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 --- 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 +- 52 files changed, 7340 insertions(+), 7344 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 (limited to 'tests') 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