msgs + (BetreeListCons (k, msg) l); + Return (st1, opt) + od) + else + (case msg of + | BetreeMessageInsert v => + do + _ <- + betree_node_lookup_first_message_for_key_back key msgs + (BetreeListCons (k, BetreeMessageInsert v) l); + Return (st0, SOME v) + od + | BetreeMessageDelete => + do + _ <- + betree_node_lookup_first_message_for_key_back key msgs + (BetreeListCons (k, BetreeMessageDelete) l); + Return (st0, NONE) + od + | BetreeMessageUpsert ufs => + do + (st1, v) <- betree_internal_lookup_in_children_fwd node key st0; + (st2, v0) <- + betree_node_apply_upserts_fwd (BetreeListCons (k, + BetreeMessageUpsert ufs) l) v key st1; + node0 <- betree_internal_lookup_in_children_back node key st0; + pending0 <- + betree_node_apply_upserts_back (BetreeListCons (k, + BetreeMessageUpsert ufs) l) v key st1; + msgs0 <- + betree_node_lookup_first_message_for_key_back key msgs pending0; + (st3, _) <- + betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2; + Return (st3, SOME v0) + od) + | BetreeListNil => + do + (st1, opt) <- betree_internal_lookup_in_children_fwd node key st0; + _ <- + betree_node_lookup_first_message_for_key_back key msgs BetreeListNil; + Return (st1, opt) + od) + od + | BetreeNodeLeaf node => + do + (st0, bindings) <- betree_load_leaf_node_fwd node.betree_leaf_id st; + opt <- betree_node_lookup_in_bindings_fwd key bindings; + Return (st0, opt) + od)) + /\ + + (** [betree::betree::Node::{5}::lookup]: backward function 0 *) + betree_node_lookup_back + (self : betree_node_t) (key : u64) (st : state) : betree_node_t result = + (case self of + | BetreeNodeInternal node => + do + (st0, msgs) <- betree_load_internal_node_fwd node.betree_internal_id st; + pending <- betree_node_lookup_first_message_for_key_fwd key msgs; + (case pending of + | BetreeListCons p l => + let (k, msg) = p in + if k <> key + then ( + do + _ <- + betree_node_lookup_first_message_for_key_back key msgs + (BetreeListCons (k, msg) l); + node0 <- betree_internal_lookup_in_children_back node key st0; + Return (BetreeNodeInternal node0) + od) + else + (case msg of + | BetreeMessageInsert v => + do + _ <- + betree_node_lookup_first_message_for_key_back key msgs + (BetreeListCons (k, BetreeMessageInsert v) l); + Return (BetreeNodeInternal node) + od + | BetreeMessageDelete => + do + _ <- + betree_node_lookup_first_message_for_key_back key msgs + (BetreeListCons (k, BetreeMessageDelete) l); + Return (BetreeNodeInternal node) + od + | BetreeMessageUpsert ufs => + do + (st1, v) <- betree_internal_lookup_in_children_fwd node key st0; + (st2, _) <- + betree_node_apply_upserts_fwd (BetreeListCons (k, + BetreeMessageUpsert ufs) l) v key st1; + node0 <- betree_internal_lookup_in_children_back node key st0; + pending0 <- + betree_node_apply_upserts_back (BetreeListCons (k, + BetreeMessageUpsert ufs) l) v key st1; + msgs0 <- + betree_node_lookup_first_message_for_key_back key msgs pending0; + _ <- + betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2; + Return (BetreeNodeInternal node0) + od) + | BetreeListNil => + do + _ <- + betree_node_lookup_first_message_for_key_back key msgs BetreeListNil; + node0 <- betree_internal_lookup_in_children_back node key st0; + Return (BetreeNodeInternal node0) + od) + od + | BetreeNodeLeaf node => + do + (_, bindings) <- betree_load_leaf_node_fwd node.betree_leaf_id st; + _ <- betree_node_lookup_in_bindings_fwd key bindings; + Return (BetreeNodeLeaf node) + od) +’ + +val [betree_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) + betree_node_filter_messages_for_key_fwd_back + (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) : + (u64 # betree_message_t) betree_list_t result + = + (case msgs of + | BetreeListCons p l => + let (k, m) = p in + if k = key + then ( + do + msgs0 <- betree_list_pop_front_back (BetreeListCons (k, m) l); + betree_node_filter_messages_for_key_fwd_back key msgs0 + od) + else Return (BetreeListCons (k, m) l) + | BetreeListNil => Return BetreeListNil) +’ + +val [betree_node_lookup_first_message_after_key_fwd_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::lookup_first_message_after_key]: forward function *) + betree_node_lookup_first_message_after_key_fwd + (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) : + (u64 # betree_message_t) betree_list_t result + = + (case msgs of + | BetreeListCons p next_msgs => + let (k, m) = p in + if k = key + then betree_node_lookup_first_message_after_key_fwd key next_msgs + else Return (BetreeListCons (k, m) next_msgs) + | BetreeListNil => Return BetreeListNil) +’ + +val [betree_node_lookup_first_message_after_key_back_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *) + betree_node_lookup_first_message_after_key_back + (key : u64) (msgs : (u64 # betree_message_t) betree_list_t) + (ret : (u64 # betree_message_t) betree_list_t) : + (u64 # betree_message_t) betree_list_t result + = + (case msgs of + | BetreeListCons p next_msgs => + let (k, m) = p in + if k = key + then ( + do + next_msgs0 <- + betree_node_lookup_first_message_after_key_back key next_msgs ret; + Return (BetreeListCons (k, m) next_msgs0) + od) + else Return ret + | BetreeListNil => Return ret) +’ + +val betree_node_apply_to_internal_fwd_back_def = Define ‘ + (** [betree::betree::Node::{5}::apply_to_internal]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) + betree_node_apply_to_internal_fwd_back + (msgs : (u64 # betree_message_t) betree_list_t) (key : u64) + (new_msg : betree_message_t) : + (u64 # betree_message_t) betree_list_t result + = + do + msgs0 <- betree_node_lookup_first_message_for_key_fwd key msgs; + b <- betree_list_head_has_key_fwd msgs0 key; + if b + then + (case new_msg of + | BetreeMessageInsert i => + do + msgs1 <- betree_node_filter_messages_for_key_fwd_back key msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 (key, BetreeMessageInsert i); + betree_node_lookup_first_message_for_key_back key msgs msgs2 + od + | BetreeMessageDelete => + do + msgs1 <- betree_node_filter_messages_for_key_fwd_back key msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 (key, BetreeMessageDelete); + betree_node_lookup_first_message_for_key_back key msgs msgs2 + od + | BetreeMessageUpsert s => + do + p <- betree_list_hd_fwd msgs0; + let (_, m) = p in + (case m of + | BetreeMessageInsert prev => + do + v <- betree_upsert_update_fwd (SOME prev) s; + msgs1 <- betree_list_pop_front_back msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 (key, BetreeMessageInsert v); + betree_node_lookup_first_message_for_key_back key msgs msgs2 + od + | BetreeMessageDelete => + do + v <- betree_upsert_update_fwd NONE s; + msgs1 <- betree_list_pop_front_back msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 (key, BetreeMessageInsert v); + betree_node_lookup_first_message_for_key_back key msgs msgs2 + od + | BetreeMessageUpsert ufs => + do + msgs1 <- betree_node_lookup_first_message_after_key_fwd key msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 (key, BetreeMessageUpsert s); + msgs3 <- + betree_node_lookup_first_message_after_key_back key msgs0 msgs2; + betree_node_lookup_first_message_for_key_back key msgs msgs3 + od) + od) + else ( + do + msgs1 <- betree_list_push_front_fwd_back msgs0 (key, new_msg); + betree_node_lookup_first_message_for_key_back key msgs msgs1 + od) + od +’ + +val [betree_node_apply_messages_to_internal_fwd_back_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) + betree_node_apply_messages_to_internal_fwd_back + (msgs : (u64 # betree_message_t) betree_list_t) + (new_msgs : (u64 # betree_message_t) betree_list_t) : + (u64 # betree_message_t) betree_list_t result + = + (case new_msgs of + | BetreeListCons new_msg new_msgs_tl => + let (i, m) = new_msg in + do + msgs0 <- betree_node_apply_to_internal_fwd_back msgs i m; + betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl + od + | BetreeListNil => Return msgs) +’ + +val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::lookup_mut_in_bindings]: forward function *) + betree_node_lookup_mut_in_bindings_fwd + (key : u64) (bindings : (u64 # u64) betree_list_t) : + (u64 # u64) betree_list_t result + = + (case bindings of + | BetreeListCons hd tl => + let (i, i0) = hd in + if u64_ge i key + then Return (BetreeListCons (i, i0) tl) + else betree_node_lookup_mut_in_bindings_fwd key tl + | BetreeListNil => Return BetreeListNil) +’ + +val [betree_node_lookup_mut_in_bindings_back_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *) + betree_node_lookup_mut_in_bindings_back + (key : u64) (bindings : (u64 # u64) betree_list_t) + (ret : (u64 # u64) betree_list_t) : + (u64 # u64) betree_list_t result + = + (case bindings of + | BetreeListCons hd tl => + let (i, i0) = hd in + if u64_ge i key + then Return ret + else ( + do + tl0 <- betree_node_lookup_mut_in_bindings_back key tl ret; + Return (BetreeListCons (i, i0) tl0) + od) + | BetreeListNil => Return ret) +’ + +val betree_node_apply_to_leaf_fwd_back_def = Define ‘ + (** [betree::betree::Node::{5}::apply_to_leaf]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) + betree_node_apply_to_leaf_fwd_back + (bindings : (u64 # u64) betree_list_t) (key : u64) + (new_msg : betree_message_t) : + (u64 # u64) betree_list_t result + = + do + bindings0 <- betree_node_lookup_mut_in_bindings_fwd key bindings; + b <- betree_list_head_has_key_fwd bindings0 key; + if b + then ( + do + hd <- betree_list_pop_front_fwd bindings0; + (case new_msg of + | BetreeMessageInsert v => + do + bindings1 <- betree_list_pop_front_back bindings0; + bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v); + betree_node_lookup_mut_in_bindings_back key bindings bindings2 + od + | BetreeMessageDelete => + do + bindings1 <- betree_list_pop_front_back bindings0; + betree_node_lookup_mut_in_bindings_back key bindings bindings1 + od + | BetreeMessageUpsert s => + let (_, i) = hd in + do + v <- betree_upsert_update_fwd (SOME i) s; + bindings1 <- betree_list_pop_front_back bindings0; + bindings2 <- betree_list_push_front_fwd_back bindings1 (key, v); + betree_node_lookup_mut_in_bindings_back key bindings bindings2 + od) + od) + else + (case new_msg of + | BetreeMessageInsert v => + do + bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v); + betree_node_lookup_mut_in_bindings_back key bindings bindings1 + od + | BetreeMessageDelete => + betree_node_lookup_mut_in_bindings_back key bindings bindings0 + | BetreeMessageUpsert s => + do + v <- betree_upsert_update_fwd NONE s; + bindings1 <- betree_list_push_front_fwd_back bindings0 (key, v); + betree_node_lookup_mut_in_bindings_back key bindings bindings1 + od) + od +’ + +val [betree_node_apply_messages_to_leaf_fwd_back_def] = DefineDiv ‘ + (** [betree::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) + betree_node_apply_messages_to_leaf_fwd_back + (bindings : (u64 # u64) betree_list_t) + (new_msgs : (u64 # betree_message_t) betree_list_t) : + (u64 # u64) betree_list_t result + = + (case new_msgs of + | BetreeListCons new_msg new_msgs_tl => + let (i, m) = new_msg in + do + bindings0 <- betree_node_apply_to_leaf_fwd_back bindings i m; + betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl + od + | BetreeListNil => Return bindings) +’ + +val [betree_internal_flush_fwd_def, betree_internal_flush_back_def, betree_node_apply_messages_fwd_def, betree_node_apply_messages_back_def] = DefineDiv ‘ + (** [betree::betree::Internal::{4}::flush]: forward function *) + (betree_internal_flush_fwd + (self : betree_internal_t) (params : betree_params_t) + (node_id_cnt : betree_node_id_counter_t) + (content : (u64 # betree_message_t) betree_list_t) (st : state) : + (state # (u64 # betree_message_t) betree_list_t) result + = + do + p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot; + let (msgs_left, msgs_right) = p in + do + len_left <- betree_list_len_fwd msgs_left; + if u64_ge len_left params.betree_params_min_flush_size + then ( + do + (st0, _) <- + betree_node_apply_messages_fwd self.betree_internal_left params + node_id_cnt msgs_left st; + (_, node_id_cnt0) <- + betree_node_apply_messages_back self.betree_internal_left params + node_id_cnt msgs_left st; + len_right <- betree_list_len_fwd msgs_right; + if u64_ge len_right params.betree_params_min_flush_size + then ( + do + (st1, _) <- + betree_node_apply_messages_fwd self.betree_internal_right params + node_id_cnt0 msgs_right st0; + _ <- + betree_node_apply_messages_back self.betree_internal_right params + node_id_cnt0 msgs_right st0; + Return (st1, BetreeListNil) + od) + else Return (st0, msgs_right) + od) + else ( + do + (st0, _) <- + betree_node_apply_messages_fwd self.betree_internal_right params + node_id_cnt msgs_right st; + _ <- + betree_node_apply_messages_back self.betree_internal_right params + node_id_cnt msgs_right st; + Return (st0, msgs_left) + od) + od + od) + /\ + + (** [betree::betree::Internal::{4}::flush]: backward function 0 *) + (betree_internal_flush_back + (self : betree_internal_t) (params : betree_params_t) + (node_id_cnt : betree_node_id_counter_t) + (content : (u64 # betree_message_t) betree_list_t) (st : state) : + (betree_internal_t # betree_node_id_counter_t) result + = + do + p <- betree_list_partition_at_pivot_fwd content self.betree_internal_pivot; + let (msgs_left, msgs_right) = p in + do + len_left <- betree_list_len_fwd msgs_left; + if u64_ge len_left params.betree_params_min_flush_size + then ( + do + (st0, _) <- + betree_node_apply_messages_fwd self.betree_internal_left params + node_id_cnt msgs_left st; + (n, node_id_cnt0) <- + betree_node_apply_messages_back self.betree_internal_left params + node_id_cnt msgs_left st; + len_right <- betree_list_len_fwd msgs_right; + if u64_ge len_right params.betree_params_min_flush_size + then ( + do + (n0, node_id_cnt1) <- + betree_node_apply_messages_back self.betree_internal_right params + node_id_cnt0 msgs_right st0; + Return + (self + with + <| + betree_internal_left := n; betree_internal_right := n0 + |>, node_id_cnt1) + od) + else Return (self with <| betree_internal_left := n |>, node_id_cnt0) + od) + else ( + do + (n, node_id_cnt0) <- + betree_node_apply_messages_back self.betree_internal_right params + node_id_cnt msgs_right st; + Return (self with <| betree_internal_right := n |>, node_id_cnt0) + od) + od + od) + /\ + + (** [betree::betree::Node::{5}::apply_messages]: forward function *) + (betree_node_apply_messages_fwd + (self : betree_node_t) (params : betree_params_t) + (node_id_cnt : betree_node_id_counter_t) + (msgs : (u64 # betree_message_t) betree_list_t) (st : state) : + (state # unit) result + = + (case self of + | BetreeNodeInternal node => + do + (st0, content) <- + betree_load_internal_node_fwd node.betree_internal_id st; + content0 <- betree_node_apply_messages_to_internal_fwd_back content msgs; + num_msgs <- betree_list_len_fwd content0; + if u64_ge num_msgs params.betree_params_min_flush_size + then ( + do + (st1, content1) <- + betree_internal_flush_fwd node params node_id_cnt content0 st0; + (node0, _) <- + betree_internal_flush_back node params node_id_cnt content0 st0; + (st2, _) <- + betree_store_internal_node_fwd node0.betree_internal_id content1 st1; + Return (st2, ()) + od) + else ( + do + (st1, _) <- + betree_store_internal_node_fwd node.betree_internal_id content0 st0; + Return (st1, ()) + od) + od + | BetreeNodeLeaf node => + do + (st0, content) <- betree_load_leaf_node_fwd node.betree_leaf_id st; + content0 <- betree_node_apply_messages_to_leaf_fwd_back content msgs; + len <- betree_list_len_fwd content0; + i <- u64_mul (int_to_u64 2) params.betree_params_split_size; + if u64_ge len i + then ( + do + (st1, _) <- betree_leaf_split_fwd node content0 params node_id_cnt st0; + (st2, _) <- + betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1; + Return (st2, ()) + od) + else ( + do + (st1, _) <- + betree_store_leaf_node_fwd node.betree_leaf_id content0 st0; + Return (st1, ()) + od) + od)) + /\ + + (** [betree::betree::Node::{5}::apply_messages]: backward function 0 *) + betree_node_apply_messages_back + (self : betree_node_t) (params : betree_params_t) + (node_id_cnt : betree_node_id_counter_t) + (msgs : (u64 # betree_message_t) betree_list_t) (st : state) : + (betree_node_t # betree_node_id_counter_t) result + = + (case self of + | BetreeNodeInternal node => + do + (st0, content) <- + betree_load_internal_node_fwd node.betree_internal_id st; + content0 <- betree_node_apply_messages_to_internal_fwd_back content msgs; + num_msgs <- betree_list_len_fwd content0; + if u64_ge num_msgs params.betree_params_min_flush_size + then ( + do + (st1, content1) <- + betree_internal_flush_fwd node params node_id_cnt content0 st0; + (node0, node_id_cnt0) <- + betree_internal_flush_back node params node_id_cnt content0 st0; + _ <- + betree_store_internal_node_fwd node0.betree_internal_id content1 st1; + Return (BetreeNodeInternal node0, node_id_cnt0) + od) + else ( + do + _ <- + betree_store_internal_node_fwd node.betree_internal_id content0 st0; + Return (BetreeNodeInternal node, node_id_cnt) + od) + od + | BetreeNodeLeaf node => + do + (st0, content) <- betree_load_leaf_node_fwd node.betree_leaf_id st; + content0 <- betree_node_apply_messages_to_leaf_fwd_back content msgs; + len <- betree_list_len_fwd content0; + i <- u64_mul (int_to_u64 2) params.betree_params_split_size; + if u64_ge len i + then ( + do + (st1, new_node) <- + betree_leaf_split_fwd node content0 params node_id_cnt st0; + _ <- betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1; + node_id_cnt0 <- + betree_leaf_split_back node content0 params node_id_cnt st0; + Return (BetreeNodeInternal new_node, node_id_cnt0) + od) + else ( + do + _ <- betree_store_leaf_node_fwd node.betree_leaf_id content0 st0; + Return (BetreeNodeLeaf (node with <| betree_leaf_size := len |>), + node_id_cnt) + od) + od) +’ + +val betree_node_apply_fwd_def = Define ‘ + (** [betree::betree::Node::{5}::apply]: forward function *) + betree_node_apply_fwd + (self : betree_node_t) (params : betree_params_t) + (node_id_cnt : betree_node_id_counter_t) (key : u64) + (new_msg : betree_message_t) (st : state) : + (state # unit) result + = + let l = BetreeListNil in + do + (st0, _) <- + betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons + (key, new_msg) l) st; + _ <- + betree_node_apply_messages_back self params node_id_cnt (BetreeListCons + (key, new_msg) l) st; + Return (st0, ()) + od +’ + +val betree_node_apply_back_def = Define ‘ + (** [betree::betree::Node::{5}::apply]: backward function 0 *) + betree_node_apply_back + (self : betree_node_t) (params : betree_params_t) + (node_id_cnt : betree_node_id_counter_t) (key : u64) + (new_msg : betree_message_t) (st : state) : + (betree_node_t # betree_node_id_counter_t) result + = + let l = BetreeListNil in + betree_node_apply_messages_back self params node_id_cnt (BetreeListCons + (key, new_msg) l) st +’ + +val betree_be_tree_new_fwd_def = Define ‘ + (** [betree::betree::BeTree::{6}::new]: forward function *) + betree_be_tree_new_fwd + (min_flush_size : u64) (split_size : u64) (st : state) : + (state # betree_be_tree_t) result + = + do + node_id_cnt <- betree_node_id_counter_new_fwd; + id <- betree_node_id_counter_fresh_id_fwd node_id_cnt; + (st0, _) <- betree_store_leaf_node_fwd id BetreeListNil st; + node_id_cnt0 <- betree_node_id_counter_fresh_id_back node_id_cnt; + Return (st0, + <| + betree_be_tree_params := + (<| + betree_params_min_flush_size := min_flush_size; + betree_params_split_size := split_size + |>); + betree_be_tree_node_id_cnt := node_id_cnt0; + betree_be_tree_root := + (BetreeNodeLeaf + (<| betree_leaf_id := id; betree_leaf_size := (int_to_u64 0) |>)) + |>) + od +’ + +val betree_be_tree_apply_fwd_def = Define ‘ + (** [betree::betree::BeTree::{6}::apply]: forward function *) + betree_be_tree_apply_fwd + (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) + : + (state # unit) result + = + do + (st0, _) <- + betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params + self.betree_be_tree_node_id_cnt key msg st; + _ <- + betree_node_apply_back self.betree_be_tree_root + self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st; + Return (st0, ()) + od +’ + +val betree_be_tree_apply_back_def = Define ‘ + (** [betree::betree::BeTree::{6}::apply]: backward function 0 *) + betree_be_tree_apply_back + (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) + : + betree_be_tree_t result + = + do + (n, nic) <- + betree_node_apply_back self.betree_be_tree_root + self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st; + Return + (self + with + <| + betree_be_tree_node_id_cnt := nic; betree_be_tree_root := n + |>) + od +’ + +val betree_be_tree_insert_fwd_def = Define ‘ + (** [betree::betree::BeTree::{6}::insert]: forward function *) + betree_be_tree_insert_fwd + (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : + (state # unit) result + = + do + (st0, _) <- + betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st; + _ <- betree_be_tree_apply_back self key (BetreeMessageInsert value) st; + Return (st0, ()) + od +’ + +val betree_be_tree_insert_back_def = Define ‘ + (** [betree::betree::BeTree::{6}::insert]: backward function 0 *) + betree_be_tree_insert_back + (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : + betree_be_tree_t result + = + betree_be_tree_apply_back self key (BetreeMessageInsert value) st +’ + +val betree_be_tree_delete_fwd_def = Define ‘ + (** [betree::betree::BeTree::{6}::delete]: forward function *) + betree_be_tree_delete_fwd + (self : betree_be_tree_t) (key : u64) (st : state) : + (state # unit) result + = + do + (st0, _) <- betree_be_tree_apply_fwd self key BetreeMessageDelete st; + _ <- betree_be_tree_apply_back self key BetreeMessageDelete st; + Return (st0, ()) + od +’ + +val betree_be_tree_delete_back_def = Define ‘ + (** [betree::betree::BeTree::{6}::delete]: backward function 0 *) + betree_be_tree_delete_back + (self : betree_be_tree_t) (key : u64) (st : state) : + betree_be_tree_t result + = + betree_be_tree_apply_back self key BetreeMessageDelete st +’ + +val betree_be_tree_upsert_fwd_def = Define ‘ + (** [betree::betree::BeTree::{6}::upsert]: forward function *) + betree_be_tree_upsert_fwd + (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) + (st : state) : + (state # unit) result + = + do + (st0, _) <- betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st; + _ <- betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st; + Return (st0, ()) + od +’ + +val betree_be_tree_upsert_back_def = Define ‘ + (** [betree::betree::BeTree::{6}::upsert]: backward function 0 *) + betree_be_tree_upsert_back + (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) + (st : state) : + betree_be_tree_t result + = + betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st +’ + +val betree_be_tree_lookup_fwd_def = Define ‘ + (** [betree::betree::BeTree::{6}::lookup]: forward function *) + betree_be_tree_lookup_fwd + (self : betree_be_tree_t) (key : u64) (st : state) : + (state # u64 option) result + = + betree_node_lookup_fwd self.betree_be_tree_root key st +’ + +val betree_be_tree_lookup_back_def = Define ‘ + (** [betree::betree::BeTree::{6}::lookup]: backward function 0 *) + betree_be_tree_lookup_back + (self : betree_be_tree_t) (key : u64) (st : state) : + betree_be_tree_t result + = + do + n <- betree_node_lookup_back self.betree_be_tree_root key st; + Return (self with <| betree_be_tree_root := n |>) + od +’ + +val main_fwd_def = Define ‘ + (** [betree::main]: forward function *) + main_fwd : unit result = + Return () +’ + +(** Unit test for [betree::main] *) +val _ = assert_return (“main_fwd”) + +val _ = export_theory () diff --git a/tests/hol4/betree/betree_FunsTheory.sig b/tests/hol4/betree/betree_FunsTheory.sig new file mode 100644 index 00000000..4127cba1 --- /dev/null +++ b/tests/hol4/betree/betree_FunsTheory.sig @@ -0,0 +1,1230 @@ +signature betree_FunsTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val betree_be_tree_apply_back_def : thm + val betree_be_tree_apply_fwd_def : thm + val betree_be_tree_delete_back_def : thm + val betree_be_tree_delete_fwd_def : thm + val betree_be_tree_insert_back_def : thm + val betree_be_tree_insert_fwd_def : thm + val betree_be_tree_lookup_back_def : thm + val betree_be_tree_lookup_fwd_def : thm + val betree_be_tree_new_fwd_def : thm + val betree_be_tree_upsert_back_def : thm + val betree_be_tree_upsert_fwd_def : thm + val betree_fresh_node_id_back_def : thm + val betree_fresh_node_id_fwd_def : thm + val betree_internal_flush_back_def : thm + val betree_internal_flush_fwd_def : thm + val betree_internal_lookup_in_children_back_def : thm + val betree_internal_lookup_in_children_fwd_def : thm + val betree_leaf_split_back_def : thm + val betree_leaf_split_fwd_def : thm + val betree_list_hd_fwd_def : thm + val betree_list_head_has_key_fwd_def : thm + val betree_list_len_fwd_def : thm + val betree_list_partition_at_pivot_fwd_def : thm + val betree_list_pop_front_back_def : thm + val betree_list_pop_front_fwd_def : thm + val betree_list_push_front_fwd_back_def : thm + val betree_list_split_at_fwd_def : thm + val betree_load_internal_node_fwd_def : thm + val betree_load_leaf_node_fwd_def : thm + val betree_node_apply_back_def : thm + val betree_node_apply_fwd_def : thm + val betree_node_apply_messages_back_def : thm + val betree_node_apply_messages_fwd_def : thm + val betree_node_apply_messages_to_internal_fwd_back_def : thm + val betree_node_apply_messages_to_leaf_fwd_back_def : thm + val betree_node_apply_to_internal_fwd_back_def : thm + val betree_node_apply_to_leaf_fwd_back_def : thm + val betree_node_apply_upserts_back_def : thm + val betree_node_apply_upserts_fwd_def : thm + val betree_node_filter_messages_for_key_fwd_back_def : thm + val betree_node_id_counter_fresh_id_back_def : thm + val betree_node_id_counter_fresh_id_fwd_def : thm + val betree_node_id_counter_new_fwd_def : thm + val betree_node_lookup_back_def : thm + val betree_node_lookup_first_message_after_key_back_def : thm + val betree_node_lookup_first_message_after_key_fwd_def : thm + val betree_node_lookup_first_message_for_key_back_def : thm + val betree_node_lookup_first_message_for_key_fwd_def : thm + val betree_node_lookup_fwd_def : thm + val betree_node_lookup_in_bindings_fwd_def : thm + val betree_node_lookup_mut_in_bindings_back_def : thm + val betree_node_lookup_mut_in_bindings_fwd_def : thm + val betree_store_internal_node_fwd_def : thm + val betree_store_leaf_node_fwd_def : thm + val betree_upsert_update_fwd_def : thm + val main_fwd_def : thm + + val betree_Funs_grammars : type_grammar.grammar * term_grammar.grammar +(* + [betree_Opaque] Parent theory of "betree_Funs" + + [betree_be_tree_apply_back_def] Definition + + ⊢ ∀self key msg st. + betree_be_tree_apply_back self key msg st = + do + (n,nic) <- + betree_node_apply_back self.betree_be_tree_root + self.betree_be_tree_params self.betree_be_tree_node_id_cnt + key msg st; + Return + (self with + <|betree_be_tree_node_id_cnt := nic; + betree_be_tree_root := n|>) + od + + [betree_be_tree_apply_fwd_def] Definition + + ⊢ ∀self key msg st. + betree_be_tree_apply_fwd self key msg st = + do + (st0,_) <- + betree_node_apply_fwd self.betree_be_tree_root + self.betree_be_tree_params self.betree_be_tree_node_id_cnt + key msg st; + monad_ignore_bind + (betree_node_apply_back self.betree_be_tree_root + self.betree_be_tree_params self.betree_be_tree_node_id_cnt + key msg st) (Return (st0,())) + od + + [betree_be_tree_delete_back_def] Definition + + ⊢ ∀self key st. + betree_be_tree_delete_back self key st = + betree_be_tree_apply_back self key BetreeMessageDelete st + + [betree_be_tree_delete_fwd_def] Definition + + ⊢ ∀self key st. + betree_be_tree_delete_fwd self key st = + do + (st0,_) <- + betree_be_tree_apply_fwd self key BetreeMessageDelete st; + monad_ignore_bind + (betree_be_tree_apply_back self key BetreeMessageDelete st) + (Return (st0,())) + od + + [betree_be_tree_insert_back_def] Definition + + ⊢ ∀self key value st. + betree_be_tree_insert_back self key value st = + betree_be_tree_apply_back self key (BetreeMessageInsert value) st + + [betree_be_tree_insert_fwd_def] Definition + + ⊢ ∀self key value st. + betree_be_tree_insert_fwd self key value st = + do + (st0,_) <- + betree_be_tree_apply_fwd self key (BetreeMessageInsert value) + st; + monad_ignore_bind + (betree_be_tree_apply_back self key + (BetreeMessageInsert value) st) (Return (st0,())) + od + + [betree_be_tree_lookup_back_def] Definition + + ⊢ ∀self key st. + betree_be_tree_lookup_back self key st = + do + n <- betree_node_lookup_back self.betree_be_tree_root key st; + Return (self with betree_be_tree_root := n) + od + + [betree_be_tree_lookup_fwd_def] Definition + + ⊢ ∀self key st. + betree_be_tree_lookup_fwd self key st = + betree_node_lookup_fwd self.betree_be_tree_root key st + + [betree_be_tree_new_fwd_def] Definition + + ⊢ ∀min_flush_size split_size st. + betree_be_tree_new_fwd min_flush_size split_size st = + do + node_id_cnt <- betree_node_id_counter_new_fwd; + id <- betree_node_id_counter_fresh_id_fwd node_id_cnt; + (st0,_) <- betree_store_leaf_node_fwd id BetreeListNil st; + node_id_cnt0 <- + betree_node_id_counter_fresh_id_back node_id_cnt; + Return + (st0, + <|betree_be_tree_params := + <|betree_params_min_flush_size := min_flush_size; + betree_params_split_size := split_size|>; + betree_be_tree_node_id_cnt := node_id_cnt0; + betree_be_tree_root := + BetreeNodeLeaf + <|betree_leaf_id := id; + betree_leaf_size := int_to_u64 0|> |>) + od + + [betree_be_tree_upsert_back_def] Definition + + ⊢ ∀self key upd st. + betree_be_tree_upsert_back self key upd st = + betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st + + [betree_be_tree_upsert_fwd_def] Definition + + ⊢ ∀self key upd st. + betree_be_tree_upsert_fwd self key upd st = + do + (st0,_) <- + betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) + st; + monad_ignore_bind + (betree_be_tree_apply_back self key (BetreeMessageUpsert upd) + st) (Return (st0,())) + od + + [betree_fresh_node_id_back_def] Definition + + ⊢ ∀counter. + betree_fresh_node_id_back counter = + u64_add counter (int_to_u64 1) + + [betree_fresh_node_id_fwd_def] Definition + + ⊢ ∀counter. + betree_fresh_node_id_fwd counter = + monad_ignore_bind (u64_add counter (int_to_u64 1)) + (Return counter) + + [betree_internal_flush_back_def] Definition + + ⊢ ∀self params node_id_cnt content st. + betree_internal_flush_back self params node_id_cnt content st = + do + p <- + betree_list_partition_at_pivot_fwd content + self.betree_internal_pivot; + (msgs_left,msgs_right) <<- p; + len_left <- betree_list_len_fwd msgs_left; + if u64_ge len_left params.betree_params_min_flush_size then + do + (st0,_) <- + betree_node_apply_messages_fwd self.betree_internal_left + params node_id_cnt msgs_left st; + (n,node_id_cnt0) <- + betree_node_apply_messages_back self.betree_internal_left + params node_id_cnt msgs_left st; + len_right <- betree_list_len_fwd msgs_right; + if + u64_ge len_right params.betree_params_min_flush_size + then + do + (n0,node_id_cnt1) <- + betree_node_apply_messages_back + self.betree_internal_right params node_id_cnt0 + msgs_right st0; + Return + (self with + <|betree_internal_left := n; + betree_internal_right := n0|>,node_id_cnt1) + od + else + Return (self with betree_internal_left := n,node_id_cnt0) + od + else + do + (n,node_id_cnt0) <- + betree_node_apply_messages_back + self.betree_internal_right params node_id_cnt + msgs_right st; + Return (self with betree_internal_right := n,node_id_cnt0) + od + od + + [betree_internal_flush_fwd_def] Definition + + ⊢ ∀self params node_id_cnt content st. + betree_internal_flush_fwd self params node_id_cnt content st = + do + p <- + betree_list_partition_at_pivot_fwd content + self.betree_internal_pivot; + (msgs_left,msgs_right) <<- p; + len_left <- betree_list_len_fwd msgs_left; + if u64_ge len_left params.betree_params_min_flush_size then + do + (st0,_) <- + betree_node_apply_messages_fwd self.betree_internal_left + params node_id_cnt msgs_left st; + (_,node_id_cnt0) <- + betree_node_apply_messages_back self.betree_internal_left + params node_id_cnt msgs_left st; + len_right <- betree_list_len_fwd msgs_right; + if + u64_ge len_right params.betree_params_min_flush_size + then + do + (st1,_) <- + betree_node_apply_messages_fwd + self.betree_internal_right params node_id_cnt0 + msgs_right st0; + monad_ignore_bind + (betree_node_apply_messages_back + self.betree_internal_right params node_id_cnt0 + msgs_right st0) (Return (st1,BetreeListNil)) + od + else Return (st0,msgs_right) + od + else + do + (st0,_) <- + betree_node_apply_messages_fwd self.betree_internal_right + params node_id_cnt msgs_right st; + monad_ignore_bind + (betree_node_apply_messages_back + self.betree_internal_right params node_id_cnt + msgs_right st) (Return (st0,msgs_left)) + od + od + + [betree_internal_lookup_in_children_back_def] Definition + + ⊢ ∀self key st. + betree_internal_lookup_in_children_back self key st = + if u64_lt key self.betree_internal_pivot then + do + n <- betree_node_lookup_back self.betree_internal_left key st; + Return (self with betree_internal_left := n) + od + else + do + n <- + betree_node_lookup_back self.betree_internal_right key st; + Return (self with betree_internal_right := n) + od + + [betree_internal_lookup_in_children_fwd_def] Definition + + ⊢ ∀self key st. + betree_internal_lookup_in_children_fwd self key st = + if u64_lt key self.betree_internal_pivot then + betree_node_lookup_fwd self.betree_internal_left key st + else betree_node_lookup_fwd self.betree_internal_right key st + + [betree_leaf_split_back_def] Definition + + ⊢ ∀self content params node_id_cnt st. + betree_leaf_split_back self content params node_id_cnt st = + do + p <- + betree_list_split_at_fwd content + params.betree_params_split_size; + (content0,content1) <<- p; + monad_ignore_bind (betree_list_hd_fwd content1) + do + id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; + node_id_cnt0 <- + betree_node_id_counter_fresh_id_back node_id_cnt; + id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; + (st0,_) <- betree_store_leaf_node_fwd id0 content0 st; + monad_ignore_bind + (betree_store_leaf_node_fwd id1 content1 st0) + (betree_node_id_counter_fresh_id_back node_id_cnt0) + od + od + + [betree_leaf_split_fwd_def] Definition + + ⊢ ∀self content params node_id_cnt st. + betree_leaf_split_fwd self content params node_id_cnt st = + do + p <- + betree_list_split_at_fwd content + params.betree_params_split_size; + (content0,content1) <<- p; + p0 <- betree_list_hd_fwd content1; + (pivot,_) <<- p0; + id0 <- betree_node_id_counter_fresh_id_fwd node_id_cnt; + node_id_cnt0 <- + betree_node_id_counter_fresh_id_back node_id_cnt; + id1 <- betree_node_id_counter_fresh_id_fwd node_id_cnt0; + (st0,_) <- betree_store_leaf_node_fwd id0 content0 st; + (st1,_) <- betree_store_leaf_node_fwd id1 content1 st0; + n <<- + BetreeNodeLeaf + <|betree_leaf_id := id0; + betree_leaf_size := params.betree_params_split_size|>; + n0 <<- + BetreeNodeLeaf + <|betree_leaf_id := id1; + betree_leaf_size := params.betree_params_split_size|>; + Return + (st1, + <|betree_internal_id := self.betree_leaf_id; + betree_internal_pivot := pivot; betree_internal_left := n; + betree_internal_right := n0|>) + od + + [betree_list_hd_fwd_def] Definition + + ⊢ ∀self. + betree_list_hd_fwd self = + case self of + BetreeListCons hd l => Return hd + | BetreeListNil => Fail Failure + + [betree_list_head_has_key_fwd_def] Definition + + ⊢ ∀self key. + betree_list_head_has_key_fwd self key = + case self of + BetreeListCons hd l => (let (i,_) = hd in Return (i = key)) + | BetreeListNil => Return F + + [betree_list_len_fwd_def] Definition + + ⊢ ∀self. + betree_list_len_fwd self = + case self of + BetreeListCons t tl => + do i <- betree_list_len_fwd tl; u64_add (int_to_u64 1) i od + | BetreeListNil => Return (int_to_u64 0) + + [betree_list_partition_at_pivot_fwd_def] Definition + + ⊢ ∀self pivot. + betree_list_partition_at_pivot_fwd self pivot = + case self of + BetreeListCons hd tl => + (let + (i,t) = hd + in + if u64_ge i pivot then + Return (BetreeListNil,BetreeListCons (i,t) tl) + else + do + p <- betree_list_partition_at_pivot_fwd tl pivot; + (ls0,ls1) <<- p; + l <<- ls0; + Return (BetreeListCons (i,t) l,ls1) + od) + | BetreeListNil => Return (BetreeListNil,BetreeListNil) + + [betree_list_pop_front_back_def] Definition + + ⊢ ∀self. + betree_list_pop_front_back self = + (let + ls = mem_replace_fwd self BetreeListNil + in + case ls of + BetreeListCons x tl => Return tl + | BetreeListNil => Fail Failure) + + [betree_list_pop_front_fwd_def] Definition + + ⊢ ∀self. + betree_list_pop_front_fwd self = + (let + ls = mem_replace_fwd self BetreeListNil + in + case ls of + BetreeListCons x tl => Return x + | BetreeListNil => Fail Failure) + + [betree_list_push_front_fwd_back_def] Definition + + ⊢ ∀self x. + betree_list_push_front_fwd_back self x = + (let + tl = mem_replace_fwd self BetreeListNil; + l = tl + in + Return (BetreeListCons x l)) + + [betree_list_split_at_fwd_def] Definition + + ⊢ ∀self n. + betree_list_split_at_fwd self n = + if n = int_to_u64 0 then Return (BetreeListNil,self) + else + case self of + BetreeListCons hd tl => + do + i <- u64_sub n (int_to_u64 1); + p <- betree_list_split_at_fwd tl i; + (ls0,ls1) <<- p; + l <<- ls0; + Return (BetreeListCons hd l,ls1) + od + | BetreeListNil => Fail Failure + + [betree_load_internal_node_fwd_def] Definition + + ⊢ ∀id st. + betree_load_internal_node_fwd id st = + betree_utils_load_internal_node_fwd id st + + [betree_load_leaf_node_fwd_def] Definition + + ⊢ ∀id st. + betree_load_leaf_node_fwd id st = + betree_utils_load_leaf_node_fwd id st + + [betree_node_apply_back_def] Definition + + ⊢ ∀self params node_id_cnt key new_msg st. + betree_node_apply_back self params node_id_cnt key new_msg st = + (let + l = BetreeListNil + in + betree_node_apply_messages_back self params node_id_cnt + (BetreeListCons (key,new_msg) l) st) + + [betree_node_apply_fwd_def] Definition + + ⊢ ∀self params node_id_cnt key new_msg st. + betree_node_apply_fwd self params node_id_cnt key new_msg st = + (let + l = BetreeListNil + in + do + (st0,_) <- + betree_node_apply_messages_fwd self params node_id_cnt + (BetreeListCons (key,new_msg) l) st; + monad_ignore_bind + (betree_node_apply_messages_back self params node_id_cnt + (BetreeListCons (key,new_msg) l) st) (Return (st0,())) + od) + + [betree_node_apply_messages_back_def] Definition + + ⊢ ∀self params node_id_cnt msgs st. + betree_node_apply_messages_back self params node_id_cnt msgs st = + case self of + BetreeNodeInternal node => + do + (st0,content) <- + betree_load_internal_node_fwd node.betree_internal_id st; + content0 <- + betree_node_apply_messages_to_internal_fwd_back content + msgs; + num_msgs <- betree_list_len_fwd content0; + if u64_ge num_msgs params.betree_params_min_flush_size then + do + (st1,content1) <- + betree_internal_flush_fwd node params node_id_cnt + content0 st0; + (node0,node_id_cnt0) <- + betree_internal_flush_back node params node_id_cnt + content0 st0; + monad_ignore_bind + (betree_store_internal_node_fwd + node0.betree_internal_id content1 st1) + (Return (BetreeNodeInternal node0,node_id_cnt0)) + od + else + monad_ignore_bind + (betree_store_internal_node_fwd node.betree_internal_id + content0 st0) + (Return (BetreeNodeInternal node,node_id_cnt)) + od + | BetreeNodeLeaf node' => + do + (st0,content) <- + betree_load_leaf_node_fwd node'.betree_leaf_id st; + content0 <- + betree_node_apply_messages_to_leaf_fwd_back content msgs; + len <- betree_list_len_fwd content0; + i <- u64_mul (int_to_u64 2) params.betree_params_split_size; + if u64_ge len i then + do + (st1,new_node) <- + betree_leaf_split_fwd node' content0 params node_id_cnt + st0; + monad_ignore_bind + (betree_store_leaf_node_fwd node'.betree_leaf_id + BetreeListNil st1) + do + node_id_cnt0 <- + betree_leaf_split_back node' content0 params + node_id_cnt st0; + Return (BetreeNodeInternal new_node,node_id_cnt0) + od + od + else + monad_ignore_bind + (betree_store_leaf_node_fwd node'.betree_leaf_id content0 + st0) + (Return + (BetreeNodeLeaf (node' with betree_leaf_size := len), + node_id_cnt)) + od + + [betree_node_apply_messages_fwd_def] Definition + + ⊢ ∀self params node_id_cnt msgs st. + betree_node_apply_messages_fwd self params node_id_cnt msgs st = + case self of + BetreeNodeInternal node => + do + (st0,content) <- + betree_load_internal_node_fwd node.betree_internal_id st; + content0 <- + betree_node_apply_messages_to_internal_fwd_back content + msgs; + num_msgs <- betree_list_len_fwd content0; + if u64_ge num_msgs params.betree_params_min_flush_size then + do + (st1,content1) <- + betree_internal_flush_fwd node params node_id_cnt + content0 st0; + (node0,_) <- + betree_internal_flush_back node params node_id_cnt + content0 st0; + (st2,_) <- + betree_store_internal_node_fwd + node0.betree_internal_id content1 st1; + Return (st2,()) + od + else + do + (st1,_) <- + betree_store_internal_node_fwd + node.betree_internal_id content0 st0; + Return (st1,()) + od + od + | BetreeNodeLeaf node' => + do + (st0,content) <- + betree_load_leaf_node_fwd node'.betree_leaf_id st; + content0 <- + betree_node_apply_messages_to_leaf_fwd_back content msgs; + len <- betree_list_len_fwd content0; + i <- u64_mul (int_to_u64 2) params.betree_params_split_size; + if u64_ge len i then + do + (st1,_) <- + betree_leaf_split_fwd node' content0 params node_id_cnt + st0; + (st2,_) <- + betree_store_leaf_node_fwd node'.betree_leaf_id + BetreeListNil st1; + Return (st2,()) + od + else + do + (st1,_) <- + betree_store_leaf_node_fwd node'.betree_leaf_id + content0 st0; + Return (st1,()) + od + od + + [betree_node_apply_messages_to_internal_fwd_back_def] Definition + + ⊢ ∀msgs new_msgs. + betree_node_apply_messages_to_internal_fwd_back msgs new_msgs = + case new_msgs of + BetreeListCons new_msg new_msgs_tl => + (let + (i,m) = new_msg + in + do + msgs0 <- betree_node_apply_to_internal_fwd_back msgs i m; + betree_node_apply_messages_to_internal_fwd_back msgs0 + new_msgs_tl + od) + | BetreeListNil => Return msgs + + [betree_node_apply_messages_to_leaf_fwd_back_def] Definition + + ⊢ ∀bindings new_msgs. + betree_node_apply_messages_to_leaf_fwd_back bindings new_msgs = + case new_msgs of + BetreeListCons new_msg new_msgs_tl => + (let + (i,m) = new_msg + in + do + bindings0 <- + betree_node_apply_to_leaf_fwd_back bindings i m; + betree_node_apply_messages_to_leaf_fwd_back bindings0 + new_msgs_tl + od) + | BetreeListNil => Return bindings + + [betree_node_apply_to_internal_fwd_back_def] Definition + + ⊢ ∀msgs key new_msg. + betree_node_apply_to_internal_fwd_back msgs key new_msg = + do + msgs0 <- betree_node_lookup_first_message_for_key_fwd key msgs; + b <- betree_list_head_has_key_fwd msgs0 key; + if b then + case new_msg of + BetreeMessageInsert i => + do + msgs1 <- + betree_node_filter_messages_for_key_fwd_back key + msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 + (key,BetreeMessageInsert i); + betree_node_lookup_first_message_for_key_back key msgs + msgs2 + od + | BetreeMessageDelete => + do + msgs1 <- + betree_node_filter_messages_for_key_fwd_back key msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 + (key,BetreeMessageDelete); + betree_node_lookup_first_message_for_key_back key msgs + msgs2 + od + | BetreeMessageUpsert s => + do + p <- betree_list_hd_fwd msgs0; + (_,m) <<- p; + case m of + BetreeMessageInsert prev => + do + v <- betree_upsert_update_fwd (SOME prev) s; + msgs1 <- betree_list_pop_front_back msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 + (key,BetreeMessageInsert v); + betree_node_lookup_first_message_for_key_back key + msgs msgs2 + od + | BetreeMessageDelete => + do + v <- betree_upsert_update_fwd NONE s; + msgs1 <- betree_list_pop_front_back msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 + (key,BetreeMessageInsert v); + betree_node_lookup_first_message_for_key_back key + msgs msgs2 + od + | BetreeMessageUpsert ufs => + do + msgs1 <- + betree_node_lookup_first_message_after_key_fwd key + msgs0; + msgs2 <- + betree_list_push_front_fwd_back msgs1 + (key,BetreeMessageUpsert s); + msgs3 <- + betree_node_lookup_first_message_after_key_back key + msgs0 msgs2; + betree_node_lookup_first_message_for_key_back key + msgs msgs3 + od + od + else + do + msgs1 <- + betree_list_push_front_fwd_back msgs0 (key,new_msg); + betree_node_lookup_first_message_for_key_back key msgs + msgs1 + od + od + + [betree_node_apply_to_leaf_fwd_back_def] Definition + + ⊢ ∀bindings key new_msg. + betree_node_apply_to_leaf_fwd_back bindings key new_msg = + do + bindings0 <- + betree_node_lookup_mut_in_bindings_fwd key bindings; + b <- betree_list_head_has_key_fwd bindings0 key; + if b then + do + hd <- betree_list_pop_front_fwd bindings0; + case new_msg of + BetreeMessageInsert v => + do + bindings1 <- betree_list_pop_front_back bindings0; + bindings2 <- + betree_list_push_front_fwd_back bindings1 (key,v); + betree_node_lookup_mut_in_bindings_back key bindings + bindings2 + od + | BetreeMessageDelete => + do + bindings1 <- betree_list_pop_front_back bindings0; + betree_node_lookup_mut_in_bindings_back key bindings + bindings1 + od + | BetreeMessageUpsert s => + (let + (_,i) = hd + in + do + v <- betree_upsert_update_fwd (SOME i) s; + bindings1 <- betree_list_pop_front_back bindings0; + bindings2 <- + betree_list_push_front_fwd_back bindings1 (key,v); + betree_node_lookup_mut_in_bindings_back key bindings + bindings2 + od) + od + else + case new_msg of + BetreeMessageInsert v => + do + bindings1 <- + betree_list_push_front_fwd_back bindings0 (key,v); + betree_node_lookup_mut_in_bindings_back key bindings + bindings1 + od + | BetreeMessageDelete => + betree_node_lookup_mut_in_bindings_back key bindings + bindings0 + | BetreeMessageUpsert s => + do + v <- betree_upsert_update_fwd NONE s; + bindings1 <- + betree_list_push_front_fwd_back bindings0 (key,v); + betree_node_lookup_mut_in_bindings_back key bindings + bindings1 + od + od + + [betree_node_apply_upserts_back_def] Definition + + ⊢ ∀msgs prev key st. + betree_node_apply_upserts_back msgs prev key st = + do + b <- betree_list_head_has_key_fwd msgs key; + if b then + do + msg <- betree_list_pop_front_fwd msgs; + (_,m) <<- msg; + case m of + BetreeMessageInsert i => Fail Failure + | BetreeMessageDelete => Fail Failure + | BetreeMessageUpsert s => + do + v <- betree_upsert_update_fwd prev s; + msgs0 <- betree_list_pop_front_back msgs; + betree_node_apply_upserts_back msgs0 (SOME v) key st + od + od + else + do + (_,v) <- core_option_option_unwrap_fwd prev st; + betree_list_push_front_fwd_back msgs + (key,BetreeMessageInsert v) + od + od + + [betree_node_apply_upserts_fwd_def] Definition + + ⊢ ∀msgs prev key st. + betree_node_apply_upserts_fwd msgs prev key st = + do + b <- betree_list_head_has_key_fwd msgs key; + if b then + do + msg <- betree_list_pop_front_fwd msgs; + (_,m) <<- msg; + case m of + BetreeMessageInsert i => Fail Failure + | BetreeMessageDelete => Fail Failure + | BetreeMessageUpsert s => + do + v <- betree_upsert_update_fwd prev s; + msgs0 <- betree_list_pop_front_back msgs; + betree_node_apply_upserts_fwd msgs0 (SOME v) key st + od + od + else + do + (st0,v) <- core_option_option_unwrap_fwd prev st; + monad_ignore_bind + (betree_list_push_front_fwd_back msgs + (key,BetreeMessageInsert v)) (Return (st0,v)) + od + od + + [betree_node_filter_messages_for_key_fwd_back_def] Definition + + ⊢ ∀key msgs. + betree_node_filter_messages_for_key_fwd_back key msgs = + case msgs of + BetreeListCons p l => + (let + (k,m) = p + in + if k = key then + do + msgs0 <- + betree_list_pop_front_back (BetreeListCons (k,m) l); + betree_node_filter_messages_for_key_fwd_back key msgs0 + od + else Return (BetreeListCons (k,m) l)) + | BetreeListNil => Return BetreeListNil + + [betree_node_id_counter_fresh_id_back_def] Definition + + ⊢ ∀self. + betree_node_id_counter_fresh_id_back self = + do + i <- + u64_add self.betree_node_id_counter_next_node_id + (int_to_u64 1); + Return <|betree_node_id_counter_next_node_id := i|> + od + + [betree_node_id_counter_fresh_id_fwd_def] Definition + + ⊢ ∀self. + betree_node_id_counter_fresh_id_fwd self = + monad_ignore_bind + (u64_add self.betree_node_id_counter_next_node_id + (int_to_u64 1)) + (Return self.betree_node_id_counter_next_node_id) + + [betree_node_id_counter_new_fwd_def] Definition + + ⊢ betree_node_id_counter_new_fwd = + Return <|betree_node_id_counter_next_node_id := int_to_u64 0|> + + [betree_node_lookup_back_def] Definition + + ⊢ ∀self key st. + betree_node_lookup_back self key st = + case self of + BetreeNodeInternal node => + do + (st0,msgs) <- + betree_load_internal_node_fwd node.betree_internal_id st; + pending <- + betree_node_lookup_first_message_for_key_fwd key msgs; + case pending of + BetreeListCons p l => + (let + (k,msg) = p + in + if k ≠ key then + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back + key msgs (BetreeListCons (k,msg) l)) + do + node0 <- + betree_internal_lookup_in_children_back node + key st0; + Return (BetreeNodeInternal node0) + od + else + case msg of + BetreeMessageInsert v => + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back + key msgs + (BetreeListCons (k,BetreeMessageInsert v) + l)) (Return (BetreeNodeInternal node)) + | BetreeMessageDelete => + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back + key msgs + (BetreeListCons (k,BetreeMessageDelete) l)) + (Return (BetreeNodeInternal node)) + | BetreeMessageUpsert ufs => + do + (st1,v) <- + betree_internal_lookup_in_children_fwd node + key st0; + (st2,_) <- + betree_node_apply_upserts_fwd + (BetreeListCons + (k,BetreeMessageUpsert ufs) l) v key + st1; + node0 <- + betree_internal_lookup_in_children_back node + key st0; + pending0 <- + betree_node_apply_upserts_back + (BetreeListCons + (k,BetreeMessageUpsert ufs) l) v key + st1; + msgs0 <- + betree_node_lookup_first_message_for_key_back + key msgs pending0; + monad_ignore_bind + (betree_store_internal_node_fwd + node0.betree_internal_id msgs0 st2) + (Return (BetreeNodeInternal node0)) + od) + | BetreeListNil => + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back key msgs + BetreeListNil) + do + node0 <- + betree_internal_lookup_in_children_back node key + st0; + Return (BetreeNodeInternal node0) + od + od + | BetreeNodeLeaf node' => + do + (_,bindings) <- + betree_load_leaf_node_fwd node'.betree_leaf_id st; + monad_ignore_bind + (betree_node_lookup_in_bindings_fwd key bindings) + (Return (BetreeNodeLeaf node')) + od + + [betree_node_lookup_first_message_after_key_back_def] Definition + + ⊢ ∀key msgs ret. + betree_node_lookup_first_message_after_key_back key msgs ret = + case msgs of + BetreeListCons p next_msgs => + (let + (k,m) = p + in + if k = key then + do + next_msgs0 <- + betree_node_lookup_first_message_after_key_back key + next_msgs ret; + Return (BetreeListCons (k,m) next_msgs0) + od + else Return ret) + | BetreeListNil => Return ret + + [betree_node_lookup_first_message_after_key_fwd_def] Definition + + ⊢ ∀key msgs. + betree_node_lookup_first_message_after_key_fwd key msgs = + case msgs of + BetreeListCons p next_msgs => + (let + (k,m) = p + in + if k = key then + betree_node_lookup_first_message_after_key_fwd key + next_msgs + else Return (BetreeListCons (k,m) next_msgs)) + | BetreeListNil => Return BetreeListNil + + [betree_node_lookup_first_message_for_key_back_def] Definition + + ⊢ ∀key msgs ret. + betree_node_lookup_first_message_for_key_back key msgs ret = + case msgs of + BetreeListCons x next_msgs => + (let + (i,m) = x + in + if u64_ge i key then Return ret + else + do + next_msgs0 <- + betree_node_lookup_first_message_for_key_back key + next_msgs ret; + Return (BetreeListCons (i,m) next_msgs0) + od) + | BetreeListNil => Return ret + + [betree_node_lookup_first_message_for_key_fwd_def] Definition + + ⊢ ∀key msgs. + betree_node_lookup_first_message_for_key_fwd key msgs = + case msgs of + BetreeListCons x next_msgs => + (let + (i,m) = x + in + if u64_ge i key then + Return (BetreeListCons (i,m) next_msgs) + else + betree_node_lookup_first_message_for_key_fwd key + next_msgs) + | BetreeListNil => Return BetreeListNil + + [betree_node_lookup_fwd_def] Definition + + ⊢ ∀self key st. + betree_node_lookup_fwd self key st = + case self of + BetreeNodeInternal node => + do + (st0,msgs) <- + betree_load_internal_node_fwd node.betree_internal_id st; + pending <- + betree_node_lookup_first_message_for_key_fwd key msgs; + case pending of + BetreeListCons p l => + (let + (k,msg) = p + in + if k ≠ key then + do + (st1,opt) <- + betree_internal_lookup_in_children_fwd node + key st0; + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back + key msgs (BetreeListCons (k,msg) l)) + (Return (st1,opt)) + od + else + case msg of + BetreeMessageInsert v => + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back + key msgs + (BetreeListCons (k,BetreeMessageInsert v) + l)) (Return (st0,SOME v)) + | BetreeMessageDelete => + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back + key msgs + (BetreeListCons (k,BetreeMessageDelete) l)) + (Return (st0,NONE)) + | BetreeMessageUpsert ufs => + do + (st1,v) <- + betree_internal_lookup_in_children_fwd node + key st0; + (st2,v0) <- + betree_node_apply_upserts_fwd + (BetreeListCons + (k,BetreeMessageUpsert ufs) l) v key + st1; + node0 <- + betree_internal_lookup_in_children_back node + key st0; + pending0 <- + betree_node_apply_upserts_back + (BetreeListCons + (k,BetreeMessageUpsert ufs) l) v key + st1; + msgs0 <- + betree_node_lookup_first_message_for_key_back + key msgs pending0; + (st3,_) <- + betree_store_internal_node_fwd + node0.betree_internal_id msgs0 st2; + Return (st3,SOME v0) + od) + | BetreeListNil => + do + (st1,opt) <- + betree_internal_lookup_in_children_fwd node key st0; + monad_ignore_bind + (betree_node_lookup_first_message_for_key_back key + msgs BetreeListNil) (Return (st1,opt)) + od + od + | BetreeNodeLeaf node' => + do + (st0,bindings) <- + betree_load_leaf_node_fwd node'.betree_leaf_id st; + opt <- betree_node_lookup_in_bindings_fwd key bindings; + Return (st0,opt) + od + + [betree_node_lookup_in_bindings_fwd_def] Definition + + ⊢ ∀key bindings. + betree_node_lookup_in_bindings_fwd key bindings = + case bindings of + BetreeListCons hd tl => + (let + (i,i0) = hd + in + if i = key then Return (SOME i0) + else if u64_gt i key then Return NONE + else betree_node_lookup_in_bindings_fwd key tl) + | BetreeListNil => Return NONE + + [betree_node_lookup_mut_in_bindings_back_def] Definition + + ⊢ ∀key bindings ret. + betree_node_lookup_mut_in_bindings_back key bindings ret = + case bindings of + BetreeListCons hd tl => + (let + (i,i0) = hd + in + if u64_ge i key then Return ret + else + do + tl0 <- + betree_node_lookup_mut_in_bindings_back key tl ret; + Return (BetreeListCons (i,i0) tl0) + od) + | BetreeListNil => Return ret + + [betree_node_lookup_mut_in_bindings_fwd_def] Definition + + ⊢ ∀key bindings. + betree_node_lookup_mut_in_bindings_fwd key bindings = + case bindings of + BetreeListCons hd tl => + (let + (i,i0) = hd + in + if u64_ge i key then Return (BetreeListCons (i,i0) tl) + else betree_node_lookup_mut_in_bindings_fwd key tl) + | BetreeListNil => Return BetreeListNil + + [betree_store_internal_node_fwd_def] Definition + + ⊢ ∀id content st. + betree_store_internal_node_fwd id content st = + do + (st0,_) <- betree_utils_store_internal_node_fwd id content st; + Return (st0,()) + od + + [betree_store_leaf_node_fwd_def] Definition + + ⊢ ∀id content st. + betree_store_leaf_node_fwd id content st = + do + (st0,_) <- betree_utils_store_leaf_node_fwd id content st; + Return (st0,()) + od + + [betree_upsert_update_fwd_def] Definition + + ⊢ ∀prev st. + betree_upsert_update_fwd prev st = + case prev of + NONE => + (case st of + BetreeUpsertFunStateAdd v => Return v + | BetreeUpsertFunStateSub i => Return (int_to_u64 0)) + | SOME prev0 => + case st of + BetreeUpsertFunStateAdd v => + do + margin <- u64_sub core_u64_max prev0; + if u64_ge margin v then u64_add prev0 v + else Return core_u64_max + od + | BetreeUpsertFunStateSub v' => + if u64_ge prev0 v' then u64_sub prev0 v' + else Return (int_to_u64 0) + + [main_fwd_def] Definition + + ⊢ main_fwd = Return () + + +*) +end diff --git a/tests/hol4/betree/betree_OpaqueScript.sml b/tests/hol4/betree/betree_OpaqueScript.sml new file mode 100644 index 00000000..d8fdf6b5 --- /dev/null +++ b/tests/hol4/betree/betree_OpaqueScript.sml @@ -0,0 +1,26 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: external function declarations *) +open primitivesLib divDefLib +open betree_TypesTheory + +val _ = new_theory "betree_Opaque" + + +(** [betree::betree_utils::load_internal_node]: forward function *)val _ = new_constant ("betree_utils_load_internal_node_fwd", + “:u64 -> state -> (state # (u64 # betree_message_t) betree_list_t) + result”) + +(** [betree::betree_utils::store_internal_node]: forward function *)val _ = new_constant ("betree_utils_store_internal_node_fwd", + “:u64 -> (u64 # betree_message_t) betree_list_t -> state -> (state # unit) + result”) + +(** [betree::betree_utils::load_leaf_node]: forward function *)val _ = new_constant ("betree_utils_load_leaf_node_fwd", + “:u64 -> state -> (state # (u64 # u64) betree_list_t) result”) + +(** [betree::betree_utils::store_leaf_node]: forward function *)val _ = new_constant ("betree_utils_store_leaf_node_fwd", + “:u64 -> (u64 # u64) betree_list_t -> state -> (state # unit) result”) + +(** [core::option::Option::{0}::unwrap]: forward function *)val _ = new_constant ("core_option_option_unwrap_fwd", + “:'t option -> state -> (state # 't) result”) + +val _ = export_theory () diff --git a/tests/hol4/betree/betree_OpaqueTheory.sig b/tests/hol4/betree/betree_OpaqueTheory.sig new file mode 100644 index 00000000..9452ff0f --- /dev/null +++ b/tests/hol4/betree/betree_OpaqueTheory.sig @@ -0,0 +1,11 @@ +signature betree_OpaqueTheory = +sig + type thm = Thm.thm + + val betree_Opaque_grammars : type_grammar.grammar * term_grammar.grammar +(* + [betree_Types] Parent theory of "betree_Opaque" + + +*) +end diff --git a/tests/hol4/betree/betree_TypesScript.sml b/tests/hol4/betree/betree_TypesScript.sml new file mode 100644 index 00000000..93be2f46 --- /dev/null +++ b/tests/hol4/betree/betree_TypesScript.sml @@ -0,0 +1,76 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree]: type definitions *) +open primitivesLib divDefLib + +val _ = new_theory "betree_Types" + + +Datatype: + (** [betree::betree::List] *) + betree_list_t = | BetreeListCons 't betree_list_t | BetreeListNil +End + +Datatype: + (** [betree::betree::UpsertFunState] *) + betree_upsert_fun_state_t = + | BetreeUpsertFunStateAdd u64 + | BetreeUpsertFunStateSub u64 +End + +Datatype: + (** [betree::betree::Message] *) + betree_message_t = + | BetreeMessageInsert u64 + | BetreeMessageDelete + | BetreeMessageUpsert betree_upsert_fun_state_t +End + +Datatype: + (** [betree::betree::Leaf] *) + betree_leaf_t = <| betree_leaf_id : u64; betree_leaf_size : u64; |> +End + +Datatype: + (** [betree::betree::Internal] *) + betree_internal_t = + <| + betree_internal_id : u64; + betree_internal_pivot : u64; + betree_internal_left : betree_node_t; + betree_internal_right : betree_node_t; + |> + ; + + (** [betree::betree::Node] *) + betree_node_t = + | BetreeNodeInternal betree_internal_t + | BetreeNodeLeaf betree_leaf_t +End + +Datatype: + (** [betree::betree::Params] *) + betree_params_t = + <| + betree_params_min_flush_size : u64; betree_params_split_size : u64; + |> +End + +Datatype: + (** [betree::betree::NodeIdCounter] *) + betree_node_id_counter_t = <| betree_node_id_counter_next_node_id : u64; |> +End + +Datatype: + (** [betree::betree::BeTree] *) + betree_be_tree_t = + <| + betree_be_tree_params : betree_params_t; + betree_be_tree_node_id_cnt : betree_node_id_counter_t; + betree_be_tree_root : betree_node_t; + |> +End + +(** The state type used in the state-error monad *) +val _ = new_type ("state", 0) + +val _ = export_theory () diff --git a/tests/hol4/betree/betree_TypesTheory.sig b/tests/hol4/betree/betree_TypesTheory.sig new file mode 100644 index 00000000..ee2ec4b5 --- /dev/null +++ b/tests/hol4/betree/betree_TypesTheory.sig @@ -0,0 +1,1751 @@ +signature betree_TypesTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val betree_be_tree_t_TY_DEF : thm + val betree_be_tree_t_betree_be_tree_node_id_cnt : thm + val betree_be_tree_t_betree_be_tree_node_id_cnt_fupd : thm + val betree_be_tree_t_betree_be_tree_params : thm + val betree_be_tree_t_betree_be_tree_params_fupd : thm + val betree_be_tree_t_betree_be_tree_root : thm + val betree_be_tree_t_betree_be_tree_root_fupd : thm + val betree_be_tree_t_case_def : thm + val betree_be_tree_t_size_def : thm + val betree_internal_t_TY_DEF : thm + val betree_internal_t_betree_internal_id : thm + val betree_internal_t_betree_internal_id_fupd : thm + val betree_internal_t_betree_internal_left : thm + val betree_internal_t_betree_internal_left_fupd : thm + val betree_internal_t_betree_internal_pivot : thm + val betree_internal_t_betree_internal_pivot_fupd : thm + val betree_internal_t_betree_internal_right : thm + val betree_internal_t_betree_internal_right_fupd : thm + val betree_internal_t_case_def : thm + val betree_internal_t_size_def : thm + val betree_leaf_t_TY_DEF : thm + val betree_leaf_t_betree_leaf_id : thm + val betree_leaf_t_betree_leaf_id_fupd : thm + val betree_leaf_t_betree_leaf_size : thm + val betree_leaf_t_betree_leaf_size_fupd : thm + val betree_leaf_t_case_def : thm + val betree_leaf_t_size_def : thm + val betree_list_t_TY_DEF : thm + val betree_list_t_case_def : thm + val betree_list_t_size_def : thm + val betree_message_t_TY_DEF : thm + val betree_message_t_case_def : thm + val betree_message_t_size_def : thm + val betree_node_id_counter_t_TY_DEF : thm + val betree_node_id_counter_t_betree_node_id_counter_next_node_id : thm + val betree_node_id_counter_t_betree_node_id_counter_next_node_id_fupd : thm + val betree_node_id_counter_t_case_def : thm + val betree_node_id_counter_t_size_def : thm + val betree_node_t_TY_DEF : thm + val betree_node_t_case_def : thm + val betree_params_t_TY_DEF : thm + val betree_params_t_betree_params_min_flush_size : thm + val betree_params_t_betree_params_min_flush_size_fupd : thm + val betree_params_t_betree_params_split_size : thm + val betree_params_t_betree_params_split_size_fupd : thm + val betree_params_t_case_def : thm + val betree_params_t_size_def : thm + val betree_upsert_fun_state_t_TY_DEF : thm + val betree_upsert_fun_state_t_case_def : thm + val betree_upsert_fun_state_t_size_def : thm + + (* Theorems *) + val EXISTS_betree_be_tree_t : thm + val EXISTS_betree_internal_t : thm + val EXISTS_betree_leaf_t : thm + val EXISTS_betree_node_id_counter_t : thm + val EXISTS_betree_params_t : thm + val FORALL_betree_be_tree_t : thm + val FORALL_betree_internal_t : thm + val FORALL_betree_leaf_t : thm + val FORALL_betree_node_id_counter_t : thm + val FORALL_betree_params_t : thm + val betree_be_tree_t_11 : thm + val betree_be_tree_t_Axiom : thm + val betree_be_tree_t_accessors : thm + val betree_be_tree_t_accfupds : thm + val betree_be_tree_t_case_cong : thm + val betree_be_tree_t_case_eq : thm + val betree_be_tree_t_component_equality : thm + val betree_be_tree_t_fn_updates : thm + val betree_be_tree_t_fupdcanon : thm + val betree_be_tree_t_fupdcanon_comp : thm + val betree_be_tree_t_fupdfupds : thm + val betree_be_tree_t_fupdfupds_comp : thm + val betree_be_tree_t_induction : thm + val betree_be_tree_t_literal_11 : thm + val betree_be_tree_t_literal_nchotomy : thm + val betree_be_tree_t_nchotomy : thm + val betree_be_tree_t_updates_eq_literal : thm + val betree_internal_t_11 : thm + val betree_internal_t_Axiom : thm + val betree_internal_t_accessors : thm + val betree_internal_t_accfupds : thm + val betree_internal_t_case_cong : thm + val betree_internal_t_case_eq : thm + val betree_internal_t_component_equality : thm + val betree_internal_t_fn_updates : thm + val betree_internal_t_fupdcanon : thm + val betree_internal_t_fupdcanon_comp : thm + val betree_internal_t_fupdfupds : thm + val betree_internal_t_fupdfupds_comp : thm + val betree_internal_t_induction : thm + val betree_internal_t_literal_11 : thm + val betree_internal_t_literal_nchotomy : thm + val betree_internal_t_nchotomy : thm + val betree_internal_t_updates_eq_literal : thm + val betree_leaf_t_11 : thm + val betree_leaf_t_Axiom : thm + val betree_leaf_t_accessors : thm + val betree_leaf_t_accfupds : thm + val betree_leaf_t_case_cong : thm + val betree_leaf_t_case_eq : thm + val betree_leaf_t_component_equality : thm + val betree_leaf_t_fn_updates : thm + val betree_leaf_t_fupdcanon : thm + val betree_leaf_t_fupdcanon_comp : thm + val betree_leaf_t_fupdfupds : thm + val betree_leaf_t_fupdfupds_comp : thm + val betree_leaf_t_induction : thm + val betree_leaf_t_literal_11 : thm + val betree_leaf_t_literal_nchotomy : thm + val betree_leaf_t_nchotomy : thm + val betree_leaf_t_updates_eq_literal : thm + val betree_list_t_11 : thm + val betree_list_t_Axiom : thm + val betree_list_t_case_cong : thm + val betree_list_t_case_eq : thm + val betree_list_t_distinct : thm + val betree_list_t_induction : thm + val betree_list_t_nchotomy : thm + val betree_message_t_11 : thm + val betree_message_t_Axiom : thm + val betree_message_t_case_cong : thm + val betree_message_t_case_eq : thm + val betree_message_t_distinct : thm + val betree_message_t_induction : thm + val betree_message_t_nchotomy : thm + val betree_node_id_counter_t_11 : thm + val betree_node_id_counter_t_Axiom : thm + val betree_node_id_counter_t_accessors : thm + val betree_node_id_counter_t_accfupds : thm + val betree_node_id_counter_t_case_cong : thm + val betree_node_id_counter_t_case_eq : thm + val betree_node_id_counter_t_component_equality : thm + val betree_node_id_counter_t_fn_updates : thm + val betree_node_id_counter_t_fupdfupds : thm + val betree_node_id_counter_t_fupdfupds_comp : thm + val betree_node_id_counter_t_induction : thm + val betree_node_id_counter_t_literal_11 : thm + val betree_node_id_counter_t_literal_nchotomy : thm + val betree_node_id_counter_t_nchotomy : thm + val betree_node_id_counter_t_updates_eq_literal : thm + val betree_node_t_11 : thm + val betree_node_t_Axiom : thm + val betree_node_t_case_cong : thm + val betree_node_t_case_eq : thm + val betree_node_t_distinct : thm + val betree_node_t_induction : thm + val betree_node_t_nchotomy : thm + val betree_params_t_11 : thm + val betree_params_t_Axiom : thm + val betree_params_t_accessors : thm + val betree_params_t_accfupds : thm + val betree_params_t_case_cong : thm + val betree_params_t_case_eq : thm + val betree_params_t_component_equality : thm + val betree_params_t_fn_updates : thm + val betree_params_t_fupdcanon : thm + val betree_params_t_fupdcanon_comp : thm + val betree_params_t_fupdfupds : thm + val betree_params_t_fupdfupds_comp : thm + val betree_params_t_induction : thm + val betree_params_t_literal_11 : thm + val betree_params_t_literal_nchotomy : thm + val betree_params_t_nchotomy : thm + val betree_params_t_updates_eq_literal : thm + val betree_upsert_fun_state_t_11 : thm + val betree_upsert_fun_state_t_Axiom : thm + val betree_upsert_fun_state_t_case_cong : thm + val betree_upsert_fun_state_t_case_eq : thm + val betree_upsert_fun_state_t_distinct : thm + val betree_upsert_fun_state_t_induction : thm + val betree_upsert_fun_state_t_nchotomy : thm + val datatype_betree_be_tree_t : thm + val datatype_betree_internal_t : thm + val datatype_betree_leaf_t : thm + val datatype_betree_list_t : thm + val datatype_betree_message_t : thm + val datatype_betree_node_id_counter_t : thm + val datatype_betree_params_t : thm + val datatype_betree_upsert_fun_state_t : thm + + val betree_Types_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "betree_Types" + + [betree_be_tree_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('betree_be_tree_t'). + (∀a0'. + (∃a0 a1 a2. + a0' = + (λa0 a1 a2. + ind_type$CONSTR 0 (a0,a1,a2) + (λn. ind_type$BOTTOM)) a0 a1 a2) ⇒ + $var$('betree_be_tree_t') a0') ⇒ + $var$('betree_be_tree_t') a0') rep + + [betree_be_tree_t_betree_be_tree_node_id_cnt] Definition + + ⊢ ∀b b0 b1. + (betree_be_tree_t b b0 b1).betree_be_tree_node_id_cnt = b0 + + [betree_be_tree_t_betree_be_tree_node_id_cnt_fupd] Definition + + ⊢ ∀f b b0 b1. + betree_be_tree_t b b0 b1 with + betree_be_tree_node_id_cnt updated_by f = + betree_be_tree_t b (f b0) b1 + + [betree_be_tree_t_betree_be_tree_params] Definition + + ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_params = b + + [betree_be_tree_t_betree_be_tree_params_fupd] Definition + + ⊢ ∀f b b0 b1. + betree_be_tree_t b b0 b1 with betree_be_tree_params updated_by f = + betree_be_tree_t (f b) b0 b1 + + [betree_be_tree_t_betree_be_tree_root] Definition + + ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_root = b1 + + [betree_be_tree_t_betree_be_tree_root_fupd] Definition + + ⊢ ∀f b b0 b1. + betree_be_tree_t b b0 b1 with betree_be_tree_root updated_by f = + betree_be_tree_t b b0 (f b1) + + [betree_be_tree_t_case_def] Definition + + ⊢ ∀a0 a1 a2 f. + betree_be_tree_t_CASE (betree_be_tree_t a0 a1 a2) f = f a0 a1 a2 + + [betree_be_tree_t_size_def] Definition + + ⊢ ∀a0 a1 a2. + betree_be_tree_t_size (betree_be_tree_t a0 a1 a2) = + 1 + + (betree_params_t_size a0 + + (betree_node_id_counter_t_size a1 + betree_node_t_size a2)) + + [betree_internal_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('betree_internal_t') $var$('betree_node_t'). + (∀a0'. + (∃a0 a1 a2 a3. + a0' = + (λa0 a1 a2 a3. + ind_type$CONSTR 0 (a0,a1,ARB) + (ind_type$FCONS a2 + (ind_type$FCONS a3 (λn. ind_type$BOTTOM)))) + a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧ + $var$('betree_node_t') a3) ⇒ + $var$('betree_internal_t') a0') ∧ + (∀a1'. + (∃a. a1' = + (λa. + ind_type$CONSTR (SUC 0) (ARB,ARB,ARB) + (ind_type$FCONS a (λn. ind_type$BOTTOM))) + a ∧ $var$('betree_internal_t') a) ∨ + (∃a. a1' = + (λa. + ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a) + (λn. ind_type$BOTTOM)) a) ⇒ + $var$('betree_node_t') a1') ⇒ + $var$('betree_internal_t') a0') rep + + [betree_internal_t_betree_internal_id] Definition + + ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_id = u + + [betree_internal_t_betree_internal_id_fupd] Definition + + ⊢ ∀f u u0 b b0. + betree_internal_t u u0 b b0 with betree_internal_id updated_by f = + betree_internal_t (f u) u0 b b0 + + [betree_internal_t_betree_internal_left] Definition + + ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_left = b + + [betree_internal_t_betree_internal_left_fupd] Definition + + ⊢ ∀f u u0 b b0. + betree_internal_t u u0 b b0 with + betree_internal_left updated_by f = + betree_internal_t u u0 (f b) b0 + + [betree_internal_t_betree_internal_pivot] Definition + + ⊢ ∀u u0 b b0. + (betree_internal_t u u0 b b0).betree_internal_pivot = u0 + + [betree_internal_t_betree_internal_pivot_fupd] Definition + + ⊢ ∀f u u0 b b0. + betree_internal_t u u0 b b0 with + betree_internal_pivot updated_by f = + betree_internal_t u (f u0) b b0 + + [betree_internal_t_betree_internal_right] Definition + + ⊢ ∀u u0 b b0. + (betree_internal_t u u0 b b0).betree_internal_right = b0 + + [betree_internal_t_betree_internal_right_fupd] Definition + + ⊢ ∀f u u0 b b0. + betree_internal_t u u0 b b0 with + betree_internal_right updated_by f = + betree_internal_t u u0 b (f b0) + + [betree_internal_t_case_def] Definition + + ⊢ ∀a0 a1 a2 a3 f. + betree_internal_t_CASE (betree_internal_t a0 a1 a2 a3) f = + f a0 a1 a2 a3 + + [betree_internal_t_size_def] Definition + + ⊢ (∀a0 a1 a2 a3. + betree_internal_t_size (betree_internal_t a0 a1 a2 a3) = + 1 + (betree_node_t_size a2 + betree_node_t_size a3)) ∧ + (∀a. betree_node_t_size (BetreeNodeInternal a) = + 1 + betree_internal_t_size a) ∧ + ∀a. betree_node_t_size (BetreeNodeLeaf a) = + 1 + betree_leaf_t_size a + + [betree_leaf_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('betree_leaf_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 (a0,a1) + (λn. ind_type$BOTTOM)) a0 a1) ⇒ + $var$('betree_leaf_t') a0') ⇒ + $var$('betree_leaf_t') a0') rep + + [betree_leaf_t_betree_leaf_id] Definition + + ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_id = u + + [betree_leaf_t_betree_leaf_id_fupd] Definition + + ⊢ ∀f u u0. + betree_leaf_t u u0 with betree_leaf_id updated_by f = + betree_leaf_t (f u) u0 + + [betree_leaf_t_betree_leaf_size] Definition + + ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_size = u0 + + [betree_leaf_t_betree_leaf_size_fupd] Definition + + ⊢ ∀f u u0. + betree_leaf_t u u0 with betree_leaf_size updated_by f = + betree_leaf_t u (f u0) + + [betree_leaf_t_case_def] Definition + + ⊢ ∀a0 a1 f. betree_leaf_t_CASE (betree_leaf_t a0 a1) f = f a0 a1 + + [betree_leaf_t_size_def] Definition + + ⊢ ∀a0 a1. betree_leaf_t_size (betree_leaf_t a0 a1) = 1 + + [betree_list_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('betree_list_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 a0 + (ind_type$FCONS a1 (λn. ind_type$BOTTOM))) + a0 a1 ∧ $var$('betree_list_t') a1) ∨ + a0' = + ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ + $var$('betree_list_t') a0') ⇒ + $var$('betree_list_t') a0') rep + + [betree_list_t_case_def] Definition + + ⊢ (∀a0 a1 f v. + betree_list_t_CASE (BetreeListCons a0 a1) f v = f a0 a1) ∧ + ∀f v. betree_list_t_CASE BetreeListNil f v = v + + [betree_list_t_size_def] Definition + + ⊢ (∀f a0 a1. + betree_list_t_size f (BetreeListCons a0 a1) = + 1 + (f a0 + betree_list_t_size f a1)) ∧ + ∀f. betree_list_t_size f BetreeListNil = 0 + + [betree_message_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('betree_message_t'). + (∀a0. + (∃a. a0 = + (λa. + ind_type$CONSTR 0 (a,ARB) + (λn. ind_type$BOTTOM)) a) ∨ + a0 = + ind_type$CONSTR (SUC 0) (ARB,ARB) + (λn. ind_type$BOTTOM) ∨ + (∃a. a0 = + (λa. + ind_type$CONSTR (SUC (SUC 0)) (ARB,a) + (λn. ind_type$BOTTOM)) a) ⇒ + $var$('betree_message_t') a0) ⇒ + $var$('betree_message_t') a0) rep + + [betree_message_t_case_def] Definition + + ⊢ (∀a f v f1. + betree_message_t_CASE (BetreeMessageInsert a) f v f1 = f a) ∧ + (∀f v f1. betree_message_t_CASE BetreeMessageDelete f v f1 = v) ∧ + ∀a f v f1. + betree_message_t_CASE (BetreeMessageUpsert a) f v f1 = f1 a + + [betree_message_t_size_def] Definition + + ⊢ (∀a. betree_message_t_size (BetreeMessageInsert a) = 1) ∧ + betree_message_t_size BetreeMessageDelete = 0 ∧ + ∀a. betree_message_t_size (BetreeMessageUpsert a) = + 1 + betree_upsert_fun_state_t_size a + + [betree_node_id_counter_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('betree_node_id_counter_t'). + (∀a0. + (∃a. a0 = + (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) + a) ⇒ + $var$('betree_node_id_counter_t') a0) ⇒ + $var$('betree_node_id_counter_t') a0) rep + + [betree_node_id_counter_t_betree_node_id_counter_next_node_id] Definition + + ⊢ ∀u. (betree_node_id_counter_t u). + betree_node_id_counter_next_node_id = + u + + [betree_node_id_counter_t_betree_node_id_counter_next_node_id_fupd] Definition + + ⊢ ∀f u. + betree_node_id_counter_t u with + betree_node_id_counter_next_node_id updated_by f = + betree_node_id_counter_t (f u) + + [betree_node_id_counter_t_case_def] Definition + + ⊢ ∀a f. + betree_node_id_counter_t_CASE (betree_node_id_counter_t a) f = + f a + + [betree_node_id_counter_t_size_def] Definition + + ⊢ ∀a. betree_node_id_counter_t_size (betree_node_id_counter_t a) = 1 + + [betree_node_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa1'. + ∀ $var$('betree_internal_t') $var$('betree_node_t'). + (∀a0'. + (∃a0 a1 a2 a3. + a0' = + (λa0 a1 a2 a3. + ind_type$CONSTR 0 (a0,a1,ARB) + (ind_type$FCONS a2 + (ind_type$FCONS a3 (λn. ind_type$BOTTOM)))) + a0 a1 a2 a3 ∧ $var$('betree_node_t') a2 ∧ + $var$('betree_node_t') a3) ⇒ + $var$('betree_internal_t') a0') ∧ + (∀a1'. + (∃a. a1' = + (λa. + ind_type$CONSTR (SUC 0) (ARB,ARB,ARB) + (ind_type$FCONS a (λn. ind_type$BOTTOM))) + a ∧ $var$('betree_internal_t') a) ∨ + (∃a. a1' = + (λa. + ind_type$CONSTR (SUC (SUC 0)) (ARB,ARB,a) + (λn. ind_type$BOTTOM)) a) ⇒ + $var$('betree_node_t') a1') ⇒ + $var$('betree_node_t') a1') rep + + [betree_node_t_case_def] Definition + + ⊢ (∀a f f1. betree_node_t_CASE (BetreeNodeInternal a) f f1 = f a) ∧ + ∀a f f1. betree_node_t_CASE (BetreeNodeLeaf a) f f1 = f1 a + + [betree_params_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('betree_params_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 (a0,a1) + (λn. ind_type$BOTTOM)) a0 a1) ⇒ + $var$('betree_params_t') a0') ⇒ + $var$('betree_params_t') a0') rep + + [betree_params_t_betree_params_min_flush_size] Definition + + ⊢ ∀u u0. (betree_params_t u u0).betree_params_min_flush_size = u + + [betree_params_t_betree_params_min_flush_size_fupd] Definition + + ⊢ ∀f u u0. + betree_params_t u u0 with + betree_params_min_flush_size updated_by f = + betree_params_t (f u) u0 + + [betree_params_t_betree_params_split_size] Definition + + ⊢ ∀u u0. (betree_params_t u u0).betree_params_split_size = u0 + + [betree_params_t_betree_params_split_size_fupd] Definition + + ⊢ ∀f u u0. + betree_params_t u u0 with betree_params_split_size updated_by f = + betree_params_t u (f u0) + + [betree_params_t_case_def] Definition + + ⊢ ∀a0 a1 f. betree_params_t_CASE (betree_params_t a0 a1) f = f a0 a1 + + [betree_params_t_size_def] Definition + + ⊢ ∀a0 a1. betree_params_t_size (betree_params_t a0 a1) = 1 + + [betree_upsert_fun_state_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('betree_upsert_fun_state_t'). + (∀a0. + (∃a. a0 = + (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) + a) ∨ + (∃a. a0 = + (λa. + ind_type$CONSTR (SUC 0) a + (λn. ind_type$BOTTOM)) a) ⇒ + $var$('betree_upsert_fun_state_t') a0) ⇒ + $var$('betree_upsert_fun_state_t') a0) rep + + [betree_upsert_fun_state_t_case_def] Definition + + ⊢ (∀a f f1. + betree_upsert_fun_state_t_CASE (BetreeUpsertFunStateAdd a) f f1 = + f a) ∧ + ∀a f f1. + betree_upsert_fun_state_t_CASE (BetreeUpsertFunStateSub a) f f1 = + f1 a + + [betree_upsert_fun_state_t_size_def] Definition + + ⊢ (∀a. betree_upsert_fun_state_t_size (BetreeUpsertFunStateAdd a) = 1) ∧ + ∀a. betree_upsert_fun_state_t_size (BetreeUpsertFunStateSub a) = 1 + + [EXISTS_betree_be_tree_t] Theorem + + ⊢ ∀P. (∃b. P b) ⇔ + ∃b2 b1 b0. + P + <|betree_be_tree_params := b2; + betree_be_tree_node_id_cnt := b1; + betree_be_tree_root := b0|> + + [EXISTS_betree_internal_t] Theorem + + ⊢ ∀P. (∃b. P b) ⇔ + ∃u0 u b1 b0. + P + <|betree_internal_id := u0; betree_internal_pivot := u; + betree_internal_left := b1; betree_internal_right := b0|> + + [EXISTS_betree_leaf_t] Theorem + + ⊢ ∀P. (∃b. P b) ⇔ + ∃u0 u. P <|betree_leaf_id := u0; betree_leaf_size := u|> + + [EXISTS_betree_node_id_counter_t] Theorem + + ⊢ ∀P. (∃b. P b) ⇔ ∃u. P <|betree_node_id_counter_next_node_id := u|> + + [EXISTS_betree_params_t] Theorem + + ⊢ ∀P. (∃b. P b) ⇔ + ∃u0 u. + P + <|betree_params_min_flush_size := u0; + betree_params_split_size := u|> + + [FORALL_betree_be_tree_t] Theorem + + ⊢ ∀P. (∀b. P b) ⇔ + ∀b2 b1 b0. + P + <|betree_be_tree_params := b2; + betree_be_tree_node_id_cnt := b1; + betree_be_tree_root := b0|> + + [FORALL_betree_internal_t] Theorem + + ⊢ ∀P. (∀b. P b) ⇔ + ∀u0 u b1 b0. + P + <|betree_internal_id := u0; betree_internal_pivot := u; + betree_internal_left := b1; betree_internal_right := b0|> + + [FORALL_betree_leaf_t] Theorem + + ⊢ ∀P. (∀b. P b) ⇔ + ∀u0 u. P <|betree_leaf_id := u0; betree_leaf_size := u|> + + [FORALL_betree_node_id_counter_t] Theorem + + ⊢ ∀P. (∀b. P b) ⇔ ∀u. P <|betree_node_id_counter_next_node_id := u|> + + [FORALL_betree_params_t] Theorem + + ⊢ ∀P. (∀b. P b) ⇔ + ∀u0 u. + P + <|betree_params_min_flush_size := u0; + betree_params_split_size := u|> + + [betree_be_tree_t_11] Theorem + + ⊢ ∀a0 a1 a2 a0' a1' a2'. + betree_be_tree_t a0 a1 a2 = betree_be_tree_t a0' a1' a2' ⇔ + a0 = a0' ∧ a1 = a1' ∧ a2 = a2' + + [betree_be_tree_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a0 a1 a2. fn (betree_be_tree_t a0 a1 a2) = f a0 a1 a2 + + [betree_be_tree_t_accessors] Theorem + + ⊢ (∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_params = b) ∧ + (∀b b0 b1. + (betree_be_tree_t b b0 b1).betree_be_tree_node_id_cnt = b0) ∧ + ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_root = b1 + + [betree_be_tree_t_accfupds] Theorem + + ⊢ (∀f b. + (b with betree_be_tree_node_id_cnt updated_by f). + betree_be_tree_params = + b.betree_be_tree_params) ∧ + (∀f b. + (b with betree_be_tree_root updated_by f).betree_be_tree_params = + b.betree_be_tree_params) ∧ + (∀f b. + (b with betree_be_tree_params updated_by f). + betree_be_tree_node_id_cnt = + b.betree_be_tree_node_id_cnt) ∧ + (∀f b. + (b with betree_be_tree_root updated_by f). + betree_be_tree_node_id_cnt = + b.betree_be_tree_node_id_cnt) ∧ + (∀f b. + (b with betree_be_tree_params updated_by f).betree_be_tree_root = + b.betree_be_tree_root) ∧ + (∀f b. + (b with betree_be_tree_node_id_cnt updated_by f). + betree_be_tree_root = + b.betree_be_tree_root) ∧ + (∀f b. + (b with betree_be_tree_params updated_by f). + betree_be_tree_params = + f b.betree_be_tree_params) ∧ + (∀f b. + (b with betree_be_tree_node_id_cnt updated_by f). + betree_be_tree_node_id_cnt = + f b.betree_be_tree_node_id_cnt) ∧ + ∀f b. + (b with betree_be_tree_root updated_by f).betree_be_tree_root = + f b.betree_be_tree_root + + [betree_be_tree_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ + (∀a0 a1 a2. + M' = betree_be_tree_t a0 a1 a2 ⇒ f a0 a1 a2 = f' a0 a1 a2) ⇒ + betree_be_tree_t_CASE M f = betree_be_tree_t_CASE M' f' + + [betree_be_tree_t_case_eq] Theorem + + ⊢ betree_be_tree_t_CASE x f = v ⇔ + ∃b b0 b1. x = betree_be_tree_t b b0 b1 ∧ f b b0 b1 = v + + [betree_be_tree_t_component_equality] Theorem + + ⊢ ∀b1 b2. + b1 = b2 ⇔ + b1.betree_be_tree_params = b2.betree_be_tree_params ∧ + b1.betree_be_tree_node_id_cnt = b2.betree_be_tree_node_id_cnt ∧ + b1.betree_be_tree_root = b2.betree_be_tree_root + + [betree_be_tree_t_fn_updates] Theorem + + ⊢ (∀f b b0 b1. + betree_be_tree_t b b0 b1 with betree_be_tree_params updated_by f = + betree_be_tree_t (f b) b0 b1) ∧ + (∀f b b0 b1. + betree_be_tree_t b b0 b1 with + betree_be_tree_node_id_cnt updated_by f = + betree_be_tree_t b (f b0) b1) ∧ + ∀f b b0 b1. + betree_be_tree_t b b0 b1 with betree_be_tree_root updated_by f = + betree_be_tree_t b b0 (f b1) + + [betree_be_tree_t_fupdcanon] Theorem + + ⊢ (∀g f b. + b with + <|betree_be_tree_node_id_cnt updated_by f; + betree_be_tree_params updated_by g|> = + b with + <|betree_be_tree_params updated_by g; + betree_be_tree_node_id_cnt updated_by f|>) ∧ + (∀g f b. + b with + <|betree_be_tree_root updated_by f; + betree_be_tree_params updated_by g|> = + b with + <|betree_be_tree_params updated_by g; + betree_be_tree_root updated_by f|>) ∧ + ∀g f b. + b with + <|betree_be_tree_root updated_by f; + betree_be_tree_node_id_cnt updated_by g|> = + b with + <|betree_be_tree_node_id_cnt updated_by g; + betree_be_tree_root updated_by f|> + + [betree_be_tree_t_fupdcanon_comp] Theorem + + ⊢ ((∀g f. + betree_be_tree_node_id_cnt_fupd f ∘ + betree_be_tree_params_fupd g = + betree_be_tree_params_fupd g ∘ + betree_be_tree_node_id_cnt_fupd f) ∧ + ∀h g f. + betree_be_tree_node_id_cnt_fupd f ∘ + betree_be_tree_params_fupd g ∘ h = + betree_be_tree_params_fupd g ∘ + betree_be_tree_node_id_cnt_fupd f ∘ h) ∧ + ((∀g f. + betree_be_tree_root_fupd f ∘ betree_be_tree_params_fupd g = + betree_be_tree_params_fupd g ∘ betree_be_tree_root_fupd f) ∧ + ∀h g f. + betree_be_tree_root_fupd f ∘ betree_be_tree_params_fupd g ∘ h = + betree_be_tree_params_fupd g ∘ betree_be_tree_root_fupd f ∘ h) ∧ + (∀g f. + betree_be_tree_root_fupd f ∘ betree_be_tree_node_id_cnt_fupd g = + betree_be_tree_node_id_cnt_fupd g ∘ betree_be_tree_root_fupd f) ∧ + ∀h g f. + betree_be_tree_root_fupd f ∘ betree_be_tree_node_id_cnt_fupd g ∘ + h = + betree_be_tree_node_id_cnt_fupd g ∘ betree_be_tree_root_fupd f ∘ + h + + [betree_be_tree_t_fupdfupds] Theorem + + ⊢ (∀g f b. + b with + <|betree_be_tree_params updated_by f; + betree_be_tree_params updated_by g|> = + b with betree_be_tree_params updated_by f ∘ g) ∧ + (∀g f b. + b with + <|betree_be_tree_node_id_cnt updated_by f; + betree_be_tree_node_id_cnt updated_by g|> = + b with betree_be_tree_node_id_cnt updated_by f ∘ g) ∧ + ∀g f b. + b with + <|betree_be_tree_root updated_by f; + betree_be_tree_root updated_by g|> = + b with betree_be_tree_root updated_by f ∘ g + + [betree_be_tree_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. + betree_be_tree_params_fupd f ∘ betree_be_tree_params_fupd g = + betree_be_tree_params_fupd (f ∘ g)) ∧ + ∀h g f. + betree_be_tree_params_fupd f ∘ betree_be_tree_params_fupd g ∘ h = + betree_be_tree_params_fupd (f ∘ g) ∘ h) ∧ + ((∀g f. + betree_be_tree_node_id_cnt_fupd f ∘ + betree_be_tree_node_id_cnt_fupd g = + betree_be_tree_node_id_cnt_fupd (f ∘ g)) ∧ + ∀h g f. + betree_be_tree_node_id_cnt_fupd f ∘ + betree_be_tree_node_id_cnt_fupd g ∘ h = + betree_be_tree_node_id_cnt_fupd (f ∘ g) ∘ h) ∧ + (∀g f. + betree_be_tree_root_fupd f ∘ betree_be_tree_root_fupd g = + betree_be_tree_root_fupd (f ∘ g)) ∧ + ∀h g f. + betree_be_tree_root_fupd f ∘ betree_be_tree_root_fupd g ∘ h = + betree_be_tree_root_fupd (f ∘ g) ∘ h + + [betree_be_tree_t_induction] Theorem + + ⊢ ∀P. (∀b b0 b1. P (betree_be_tree_t b b0 b1)) ⇒ ∀b. P b + + [betree_be_tree_t_literal_11] Theorem + + ⊢ ∀b21 b11 b01 b22 b12 b02. + <|betree_be_tree_params := b21; + betree_be_tree_node_id_cnt := b11; betree_be_tree_root := b01|> = + <|betree_be_tree_params := b22; + betree_be_tree_node_id_cnt := b12; betree_be_tree_root := b02|> ⇔ + b21 = b22 ∧ b11 = b12 ∧ b01 = b02 + + [betree_be_tree_t_literal_nchotomy] Theorem + + ⊢ ∀b. ∃b2 b1 b0. + b = + <|betree_be_tree_params := b2; betree_be_tree_node_id_cnt := b1; + betree_be_tree_root := b0|> + + [betree_be_tree_t_nchotomy] Theorem + + ⊢ ∀bb. ∃b b0 b1. bb = betree_be_tree_t b b0 b1 + + [betree_be_tree_t_updates_eq_literal] Theorem + + ⊢ ∀b b2 b1 b0. + b with + <|betree_be_tree_params := b2; betree_be_tree_node_id_cnt := b1; + betree_be_tree_root := b0|> = + <|betree_be_tree_params := b2; betree_be_tree_node_id_cnt := b1; + betree_be_tree_root := b0|> + + [betree_internal_t_11] Theorem + + ⊢ ∀a0 a1 a2 a3 a0' a1' a2' a3'. + betree_internal_t a0 a1 a2 a3 = betree_internal_t a0' a1' a2' a3' ⇔ + a0 = a0' ∧ a1 = a1' ∧ a2 = a2' ∧ a3 = a3' + + [betree_internal_t_Axiom] Theorem + + ⊢ ∀f0 f1 f2. ∃fn0 fn1. + (∀a0 a1 a2 a3. + fn0 (betree_internal_t a0 a1 a2 a3) = + f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧ + (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧ + ∀a. fn1 (BetreeNodeLeaf a) = f2 a + + [betree_internal_t_accessors] Theorem + + ⊢ (∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_id = u) ∧ + (∀u u0 b b0. + (betree_internal_t u u0 b b0).betree_internal_pivot = u0) ∧ + (∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_left = b) ∧ + ∀u u0 b b0. + (betree_internal_t u u0 b b0).betree_internal_right = b0 + + [betree_internal_t_accfupds] Theorem + + ⊢ (∀f b. + (b with betree_internal_pivot updated_by f).betree_internal_id = + b.betree_internal_id) ∧ + (∀f b. + (b with betree_internal_left updated_by f).betree_internal_id = + b.betree_internal_id) ∧ + (∀f b. + (b with betree_internal_right updated_by f).betree_internal_id = + b.betree_internal_id) ∧ + (∀f b. + (b with betree_internal_id updated_by f).betree_internal_pivot = + b.betree_internal_pivot) ∧ + (∀f b. + (b with betree_internal_left updated_by f).betree_internal_pivot = + b.betree_internal_pivot) ∧ + (∀f b. + (b with betree_internal_right updated_by f). + betree_internal_pivot = + b.betree_internal_pivot) ∧ + (∀f b. + (b with betree_internal_id updated_by f).betree_internal_left = + b.betree_internal_left) ∧ + (∀f b. + (b with betree_internal_pivot updated_by f).betree_internal_left = + b.betree_internal_left) ∧ + (∀f b. + (b with betree_internal_right updated_by f).betree_internal_left = + b.betree_internal_left) ∧ + (∀f b. + (b with betree_internal_id updated_by f).betree_internal_right = + b.betree_internal_right) ∧ + (∀f b. + (b with betree_internal_pivot updated_by f). + betree_internal_right = + b.betree_internal_right) ∧ + (∀f b. + (b with betree_internal_left updated_by f).betree_internal_right = + b.betree_internal_right) ∧ + (∀f b. + (b with betree_internal_id updated_by f).betree_internal_id = + f b.betree_internal_id) ∧ + (∀f b. + (b with betree_internal_pivot updated_by f). + betree_internal_pivot = + f b.betree_internal_pivot) ∧ + (∀f b. + (b with betree_internal_left updated_by f).betree_internal_left = + f b.betree_internal_left) ∧ + ∀f b. + (b with betree_internal_right updated_by f).betree_internal_right = + f b.betree_internal_right + + [betree_internal_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ + (∀a0 a1 a2 a3. + M' = betree_internal_t a0 a1 a2 a3 ⇒ + f a0 a1 a2 a3 = f' a0 a1 a2 a3) ⇒ + betree_internal_t_CASE M f = betree_internal_t_CASE M' f' + + [betree_internal_t_case_eq] Theorem + + ⊢ betree_internal_t_CASE x f = v ⇔ + ∃u0 u b b0. x = betree_internal_t u0 u b b0 ∧ f u0 u b b0 = v + + [betree_internal_t_component_equality] Theorem + + ⊢ ∀b1 b2. + b1 = b2 ⇔ + b1.betree_internal_id = b2.betree_internal_id ∧ + b1.betree_internal_pivot = b2.betree_internal_pivot ∧ + b1.betree_internal_left = b2.betree_internal_left ∧ + b1.betree_internal_right = b2.betree_internal_right + + [betree_internal_t_fn_updates] Theorem + + ⊢ (∀f u u0 b b0. + betree_internal_t u u0 b b0 with betree_internal_id updated_by f = + betree_internal_t (f u) u0 b b0) ∧ + (∀f u u0 b b0. + betree_internal_t u u0 b b0 with + betree_internal_pivot updated_by f = + betree_internal_t u (f u0) b b0) ∧ + (∀f u u0 b b0. + betree_internal_t u u0 b b0 with + betree_internal_left updated_by f = + betree_internal_t u u0 (f b) b0) ∧ + ∀f u u0 b b0. + betree_internal_t u u0 b b0 with + betree_internal_right updated_by f = + betree_internal_t u u0 b (f b0) + + [betree_internal_t_fupdcanon] Theorem + + ⊢ (∀g f b. + b with + <|betree_internal_pivot updated_by f; + betree_internal_id updated_by g|> = + b with + <|betree_internal_id updated_by g; + betree_internal_pivot updated_by f|>) ∧ + (∀g f b. + b with + <|betree_internal_left updated_by f; + betree_internal_id updated_by g|> = + b with + <|betree_internal_id updated_by g; + betree_internal_left updated_by f|>) ∧ + (∀g f b. + b with + <|betree_internal_left updated_by f; + betree_internal_pivot updated_by g|> = + b with + <|betree_internal_pivot updated_by g; + betree_internal_left updated_by f|>) ∧ + (∀g f b. + b with + <|betree_internal_right updated_by f; + betree_internal_id updated_by g|> = + b with + <|betree_internal_id updated_by g; + betree_internal_right updated_by f|>) ∧ + (∀g f b. + b with + <|betree_internal_right updated_by f; + betree_internal_pivot updated_by g|> = + b with + <|betree_internal_pivot updated_by g; + betree_internal_right updated_by f|>) ∧ + ∀g f b. + b with + <|betree_internal_right updated_by f; + betree_internal_left updated_by g|> = + b with + <|betree_internal_left updated_by g; + betree_internal_right updated_by f|> + + [betree_internal_t_fupdcanon_comp] Theorem + + ⊢ ((∀g f. + betree_internal_pivot_fupd f ∘ betree_internal_id_fupd g = + betree_internal_id_fupd g ∘ betree_internal_pivot_fupd f) ∧ + ∀h g f. + betree_internal_pivot_fupd f ∘ betree_internal_id_fupd g ∘ h = + betree_internal_id_fupd g ∘ betree_internal_pivot_fupd f ∘ h) ∧ + ((∀g f. + betree_internal_left_fupd f ∘ betree_internal_id_fupd g = + betree_internal_id_fupd g ∘ betree_internal_left_fupd f) ∧ + ∀h g f. + betree_internal_left_fupd f ∘ betree_internal_id_fupd g ∘ h = + betree_internal_id_fupd g ∘ betree_internal_left_fupd f ∘ h) ∧ + ((∀g f. + betree_internal_left_fupd f ∘ betree_internal_pivot_fupd g = + betree_internal_pivot_fupd g ∘ betree_internal_left_fupd f) ∧ + ∀h g f. + betree_internal_left_fupd f ∘ betree_internal_pivot_fupd g ∘ h = + betree_internal_pivot_fupd g ∘ betree_internal_left_fupd f ∘ h) ∧ + ((∀g f. + betree_internal_right_fupd f ∘ betree_internal_id_fupd g = + betree_internal_id_fupd g ∘ betree_internal_right_fupd f) ∧ + ∀h g f. + betree_internal_right_fupd f ∘ betree_internal_id_fupd g ∘ h = + betree_internal_id_fupd g ∘ betree_internal_right_fupd f ∘ h) ∧ + ((∀g f. + betree_internal_right_fupd f ∘ betree_internal_pivot_fupd g = + betree_internal_pivot_fupd g ∘ betree_internal_right_fupd f) ∧ + ∀h g f. + betree_internal_right_fupd f ∘ betree_internal_pivot_fupd g ∘ h = + betree_internal_pivot_fupd g ∘ betree_internal_right_fupd f ∘ h) ∧ + (∀g f. + betree_internal_right_fupd f ∘ betree_internal_left_fupd g = + betree_internal_left_fupd g ∘ betree_internal_right_fupd f) ∧ + ∀h g f. + betree_internal_right_fupd f ∘ betree_internal_left_fupd g ∘ h = + betree_internal_left_fupd g ∘ betree_internal_right_fupd f ∘ h + + [betree_internal_t_fupdfupds] Theorem + + ⊢ (∀g f b. + b with + <|betree_internal_id updated_by f; + betree_internal_id updated_by g|> = + b with betree_internal_id updated_by f ∘ g) ∧ + (∀g f b. + b with + <|betree_internal_pivot updated_by f; + betree_internal_pivot updated_by g|> = + b with betree_internal_pivot updated_by f ∘ g) ∧ + (∀g f b. + b with + <|betree_internal_left updated_by f; + betree_internal_left updated_by g|> = + b with betree_internal_left updated_by f ∘ g) ∧ + ∀g f b. + b with + <|betree_internal_right updated_by f; + betree_internal_right updated_by g|> = + b with betree_internal_right updated_by f ∘ g + + [betree_internal_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. + betree_internal_id_fupd f ∘ betree_internal_id_fupd g = + betree_internal_id_fupd (f ∘ g)) ∧ + ∀h g f. + betree_internal_id_fupd f ∘ betree_internal_id_fupd g ∘ h = + betree_internal_id_fupd (f ∘ g) ∘ h) ∧ + ((∀g f. + betree_internal_pivot_fupd f ∘ betree_internal_pivot_fupd g = + betree_internal_pivot_fupd (f ∘ g)) ∧ + ∀h g f. + betree_internal_pivot_fupd f ∘ betree_internal_pivot_fupd g ∘ h = + betree_internal_pivot_fupd (f ∘ g) ∘ h) ∧ + ((∀g f. + betree_internal_left_fupd f ∘ betree_internal_left_fupd g = + betree_internal_left_fupd (f ∘ g)) ∧ + ∀h g f. + betree_internal_left_fupd f ∘ betree_internal_left_fupd g ∘ h = + betree_internal_left_fupd (f ∘ g) ∘ h) ∧ + (∀g f. + betree_internal_right_fupd f ∘ betree_internal_right_fupd g = + betree_internal_right_fupd (f ∘ g)) ∧ + ∀h g f. + betree_internal_right_fupd f ∘ betree_internal_right_fupd g ∘ h = + betree_internal_right_fupd (f ∘ g) ∘ h + + [betree_internal_t_induction] Theorem + + ⊢ ∀P0 P1. + (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧ + (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧ + (∀b. P1 (BetreeNodeLeaf b)) ⇒ + (∀b. P0 b) ∧ ∀b. P1 b + + [betree_internal_t_literal_11] Theorem + + ⊢ ∀u01 u1 b11 b01 u02 u2 b12 b02. + <|betree_internal_id := u01; betree_internal_pivot := u1; + betree_internal_left := b11; betree_internal_right := b01|> = + <|betree_internal_id := u02; betree_internal_pivot := u2; + betree_internal_left := b12; betree_internal_right := b02|> ⇔ + u01 = u02 ∧ u1 = u2 ∧ b11 = b12 ∧ b01 = b02 + + [betree_internal_t_literal_nchotomy] Theorem + + ⊢ ∀b. ∃u0 u b1 b0. + b = + <|betree_internal_id := u0; betree_internal_pivot := u; + betree_internal_left := b1; betree_internal_right := b0|> + + [betree_internal_t_nchotomy] Theorem + + ⊢ ∀bb. ∃u0 u b b0. bb = betree_internal_t u0 u b b0 + + [betree_internal_t_updates_eq_literal] Theorem + + ⊢ ∀b u0 u b1 b0. + b with + <|betree_internal_id := u0; betree_internal_pivot := u; + betree_internal_left := b1; betree_internal_right := b0|> = + <|betree_internal_id := u0; betree_internal_pivot := u; + betree_internal_left := b1; betree_internal_right := b0|> + + [betree_leaf_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + betree_leaf_t a0 a1 = betree_leaf_t a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [betree_leaf_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a0 a1. fn (betree_leaf_t a0 a1) = f a0 a1 + + [betree_leaf_t_accessors] Theorem + + ⊢ (∀u u0. (betree_leaf_t u u0).betree_leaf_id = u) ∧ + ∀u u0. (betree_leaf_t u u0).betree_leaf_size = u0 + + [betree_leaf_t_accfupds] Theorem + + ⊢ (∀f b. + (b with betree_leaf_size updated_by f).betree_leaf_id = + b.betree_leaf_id) ∧ + (∀f b. + (b with betree_leaf_id updated_by f).betree_leaf_size = + b.betree_leaf_size) ∧ + (∀f b. + (b with betree_leaf_id updated_by f).betree_leaf_id = + f b.betree_leaf_id) ∧ + ∀f b. + (b with betree_leaf_size updated_by f).betree_leaf_size = + f b.betree_leaf_size + + [betree_leaf_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a0 a1. M' = betree_leaf_t a0 a1 ⇒ f a0 a1 = f' a0 a1) ⇒ + betree_leaf_t_CASE M f = betree_leaf_t_CASE M' f' + + [betree_leaf_t_case_eq] Theorem + + ⊢ betree_leaf_t_CASE x f = v ⇔ + ∃u u0. x = betree_leaf_t u u0 ∧ f u u0 = v + + [betree_leaf_t_component_equality] Theorem + + ⊢ ∀b1 b2. + b1 = b2 ⇔ + b1.betree_leaf_id = b2.betree_leaf_id ∧ + b1.betree_leaf_size = b2.betree_leaf_size + + [betree_leaf_t_fn_updates] Theorem + + ⊢ (∀f u u0. + betree_leaf_t u u0 with betree_leaf_id updated_by f = + betree_leaf_t (f u) u0) ∧ + ∀f u u0. + betree_leaf_t u u0 with betree_leaf_size updated_by f = + betree_leaf_t u (f u0) + + [betree_leaf_t_fupdcanon] Theorem + + ⊢ ∀g f b. + b with + <|betree_leaf_size updated_by f; betree_leaf_id updated_by g|> = + b with + <|betree_leaf_id updated_by g; betree_leaf_size updated_by f|> + + [betree_leaf_t_fupdcanon_comp] Theorem + + ⊢ (∀g f. + betree_leaf_size_fupd f ∘ betree_leaf_id_fupd g = + betree_leaf_id_fupd g ∘ betree_leaf_size_fupd f) ∧ + ∀h g f. + betree_leaf_size_fupd f ∘ betree_leaf_id_fupd g ∘ h = + betree_leaf_id_fupd g ∘ betree_leaf_size_fupd f ∘ h + + [betree_leaf_t_fupdfupds] Theorem + + ⊢ (∀g f b. + b with + <|betree_leaf_id updated_by f; betree_leaf_id updated_by g|> = + b with betree_leaf_id updated_by f ∘ g) ∧ + ∀g f b. + b with + <|betree_leaf_size updated_by f; betree_leaf_size updated_by g|> = + b with betree_leaf_size updated_by f ∘ g + + [betree_leaf_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. + betree_leaf_id_fupd f ∘ betree_leaf_id_fupd g = + betree_leaf_id_fupd (f ∘ g)) ∧ + ∀h g f. + betree_leaf_id_fupd f ∘ betree_leaf_id_fupd g ∘ h = + betree_leaf_id_fupd (f ∘ g) ∘ h) ∧ + (∀g f. + betree_leaf_size_fupd f ∘ betree_leaf_size_fupd g = + betree_leaf_size_fupd (f ∘ g)) ∧ + ∀h g f. + betree_leaf_size_fupd f ∘ betree_leaf_size_fupd g ∘ h = + betree_leaf_size_fupd (f ∘ g) ∘ h + + [betree_leaf_t_induction] Theorem + + ⊢ ∀P. (∀u u0. P (betree_leaf_t u u0)) ⇒ ∀b. P b + + [betree_leaf_t_literal_11] Theorem + + ⊢ ∀u01 u1 u02 u2. + <|betree_leaf_id := u01; betree_leaf_size := u1|> = + <|betree_leaf_id := u02; betree_leaf_size := u2|> ⇔ + u01 = u02 ∧ u1 = u2 + + [betree_leaf_t_literal_nchotomy] Theorem + + ⊢ ∀b. ∃u0 u. b = <|betree_leaf_id := u0; betree_leaf_size := u|> + + [betree_leaf_t_nchotomy] Theorem + + ⊢ ∀bb. ∃u u0. bb = betree_leaf_t u u0 + + [betree_leaf_t_updates_eq_literal] Theorem + + ⊢ ∀b u0 u. + b with <|betree_leaf_id := u0; betree_leaf_size := u|> = + <|betree_leaf_id := u0; betree_leaf_size := u|> + + [betree_list_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + BetreeListCons a0 a1 = BetreeListCons a0' a1' ⇔ + a0 = a0' ∧ a1 = a1' + + [betree_list_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a0 a1. fn (BetreeListCons a0 a1) = f0 a0 a1 (fn a1)) ∧ + fn BetreeListNil = f1 + + [betree_list_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ + (∀a0 a1. M' = BetreeListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ + (M' = BetreeListNil ⇒ v = v') ⇒ + betree_list_t_CASE M f v = betree_list_t_CASE M' f' v' + + [betree_list_t_case_eq] Theorem + + ⊢ betree_list_t_CASE x f v = v' ⇔ + (∃t b. x = BetreeListCons t b ∧ f t b = v') ∨ + x = BetreeListNil ∧ v = v' + + [betree_list_t_distinct] Theorem + + ⊢ ∀a1 a0. BetreeListCons a0 a1 ≠ BetreeListNil + + [betree_list_t_induction] Theorem + + ⊢ ∀P. (∀b. P b ⇒ ∀t. P (BetreeListCons t b)) ∧ P BetreeListNil ⇒ + ∀b. P b + + [betree_list_t_nchotomy] Theorem + + ⊢ ∀bb. (∃t b. bb = BetreeListCons t b) ∨ bb = BetreeListNil + + [betree_message_t_11] Theorem + + ⊢ (∀a a'. BetreeMessageInsert a = BetreeMessageInsert a' ⇔ a = a') ∧ + ∀a a'. BetreeMessageUpsert a = BetreeMessageUpsert a' ⇔ a = a' + + [betree_message_t_Axiom] Theorem + + ⊢ ∀f0 f1 f2. ∃fn. + (∀a. fn (BetreeMessageInsert a) = f0 a) ∧ + fn BetreeMessageDelete = f1 ∧ + ∀a. fn (BetreeMessageUpsert a) = f2 a + + [betree_message_t_case_cong] Theorem + + ⊢ ∀M M' f v f1. + M = M' ∧ (∀a. M' = BetreeMessageInsert a ⇒ f a = f' a) ∧ + (M' = BetreeMessageDelete ⇒ v = v') ∧ + (∀a. M' = BetreeMessageUpsert a ⇒ f1 a = f1' a) ⇒ + betree_message_t_CASE M f v f1 = + betree_message_t_CASE M' f' v' f1' + + [betree_message_t_case_eq] Theorem + + ⊢ betree_message_t_CASE x f v f1 = v' ⇔ + (∃u. x = BetreeMessageInsert u ∧ f u = v') ∨ + x = BetreeMessageDelete ∧ v = v' ∨ + ∃b. x = BetreeMessageUpsert b ∧ f1 b = v' + + [betree_message_t_distinct] Theorem + + ⊢ (∀a. BetreeMessageInsert a ≠ BetreeMessageDelete) ∧ + (∀a' a. BetreeMessageInsert a ≠ BetreeMessageUpsert a') ∧ + ∀a. BetreeMessageDelete ≠ BetreeMessageUpsert a + + [betree_message_t_induction] Theorem + + ⊢ ∀P. (∀u. P (BetreeMessageInsert u)) ∧ P BetreeMessageDelete ∧ + (∀b. P (BetreeMessageUpsert b)) ⇒ + ∀b. P b + + [betree_message_t_nchotomy] Theorem + + ⊢ ∀bb. + (∃u. bb = BetreeMessageInsert u) ∨ bb = BetreeMessageDelete ∨ + ∃b. bb = BetreeMessageUpsert b + + [betree_node_id_counter_t_11] Theorem + + ⊢ ∀a a'. + betree_node_id_counter_t a = betree_node_id_counter_t a' ⇔ a = a' + + [betree_node_id_counter_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a. fn (betree_node_id_counter_t a) = f a + + [betree_node_id_counter_t_accessors] Theorem + + ⊢ ∀u. (betree_node_id_counter_t u). + betree_node_id_counter_next_node_id = + u + + [betree_node_id_counter_t_accfupds] Theorem + + ⊢ ∀f b. + (b with betree_node_id_counter_next_node_id updated_by f). + betree_node_id_counter_next_node_id = + f b.betree_node_id_counter_next_node_id + + [betree_node_id_counter_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a. M' = betree_node_id_counter_t a ⇒ f a = f' a) ⇒ + betree_node_id_counter_t_CASE M f = + betree_node_id_counter_t_CASE M' f' + + [betree_node_id_counter_t_case_eq] Theorem + + ⊢ betree_node_id_counter_t_CASE x f = v ⇔ + ∃u. x = betree_node_id_counter_t u ∧ f u = v + + [betree_node_id_counter_t_component_equality] Theorem + + ⊢ ∀b1 b2. + b1 = b2 ⇔ + b1.betree_node_id_counter_next_node_id = + b2.betree_node_id_counter_next_node_id + + [betree_node_id_counter_t_fn_updates] Theorem + + ⊢ ∀f u. + betree_node_id_counter_t u with + betree_node_id_counter_next_node_id updated_by f = + betree_node_id_counter_t (f u) + + [betree_node_id_counter_t_fupdfupds] Theorem + + ⊢ ∀g f b. + b with + <|betree_node_id_counter_next_node_id updated_by f; + betree_node_id_counter_next_node_id updated_by g|> = + b with betree_node_id_counter_next_node_id updated_by f ∘ g + + [betree_node_id_counter_t_fupdfupds_comp] Theorem + + ⊢ (∀g f. + betree_node_id_counter_next_node_id_fupd f ∘ + betree_node_id_counter_next_node_id_fupd g = + betree_node_id_counter_next_node_id_fupd (f ∘ g)) ∧ + ∀h g f. + betree_node_id_counter_next_node_id_fupd f ∘ + betree_node_id_counter_next_node_id_fupd g ∘ h = + betree_node_id_counter_next_node_id_fupd (f ∘ g) ∘ h + + [betree_node_id_counter_t_induction] Theorem + + ⊢ ∀P. (∀u. P (betree_node_id_counter_t u)) ⇒ ∀b. P b + + [betree_node_id_counter_t_literal_11] Theorem + + ⊢ ∀u1 u2. + <|betree_node_id_counter_next_node_id := u1|> = + <|betree_node_id_counter_next_node_id := u2|> ⇔ u1 = u2 + + [betree_node_id_counter_t_literal_nchotomy] Theorem + + ⊢ ∀b. ∃u. b = <|betree_node_id_counter_next_node_id := u|> + + [betree_node_id_counter_t_nchotomy] Theorem + + ⊢ ∀bb. ∃u. bb = betree_node_id_counter_t u + + [betree_node_id_counter_t_updates_eq_literal] Theorem + + ⊢ ∀b u. + b with betree_node_id_counter_next_node_id := u = + <|betree_node_id_counter_next_node_id := u|> + + [betree_node_t_11] Theorem + + ⊢ (∀a a'. BetreeNodeInternal a = BetreeNodeInternal a' ⇔ a = a') ∧ + ∀a a'. BetreeNodeLeaf a = BetreeNodeLeaf a' ⇔ a = a' + + [betree_node_t_Axiom] Theorem + + ⊢ ∀f0 f1 f2. ∃fn0 fn1. + (∀a0 a1 a2 a3. + fn0 (betree_internal_t a0 a1 a2 a3) = + f0 a0 a1 a2 a3 (fn1 a2) (fn1 a3)) ∧ + (∀a. fn1 (BetreeNodeInternal a) = f1 a (fn0 a)) ∧ + ∀a. fn1 (BetreeNodeLeaf a) = f2 a + + [betree_node_t_case_cong] Theorem + + ⊢ ∀M M' f f1. + M = M' ∧ (∀a. M' = BetreeNodeInternal a ⇒ f a = f' a) ∧ + (∀a. M' = BetreeNodeLeaf a ⇒ f1 a = f1' a) ⇒ + betree_node_t_CASE M f f1 = betree_node_t_CASE M' f' f1' + + [betree_node_t_case_eq] Theorem + + ⊢ betree_node_t_CASE x f f1 = v ⇔ + (∃b. x = BetreeNodeInternal b ∧ f b = v) ∨ + ∃b. x = BetreeNodeLeaf b ∧ f1 b = v + + [betree_node_t_distinct] Theorem + + ⊢ ∀a' a. BetreeNodeInternal a ≠ BetreeNodeLeaf a' + + [betree_node_t_induction] Theorem + + ⊢ ∀P0 P1. + (∀b b0. P1 b ∧ P1 b0 ⇒ ∀u u0. P0 (betree_internal_t u0 u b b0)) ∧ + (∀b. P0 b ⇒ P1 (BetreeNodeInternal b)) ∧ + (∀b. P1 (BetreeNodeLeaf b)) ⇒ + (∀b. P0 b) ∧ ∀b. P1 b + + [betree_node_t_nchotomy] Theorem + + ⊢ ∀bb. (∃b. bb = BetreeNodeInternal b) ∨ ∃b. bb = BetreeNodeLeaf b + + [betree_params_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + betree_params_t a0 a1 = betree_params_t a0' a1' ⇔ + a0 = a0' ∧ a1 = a1' + + [betree_params_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a0 a1. fn (betree_params_t a0 a1) = f a0 a1 + + [betree_params_t_accessors] Theorem + + ⊢ (∀u u0. (betree_params_t u u0).betree_params_min_flush_size = u) ∧ + ∀u u0. (betree_params_t u u0).betree_params_split_size = u0 + + [betree_params_t_accfupds] Theorem + + ⊢ (∀f b. + (b with betree_params_split_size updated_by f). + betree_params_min_flush_size = + b.betree_params_min_flush_size) ∧ + (∀f b. + (b with betree_params_min_flush_size updated_by f). + betree_params_split_size = + b.betree_params_split_size) ∧ + (∀f b. + (b with betree_params_min_flush_size updated_by f). + betree_params_min_flush_size = + f b.betree_params_min_flush_size) ∧ + ∀f b. + (b with betree_params_split_size updated_by f). + betree_params_split_size = + f b.betree_params_split_size + + [betree_params_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ + (∀a0 a1. M' = betree_params_t a0 a1 ⇒ f a0 a1 = f' a0 a1) ⇒ + betree_params_t_CASE M f = betree_params_t_CASE M' f' + + [betree_params_t_case_eq] Theorem + + ⊢ betree_params_t_CASE x f = v ⇔ + ∃u u0. x = betree_params_t u u0 ∧ f u u0 = v + + [betree_params_t_component_equality] Theorem + + ⊢ ∀b1 b2. + b1 = b2 ⇔ + b1.betree_params_min_flush_size = b2.betree_params_min_flush_size ∧ + b1.betree_params_split_size = b2.betree_params_split_size + + [betree_params_t_fn_updates] Theorem + + ⊢ (∀f u u0. + betree_params_t u u0 with + betree_params_min_flush_size updated_by f = + betree_params_t (f u) u0) ∧ + ∀f u u0. + betree_params_t u u0 with betree_params_split_size updated_by f = + betree_params_t u (f u0) + + [betree_params_t_fupdcanon] Theorem + + ⊢ ∀g f b. + b with + <|betree_params_split_size updated_by f; + betree_params_min_flush_size updated_by g|> = + b with + <|betree_params_min_flush_size updated_by g; + betree_params_split_size updated_by f|> + + [betree_params_t_fupdcanon_comp] Theorem + + ⊢ (∀g f. + betree_params_split_size_fupd f ∘ + betree_params_min_flush_size_fupd g = + betree_params_min_flush_size_fupd g ∘ + betree_params_split_size_fupd f) ∧ + ∀h g f. + betree_params_split_size_fupd f ∘ + betree_params_min_flush_size_fupd g ∘ h = + betree_params_min_flush_size_fupd g ∘ + betree_params_split_size_fupd f ∘ h + + [betree_params_t_fupdfupds] Theorem + + ⊢ (∀g f b. + b with + <|betree_params_min_flush_size updated_by f; + betree_params_min_flush_size updated_by g|> = + b with betree_params_min_flush_size updated_by f ∘ g) ∧ + ∀g f b. + b with + <|betree_params_split_size updated_by f; + betree_params_split_size updated_by g|> = + b with betree_params_split_size updated_by f ∘ g + + [betree_params_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. + betree_params_min_flush_size_fupd f ∘ + betree_params_min_flush_size_fupd g = + betree_params_min_flush_size_fupd (f ∘ g)) ∧ + ∀h g f. + betree_params_min_flush_size_fupd f ∘ + betree_params_min_flush_size_fupd g ∘ h = + betree_params_min_flush_size_fupd (f ∘ g) ∘ h) ∧ + (∀g f. + betree_params_split_size_fupd f ∘ + betree_params_split_size_fupd g = + betree_params_split_size_fupd (f ∘ g)) ∧ + ∀h g f. + betree_params_split_size_fupd f ∘ + betree_params_split_size_fupd g ∘ h = + betree_params_split_size_fupd (f ∘ g) ∘ h + + [betree_params_t_induction] Theorem + + ⊢ ∀P. (∀u u0. P (betree_params_t u u0)) ⇒ ∀b. P b + + [betree_params_t_literal_11] Theorem + + ⊢ ∀u01 u1 u02 u2. + <|betree_params_min_flush_size := u01; + betree_params_split_size := u1|> = + <|betree_params_min_flush_size := u02; + betree_params_split_size := u2|> ⇔ u01 = u02 ∧ u1 = u2 + + [betree_params_t_literal_nchotomy] Theorem + + ⊢ ∀b. ∃u0 u. + b = + <|betree_params_min_flush_size := u0; + betree_params_split_size := u|> + + [betree_params_t_nchotomy] Theorem + + ⊢ ∀bb. ∃u u0. bb = betree_params_t u u0 + + [betree_params_t_updates_eq_literal] Theorem + + ⊢ ∀b u0 u. + b with + <|betree_params_min_flush_size := u0; + betree_params_split_size := u|> = + <|betree_params_min_flush_size := u0; + betree_params_split_size := u|> + + [betree_upsert_fun_state_t_11] Theorem + + ⊢ (∀a a'. + BetreeUpsertFunStateAdd a = BetreeUpsertFunStateAdd a' ⇔ a = a') ∧ + ∀a a'. + BetreeUpsertFunStateSub a = BetreeUpsertFunStateSub a' ⇔ a = a' + + [betree_upsert_fun_state_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a. fn (BetreeUpsertFunStateAdd a) = f0 a) ∧ + ∀a. fn (BetreeUpsertFunStateSub a) = f1 a + + [betree_upsert_fun_state_t_case_cong] Theorem + + ⊢ ∀M M' f f1. + M = M' ∧ (∀a. M' = BetreeUpsertFunStateAdd a ⇒ f a = f' a) ∧ + (∀a. M' = BetreeUpsertFunStateSub a ⇒ f1 a = f1' a) ⇒ + betree_upsert_fun_state_t_CASE M f f1 = + betree_upsert_fun_state_t_CASE M' f' f1' + + [betree_upsert_fun_state_t_case_eq] Theorem + + ⊢ betree_upsert_fun_state_t_CASE x f f1 = v ⇔ + (∃u. x = BetreeUpsertFunStateAdd u ∧ f u = v) ∨ + ∃u. x = BetreeUpsertFunStateSub u ∧ f1 u = v + + [betree_upsert_fun_state_t_distinct] Theorem + + ⊢ ∀a' a. BetreeUpsertFunStateAdd a ≠ BetreeUpsertFunStateSub a' + + [betree_upsert_fun_state_t_induction] Theorem + + ⊢ ∀P. (∀u. P (BetreeUpsertFunStateAdd u)) ∧ + (∀u. P (BetreeUpsertFunStateSub u)) ⇒ + ∀b. P b + + [betree_upsert_fun_state_t_nchotomy] Theorem + + ⊢ ∀bb. + (∃u. bb = BetreeUpsertFunStateAdd u) ∨ + ∃u. bb = BetreeUpsertFunStateSub u + + [datatype_betree_be_tree_t] Theorem + + ⊢ DATATYPE + (record betree_be_tree_t betree_be_tree_params + betree_be_tree_node_id_cnt betree_be_tree_root) + + [datatype_betree_internal_t] Theorem + + ⊢ DATATYPE + (record betree_internal_t betree_internal_id + betree_internal_pivot betree_internal_left + betree_internal_right ∧ + betree_node_t BetreeNodeInternal BetreeNodeLeaf) + + [datatype_betree_leaf_t] Theorem + + ⊢ DATATYPE (record betree_leaf_t betree_leaf_id betree_leaf_size) + + [datatype_betree_list_t] Theorem + + ⊢ DATATYPE (betree_list_t BetreeListCons BetreeListNil) + + [datatype_betree_message_t] Theorem + + ⊢ DATATYPE + (betree_message_t BetreeMessageInsert BetreeMessageDelete + BetreeMessageUpsert) + + [datatype_betree_node_id_counter_t] Theorem + + ⊢ DATATYPE + (record betree_node_id_counter_t + betree_node_id_counter_next_node_id) + + [datatype_betree_params_t] Theorem + + ⊢ DATATYPE + (record betree_params_t betree_params_min_flush_size + betree_params_split_size) + + [datatype_betree_upsert_fun_state_t] Theorem + + ⊢ DATATYPE + (betree_upsert_fun_state_t BetreeUpsertFunStateAdd + BetreeUpsertFunStateSub) + + +*) +end diff --git a/tests/lean/Betree/Funs.lean b/tests/lean/Betree/Funs.lean new file mode 100644 index 00000000..8612ccbc --- /dev/null +++ b/tests/lean/Betree/Funs.lean @@ -0,0 +1,699 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [betree]: function definitions +import Base +import Betree.Types +import Betree.FunsExternal +open Primitives + +namespace betree + +/- [betree::betree::load_internal_node]: + Source: 'src/betree.rs', lines 36:0-36:52 -/ +def betree.load_internal_node + (id : U64) (st : State) : + Result (State × (betree.List (U64 × betree.Message))) + := + betree_utils.load_internal_node id st + +/- [betree::betree::store_internal_node]: + Source: 'src/betree.rs', lines 41:0-41:60 -/ +def betree.store_internal_node + (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) : + Result (State × Unit) + := + betree_utils.store_internal_node id content st + +/- [betree::betree::load_leaf_node]: + Source: 'src/betree.rs', lines 46:0-46:44 -/ +def betree.load_leaf_node + (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) := + betree_utils.load_leaf_node id st + +/- [betree::betree::store_leaf_node]: + Source: 'src/betree.rs', lines 51:0-51:52 -/ +def betree.store_leaf_node + (id : U64) (content : betree.List (U64 × U64)) (st : State) : + Result (State × Unit) + := + betree_utils.store_leaf_node id content st + +/- [betree::betree::fresh_node_id]: + Source: 'src/betree.rs', lines 55:0-55:48 -/ +def betree.fresh_node_id (counter : U64) : Result (U64 × U64) := + do + let counter1 ← counter + 1#u64 + Result.ok (counter, counter1) + +/- [betree::betree::{betree::betree::NodeIdCounter}::new]: + Source: 'src/betree.rs', lines 206:4-206:20 -/ +def betree.NodeIdCounter.new : Result betree.NodeIdCounter := + Result.ok { next_node_id := 0#u64 } + +/- [betree::betree::{betree::betree::NodeIdCounter}::fresh_id]: + Source: 'src/betree.rs', lines 210:4-210:36 -/ +def betree.NodeIdCounter.fresh_id + (self : betree.NodeIdCounter) : Result (U64 × betree.NodeIdCounter) := + do + let i ← self.next_node_id + 1#u64 + Result.ok (self.next_node_id, { next_node_id := i }) + +/- [betree::betree::upsert_update]: + Source: 'src/betree.rs', lines 234:0-234:70 -/ +def betree.upsert_update + (prev : Option U64) (st : betree.UpsertFunState) : Result U64 := + match prev with + | none => + match st with + | betree.UpsertFunState.Add v => Result.ok v + | betree.UpsertFunState.Sub _ => Result.ok 0#u64 + | some prev1 => + match st with + | betree.UpsertFunState.Add v => + do + let margin ← core_u64_max - prev1 + if margin >= v + then prev1 + v + else Result.ok core_u64_max + | betree.UpsertFunState.Sub v => + if prev1 >= v + then prev1 - v + else Result.ok 0#u64 + +/- [betree::betree::{betree::betree::List#1}::len]: + Source: 'src/betree.rs', lines 276:4-276:24 -/ +divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 := + match self with + | betree.List.Cons _ tl => do + let i ← betree.List.len T tl + 1#u64 + i + | betree.List.Nil => Result.ok 0#u64 + +/- [betree::betree::{betree::betree::List#1}::split_at]: + Source: 'src/betree.rs', lines 284:4-284:51 -/ +divergent def betree.List.split_at + (T : Type) (self : betree.List T) (n : U64) : + Result ((betree.List T) × (betree.List T)) + := + if n = 0#u64 + then Result.ok (betree.List.Nil, self) + else + match self with + | betree.List.Cons hd tl => + do + let i ← n - 1#u64 + let p ← betree.List.split_at T tl i + let (ls0, ls1) := p + Result.ok (betree.List.Cons hd ls0, ls1) + | betree.List.Nil => Result.fail .panic + +/- [betree::betree::{betree::betree::List#1}::push_front]: + Source: 'src/betree.rs', lines 299:4-299:34 -/ +def betree.List.push_front + (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) := + let (tl, _) := core.mem.replace (betree.List T) self betree.List.Nil + Result.ok (betree.List.Cons x tl) + +/- [betree::betree::{betree::betree::List#1}::pop_front]: + Source: 'src/betree.rs', lines 306:4-306:32 -/ +def betree.List.pop_front + (T : Type) (self : betree.List T) : Result (T × (betree.List T)) := + let (ls, _) := core.mem.replace (betree.List T) self betree.List.Nil + match ls with + | betree.List.Cons x tl => Result.ok (x, tl) + | betree.List.Nil => Result.fail .panic + +/- [betree::betree::{betree::betree::List#1}::hd]: + Source: 'src/betree.rs', lines 318:4-318:22 -/ +def betree.List.hd (T : Type) (self : betree.List T) : Result T := + match self with + | betree.List.Cons hd _ => Result.ok hd + | betree.List.Nil => Result.fail .panic + +/- [betree::betree::{betree::betree::List<(u64, T)>#2}::head_has_key]: + Source: 'src/betree.rs', lines 327:4-327:44 -/ +def betree.ListPairU64T.head_has_key + (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool := + match self with + | betree.List.Cons hd _ => let (i, _) := hd + Result.ok (i = key) + | betree.List.Nil => Result.ok false + +/- [betree::betree::{betree::betree::List<(u64, T)>#2}::partition_at_pivot]: + Source: 'src/betree.rs', lines 339:4-339:73 -/ +divergent def betree.ListPairU64T.partition_at_pivot + (T : Type) (self : betree.List (U64 × T)) (pivot : U64) : + Result ((betree.List (U64 × T)) × (betree.List (U64 × T))) + := + match self with + | betree.List.Cons hd tl => + let (i, t) := hd + if i >= pivot + then Result.ok (betree.List.Nil, betree.List.Cons (i, t) tl) + else + do + let p ← betree.ListPairU64T.partition_at_pivot T tl pivot + let (ls0, ls1) := p + Result.ok (betree.List.Cons (i, t) ls0, ls1) + | betree.List.Nil => Result.ok (betree.List.Nil, betree.List.Nil) + +/- [betree::betree::{betree::betree::Leaf#3}::split]: + Source: 'src/betree.rs', lines 359:4-364:17 -/ +def betree.Leaf.split + (self : betree.Leaf) (content : betree.List (U64 × U64)) + (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) : + Result (State × (betree.Internal × betree.NodeIdCounter)) + := + do + let p ← betree.List.split_at (U64 × U64) content params.split_size + let (content0, content1) := p + let p1 ← betree.List.hd (U64 × U64) content1 + let (pivot, _) := p1 + let (id0, node_id_cnt1) ← betree.NodeIdCounter.fresh_id node_id_cnt + let (id1, node_id_cnt2) ← betree.NodeIdCounter.fresh_id node_id_cnt1 + let (st1, _) ← betree.store_leaf_node id0 content0 st + let (st2, _) ← betree.store_leaf_node id1 content1 st1 + let n := betree.Node.Leaf { id := id0, size := params.split_size } + let n1 := betree.Node.Leaf { id := id1, size := params.split_size } + Result.ok (st2, (betree.Internal.mk self.id pivot n n1, node_id_cnt2)) + +/- [betree::betree::{betree::betree::Node#5}::lookup_first_message_for_key]: + Source: 'src/betree.rs', lines 789:4-792:34 -/ +divergent def betree.Node.lookup_first_message_for_key + (key : U64) (msgs : betree.List (U64 × betree.Message)) : + Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 × + betree.Message) → Result (betree.List (U64 × betree.Message)))) + := + match msgs with + | betree.List.Cons x next_msgs => + let (i, m) := x + if i >= key + then Result.ok (betree.List.Cons (i, m) next_msgs, Result.ok) + else + do + let (l, lookup_first_message_for_key_back) ← + betree.Node.lookup_first_message_for_key key next_msgs + let back := + fun ret => + do + let next_msgs1 ← lookup_first_message_for_key_back ret + Result.ok (betree.List.Cons (i, m) next_msgs1) + Result.ok (l, back) + | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok) + +/- [betree::betree::{betree::betree::Node#5}::lookup_in_bindings]: + Source: 'src/betree.rs', lines 636:4-636:80 -/ +divergent def betree.Node.lookup_in_bindings + (key : U64) (bindings : betree.List (U64 × U64)) : Result (Option U64) := + match bindings with + | betree.List.Cons hd tl => + let (i, i1) := hd + if i = key + then Result.ok (some i1) + else + if i > key + then Result.ok none + else betree.Node.lookup_in_bindings key tl + | betree.List.Nil => Result.ok none + +/- [betree::betree::{betree::betree::Node#5}::apply_upserts]: + Source: 'src/betree.rs', lines 819:4-819:90 -/ +divergent def betree.Node.apply_upserts + (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64) + : + Result (U64 × (betree.List (U64 × betree.Message))) + := + do + let b ← betree.ListPairU64T.head_has_key betree.Message msgs key + if b + then + do + let (msg, msgs1) ← betree.List.pop_front (U64 × betree.Message) msgs + let (_, m) := msg + match m with + | betree.Message.Insert _ => Result.fail .panic + | betree.Message.Delete => Result.fail .panic + | betree.Message.Upsert s => + do + let v ← betree.upsert_update prev s + betree.Node.apply_upserts msgs1 (some v) key + else + do + let v ← core.option.Option.unwrap U64 prev + let msgs1 ← + betree.List.push_front (U64 × betree.Message) msgs (key, + betree.Message.Insert v) + Result.ok (v, msgs1) + +/- [betree::betree::{betree::betree::Internal#4}::lookup_in_children]: + Source: 'src/betree.rs', lines 395:4-395:63 -/ +mutual divergent def betree.Internal.lookup_in_children + (self : betree.Internal) (key : U64) (st : State) : + Result (State × ((Option U64) × betree.Internal)) + := + if key < self.pivot + then + do + let (st1, (o, n)) ← betree.Node.lookup self.left key st + Result.ok (st1, (o, betree.Internal.mk self.id self.pivot n self.right)) + else + do + let (st1, (o, n)) ← betree.Node.lookup self.right key st + Result.ok (st1, (o, betree.Internal.mk self.id self.pivot self.left n)) + +/- [betree::betree::{betree::betree::Node#5}::lookup]: + Source: 'src/betree.rs', lines 709:4-709:58 -/ +divergent def betree.Node.lookup + (self : betree.Node) (key : U64) (st : State) : + Result (State × ((Option U64) × betree.Node)) + := + match self with + | betree.Node.Internal node => + do + let (st1, msgs) ← betree.load_internal_node node.id st + let (pending, lookup_first_message_for_key_back) ← + betree.Node.lookup_first_message_for_key key msgs + match pending with + | betree.List.Cons p l => + let (k, msg) := p + if k != key + then + do + let (st2, (o, node1)) ← + betree.Internal.lookup_in_children node key st1 + let _ ← + lookup_first_message_for_key_back (betree.List.Cons (k, msg) l) + Result.ok (st2, (o, betree.Node.Internal node1)) + else + match msg with + | betree.Message.Insert v => + do + let _ ← + lookup_first_message_for_key_back (betree.List.Cons (k, + betree.Message.Insert v) l) + Result.ok (st1, (some v, betree.Node.Internal node)) + | betree.Message.Delete => + do + let _ ← + lookup_first_message_for_key_back (betree.List.Cons (k, + betree.Message.Delete) l) + Result.ok (st1, (none, betree.Node.Internal node)) + | betree.Message.Upsert ufs => + do + let (st2, (v, node1)) ← + betree.Internal.lookup_in_children node key st1 + let (v1, pending1) ← + betree.Node.apply_upserts (betree.List.Cons (k, + betree.Message.Upsert ufs) l) v key + let msgs1 ← lookup_first_message_for_key_back pending1 + let (st3, _) ← betree.store_internal_node node1.id msgs1 st2 + Result.ok (st3, (some v1, betree.Node.Internal node1)) + | betree.List.Nil => + do + let (st2, (o, node1)) ← betree.Internal.lookup_in_children node key st1 + let _ ← lookup_first_message_for_key_back betree.List.Nil + Result.ok (st2, (o, betree.Node.Internal node1)) + | betree.Node.Leaf node => + do + let (st1, bindings) ← betree.load_leaf_node node.id st + let o ← betree.Node.lookup_in_bindings key bindings + Result.ok (st1, (o, betree.Node.Leaf node)) + +end + +/- [betree::betree::{betree::betree::Node#5}::filter_messages_for_key]: + Source: 'src/betree.rs', lines 674:4-674:77 -/ +divergent def betree.Node.filter_messages_for_key + (key : U64) (msgs : betree.List (U64 × betree.Message)) : + Result (betree.List (U64 × betree.Message)) + := + match msgs with + | betree.List.Cons p l => + let (k, m) := p + if k = key + then + do + let (_, msgs1) ← + betree.List.pop_front (U64 × betree.Message) (betree.List.Cons (k, m) + l) + betree.Node.filter_messages_for_key key msgs1 + else Result.ok (betree.List.Cons (k, m) l) + | betree.List.Nil => Result.ok betree.List.Nil + +/- [betree::betree::{betree::betree::Node#5}::lookup_first_message_after_key]: + Source: 'src/betree.rs', lines 689:4-692:34 -/ +divergent def betree.Node.lookup_first_message_after_key + (key : U64) (msgs : betree.List (U64 × betree.Message)) : + Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 × + betree.Message) → Result (betree.List (U64 × betree.Message)))) + := + match msgs with + | betree.List.Cons p next_msgs => + let (k, m) := p + if k = key + then + do + let (l, lookup_first_message_after_key_back) ← + betree.Node.lookup_first_message_after_key key next_msgs + let back := + fun ret => + do + let next_msgs1 ← lookup_first_message_after_key_back ret + Result.ok (betree.List.Cons (k, m) next_msgs1) + Result.ok (l, back) + else Result.ok (betree.List.Cons (k, m) next_msgs, Result.ok) + | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok) + +/- [betree::betree::{betree::betree::Node#5}::apply_to_internal]: + Source: 'src/betree.rs', lines 521:4-521:89 -/ +def betree.Node.apply_to_internal + (msgs : betree.List (U64 × betree.Message)) (key : U64) + (new_msg : betree.Message) : + Result (betree.List (U64 × betree.Message)) + := + do + let (msgs1, lookup_first_message_for_key_back) ← + betree.Node.lookup_first_message_for_key key msgs + let b ← betree.ListPairU64T.head_has_key betree.Message msgs1 key + if b + then + match new_msg with + | betree.Message.Insert i => + do + let msgs2 ← betree.Node.filter_messages_for_key key msgs1 + let msgs3 ← + betree.List.push_front (U64 × betree.Message) msgs2 (key, + betree.Message.Insert i) + lookup_first_message_for_key_back msgs3 + | betree.Message.Delete => + do + let msgs2 ← betree.Node.filter_messages_for_key key msgs1 + let msgs3 ← + betree.List.push_front (U64 × betree.Message) msgs2 (key, + betree.Message.Delete) + lookup_first_message_for_key_back msgs3 + | betree.Message.Upsert s => + do + let p ← betree.List.hd (U64 × betree.Message) msgs1 + let (_, m) := p + match m with + | betree.Message.Insert prev => + do + let v ← betree.upsert_update (some prev) s + let (_, msgs2) ← betree.List.pop_front (U64 × betree.Message) msgs1 + let msgs3 ← + betree.List.push_front (U64 × betree.Message) msgs2 (key, + betree.Message.Insert v) + lookup_first_message_for_key_back msgs3 + | betree.Message.Delete => + do + let (_, msgs2) ← betree.List.pop_front (U64 × betree.Message) msgs1 + let v ← betree.upsert_update none s + let msgs3 ← + betree.List.push_front (U64 × betree.Message) msgs2 (key, + betree.Message.Insert v) + lookup_first_message_for_key_back msgs3 + | betree.Message.Upsert _ => + do + let (msgs2, lookup_first_message_after_key_back) ← + betree.Node.lookup_first_message_after_key key msgs1 + let msgs3 ← + betree.List.push_front (U64 × betree.Message) msgs2 (key, + betree.Message.Upsert s) + let msgs4 ← lookup_first_message_after_key_back msgs3 + lookup_first_message_for_key_back msgs4 + else + do + let msgs2 ← + betree.List.push_front (U64 × betree.Message) msgs1 (key, new_msg) + lookup_first_message_for_key_back msgs2 + +/- [betree::betree::{betree::betree::Node#5}::apply_messages_to_internal]: + Source: 'src/betree.rs', lines 502:4-505:5 -/ +divergent def betree.Node.apply_messages_to_internal + (msgs : betree.List (U64 × betree.Message)) + (new_msgs : betree.List (U64 × betree.Message)) : + Result (betree.List (U64 × betree.Message)) + := + match new_msgs with + | betree.List.Cons new_msg new_msgs_tl => + do + let (i, m) := new_msg + let msgs1 ← betree.Node.apply_to_internal msgs i m + betree.Node.apply_messages_to_internal msgs1 new_msgs_tl + | betree.List.Nil => Result.ok msgs + +/- [betree::betree::{betree::betree::Node#5}::lookup_mut_in_bindings]: + Source: 'src/betree.rs', lines 653:4-656:32 -/ +divergent def betree.Node.lookup_mut_in_bindings + (key : U64) (bindings : betree.List (U64 × U64)) : + Result ((betree.List (U64 × U64)) × (betree.List (U64 × U64) → Result + (betree.List (U64 × U64)))) + := + match bindings with + | betree.List.Cons hd tl => + let (i, i1) := hd + if i >= key + then Result.ok (betree.List.Cons (i, i1) tl, Result.ok) + else + do + let (l, lookup_mut_in_bindings_back) ← + betree.Node.lookup_mut_in_bindings key tl + let back := + fun ret => + do + let tl1 ← lookup_mut_in_bindings_back ret + Result.ok (betree.List.Cons (i, i1) tl1) + Result.ok (l, back) + | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok) + +/- [betree::betree::{betree::betree::Node#5}::apply_to_leaf]: + Source: 'src/betree.rs', lines 460:4-460:87 -/ +def betree.Node.apply_to_leaf + (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message) + : + Result (betree.List (U64 × U64)) + := + do + let (bindings1, lookup_mut_in_bindings_back) ← + betree.Node.lookup_mut_in_bindings key bindings + let b ← betree.ListPairU64T.head_has_key U64 bindings1 key + if b + then + do + let (hd, bindings2) ← betree.List.pop_front (U64 × U64) bindings1 + match new_msg with + | betree.Message.Insert v => + do + let bindings3 ← betree.List.push_front (U64 × U64) bindings2 (key, v) + lookup_mut_in_bindings_back bindings3 + | betree.Message.Delete => lookup_mut_in_bindings_back bindings2 + | betree.Message.Upsert s => + do + let (_, i) := hd + let v ← betree.upsert_update (some i) s + let bindings3 ← betree.List.push_front (U64 × U64) bindings2 (key, v) + lookup_mut_in_bindings_back bindings3 + else + match new_msg with + | betree.Message.Insert v => + do + let bindings2 ← betree.List.push_front (U64 × U64) bindings1 (key, v) + lookup_mut_in_bindings_back bindings2 + | betree.Message.Delete => lookup_mut_in_bindings_back bindings1 + | betree.Message.Upsert s => + do + let v ← betree.upsert_update none s + let bindings2 ← betree.List.push_front (U64 × U64) bindings1 (key, v) + lookup_mut_in_bindings_back bindings2 + +/- [betree::betree::{betree::betree::Node#5}::apply_messages_to_leaf]: + Source: 'src/betree.rs', lines 444:4-447:5 -/ +divergent def betree.Node.apply_messages_to_leaf + (bindings : betree.List (U64 × U64)) + (new_msgs : betree.List (U64 × betree.Message)) : + Result (betree.List (U64 × U64)) + := + match new_msgs with + | betree.List.Cons new_msg new_msgs_tl => + do + let (i, m) := new_msg + let bindings1 ← betree.Node.apply_to_leaf bindings i m + betree.Node.apply_messages_to_leaf bindings1 new_msgs_tl + | betree.List.Nil => Result.ok bindings + +/- [betree::betree::{betree::betree::Internal#4}::flush]: + Source: 'src/betree.rs', lines 410:4-415:26 -/ +mutual divergent def betree.Internal.flush + (self : betree.Internal) (params : betree.Params) + (node_id_cnt : betree.NodeIdCounter) + (content : betree.List (U64 × betree.Message)) (st : State) : + Result (State × ((betree.List (U64 × betree.Message)) × (betree.Internal + × betree.NodeIdCounter))) + := + do + let p ← + betree.ListPairU64T.partition_at_pivot betree.Message content self.pivot + let (msgs_left, msgs_right) := p + let len_left ← betree.List.len (U64 × betree.Message) msgs_left + if len_left >= params.min_flush_size + then + do + let (st1, p1) ← + betree.Node.apply_messages self.left params node_id_cnt msgs_left st + let (n, node_id_cnt1) := p1 + let len_right ← betree.List.len (U64 × betree.Message) msgs_right + if len_right >= params.min_flush_size + then + do + let (st2, p2) ← + betree.Node.apply_messages self.right params node_id_cnt1 msgs_right + st1 + let (n1, node_id_cnt2) := p2 + Result.ok (st2, (betree.List.Nil, (betree.Internal.mk self.id self.pivot + n n1, node_id_cnt2))) + else + Result.ok (st1, (msgs_right, (betree.Internal.mk self.id self.pivot n + self.right, node_id_cnt1))) + else + do + let (st1, p1) ← + betree.Node.apply_messages self.right params node_id_cnt msgs_right st + let (n, node_id_cnt1) := p1 + Result.ok (st1, (msgs_left, (betree.Internal.mk self.id self.pivot + self.left n, node_id_cnt1))) + +/- [betree::betree::{betree::betree::Node#5}::apply_messages]: + Source: 'src/betree.rs', lines 588:4-593:5 -/ +divergent def betree.Node.apply_messages + (self : betree.Node) (params : betree.Params) + (node_id_cnt : betree.NodeIdCounter) + (msgs : betree.List (U64 × betree.Message)) (st : State) : + Result (State × (betree.Node × betree.NodeIdCounter)) + := + match self with + | betree.Node.Internal node => + do + let (st1, content) ← betree.load_internal_node node.id st + let content1 ← betree.Node.apply_messages_to_internal content msgs + let num_msgs ← betree.List.len (U64 × betree.Message) content1 + if num_msgs >= params.min_flush_size + then + do + let (st2, (content2, p)) ← + betree.Internal.flush node params node_id_cnt content1 st1 + let (node1, node_id_cnt1) := p + let (st3, _) ← betree.store_internal_node node1.id content2 st2 + Result.ok (st3, (betree.Node.Internal node1, node_id_cnt1)) + else + do + let (st2, _) ← betree.store_internal_node node.id content1 st1 + Result.ok (st2, (betree.Node.Internal node, node_id_cnt)) + | betree.Node.Leaf node => + do + let (st1, content) ← betree.load_leaf_node node.id st + let content1 ← betree.Node.apply_messages_to_leaf content msgs + let len ← betree.List.len (U64 × U64) content1 + let i ← 2#u64 * params.split_size + if len >= i + then + do + let (st2, (new_node, node_id_cnt1)) ← + betree.Leaf.split node content1 params node_id_cnt st1 + let (st3, _) ← betree.store_leaf_node node.id betree.List.Nil st2 + Result.ok (st3, (betree.Node.Internal new_node, node_id_cnt1)) + else + do + let (st2, _) ← betree.store_leaf_node node.id content1 st1 + Result.ok (st2, (betree.Node.Leaf { node with size := len }, + node_id_cnt)) + +end + +/- [betree::betree::{betree::betree::Node#5}::apply]: + Source: 'src/betree.rs', lines 576:4-582:5 -/ +def betree.Node.apply + (self : betree.Node) (params : betree.Params) + (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message) + (st : State) : + Result (State × (betree.Node × betree.NodeIdCounter)) + := + do + let (st1, p) ← + betree.Node.apply_messages self params node_id_cnt (betree.List.Cons (key, + new_msg) betree.List.Nil) st + let (self1, node_id_cnt1) := p + Result.ok (st1, (self1, node_id_cnt1)) + +/- [betree::betree::{betree::betree::BeTree#6}::new]: + Source: 'src/betree.rs', lines 849:4-849:60 -/ +def betree.BeTree.new + (min_flush_size : U64) (split_size : U64) (st : State) : + Result (State × betree.BeTree) + := + do + let node_id_cnt ← betree.NodeIdCounter.new + let (id, node_id_cnt1) ← betree.NodeIdCounter.fresh_id node_id_cnt + let (st1, _) ← betree.store_leaf_node id betree.List.Nil st + Result.ok (st1, + { + params := { min_flush_size := min_flush_size, split_size := split_size }, + node_id_cnt := node_id_cnt1, + root := (betree.Node.Leaf { id := id, size := 0#u64 }) + }) + +/- [betree::betree::{betree::betree::BeTree#6}::apply]: + Source: 'src/betree.rs', lines 868:4-868:47 -/ +def betree.BeTree.apply + (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) : + Result (State × betree.BeTree) + := + do + let (st1, p) ← + betree.Node.apply self.root self.params self.node_id_cnt key msg st + let (n, nic) := p + Result.ok (st1, { self with node_id_cnt := nic, root := n }) + +/- [betree::betree::{betree::betree::BeTree#6}::insert]: + Source: 'src/betree.rs', lines 874:4-874:52 -/ +def betree.BeTree.insert + (self : betree.BeTree) (key : U64) (value : U64) (st : State) : + Result (State × betree.BeTree) + := + betree.BeTree.apply self key (betree.Message.Insert value) st + +/- [betree::betree::{betree::betree::BeTree#6}::delete]: + Source: 'src/betree.rs', lines 880:4-880:38 -/ +def betree.BeTree.delete + (self : betree.BeTree) (key : U64) (st : State) : + Result (State × betree.BeTree) + := + betree.BeTree.apply self key betree.Message.Delete st + +/- [betree::betree::{betree::betree::BeTree#6}::upsert]: + Source: 'src/betree.rs', lines 886:4-886:59 -/ +def betree.BeTree.upsert + (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State) + : + Result (State × betree.BeTree) + := + betree.BeTree.apply self key (betree.Message.Upsert upd) st + +/- [betree::betree::{betree::betree::BeTree#6}::lookup]: + Source: 'src/betree.rs', lines 895:4-895:62 -/ +def betree.BeTree.lookup + (self : betree.BeTree) (key : U64) (st : State) : + Result (State × ((Option U64) × betree.BeTree)) + := + do + let (st1, (o, n)) ← betree.Node.lookup self.root key st + Result.ok (st1, (o, { self with root := n })) + +/- [betree::main]: + Source: 'src/main.rs', lines 4:0-4:9 -/ +def main : Result Unit := + Result.ok () + +/- Unit test for [betree::main] -/ +#assert (main == Result.ok ()) + +end betree diff --git a/tests/lean/Betree/FunsExternal.lean b/tests/lean/Betree/FunsExternal.lean new file mode 100644 index 00000000..859cbd68 --- /dev/null +++ b/tests/lean/Betree/FunsExternal.lean @@ -0,0 +1,30 @@ +-- [betree]: external functions. +import Base +import Betree.Types +open Primitives +open betree + +-- TODO: fill those bodies + +/- [betree::betree_utils::load_internal_node] -/ +def betree_utils.load_internal_node + : + U64 → State → Result (State × (betree.List (U64 × betree.Message))) := + fun _ _ => .fail .panic + +/- [betree::betree_utils::store_internal_node] -/ +def betree_utils.store_internal_node + : + U64 → betree.List (U64 × betree.Message) → State → Result (State + × Unit) := + fun _ _ _ => .fail .panic + +/- [betree::betree_utils::load_leaf_node] -/ +def betree_utils.load_leaf_node + : U64 → State → Result (State × (betree.List (U64 × U64))) := + fun _ _ => .fail .panic + +/- [betree::betree_utils::store_leaf_node] -/ +def betree_utils.store_leaf_node + : U64 → betree.List (U64 × U64) → State → Result (State × Unit) := + fun _ _ _ => .fail .panic diff --git a/tests/lean/Betree/FunsExternal_Template.lean b/tests/lean/Betree/FunsExternal_Template.lean new file mode 100644 index 00000000..014f0d83 --- /dev/null +++ b/tests/lean/Betree/FunsExternal_Template.lean @@ -0,0 +1,30 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [betree]: external functions. +-- This is a template file: rename it to "FunsExternal.lean" and fill the holes. +import Base +import Betree.Types +open Primitives +open betree + +/- [betree::betree_utils::load_internal_node]: + Source: 'src/betree_utils.rs', lines 98:0-98:63 -/ +axiom betree_utils.load_internal_node + : U64 → State → Result (State × (betree.List (U64 × betree.Message))) + +/- [betree::betree_utils::store_internal_node]: + Source: 'src/betree_utils.rs', lines 115:0-115:71 -/ +axiom betree_utils.store_internal_node + : + U64 → betree.List (U64 × betree.Message) → State → Result (State × + Unit) + +/- [betree::betree_utils::load_leaf_node]: + Source: 'src/betree_utils.rs', lines 132:0-132:55 -/ +axiom betree_utils.load_leaf_node + : U64 → State → Result (State × (betree.List (U64 × U64))) + +/- [betree::betree_utils::store_leaf_node]: + Source: 'src/betree_utils.rs', lines 145:0-145:63 -/ +axiom betree_utils.store_leaf_node + : U64 → betree.List (U64 × U64) → State → Result (State × Unit) + diff --git a/tests/lean/Betree/Types.lean b/tests/lean/Betree/Types.lean new file mode 100644 index 00000000..3b46c00c --- /dev/null +++ b/tests/lean/Betree/Types.lean @@ -0,0 +1,83 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [betree]: type definitions +import Base +import Betree.TypesExternal +open Primitives + +namespace betree + +/- [betree::betree::List] + Source: 'src/betree.rs', lines 17:0-17:23 -/ +inductive betree.List (T : Type) := +| Cons : T → betree.List T → betree.List T +| Nil : betree.List T + +/- [betree::betree::UpsertFunState] + Source: 'src/betree.rs', lines 63:0-63:23 -/ +inductive betree.UpsertFunState := +| Add : U64 → betree.UpsertFunState +| Sub : U64 → betree.UpsertFunState + +/- [betree::betree::Message] + Source: 'src/betree.rs', lines 69:0-69:23 -/ +inductive betree.Message := +| Insert : U64 → betree.Message +| Delete : betree.Message +| Upsert : betree.UpsertFunState → betree.Message + +/- [betree::betree::Leaf] + Source: 'src/betree.rs', lines 167:0-167:11 -/ +structure betree.Leaf where + id : U64 + size : U64 + +mutual + +/- [betree::betree::Internal] + Source: 'src/betree.rs', lines 156:0-156:15 -/ +inductive betree.Internal := +| mk : U64 → U64 → betree.Node → betree.Node → betree.Internal + +/- [betree::betree::Node] + Source: 'src/betree.rs', lines 179:0-179:9 -/ +inductive betree.Node := +| Internal : betree.Internal → betree.Node +| Leaf : betree.Leaf → betree.Node + +end + +@[simp, reducible] +def betree.Internal.id (x : betree.Internal) := + match x with | betree.Internal.mk x1 _ _ _ => x1 + +@[simp, reducible] +def betree.Internal.pivot (x : betree.Internal) := + match x with | betree.Internal.mk _ x1 _ _ => x1 + +@[simp, reducible] +def betree.Internal.left (x : betree.Internal) := + match x with | betree.Internal.mk _ _ x1 _ => x1 + +@[simp, reducible] +def betree.Internal.right (x : betree.Internal) := + match x with | betree.Internal.mk _ _ _ x1 => x1 + +/- [betree::betree::Params] + Source: 'src/betree.rs', lines 187:0-187:13 -/ +structure betree.Params where + min_flush_size : U64 + split_size : U64 + +/- [betree::betree::NodeIdCounter] + Source: 'src/betree.rs', lines 201:0-201:20 -/ +structure betree.NodeIdCounter where + next_node_id : U64 + +/- [betree::betree::BeTree] + Source: 'src/betree.rs', lines 218:0-218:17 -/ +structure betree.BeTree where + params : betree.Params + node_id_cnt : betree.NodeIdCounter + root : betree.Node + +end betree diff --git a/tests/lean/Betree/TypesExternal.lean b/tests/lean/Betree/TypesExternal.lean new file mode 100644 index 00000000..34170271 --- /dev/null +++ b/tests/lean/Betree/TypesExternal.lean @@ -0,0 +1,7 @@ +-- [betree]: external types. +import Base +open Primitives + +/- The state type used in the state-error monad -/ +axiom State : Type + diff --git a/tests/lean/Betree/TypesExternal_Template.lean b/tests/lean/Betree/TypesExternal_Template.lean new file mode 100644 index 00000000..12fce657 --- /dev/null +++ b/tests/lean/Betree/TypesExternal_Template.lean @@ -0,0 +1,9 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [betree]: external types. +-- This is a template file: rename it to "TypesExternal.lean" and fill the holes. +import Base +open Primitives + +/- The state type used in the state-error monad -/ +axiom State : Type + diff --git a/tests/lean/BetreeMain.lean b/tests/lean/BetreeMain.lean deleted file mode 100644 index 5f307877..00000000 --- a/tests/lean/BetreeMain.lean +++ /dev/null @@ -1 +0,0 @@ -import BetreeMain.Funs diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean deleted file mode 100644 index f6fda6db..00000000 --- a/tests/lean/BetreeMain/Funs.lean +++ /dev/null @@ -1,699 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: function definitions -import Base -import BetreeMain.Types -import BetreeMain.FunsExternal -open Primitives - -namespace betree_main - -/- [betree_main::betree::load_internal_node]: - Source: 'src/betree.rs', lines 36:0-36:52 -/ -def betree.load_internal_node - (id : U64) (st : State) : - Result (State × (betree.List (U64 × betree.Message))) - := - betree_utils.load_internal_node id st - -/- [betree_main::betree::store_internal_node]: - Source: 'src/betree.rs', lines 41:0-41:60 -/ -def betree.store_internal_node - (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) : - Result (State × Unit) - := - betree_utils.store_internal_node id content st - -/- [betree_main::betree::load_leaf_node]: - Source: 'src/betree.rs', lines 46:0-46:44 -/ -def betree.load_leaf_node - (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) := - betree_utils.load_leaf_node id st - -/- [betree_main::betree::store_leaf_node]: - Source: 'src/betree.rs', lines 51:0-51:52 -/ -def betree.store_leaf_node - (id : U64) (content : betree.List (U64 × U64)) (st : State) : - Result (State × Unit) - := - betree_utils.store_leaf_node id content st - -/- [betree_main::betree::fresh_node_id]: - Source: 'src/betree.rs', lines 55:0-55:48 -/ -def betree.fresh_node_id (counter : U64) : Result (U64 × U64) := - do - let counter1 ← counter + 1#u64 - Result.ok (counter, counter1) - -/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: - Source: 'src/betree.rs', lines 206:4-206:20 -/ -def betree.NodeIdCounter.new : Result betree.NodeIdCounter := - Result.ok { next_node_id := 0#u64 } - -/- [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: - Source: 'src/betree.rs', lines 210:4-210:36 -/ -def betree.NodeIdCounter.fresh_id - (self : betree.NodeIdCounter) : Result (U64 × betree.NodeIdCounter) := - do - let i ← self.next_node_id + 1#u64 - Result.ok (self.next_node_id, { next_node_id := i }) - -/- [betree_main::betree::upsert_update]: - Source: 'src/betree.rs', lines 234:0-234:70 -/ -def betree.upsert_update - (prev : Option U64) (st : betree.UpsertFunState) : Result U64 := - match prev with - | none => - match st with - | betree.UpsertFunState.Add v => Result.ok v - | betree.UpsertFunState.Sub _ => Result.ok 0#u64 - | some prev1 => - match st with - | betree.UpsertFunState.Add v => - do - let margin ← core_u64_max - prev1 - if margin >= v - then prev1 + v - else Result.ok core_u64_max - | betree.UpsertFunState.Sub v => - if prev1 >= v - then prev1 - v - else Result.ok 0#u64 - -/- [betree_main::betree::{betree_main::betree::List#1}::len]: - Source: 'src/betree.rs', lines 276:4-276:24 -/ -divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 := - match self with - | betree.List.Cons _ tl => do - let i ← betree.List.len T tl - 1#u64 + i - | betree.List.Nil => Result.ok 0#u64 - -/- [betree_main::betree::{betree_main::betree::List#1}::split_at]: - Source: 'src/betree.rs', lines 284:4-284:51 -/ -divergent def betree.List.split_at - (T : Type) (self : betree.List T) (n : U64) : - Result ((betree.List T) × (betree.List T)) - := - if n = 0#u64 - then Result.ok (betree.List.Nil, self) - else - match self with - | betree.List.Cons hd tl => - do - let i ← n - 1#u64 - let p ← betree.List.split_at T tl i - let (ls0, ls1) := p - Result.ok (betree.List.Cons hd ls0, ls1) - | betree.List.Nil => Result.fail .panic - -/- [betree_main::betree::{betree_main::betree::List#1}::push_front]: - Source: 'src/betree.rs', lines 299:4-299:34 -/ -def betree.List.push_front - (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) := - let (tl, _) := core.mem.replace (betree.List T) self betree.List.Nil - Result.ok (betree.List.Cons x tl) - -/- [betree_main::betree::{betree_main::betree::List#1}::pop_front]: - Source: 'src/betree.rs', lines 306:4-306:32 -/ -def betree.List.pop_front - (T : Type) (self : betree.List T) : Result (T × (betree.List T)) := - let (ls, _) := core.mem.replace (betree.List T) self betree.List.Nil - match ls with - | betree.List.Cons x tl => Result.ok (x, tl) - | betree.List.Nil => Result.fail .panic - -/- [betree_main::betree::{betree_main::betree::List#1}::hd]: - Source: 'src/betree.rs', lines 318:4-318:22 -/ -def betree.List.hd (T : Type) (self : betree.List T) : Result T := - match self with - | betree.List.Cons hd _ => Result.ok hd - | betree.List.Nil => Result.fail .panic - -/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: - Source: 'src/betree.rs', lines 327:4-327:44 -/ -def betree.ListPairU64T.head_has_key - (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool := - match self with - | betree.List.Cons hd _ => let (i, _) := hd - Result.ok (i = key) - | betree.List.Nil => Result.ok false - -/- [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: - Source: 'src/betree.rs', lines 339:4-339:73 -/ -divergent def betree.ListPairU64T.partition_at_pivot - (T : Type) (self : betree.List (U64 × T)) (pivot : U64) : - Result ((betree.List (U64 × T)) × (betree.List (U64 × T))) - := - match self with - | betree.List.Cons hd tl => - let (i, t) := hd - if i >= pivot - then Result.ok (betree.List.Nil, betree.List.Cons (i, t) tl) - else - do - let p ← betree.ListPairU64T.partition_at_pivot T tl pivot - let (ls0, ls1) := p - Result.ok (betree.List.Cons (i, t) ls0, ls1) - | betree.List.Nil => Result.ok (betree.List.Nil, betree.List.Nil) - -/- [betree_main::betree::{betree_main::betree::Leaf#3}::split]: - Source: 'src/betree.rs', lines 359:4-364:17 -/ -def betree.Leaf.split - (self : betree.Leaf) (content : betree.List (U64 × U64)) - (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) : - Result (State × (betree.Internal × betree.NodeIdCounter)) - := - do - let p ← betree.List.split_at (U64 × U64) content params.split_size - let (content0, content1) := p - let p1 ← betree.List.hd (U64 × U64) content1 - let (pivot, _) := p1 - let (id0, node_id_cnt1) ← betree.NodeIdCounter.fresh_id node_id_cnt - let (id1, node_id_cnt2) ← betree.NodeIdCounter.fresh_id node_id_cnt1 - let (st1, _) ← betree.store_leaf_node id0 content0 st - let (st2, _) ← betree.store_leaf_node id1 content1 st1 - let n := betree.Node.Leaf { id := id0, size := params.split_size } - let n1 := betree.Node.Leaf { id := id1, size := params.split_size } - Result.ok (st2, (betree.Internal.mk self.id pivot n n1, node_id_cnt2)) - -/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: - Source: 'src/betree.rs', lines 789:4-792:34 -/ -divergent def betree.Node.lookup_first_message_for_key - (key : U64) (msgs : betree.List (U64 × betree.Message)) : - Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 × - betree.Message) → Result (betree.List (U64 × betree.Message)))) - := - match msgs with - | betree.List.Cons x next_msgs => - let (i, m) := x - if i >= key - then Result.ok (betree.List.Cons (i, m) next_msgs, Result.ok) - else - do - let (l, lookup_first_message_for_key_back) ← - betree.Node.lookup_first_message_for_key key next_msgs - let back := - fun ret => - do - let next_msgs1 ← lookup_first_message_for_key_back ret - Result.ok (betree.List.Cons (i, m) next_msgs1) - Result.ok (l, back) - | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok) - -/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: - Source: 'src/betree.rs', lines 636:4-636:80 -/ -divergent def betree.Node.lookup_in_bindings - (key : U64) (bindings : betree.List (U64 × U64)) : Result (Option U64) := - match bindings with - | betree.List.Cons hd tl => - let (i, i1) := hd - if i = key - then Result.ok (some i1) - else - if i > key - then Result.ok none - else betree.Node.lookup_in_bindings key tl - | betree.List.Nil => Result.ok none - -/- [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: - Source: 'src/betree.rs', lines 819:4-819:90 -/ -divergent def betree.Node.apply_upserts - (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64) - : - Result (U64 × (betree.List (U64 × betree.Message))) - := - do - let b ← betree.ListPairU64T.head_has_key betree.Message msgs key - if b - then - do - let (msg, msgs1) ← betree.List.pop_front (U64 × betree.Message) msgs - let (_, m) := msg - match m with - | betree.Message.Insert _ => Result.fail .panic - | betree.Message.Delete => Result.fail .panic - | betree.Message.Upsert s => - do - let v ← betree.upsert_update prev s - betree.Node.apply_upserts msgs1 (some v) key - else - do - let v ← core.option.Option.unwrap U64 prev - let msgs1 ← - betree.List.push_front (U64 × betree.Message) msgs (key, - betree.Message.Insert v) - Result.ok (v, msgs1) - -/- [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: - Source: 'src/betree.rs', lines 395:4-395:63 -/ -mutual divergent def betree.Internal.lookup_in_children - (self : betree.Internal) (key : U64) (st : State) : - Result (State × ((Option U64) × betree.Internal)) - := - if key < self.pivot - then - do - let (st1, (o, n)) ← betree.Node.lookup self.left key st - Result.ok (st1, (o, betree.Internal.mk self.id self.pivot n self.right)) - else - do - let (st1, (o, n)) ← betree.Node.lookup self.right key st - Result.ok (st1, (o, betree.Internal.mk self.id self.pivot self.left n)) - -/- [betree_main::betree::{betree_main::betree::Node#5}::lookup]: - Source: 'src/betree.rs', lines 709:4-709:58 -/ -divergent def betree.Node.lookup - (self : betree.Node) (key : U64) (st : State) : - Result (State × ((Option U64) × betree.Node)) - := - match self with - | betree.Node.Internal node => - do - let (st1, msgs) ← betree.load_internal_node node.id st - let (pending, lookup_first_message_for_key_back) ← - betree.Node.lookup_first_message_for_key key msgs - match pending with - | betree.List.Cons p l => - let (k, msg) := p - if k != key - then - do - let (st2, (o, node1)) ← - betree.Internal.lookup_in_children node key st1 - let _ ← - lookup_first_message_for_key_back (betree.List.Cons (k, msg) l) - Result.ok (st2, (o, betree.Node.Internal node1)) - else - match msg with - | betree.Message.Insert v => - do - let _ ← - lookup_first_message_for_key_back (betree.List.Cons (k, - betree.Message.Insert v) l) - Result.ok (st1, (some v, betree.Node.Internal node)) - | betree.Message.Delete => - do - let _ ← - lookup_first_message_for_key_back (betree.List.Cons (k, - betree.Message.Delete) l) - Result.ok (st1, (none, betree.Node.Internal node)) - | betree.Message.Upsert ufs => - do - let (st2, (v, node1)) ← - betree.Internal.lookup_in_children node key st1 - let (v1, pending1) ← - betree.Node.apply_upserts (betree.List.Cons (k, - betree.Message.Upsert ufs) l) v key - let msgs1 ← lookup_first_message_for_key_back pending1 - let (st3, _) ← betree.store_internal_node node1.id msgs1 st2 - Result.ok (st3, (some v1, betree.Node.Internal node1)) - | betree.List.Nil => - do - let (st2, (o, node1)) ← betree.Internal.lookup_in_children node key st1 - let _ ← lookup_first_message_for_key_back betree.List.Nil - Result.ok (st2, (o, betree.Node.Internal node1)) - | betree.Node.Leaf node => - do - let (st1, bindings) ← betree.load_leaf_node node.id st - let o ← betree.Node.lookup_in_bindings key bindings - Result.ok (st1, (o, betree.Node.Leaf node)) - -end - -/- [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: - Source: 'src/betree.rs', lines 674:4-674:77 -/ -divergent def betree.Node.filter_messages_for_key - (key : U64) (msgs : betree.List (U64 × betree.Message)) : - Result (betree.List (U64 × betree.Message)) - := - match msgs with - | betree.List.Cons p l => - let (k, m) := p - if k = key - then - do - let (_, msgs1) ← - betree.List.pop_front (U64 × betree.Message) (betree.List.Cons (k, m) - l) - betree.Node.filter_messages_for_key key msgs1 - else Result.ok (betree.List.Cons (k, m) l) - | betree.List.Nil => Result.ok betree.List.Nil - -/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: - Source: 'src/betree.rs', lines 689:4-692:34 -/ -divergent def betree.Node.lookup_first_message_after_key - (key : U64) (msgs : betree.List (U64 × betree.Message)) : - Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 × - betree.Message) → Result (betree.List (U64 × betree.Message)))) - := - match msgs with - | betree.List.Cons p next_msgs => - let (k, m) := p - if k = key - then - do - let (l, lookup_first_message_after_key_back) ← - betree.Node.lookup_first_message_after_key key next_msgs - let back := - fun ret => - do - let next_msgs1 ← lookup_first_message_after_key_back ret - Result.ok (betree.List.Cons (k, m) next_msgs1) - Result.ok (l, back) - else Result.ok (betree.List.Cons (k, m) next_msgs, Result.ok) - | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok) - -/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: - Source: 'src/betree.rs', lines 521:4-521:89 -/ -def betree.Node.apply_to_internal - (msgs : betree.List (U64 × betree.Message)) (key : U64) - (new_msg : betree.Message) : - Result (betree.List (U64 × betree.Message)) - := - do - let (msgs1, lookup_first_message_for_key_back) ← - betree.Node.lookup_first_message_for_key key msgs - let b ← betree.ListPairU64T.head_has_key betree.Message msgs1 key - if b - then - match new_msg with - | betree.Message.Insert i => - do - let msgs2 ← betree.Node.filter_messages_for_key key msgs1 - let msgs3 ← - betree.List.push_front (U64 × betree.Message) msgs2 (key, - betree.Message.Insert i) - lookup_first_message_for_key_back msgs3 - | betree.Message.Delete => - do - let msgs2 ← betree.Node.filter_messages_for_key key msgs1 - let msgs3 ← - betree.List.push_front (U64 × betree.Message) msgs2 (key, - betree.Message.Delete) - lookup_first_message_for_key_back msgs3 - | betree.Message.Upsert s => - do - let p ← betree.List.hd (U64 × betree.Message) msgs1 - let (_, m) := p - match m with - | betree.Message.Insert prev => - do - let v ← betree.upsert_update (some prev) s - let (_, msgs2) ← betree.List.pop_front (U64 × betree.Message) msgs1 - let msgs3 ← - betree.List.push_front (U64 × betree.Message) msgs2 (key, - betree.Message.Insert v) - lookup_first_message_for_key_back msgs3 - | betree.Message.Delete => - do - let (_, msgs2) ← betree.List.pop_front (U64 × betree.Message) msgs1 - let v ← betree.upsert_update none s - let msgs3 ← - betree.List.push_front (U64 × betree.Message) msgs2 (key, - betree.Message.Insert v) - lookup_first_message_for_key_back msgs3 - | betree.Message.Upsert _ => - do - let (msgs2, lookup_first_message_after_key_back) ← - betree.Node.lookup_first_message_after_key key msgs1 - let msgs3 ← - betree.List.push_front (U64 × betree.Message) msgs2 (key, - betree.Message.Upsert s) - let msgs4 ← lookup_first_message_after_key_back msgs3 - lookup_first_message_for_key_back msgs4 - else - do - let msgs2 ← - betree.List.push_front (U64 × betree.Message) msgs1 (key, new_msg) - lookup_first_message_for_key_back msgs2 - -/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: - Source: 'src/betree.rs', lines 502:4-505:5 -/ -divergent def betree.Node.apply_messages_to_internal - (msgs : betree.List (U64 × betree.Message)) - (new_msgs : betree.List (U64 × betree.Message)) : - Result (betree.List (U64 × betree.Message)) - := - match new_msgs with - | betree.List.Cons new_msg new_msgs_tl => - do - let (i, m) := new_msg - let msgs1 ← betree.Node.apply_to_internal msgs i m - betree.Node.apply_messages_to_internal msgs1 new_msgs_tl - | betree.List.Nil => Result.ok msgs - -/- [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: - Source: 'src/betree.rs', lines 653:4-656:32 -/ -divergent def betree.Node.lookup_mut_in_bindings - (key : U64) (bindings : betree.List (U64 × U64)) : - Result ((betree.List (U64 × U64)) × (betree.List (U64 × U64) → Result - (betree.List (U64 × U64)))) - := - match bindings with - | betree.List.Cons hd tl => - let (i, i1) := hd - if i >= key - then Result.ok (betree.List.Cons (i, i1) tl, Result.ok) - else - do - let (l, lookup_mut_in_bindings_back) ← - betree.Node.lookup_mut_in_bindings key tl - let back := - fun ret => - do - let tl1 ← lookup_mut_in_bindings_back ret - Result.ok (betree.List.Cons (i, i1) tl1) - Result.ok (l, back) - | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok) - -/- [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: - Source: 'src/betree.rs', lines 460:4-460:87 -/ -def betree.Node.apply_to_leaf - (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message) - : - Result (betree.List (U64 × U64)) - := - do - let (bindings1, lookup_mut_in_bindings_back) ← - betree.Node.lookup_mut_in_bindings key bindings - let b ← betree.ListPairU64T.head_has_key U64 bindings1 key - if b - then - do - let (hd, bindings2) ← betree.List.pop_front (U64 × U64) bindings1 - match new_msg with - | betree.Message.Insert v => - do - let bindings3 ← betree.List.push_front (U64 × U64) bindings2 (key, v) - lookup_mut_in_bindings_back bindings3 - | betree.Message.Delete => lookup_mut_in_bindings_back bindings2 - | betree.Message.Upsert s => - do - let (_, i) := hd - let v ← betree.upsert_update (some i) s - let bindings3 ← betree.List.push_front (U64 × U64) bindings2 (key, v) - lookup_mut_in_bindings_back bindings3 - else - match new_msg with - | betree.Message.Insert v => - do - let bindings2 ← betree.List.push_front (U64 × U64) bindings1 (key, v) - lookup_mut_in_bindings_back bindings2 - | betree.Message.Delete => lookup_mut_in_bindings_back bindings1 - | betree.Message.Upsert s => - do - let v ← betree.upsert_update none s - let bindings2 ← betree.List.push_front (U64 × U64) bindings1 (key, v) - lookup_mut_in_bindings_back bindings2 - -/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: - Source: 'src/betree.rs', lines 444:4-447:5 -/ -divergent def betree.Node.apply_messages_to_leaf - (bindings : betree.List (U64 × U64)) - (new_msgs : betree.List (U64 × betree.Message)) : - Result (betree.List (U64 × U64)) - := - match new_msgs with - | betree.List.Cons new_msg new_msgs_tl => - do - let (i, m) := new_msg - let bindings1 ← betree.Node.apply_to_leaf bindings i m - betree.Node.apply_messages_to_leaf bindings1 new_msgs_tl - | betree.List.Nil => Result.ok bindings - -/- [betree_main::betree::{betree_main::betree::Internal#4}::flush]: - Source: 'src/betree.rs', lines 410:4-415:26 -/ -mutual divergent def betree.Internal.flush - (self : betree.Internal) (params : betree.Params) - (node_id_cnt : betree.NodeIdCounter) - (content : betree.List (U64 × betree.Message)) (st : State) : - Result (State × ((betree.List (U64 × betree.Message)) × (betree.Internal - × betree.NodeIdCounter))) - := - do - let p ← - betree.ListPairU64T.partition_at_pivot betree.Message content self.pivot - let (msgs_left, msgs_right) := p - let len_left ← betree.List.len (U64 × betree.Message) msgs_left - if len_left >= params.min_flush_size - then - do - let (st1, p1) ← - betree.Node.apply_messages self.left params node_id_cnt msgs_left st - let (n, node_id_cnt1) := p1 - let len_right ← betree.List.len (U64 × betree.Message) msgs_right - if len_right >= params.min_flush_size - then - do - let (st2, p2) ← - betree.Node.apply_messages self.right params node_id_cnt1 msgs_right - st1 - let (n1, node_id_cnt2) := p2 - Result.ok (st2, (betree.List.Nil, (betree.Internal.mk self.id self.pivot - n n1, node_id_cnt2))) - else - Result.ok (st1, (msgs_right, (betree.Internal.mk self.id self.pivot n - self.right, node_id_cnt1))) - else - do - let (st1, p1) ← - betree.Node.apply_messages self.right params node_id_cnt msgs_right st - let (n, node_id_cnt1) := p1 - Result.ok (st1, (msgs_left, (betree.Internal.mk self.id self.pivot - self.left n, node_id_cnt1))) - -/- [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: - Source: 'src/betree.rs', lines 588:4-593:5 -/ -divergent def betree.Node.apply_messages - (self : betree.Node) (params : betree.Params) - (node_id_cnt : betree.NodeIdCounter) - (msgs : betree.List (U64 × betree.Message)) (st : State) : - Result (State × (betree.Node × betree.NodeIdCounter)) - := - match self with - | betree.Node.Internal node => - do - let (st1, content) ← betree.load_internal_node node.id st - let content1 ← betree.Node.apply_messages_to_internal content msgs - let num_msgs ← betree.List.len (U64 × betree.Message) content1 - if num_msgs >= params.min_flush_size - then - do - let (st2, (content2, p)) ← - betree.Internal.flush node params node_id_cnt content1 st1 - let (node1, node_id_cnt1) := p - let (st3, _) ← betree.store_internal_node node1.id content2 st2 - Result.ok (st3, (betree.Node.Internal node1, node_id_cnt1)) - else - do - let (st2, _) ← betree.store_internal_node node.id content1 st1 - Result.ok (st2, (betree.Node.Internal node, node_id_cnt)) - | betree.Node.Leaf node => - do - let (st1, content) ← betree.load_leaf_node node.id st - let content1 ← betree.Node.apply_messages_to_leaf content msgs - let len ← betree.List.len (U64 × U64) content1 - let i ← 2#u64 * params.split_size - if len >= i - then - do - let (st2, (new_node, node_id_cnt1)) ← - betree.Leaf.split node content1 params node_id_cnt st1 - let (st3, _) ← betree.store_leaf_node node.id betree.List.Nil st2 - Result.ok (st3, (betree.Node.Internal new_node, node_id_cnt1)) - else - do - let (st2, _) ← betree.store_leaf_node node.id content1 st1 - Result.ok (st2, (betree.Node.Leaf { node with size := len }, - node_id_cnt)) - -end - -/- [betree_main::betree::{betree_main::betree::Node#5}::apply]: - Source: 'src/betree.rs', lines 576:4-582:5 -/ -def betree.Node.apply - (self : betree.Node) (params : betree.Params) - (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message) - (st : State) : - Result (State × (betree.Node × betree.NodeIdCounter)) - := - do - let (st1, p) ← - betree.Node.apply_messages self params node_id_cnt (betree.List.Cons (key, - new_msg) betree.List.Nil) st - let (self1, node_id_cnt1) := p - Result.ok (st1, (self1, node_id_cnt1)) - -/- [betree_main::betree::{betree_main::betree::BeTree#6}::new]: - Source: 'src/betree.rs', lines 849:4-849:60 -/ -def betree.BeTree.new - (min_flush_size : U64) (split_size : U64) (st : State) : - Result (State × betree.BeTree) - := - do - let node_id_cnt ← betree.NodeIdCounter.new - let (id, node_id_cnt1) ← betree.NodeIdCounter.fresh_id node_id_cnt - let (st1, _) ← betree.store_leaf_node id betree.List.Nil st - Result.ok (st1, - { - params := { min_flush_size := min_flush_size, split_size := split_size }, - node_id_cnt := node_id_cnt1, - root := (betree.Node.Leaf { id := id, size := 0#u64 }) - }) - -/- [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: - Source: 'src/betree.rs', lines 868:4-868:47 -/ -def betree.BeTree.apply - (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) : - Result (State × betree.BeTree) - := - do - let (st1, p) ← - betree.Node.apply self.root self.params self.node_id_cnt key msg st - let (n, nic) := p - Result.ok (st1, { self with node_id_cnt := nic, root := n }) - -/- [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: - Source: 'src/betree.rs', lines 874:4-874:52 -/ -def betree.BeTree.insert - (self : betree.BeTree) (key : U64) (value : U64) (st : State) : - Result (State × betree.BeTree) - := - betree.BeTree.apply self key (betree.Message.Insert value) st - -/- [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: - Source: 'src/betree.rs', lines 880:4-880:38 -/ -def betree.BeTree.delete - (self : betree.BeTree) (key : U64) (st : State) : - Result (State × betree.BeTree) - := - betree.BeTree.apply self key betree.Message.Delete st - -/- [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: - Source: 'src/betree.rs', lines 886:4-886:59 -/ -def betree.BeTree.upsert - (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State) - : - Result (State × betree.BeTree) - := - betree.BeTree.apply self key (betree.Message.Upsert upd) st - -/- [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: - Source: 'src/betree.rs', lines 895:4-895:62 -/ -def betree.BeTree.lookup - (self : betree.BeTree) (key : U64) (st : State) : - Result (State × ((Option U64) × betree.BeTree)) - := - do - let (st1, (o, n)) ← betree.Node.lookup self.root key st - Result.ok (st1, (o, { self with root := n })) - -/- [betree_main::main]: - Source: 'src/main.rs', lines 4:0-4:9 -/ -def main : Result Unit := - Result.ok () - -/- Unit test for [betree_main::main] -/ -#assert (main == Result.ok ()) - -end betree_main diff --git a/tests/lean/BetreeMain/FunsExternal.lean b/tests/lean/BetreeMain/FunsExternal.lean deleted file mode 100644 index d26177fb..00000000 --- a/tests/lean/BetreeMain/FunsExternal.lean +++ /dev/null @@ -1,30 +0,0 @@ --- [betree_main]: external functions. -import Base -import BetreeMain.Types -open Primitives -open betree_main - --- TODO: fill those bodies - -/- [betree_main::betree_utils::load_internal_node] -/ -def betree_utils.load_internal_node - : - U64 → State → Result (State × (betree.List (U64 × betree.Message))) := - fun _ _ => .fail .panic - -/- [betree_main::betree_utils::store_internal_node] -/ -def betree_utils.store_internal_node - : - U64 → betree.List (U64 × betree.Message) → State → Result (State - × Unit) := - fun _ _ _ => .fail .panic - -/- [betree_main::betree_utils::load_leaf_node] -/ -def betree_utils.load_leaf_node - : U64 → State → Result (State × (betree.List (U64 × U64))) := - fun _ _ => .fail .panic - -/- [betree_main::betree_utils::store_leaf_node] -/ -def betree_utils.store_leaf_node - : U64 → betree.List (U64 × U64) → State → Result (State × Unit) := - fun _ _ _ => .fail .panic diff --git a/tests/lean/BetreeMain/FunsExternal_Template.lean b/tests/lean/BetreeMain/FunsExternal_Template.lean deleted file mode 100644 index 0dcce5ca..00000000 --- a/tests/lean/BetreeMain/FunsExternal_Template.lean +++ /dev/null @@ -1,30 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: external functions. --- This is a template file: rename it to "FunsExternal.lean" and fill the holes. -import Base -import BetreeMain.Types -open Primitives -open betree_main - -/- [betree_main::betree_utils::load_internal_node]: - Source: 'src/betree_utils.rs', lines 98:0-98:63 -/ -axiom betree_utils.load_internal_node - : U64 → State → Result (State × (betree.List (U64 × betree.Message))) - -/- [betree_main::betree_utils::store_internal_node]: - Source: 'src/betree_utils.rs', lines 115:0-115:71 -/ -axiom betree_utils.store_internal_node - : - U64 → betree.List (U64 × betree.Message) → State → Result (State × - Unit) - -/- [betree_main::betree_utils::load_leaf_node]: - Source: 'src/betree_utils.rs', lines 132:0-132:55 -/ -axiom betree_utils.load_leaf_node - : U64 → State → Result (State × (betree.List (U64 × U64))) - -/- [betree_main::betree_utils::store_leaf_node]: - Source: 'src/betree_utils.rs', lines 145:0-145:63 -/ -axiom betree_utils.store_leaf_node - : U64 → betree.List (U64 × U64) → State → Result (State × Unit) - diff --git a/tests/lean/BetreeMain/Types.lean b/tests/lean/BetreeMain/Types.lean deleted file mode 100644 index e79da43f..00000000 --- a/tests/lean/BetreeMain/Types.lean +++ /dev/null @@ -1,83 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: type definitions -import Base -import BetreeMain.TypesExternal -open Primitives - -namespace betree_main - -/- [betree_main::betree::List] - Source: 'src/betree.rs', lines 17:0-17:23 -/ -inductive betree.List (T : Type) := -| Cons : T → betree.List T → betree.List T -| Nil : betree.List T - -/- [betree_main::betree::UpsertFunState] - Source: 'src/betree.rs', lines 63:0-63:23 -/ -inductive betree.UpsertFunState := -| Add : U64 → betree.UpsertFunState -| Sub : U64 → betree.UpsertFunState - -/- [betree_main::betree::Message] - Source: 'src/betree.rs', lines 69:0-69:23 -/ -inductive betree.Message := -| Insert : U64 → betree.Message -| Delete : betree.Message -| Upsert : betree.UpsertFunState → betree.Message - -/- [betree_main::betree::Leaf] - Source: 'src/betree.rs', lines 167:0-167:11 -/ -structure betree.Leaf where - id : U64 - size : U64 - -mutual - -/- [betree_main::betree::Internal] - Source: 'src/betree.rs', lines 156:0-156:15 -/ -inductive betree.Internal := -| mk : U64 → U64 → betree.Node → betree.Node → betree.Internal - -/- [betree_main::betree::Node] - Source: 'src/betree.rs', lines 179:0-179:9 -/ -inductive betree.Node := -| Internal : betree.Internal → betree.Node -| Leaf : betree.Leaf → betree.Node - -end - -@[simp, reducible] -def betree.Internal.id (x : betree.Internal) := - match x with | betree.Internal.mk x1 _ _ _ => x1 - -@[simp, reducible] -def betree.Internal.pivot (x : betree.Internal) := - match x with | betree.Internal.mk _ x1 _ _ => x1 - -@[simp, reducible] -def betree.Internal.left (x : betree.Internal) := - match x with | betree.Internal.mk _ _ x1 _ => x1 - -@[simp, reducible] -def betree.Internal.right (x : betree.Internal) := - match x with | betree.Internal.mk _ _ _ x1 => x1 - -/- [betree_main::betree::Params] - Source: 'src/betree.rs', lines 187:0-187:13 -/ -structure betree.Params where - min_flush_size : U64 - split_size : U64 - -/- [betree_main::betree::NodeIdCounter] - Source: 'src/betree.rs', lines 201:0-201:20 -/ -structure betree.NodeIdCounter where - next_node_id : U64 - -/- [betree_main::betree::BeTree] - Source: 'src/betree.rs', lines 218:0-218:17 -/ -structure betree.BeTree where - params : betree.Params - node_id_cnt : betree.NodeIdCounter - root : betree.Node - -end betree_main diff --git a/tests/lean/BetreeMain/TypesExternal.lean b/tests/lean/BetreeMain/TypesExternal.lean deleted file mode 100644 index 1701eaaf..00000000 --- a/tests/lean/BetreeMain/TypesExternal.lean +++ /dev/null @@ -1,7 +0,0 @@ --- [betree_main]: external types. -import Base -open Primitives - -/- The state type used in the state-error monad -/ -axiom State : Type - diff --git a/tests/lean/BetreeMain/TypesExternal_Template.lean b/tests/lean/BetreeMain/TypesExternal_Template.lean deleted file mode 100644 index bbac7e99..00000000 --- a/tests/lean/BetreeMain/TypesExternal_Template.lean +++ /dev/null @@ -1,9 +0,0 @@ --- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS --- [betree_main]: external types. --- This is a template file: rename it to "TypesExternal.lean" and fill the holes. -import Base -open Primitives - -/- The state type used in the state-error monad -/ -axiom State : Type - diff --git a/tests/lean/lakefile.lean b/tests/lean/lakefile.lean index bb13ddf2..ba336a4a 100644 --- a/tests/lean/lakefile.lean +++ b/tests/lean/lakefile.lean @@ -9,7 +9,7 @@ require base from "../../backends/lean" package «tests» {} @[default_target] lean_lib Tutorial -@[default_target] lean_lib BetreeMain +@[default_target] lean_lib Betree @[default_target] lean_lib Constants @[default_target] lean_lib External @[default_target] lean_lib Hashmap diff --git a/tests/test_runner/run_test.ml b/tests/test_runner/run_test.ml index 1c885d4b..a7b83e88 100644 --- a/tests/test_runner/run_test.ml +++ b/tests/test_runner/run_test.ml @@ -122,8 +122,7 @@ let aeneas_options_for_test backend test_name = (* File-specific options *) let charon_options_for_test test_name = match test_name with - | "betree" -> - [ "--polonius"; "--opaque=betree_utils"; "--crate"; "betree_main" ] + | "betree" -> [ "--polonius"; "--opaque=betree_utils" ] | _ -> [] (* The data for a specific test input *) @@ -257,10 +256,8 @@ end (* Run Aeneas on a specific input with the given options *) let run_aeneas (env : runner_env) (case : Input.t) (backend : Backend.t) = - (* FIXME: remove this special case *) let backend_str = Backend.to_string backend in - let test_name = if case.name = "betree" then "betree_main" else case.name in - let input_file = concat_path [ env.llbc_dir; test_name ] ^ ".llbc" in + let input_file = concat_path [ env.llbc_dir; case.name ] ^ ".llbc" in let output_file = Filename.remove_extension case.path ^ "." ^ backend_str ^ ".out" in -- cgit v1.2.3 From 9cc69020773cc77965a6faa6f0d46f179de3d8b8 Mon Sep 17 00:00:00 2001 From: Nadrieril Date: Mon, 27 May 2024 17:22:07 +0200 Subject: runner: Store options for crate tests in a separate file --- tests/src/betree/aeneas-test-options | 4 ++++ tests/test_runner/run_test.ml | 40 +++++++++--------------------------- 2 files changed, 14 insertions(+), 30 deletions(-) create mode 100644 tests/src/betree/aeneas-test-options diff --git a/tests/src/betree/aeneas-test-options b/tests/src/betree/aeneas-test-options new file mode 100644 index 00000000..c71e01df --- /dev/null +++ b/tests/src/betree/aeneas-test-options @@ -0,0 +1,4 @@ +charon-args=--polonius --opaque=betree_utils +aeneas-args=-backward-no-state-update -test-trans-units -state -split-files +[coq] aeneas-args=-use-fuel +[fstar] aeneas-args=-decreases-clauses -template-clauses diff --git a/tests/test_runner/run_test.ml b/tests/test_runner/run_test.ml index a7b83e88..c626b4d1 100644 --- a/tests/test_runner/run_test.ml +++ b/tests/test_runner/run_test.ml @@ -100,31 +100,6 @@ module Command = struct | Failure -> () end -let aeneas_options_for_test backend test_name = - if test_name = "betree" then - let options = - [ - "-backward-no-state-update"; - "-test-trans-units"; - "-state"; - "-split-files"; - ] - in - let extra_options = - match backend with - | Backend.Coq -> [ "-use-fuel" ] - | Backend.FStar -> [ "-decreases-clauses"; "-template-clauses" ] - | _ -> [] - in - List.append extra_options options - else [] - -(* File-specific options *) -let charon_options_for_test test_name = - match test_name with - | "betree" -> [ "--polonius"; "--opaque=betree_utils" ] - | _ -> [] - (* The data for a specific test input *) module Input = struct type kind = SingleFile | Crate @@ -218,13 +193,10 @@ module Input = struct else failwith ("`" ^ path ^ "` is not a file or a directory.") in let actions = BackendMap.make (fun _ -> Normal) in - let charon_options = charon_options_for_test name in let subdirs = BackendMap.make (fun backend -> default_subdir backend name) in - let aeneas_options = - BackendMap.make (fun backend -> aeneas_options_for_test backend name) - in + let aeneas_options = BackendMap.make (fun _ -> []) in let check_output = BackendMap.make (fun _ -> true) in let input = { @@ -232,12 +204,14 @@ module Input = struct name; kind; actions; - charon_options; + charon_options = []; subdirs; aeneas_options; check_output; } in + (* For crates, we store the special comments in a separate file. *) + let crate_config_file = Filename.concat path "aeneas-test-options" in match kind with | SingleFile -> let file_lines = Core.In_channel.read_lines path in @@ -251,6 +225,11 @@ module Input = struct List.fold_left (fun input comment -> apply_special_comment comment input) input special_comments + | Crate when Sys.file_exists crate_config_file -> + let special_comments = Core.In_channel.read_lines crate_config_file in + List.fold_left + (fun input comment -> apply_special_comment comment input) + input special_comments | Crate -> input end @@ -300,6 +279,7 @@ let run_aeneas (env : runner_env) (case : Input.t) (backend : Backend.t) = let cmd = { cmd with redirect_out = Some out } in Command.run_command_expecting_failure cmd; Unix.close out + (* Run Charon on a specific input with the given options *) let run_charon (env : runner_env) (case : Input.t) = match case.kind with -- cgit v1.2.3 From c81c96f20b1dbf428a9ed42e83b910e798e1a225 Mon Sep 17 00:00:00 2001 From: Nadrieril Date: Mon, 27 May 2024 17:33:56 +0200 Subject: Add some tests --- tests/coq/misc/Issue194RecursiveStructProjector.v | 54 ++++++++++++++++++++++ .../misc/Issue194RecursiveStructProjector.fst | 24 ++++++++++ tests/fstar/misc/Matches.fst | 12 +++++ tests/lean/Issue194RecursiveStructProjector.lean | 35 ++++++++++++++ tests/lean/Matches.lean | 16 +++++++ tests/src/infinite-loop.rs | 11 +++++ tests/src/issue-194-recursive-struct-projector.rs | 16 +++++++ tests/src/matches.rs | 10 ++++ 8 files changed, 178 insertions(+) create mode 100644 tests/coq/misc/Issue194RecursiveStructProjector.v create mode 100644 tests/fstar/misc/Issue194RecursiveStructProjector.fst create mode 100644 tests/fstar/misc/Matches.fst create mode 100644 tests/lean/Issue194RecursiveStructProjector.lean create mode 100644 tests/lean/Matches.lean create mode 100644 tests/src/infinite-loop.rs create mode 100644 tests/src/issue-194-recursive-struct-projector.rs create mode 100644 tests/src/matches.rs diff --git a/tests/coq/misc/Issue194RecursiveStructProjector.v b/tests/coq/misc/Issue194RecursiveStructProjector.v new file mode 100644 index 00000000..d1a07449 --- /dev/null +++ b/tests/coq/misc/Issue194RecursiveStructProjector.v @@ -0,0 +1,54 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [issue_194_recursive_struct_projector] *) +Require Import Primitives. +Import Primitives. +Require Import Coq.ZArith.ZArith. +Require Import List. +Import ListNotations. +Local Open Scope Primitives_scope. +Module Issue194RecursiveStructProjector. + +(** [issue_194_recursive_struct_projector::AVLNode] + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 2:0-2:17 *) +Inductive AVLNode_t (T : Type) := +| mkAVLNode_t : + T -> + option (AVLNode_t T) -> + option (AVLNode_t T) -> + AVLNode_t T +. + +Arguments mkAVLNode_t { _ }. + +Definition aVLNode_value {T : Type} (x : AVLNode_t T) := + match x with | mkAVLNode_t x1 _ _ => x1 end +. + +Notation "x2 .(aVLNode_value)" := (aVLNode_value x2) (at level 9). + +Definition aVLNode_left {T : Type} (x : AVLNode_t T) := + match x with | mkAVLNode_t _ x1 _ => x1 end +. + +Notation "x2 .(aVLNode_left)" := (aVLNode_left x2) (at level 9). + +Definition aVLNode_right {T : Type} (x : AVLNode_t T) := + match x with | mkAVLNode_t _ _ x1 => x1 end +. + +Notation "x2 .(aVLNode_right)" := (aVLNode_right x2) (at level 9). + +(** [issue_194_recursive_struct_projector::get_val]: + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 10:0-10:33 *) +Definition get_val (T : Type) (x : AVLNode_t T) : result T := + Ok x.(aVLNode_value) +. + +(** [issue_194_recursive_struct_projector::get_left]: + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 14:0-14:43 *) +Definition get_left + (T : Type) (x : AVLNode_t T) : result (option (AVLNode_t T)) := + Ok x.(aVLNode_left) +. + +End Issue194RecursiveStructProjector. diff --git a/tests/fstar/misc/Issue194RecursiveStructProjector.fst b/tests/fstar/misc/Issue194RecursiveStructProjector.fst new file mode 100644 index 00000000..76368f04 --- /dev/null +++ b/tests/fstar/misc/Issue194RecursiveStructProjector.fst @@ -0,0 +1,24 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [issue_194_recursive_struct_projector] *) +module Issue194RecursiveStructProjector +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [issue_194_recursive_struct_projector::AVLNode] + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 2:0-2:17 *) +type aVLNode_t (t : Type0) = +{ + value : t; left : option (aVLNode_t t); right : option (aVLNode_t t); +} + +(** [issue_194_recursive_struct_projector::get_val]: + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 10:0-10:33 *) +let get_val (t : Type0) (x : aVLNode_t t) : result t = + Ok x.value + +(** [issue_194_recursive_struct_projector::get_left]: + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 14:0-14:43 *) +let get_left (t : Type0) (x : aVLNode_t t) : result (option (aVLNode_t t)) = + Ok x.left + diff --git a/tests/fstar/misc/Matches.fst b/tests/fstar/misc/Matches.fst new file mode 100644 index 00000000..06a9b6df --- /dev/null +++ b/tests/fstar/misc/Matches.fst @@ -0,0 +1,12 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [matches] *) +module Matches +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [matches::match_u32]: + Source: 'tests/src/matches.rs', lines 4:0-4:27 *) +let match_u32 (x : u32) : result u32 = + begin match x with | 0 -> Ok 0 | 1 -> Ok 1 | _ -> Ok 2 end + diff --git a/tests/lean/Issue194RecursiveStructProjector.lean b/tests/lean/Issue194RecursiveStructProjector.lean new file mode 100644 index 00000000..4eb23934 --- /dev/null +++ b/tests/lean/Issue194RecursiveStructProjector.lean @@ -0,0 +1,35 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [issue_194_recursive_struct_projector] +import Base +open Primitives + +namespace issue_194_recursive_struct_projector + +/- [issue_194_recursive_struct_projector::AVLNode] + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 2:0-2:17 -/ +inductive AVLNode (T : Type) := +| mk : T → Option (AVLNode T) → Option (AVLNode T) → AVLNode T + +@[simp, reducible] +def AVLNode.value {T : Type} (x : AVLNode T) := + match x with | AVLNode.mk x1 _ _ => x1 + +@[simp, reducible] +def AVLNode.left {T : Type} (x : AVLNode T) := + match x with | AVLNode.mk _ x1 _ => x1 + +@[simp, reducible] +def AVLNode.right {T : Type} (x : AVLNode T) := + match x with | AVLNode.mk _ _ x1 => x1 + +/- [issue_194_recursive_struct_projector::get_val]: + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 10:0-10:33 -/ +def get_val (T : Type) (x : AVLNode T) : Result T := + Result.ok x.value + +/- [issue_194_recursive_struct_projector::get_left]: + Source: 'tests/src/issue-194-recursive-struct-projector.rs', lines 14:0-14:43 -/ +def get_left (T : Type) (x : AVLNode T) : Result (Option (AVLNode T)) := + Result.ok x.left + +end issue_194_recursive_struct_projector diff --git a/tests/lean/Matches.lean b/tests/lean/Matches.lean new file mode 100644 index 00000000..3e3a558b --- /dev/null +++ b/tests/lean/Matches.lean @@ -0,0 +1,16 @@ +-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS +-- [matches] +import Base +open Primitives + +namespace matches + +/- [matches::match_u32]: + Source: 'tests/src/matches.rs', lines 4:0-4:27 -/ +def match_u32 (x : U32) : Result U32 := + match x with + | 0#u32 => Result.ok 0#u32 + | 1#u32 => Result.ok 1#u32 + | _ => Result.ok 2#u32 + +end matches diff --git a/tests/src/infinite-loop.rs b/tests/src/infinite-loop.rs new file mode 100644 index 00000000..906fc1fa --- /dev/null +++ b/tests/src/infinite-loop.rs @@ -0,0 +1,11 @@ +//@ [coq,fstar,lean] skip +//@ [coq,fstar] aeneas-args=-use-fuel +//@ [coq,fstar] subdir=misc +// FIXME: make it work +fn bar() {} + +fn foo() { + loop { + bar() + } +} diff --git a/tests/src/issue-194-recursive-struct-projector.rs b/tests/src/issue-194-recursive-struct-projector.rs new file mode 100644 index 00000000..9ebdc2bc --- /dev/null +++ b/tests/src/issue-194-recursive-struct-projector.rs @@ -0,0 +1,16 @@ +//@ [coq,fstar] subdir=misc +struct AVLNode { + value: T, + left: AVLTree, + right: AVLTree, +} + +type AVLTree = Option>>; + +fn get_val(x: AVLNode) -> T { + x.value +} + +fn get_left(x: AVLNode) -> AVLTree { + x.left +} diff --git a/tests/src/matches.rs b/tests/src/matches.rs new file mode 100644 index 00000000..5710a604 --- /dev/null +++ b/tests/src/matches.rs @@ -0,0 +1,10 @@ +//@ [coq] skip +//@ [coq,fstar] subdir=misc +//^ note: coq gives "invalid notation for pattern" +fn match_u32(x: u32) -> u32 { + match x { + 0 => 0, + 1 => 1, + _ => 2, + } +} -- cgit v1.2.3 From c4d2af051c18c4c81b1e57a45210c37c89c8330f Mon Sep 17 00:00:00 2001 From: Nadrieril Date: Tue, 28 May 2024 11:18:35 +0200 Subject: tests: Rename hashmap_utils -> utils --- tests/coq/hashmap/Hashmap_Funs.v | 4 ++-- tests/coq/hashmap/Hashmap_FunsExternal.v | 8 ++++---- tests/coq/hashmap/Hashmap_FunsExternal_Template.v | 9 ++++----- tests/fstar/hashmap/Hashmap.Funs.fst | 4 ++-- tests/fstar/hashmap/Hashmap.FunsExternal.fsti | 8 ++++---- tests/fstar/hashmap/Hashmap.Properties.fst | 8 ++++---- tests/hol4/hashmap_main/hashmapMain_FunsScript.sml | 4 ++-- tests/hol4/hashmap_main/hashmapMain_FunsTheory.sig | 4 ++-- tests/hol4/hashmap_main/hashmapMain_OpaqueScript.sml | 4 ++-- tests/lean/Hashmap/Funs.lean | 4 ++-- tests/lean/Hashmap/FunsExternal.lean | 8 ++++---- tests/lean/Hashmap/FunsExternal_Template.lean | 9 ++++----- tests/src/hashmap.rs | 8 ++++---- 13 files changed, 40 insertions(+), 42 deletions(-) diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v index 89f90210..04df873a 100644 --- a/tests/coq/hashmap/Hashmap_Funs.v +++ b/tests/coq/hashmap/Hashmap_Funs.v @@ -508,10 +508,10 @@ Definition hashMap_remove Source: 'tests/src/hashmap.rs', lines 335:0-335:43 *) Definition insert_on_disk (n : nat) (key : usize) (value : u64) (st : state) : result (state * unit) := - p <- hashmap_utils_deserialize st; + p <- utils_deserialize st; let (st1, hm) := p in hm1 <- hashMap_insert u64 n hm key value; - hashmap_utils_serialize hm1 st1 + utils_serialize hm1 st1 . (** [hashmap::test1]: diff --git a/tests/coq/hashmap/Hashmap_FunsExternal.v b/tests/coq/hashmap/Hashmap_FunsExternal.v index bcf12c17..3bc6c98a 100644 --- a/tests/coq/hashmap/Hashmap_FunsExternal.v +++ b/tests/coq/hashmap/Hashmap_FunsExternal.v @@ -9,13 +9,13 @@ Require Export Hashmap_Types. Import Hashmap_Types. Module Hashmap_FunsExternal. -(** [hashmap::hashmap_utils::deserialize]: +(** [hashmap::utils::deserialize]: Source: 'tests/src/hashmap.rs', lines 330:4-330:47 *) -Axiom hashmap_utils_deserialize : state -> result (state * (HashMap_t u64)). +Axiom utils_deserialize : state -> result (state * (HashMap_t u64)). -(** [hashmap::hashmap_utils::serialize]: +(** [hashmap::utils::serialize]: Source: 'tests/src/hashmap.rs', lines 325:4-325:46 *) -Axiom hashmap_utils_serialize : HashMap_t u64 -> state -> result (state * unit) +Axiom utils_serialize : HashMap_t u64 -> state -> result (state * unit) . End Hashmap_FunsExternal. diff --git a/tests/coq/hashmap/Hashmap_FunsExternal_Template.v b/tests/coq/hashmap/Hashmap_FunsExternal_Template.v index c35b8e14..c58b021d 100644 --- a/tests/coq/hashmap/Hashmap_FunsExternal_Template.v +++ b/tests/coq/hashmap/Hashmap_FunsExternal_Template.v @@ -11,13 +11,12 @@ Require Import Hashmap_Types. Include Hashmap_Types. Module Hashmap_FunsExternal_Template. -(** [hashmap::hashmap_utils::deserialize]: +(** [hashmap::utils::deserialize]: Source: 'tests/src/hashmap.rs', lines 330:4-330:47 *) -Axiom hashmap_utils_deserialize : state -> result (state * (HashMap_t u64)). +Axiom utils_deserialize : state -> result (state * (HashMap_t u64)). -(** [hashmap::hashmap_utils::serialize]: +(** [hashmap::utils::serialize]: Source: 'tests/src/hashmap.rs', lines 325:4-325:46 *) -Axiom hashmap_utils_serialize : HashMap_t u64 -> state -> result (state * unit) -. +Axiom utils_serialize : HashMap_t u64 -> state -> result (state * unit). End Hashmap_FunsExternal_Template. diff --git a/tests/fstar/hashmap/Hashmap.Funs.fst b/tests/fstar/hashmap/Hashmap.Funs.fst index a85be4ed..0e991720 100644 --- a/tests/fstar/hashmap/Hashmap.Funs.fst +++ b/tests/fstar/hashmap/Hashmap.Funs.fst @@ -380,9 +380,9 @@ let hashMap_remove Source: 'tests/src/hashmap.rs', lines 335:0-335:43 *) let insert_on_disk (key : usize) (value : u64) (st : state) : result (state & unit) = - let* (st1, hm) = hashmap_utils_deserialize st in + let* (st1, hm) = utils_deserialize st in let* hm1 = hashMap_insert u64 hm key value in - hashmap_utils_serialize hm1 st1 + utils_serialize hm1 st1 (** [hashmap::test1]: Source: 'tests/src/hashmap.rs', lines 350:0-350:10 *) diff --git a/tests/fstar/hashmap/Hashmap.FunsExternal.fsti b/tests/fstar/hashmap/Hashmap.FunsExternal.fsti index 6e3964c7..f2f305e6 100644 --- a/tests/fstar/hashmap/Hashmap.FunsExternal.fsti +++ b/tests/fstar/hashmap/Hashmap.FunsExternal.fsti @@ -6,11 +6,11 @@ include Hashmap.Types #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" -(** [hashmap::hashmap_utils::deserialize]: +(** [hashmap::utils::deserialize]: Source: 'tests/src/hashmap.rs', lines 330:4-330:47 *) -val hashmap_utils_deserialize : state -> result (state & (hashMap_t u64)) +val utils_deserialize : state -> result (state & (hashMap_t u64)) -(** [hashmap::hashmap_utils::serialize]: +(** [hashmap::utils::serialize]: Source: 'tests/src/hashmap.rs', lines 325:4-325:46 *) -val hashmap_utils_serialize : hashMap_t u64 -> state -> result (state & unit) +val utils_serialize : hashMap_t u64 -> state -> result (state & unit) diff --git a/tests/fstar/hashmap/Hashmap.Properties.fst b/tests/fstar/hashmap/Hashmap.Properties.fst index 0d6372c1..ed118c46 100644 --- a/tests/fstar/hashmap/Hashmap.Properties.fst +++ b/tests/fstar/hashmap/Hashmap.Properties.fst @@ -18,18 +18,18 @@ val state_v : state -> hashMap_t u64 /// [serialize] updates the hash map stored on disk assume val serialize_lem (hm : hashMap_t u64) (st : state) : Lemma ( - match hashmap_utils_serialize hm st with + match utils_serialize hm st with | Fail _ -> True | Ok (st', ()) -> state_v st' == hm) - [SMTPat (hashmap_utils_serialize hm st)] + [SMTPat (utils_serialize hm st)] /// [deserialize] gives us the hash map stored on disk, without updating it assume val deserialize_lem (st : state) : Lemma ( - match hashmap_utils_deserialize st with + match utils_deserialize st with | Fail _ -> True | Ok (st', hm) -> hm == state_v st /\ st' == st) - [SMTPat (hashmap_utils_deserialize st)] + [SMTPat (utils_deserialize st)] (*** Lemmas *) diff --git a/tests/hol4/hashmap_main/hashmapMain_FunsScript.sml b/tests/hol4/hashmap_main/hashmapMain_FunsScript.sml index c1e30aa6..2a17d185 100644 --- a/tests/hol4/hashmap_main/hashmapMain_FunsScript.sml +++ b/tests/hol4/hashmap_main/hashmapMain_FunsScript.sml @@ -628,9 +628,9 @@ val insert_on_disk_fwd_def = Define ‘ insert_on_disk_fwd (key : usize) (value : u64) (st : state) : (state # unit) result = do - (st0, hm) <- hashmap_utils_deserialize_fwd st; + (st0, hm) <- utils_deserialize_fwd st; hm0 <- hashmap_hash_map_insert_fwd_back hm key value; - (st1, _) <- hashmap_utils_serialize_fwd hm0 st0; + (st1, _) <- utils_serialize_fwd hm0 st0; Return (st1, ()) od ’ diff --git a/tests/hol4/hashmap_main/hashmapMain_FunsTheory.sig b/tests/hol4/hashmap_main/hashmapMain_FunsTheory.sig index d4e43d9a..c19673bb 100644 --- a/tests/hol4/hashmap_main/hashmapMain_FunsTheory.sig +++ b/tests/hol4/hashmap_main/hashmapMain_FunsTheory.sig @@ -583,9 +583,9 @@ sig ⊢ ∀key value st. insert_on_disk_fwd key value st = do - (st0,hm) <- hashmap_utils_deserialize_fwd st; + (st0,hm) <- utils_deserialize_fwd st; hm0 <- hashmap_hash_map_insert_fwd_back hm key value; - (st1,_) <- hashmap_utils_serialize_fwd hm0 st0; + (st1,_) <- utils_serialize_fwd hm0 st0; Return (st1,()) od diff --git a/tests/hol4/hashmap_main/hashmapMain_OpaqueScript.sml b/tests/hol4/hashmap_main/hashmapMain_OpaqueScript.sml index f7221d92..9c29c0e0 100644 --- a/tests/hol4/hashmap_main/hashmapMain_OpaqueScript.sml +++ b/tests/hol4/hashmap_main/hashmapMain_OpaqueScript.sml @@ -6,10 +6,10 @@ open hashmapMain_TypesTheory val _ = new_theory "hashmapMain_Opaque" -(** [hashmap_main::hashmap_utils::deserialize]: forward function *)val _ = new_constant ("hashmap_utils_deserialize_fwd", +(** [hashmap_main::utils::deserialize]: forward function *)val _ = new_constant ("utils_deserialize_fwd", “:state -> (state # u64 hashmap_hash_map_t) result”) -(** [hashmap_main::hashmap_utils::serialize]: forward function *)val _ = new_constant ("hashmap_utils_serialize_fwd", +(** [hashmap_main::utils::serialize]: forward function *)val _ = new_constant ("utils_serialize_fwd", “:u64 hashmap_hash_map_t -> state -> (state # unit) result”) val _ = export_theory () diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean index e76912cc..d7ac3b05 100644 --- a/tests/lean/Hashmap/Funs.lean +++ b/tests/lean/Hashmap/Funs.lean @@ -386,9 +386,9 @@ def HashMap.remove def insert_on_disk (key : Usize) (value : U64) (st : State) : Result (State × Unit) := do - let (st1, hm) ← hashmap_utils.deserialize st + let (st1, hm) ← utils.deserialize st let hm1 ← HashMap.insert U64 hm key value - hashmap_utils.serialize hm1 st1 + utils.serialize hm1 st1 /- [hashmap::test1]: Source: 'tests/src/hashmap.rs', lines 350:0-350:10 -/ diff --git a/tests/lean/Hashmap/FunsExternal.lean b/tests/lean/Hashmap/FunsExternal.lean index 7454696b..329e5d82 100644 --- a/tests/lean/Hashmap/FunsExternal.lean +++ b/tests/lean/Hashmap/FunsExternal.lean @@ -6,14 +6,14 @@ open hashmap -- TODO: fill those bodies -/- [hashmap::hashmap_utils::deserialize]: +/- [hashmap::utils::deserialize]: Source: 'tests/src/hashmap.rs', lines 330:4-330:47 -/ -def hashmap_utils.deserialize +def utils.deserialize : State → Result (State × (HashMap U64)) := fun _ => .fail .panic -/- [hashmap::hashmap_utils::serialize]: +/- [hashmap::utils::serialize]: Source: 'tests/src/hashmap.rs', lines 325:4-325:46 -/ -def hashmap_utils.serialize +def utils.serialize : HashMap U64 → State → Result (State × Unit) := fun _ _ => .fail .panic diff --git a/tests/lean/Hashmap/FunsExternal_Template.lean b/tests/lean/Hashmap/FunsExternal_Template.lean index 16b4b6af..2af57d10 100644 --- a/tests/lean/Hashmap/FunsExternal_Template.lean +++ b/tests/lean/Hashmap/FunsExternal_Template.lean @@ -6,12 +6,11 @@ import Hashmap.Types open Primitives open hashmap -/- [hashmap::hashmap_utils::deserialize]: +/- [hashmap::utils::deserialize]: Source: 'tests/src/hashmap.rs', lines 330:4-330:47 -/ -axiom hashmap_utils.deserialize : State → Result (State × (HashMap U64)) +axiom utils.deserialize : State → Result (State × (HashMap U64)) -/- [hashmap::hashmap_utils::serialize]: +/- [hashmap::utils::serialize]: Source: 'tests/src/hashmap.rs', lines 325:4-325:46 -/ -axiom hashmap_utils.serialize - : HashMap U64 → State → Result (State × Unit) +axiom utils.serialize : HashMap U64 → State → Result (State × Unit) diff --git a/tests/src/hashmap.rs b/tests/src/hashmap.rs index ccb96e1e..19832a84 100644 --- a/tests/src/hashmap.rs +++ b/tests/src/hashmap.rs @@ -1,4 +1,4 @@ -//@ charon-args=--opaque=hashmap_utils +//@ charon-args=--opaque=utils //@ aeneas-args=-state -split-files //@ [coq] aeneas-args=-use-fuel //@ [fstar] aeneas-args=-decreases-clauses -template-clauses @@ -317,7 +317,7 @@ impl HashMap { } // This is a module so we can tell charon to leave it opaque -mod hashmap_utils { +mod utils { use crate::*; /// Serialize a hash map - we don't have traits, so we fix the type of the @@ -334,11 +334,11 @@ mod hashmap_utils { pub fn insert_on_disk(key: Key, value: u64) { // Deserialize - let mut hm = hashmap_utils::deserialize(); + let mut hm = utils::deserialize(); // Update hm.insert(key, value); // Serialize - hashmap_utils::serialize(hm); + utils::serialize(hm); } /// I currently can't retrieve functions marked with the attribute #[test], -- cgit v1.2.3