From 6db835db88c4bcf0e00ce1a7a6bc396382b393c3 Mon Sep 17 00:00:00 2001 From: Son Ho Date: Fri, 11 Nov 2022 21:34:29 +0100 Subject: Reorganize the project to prepare for new backends --- tests/betree/BetreeMain.Clauses.Template.fst | 106 -- tests/betree/BetreeMain.Clauses.fst | 210 ---- tests/betree/BetreeMain.Funs.fst | 1654 -------------------------- tests/betree/BetreeMain.Opaque.fsti | 30 - tests/betree/BetreeMain.Types.fsti | 64 - tests/betree/Makefile | 47 - tests/betree/Primitives.fst | 287 ----- 7 files changed, 2398 deletions(-) delete mode 100644 tests/betree/BetreeMain.Clauses.Template.fst delete mode 100644 tests/betree/BetreeMain.Clauses.fst delete mode 100644 tests/betree/BetreeMain.Funs.fst delete mode 100644 tests/betree/BetreeMain.Opaque.fsti delete mode 100644 tests/betree/BetreeMain.Types.fsti delete mode 100644 tests/betree/Makefile delete mode 100644 tests/betree/Primitives.fst (limited to 'tests/betree') diff --git a/tests/betree/BetreeMain.Clauses.Template.fst b/tests/betree/BetreeMain.Clauses.Template.fst deleted file mode 100644 index d48213d3..00000000 --- a/tests/betree/BetreeMain.Clauses.Template.fst +++ /dev/null @@ -1,106 +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" - -(** [core::num::u64::{10}::MAX] *) -let core_num_u64_max_body : result u64 = Return 18446744073709551615 -let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body - -(** [betree_main::betree::List::{1}::len]: decreases clause *) -unfold -let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat = - admit () - -(** [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 = - admit () - -(** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) -unfold -let betree_list_partition_at_pivot_decreases (t : Type0) - (self : betree_list_t (u64 & t)) (pivot : u64) : nat = - admit () - -(** [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)) : nat = - admit () - -(** [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)) : nat = - admit () - -(** [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) (st : state) : nat = - admit () - -(** [betree_main::betree::Node::{5}::lookup]: decreases clause *) -unfold -let betree_node_lookup_decreases (self : betree_node_t) (key : u64) - (st : state) : nat = - admit () - -(** [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) : nat = - admit () - -(** [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)) : nat = - admit () - -(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases clause *) -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::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)) : nat = - admit () - -(** [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)) : nat = - admit () - -(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases clause *) -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::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_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat = - admit () - -(** [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_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat = - admit () - diff --git a/tests/betree/BetreeMain.Clauses.fst b/tests/betree/BetreeMain.Clauses.fst deleted file mode 100644 index 07484711..00000000 --- a/tests/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_list_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) (st : state) : 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 - | BetreeNodeInternal node -> 1 + betree_internal_size node - | BetreeNodeLeaf _ -> 1 - -and betree_internal_size (node : betree_internal_t) : nat = - 1 + betree_size node.betree_internal_left + betree_size node.betree_internal_right - -let rec betree_list_len (#a : Type0) (ls : betree_list_t a) : nat = - match ls with - | BetreeListCons _ tl -> 1 + betree_list_len tl - | BetreeListNil -> 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_node_id_counter_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_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair = - (|betree_size self, betree_list_len msgs|) diff --git a/tests/betree/BetreeMain.Funs.fst b/tests/betree/BetreeMain.Funs.fst deleted file mode 100644 index 9ba5d3e7..00000000 --- a/tests/betree/BetreeMain.Funs.fst +++ /dev/null @@ -1,1654 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: function definitions *) -module BetreeMain.Funs -open Primitives -include BetreeMain.Types -include BetreeMain.Opaque -include BetreeMain.Clauses - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [betree_main::betree::load_internal_node] *) -let betree_load_internal_node_fwd - (id : u64) (st : state) : - result (state & (betree_list_t (u64 & betree_message_t))) - = - begin match betree_utils_load_internal_node_fwd id st with - | Fail -> Fail - | Return (st0, l) -> Return (st0, l) - end - -(** [betree_main::betree::store_internal_node] *) -let betree_store_internal_node_fwd - (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) : - result (state & unit) - = - begin match betree_utils_store_internal_node_fwd id content st with - | Fail -> Fail - | Return (st0, _) -> Return (st0, ()) - end - -(** [betree_main::betree::load_leaf_node] *) -let betree_load_leaf_node_fwd - (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) = - begin match betree_utils_load_leaf_node_fwd id st with - | Fail -> Fail - | Return (st0, l) -> Return (st0, l) - end - -(** [betree_main::betree::store_leaf_node] *) -let betree_store_leaf_node_fwd - (id : u64) (content : betree_list_t (u64 & u64)) (st : state) : - result (state & unit) - = - begin match betree_utils_store_leaf_node_fwd id content st with - | Fail -> Fail - | Return (st0, _) -> Return (st0, ()) - end - -(** [betree_main::betree::fresh_node_id] *) -let betree_fresh_node_id_fwd (counter : u64) : result u64 = - begin match u64_add counter 1 with - | Fail -> Fail - | Return _ -> Return counter - end - -(** [betree_main::betree::fresh_node_id] *) -let betree_fresh_node_id_back (counter : u64) : result u64 = - begin match u64_add counter 1 with - | Fail -> Fail - | Return counter0 -> Return counter0 - end - -(** [betree_main::betree::NodeIdCounter::{0}::new] *) -let betree_node_id_counter_new_fwd : result betree_node_id_counter_t = - Return (Mkbetree_node_id_counter_t 0) - -(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *) -let betree_node_id_counter_fresh_id_fwd - (self : betree_node_id_counter_t) : result u64 = - begin match u64_add self.betree_node_id_counter_next_node_id 1 with - | Fail -> Fail - | Return _ -> Return self.betree_node_id_counter_next_node_id - end - -(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *) -let betree_node_id_counter_fresh_id_back - (self : betree_node_id_counter_t) : result betree_node_id_counter_t = - begin match u64_add self.betree_node_id_counter_next_node_id 1 with - | Fail -> Fail - | Return i -> Return (Mkbetree_node_id_counter_t i) - end - -(** [core::num::u64::{10}::MAX] *) -let core_num_u64_max_body : result u64 = Return 18446744073709551615 -let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body - -(** [betree_main::betree::upsert_update] *) -let betree_upsert_update_fwd - (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 = - begin match prev with - | None -> - begin match st with - | BetreeUpsertFunStateAdd v -> Return v - | BetreeUpsertFunStateSub i -> Return 0 - end - | Some prev0 -> - begin match st with - | BetreeUpsertFunStateAdd v -> - begin match u64_sub core_num_u64_max_c prev0 with - | Fail -> Fail - | Return margin -> - if margin >= v - then - begin match u64_add prev0 v with - | Fail -> Fail - | Return i -> Return i - end - else Return core_num_u64_max_c - end - | BetreeUpsertFunStateSub v -> - if prev0 >= v - then - begin match u64_sub prev0 v with - | Fail -> Fail - | Return i -> Return i - end - else Return 0 - end - end - -(** [betree_main::betree::List::{1}::len] *) -let rec betree_list_len_fwd - (t : Type0) (self : betree_list_t t) : - Tot (result u64) (decreases (betree_list_len_decreases t self)) - = - begin match self with - | BetreeListCons x tl -> - begin match betree_list_len_fwd t tl with - | Fail -> Fail - | Return i -> - begin match u64_add 1 i with | Fail -> Fail | Return i0 -> Return i0 end - end - | BetreeListNil -> Return 0 - end - -(** [betree_main::betree::List::{1}::split_at] *) -let rec betree_list_split_at_fwd - (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 Return (BetreeListNil, self) - else - begin match self with - | BetreeListCons hd tl -> - begin match u64_sub n 1 with - | Fail -> Fail - | Return i -> - begin match betree_list_split_at_fwd t tl i with - | Fail -> Fail - | Return p -> - let (ls0, ls1) = p in - let l = ls0 in Return (BetreeListCons hd l, ls1) - end - end - | BetreeListNil -> Fail - end - -(** [betree_main::betree::List::{1}::push_front] *) -let betree_list_push_front_fwd_back - (t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) = - let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in - let l = tl in Return (BetreeListCons x l) - -(** [betree_main::betree::List::{1}::pop_front] *) -let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t = - let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in - begin match ls with - | BetreeListCons x tl -> Return x - | BetreeListNil -> Fail - end - -(** [betree_main::betree::List::{1}::pop_front] *) -let betree_list_pop_front_back - (t : Type0) (self : betree_list_t t) : result (betree_list_t t) = - let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in - begin match ls with - | BetreeListCons x tl -> Return tl - | BetreeListNil -> Fail - end - -(** [betree_main::betree::List::{1}::hd] *) -let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t = - begin match self with - | BetreeListCons hd l -> Return hd - | BetreeListNil -> Fail - end - -(** [betree_main::betree::List::{2}::head_has_key] *) -let betree_list_head_has_key_fwd - (t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool = - begin match self with - | BetreeListCons hd l -> let (i, _) = hd in Return (i = key) - | BetreeListNil -> Return false - end - -(** [betree_main::betree::List::{2}::partition_at_pivot] *) -let rec betree_list_partition_at_pivot_fwd - (t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) : - Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t)))) - (decreases (betree_list_partition_at_pivot_decreases t self pivot)) - = - begin match self with - | BetreeListCons hd tl -> - let (i, x) = hd in - if i >= pivot - then Return (BetreeListNil, BetreeListCons (i, x) tl) - else - begin match betree_list_partition_at_pivot_fwd t tl pivot with - | Fail -> Fail - | Return p -> - let (ls0, ls1) = p in - let l = ls0 in Return (BetreeListCons (i, x) l, ls1) - end - | BetreeListNil -> Return (BetreeListNil, BetreeListNil) - end - -(** [betree_main::betree::Leaf::{3}::split] *) -let betree_leaf_split_fwd - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : state) : - result (state & betree_internal_t) - = - begin match - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size with - | Fail -> Fail - | Return p -> - let (content0, content1) = p in - begin match betree_list_hd_fwd (u64 & u64) content1 with - | Fail -> Fail - | Return p0 -> - let (pivot, _) = p0 in - begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with - | Fail -> Fail - | Return id0 -> - begin match betree_node_id_counter_fresh_id_back node_id_cnt with - | Fail -> Fail - | Return node_id_cnt0 -> - begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with - | Fail -> Fail - | Return id1 -> - begin match betree_store_leaf_node_fwd id0 content0 st with - | Fail -> Fail - | Return (st0, _) -> - begin match betree_store_leaf_node_fwd id1 content1 st0 with - | Fail -> Fail - | Return (st1, _) -> - let n = BetreeNodeLeaf (Mkbetree_leaf_t id0 - params.betree_params_split_size) in - let n0 = BetreeNodeLeaf (Mkbetree_leaf_t id1 - params.betree_params_split_size) in - Return - (st1, - Mkbetree_internal_t - self.betree_leaf_id - pivot - n - n0) - end - end - end - end - end - end - end - -(** [betree_main::betree::Leaf::{3}::split] *) -let betree_leaf_split_back - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (st : state) : - result betree_node_id_counter_t - = - begin match - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size with - | Fail -> Fail - | Return p -> - let (content0, content1) = p in - begin match betree_list_hd_fwd (u64 & u64) content1 with - | Fail -> Fail - | Return _ -> - begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with - | Fail -> Fail - | Return id0 -> - begin match betree_node_id_counter_fresh_id_back node_id_cnt with - | Fail -> Fail - | Return node_id_cnt0 -> - begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with - | Fail -> Fail - | Return id1 -> - begin match betree_store_leaf_node_fwd id0 content0 st with - | Fail -> Fail - | Return (st0, _) -> - begin match betree_store_leaf_node_fwd id1 content1 st0 with - | Fail -> Fail - | Return (_, _) -> - begin match betree_node_id_counter_fresh_id_back node_id_cnt0 - with - | Fail -> Fail - | Return node_id_cnt1 -> Return node_id_cnt1 - end - end - end - end - end - end - end - end - -(** [betree_main::betree::Node::{5}::lookup_in_bindings] *) -let rec betree_node_lookup_in_bindings_fwd - (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 - | BetreeListCons hd tl -> - let (i, i0) = hd in - if i = key - then Return (Some i0) - else - if i > key - then Return None - else - begin match betree_node_lookup_in_bindings_fwd key tl with - | Fail -> Fail - | Return opt -> Return opt - end - | BetreeListNil -> Return None - end - -(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *) -let rec betree_node_lookup_first_message_for_key_fwd - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_for_key_decreases key msgs)) - = - begin match msgs with - | BetreeListCons x next_msgs -> - let (i, m) = x in - if i >= key - then Return (BetreeListCons (i, m) next_msgs) - else - begin match betree_node_lookup_first_message_for_key_fwd key next_msgs - with - | Fail -> Fail - | Return l -> Return l - end - | BetreeListNil -> Return BetreeListNil - end - -(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *) -let rec betree_node_lookup_first_message_for_key_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) - (ret : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_for_key_decreases key msgs)) - = - begin match msgs with - | BetreeListCons x next_msgs -> - let (i, m) = x in - if i >= key - then Return ret - else - begin match - betree_node_lookup_first_message_for_key_back key next_msgs ret with - | Fail -> Fail - | Return next_msgs0 -> Return (BetreeListCons (i, m) next_msgs0) - end - | BetreeListNil -> Return ret - end - -(** [betree_main::betree::Node::{5}::apply_upserts] *) -let rec betree_node_apply_upserts_fwd - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) - (key : u64) (st : state) : - Tot (result (state & u64)) - (decreases (betree_node_apply_upserts_decreases msgs prev key st)) - = - begin match betree_list_head_has_key_fwd betree_message_t msgs key with - | Fail -> Fail - | Return b -> - if b - then - begin match betree_list_pop_front_fwd (u64 & betree_message_t) msgs with - | Fail -> Fail - | Return msg -> - let (_, m) = msg in - begin match m with - | BetreeMessageInsert i -> Fail - | BetreeMessageDelete -> Fail - | BetreeMessageUpsert s -> - begin match betree_upsert_update_fwd prev s with - | Fail -> Fail - | Return v -> - begin match - betree_list_pop_front_back (u64 & betree_message_t) msgs with - | Fail -> Fail - | Return msgs0 -> - begin match betree_node_apply_upserts_fwd msgs0 (Some v) key st - with - | Fail -> Fail - | Return (st0, i) -> Return (st0, i) - end - end - end - end - end - else - begin match core_option_option_unwrap_fwd u64 prev st with - | Fail -> Fail - | Return (st0, v) -> - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key, - BetreeMessageInsert v) with - | Fail -> Fail - | Return _ -> Return (st0, v) - end - end - end - -(** [betree_main::betree::Node::{5}::apply_upserts] *) -let rec betree_node_apply_upserts_back - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) - (key : u64) (st : state) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_apply_upserts_decreases msgs prev key st)) - = - begin match betree_list_head_has_key_fwd betree_message_t msgs key with - | Fail -> Fail - | Return b -> - if b - then - begin match betree_list_pop_front_fwd (u64 & betree_message_t) msgs with - | Fail -> Fail - | Return msg -> - let (_, m) = msg in - begin match m with - | BetreeMessageInsert i -> Fail - | BetreeMessageDelete -> Fail - | BetreeMessageUpsert s -> - begin match betree_upsert_update_fwd prev s with - | Fail -> Fail - | Return v -> - begin match - betree_list_pop_front_back (u64 & betree_message_t) msgs with - | Fail -> Fail - | Return msgs0 -> - begin match betree_node_apply_upserts_back msgs0 (Some v) key st - with - | Fail -> Fail - | Return msgs1 -> Return msgs1 - end - end - end - end - end - else - begin match core_option_option_unwrap_fwd u64 prev st with - | Fail -> Fail - | Return (_, v) -> - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key, - BetreeMessageInsert v) with - | Fail -> Fail - | Return msgs0 -> Return msgs0 - end - end - end - -(** [betree_main::betree::Node::{5}::lookup] *) -let rec betree_node_lookup_fwd - (self : betree_node_t) (key : u64) (st : state) : - Tot (result (state & (option u64))) - (decreases (betree_node_lookup_decreases self key st)) - = - begin match self with - | BetreeNodeInternal node -> - begin match betree_load_internal_node_fwd node.betree_internal_id st with - | Fail -> Fail - | Return (st0, msgs) -> - begin match betree_node_lookup_first_message_for_key_fwd key msgs with - | Fail -> Fail - | Return pending -> - begin match pending with - | BetreeListCons p l -> - let (k, msg) = p in - if k <> key - then - begin match betree_internal_lookup_in_children_fwd node key st0 - with - | Fail -> Fail - | Return (st1, opt) -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l) with - | Fail -> Fail - | Return _ -> Return (st1, opt) - end - end - else - begin match msg with - | BetreeMessageInsert v -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l) with - | Fail -> Fail - | Return _ -> Return (st0, Some v) - end - | BetreeMessageDelete -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l) with - | Fail -> Fail - | Return _ -> Return (st0, None) - end - | BetreeMessageUpsert ufs -> - begin match betree_internal_lookup_in_children_fwd node key st0 - with - | Fail -> Fail - | Return (st1, v) -> - begin match - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 with - | Fail -> Fail - | Return (st2, v0) -> - begin match - betree_internal_lookup_in_children_back node key st0 with - | Fail -> Fail - | Return node0 -> - begin match - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 with - | Fail -> Fail - | Return pending0 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - pending0 with - | Fail -> Fail - | Return msgs0 -> - begin match - betree_store_internal_node_fwd - node0.betree_internal_id msgs0 st2 with - | Fail -> Fail - | Return (st3, _) -> Return (st3, Some v0) - end - end - end - end - end - end - end - | BetreeListNil -> - begin match betree_internal_lookup_in_children_fwd node key st0 with - | Fail -> Fail - | Return (st1, opt) -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - BetreeListNil with - | Fail -> Fail - | Return _ -> Return (st1, opt) - end - end - end - end - end - | BetreeNodeLeaf node -> - begin match betree_load_leaf_node_fwd node.betree_leaf_id st with - | Fail -> Fail - | Return (st0, bindings) -> - begin match betree_node_lookup_in_bindings_fwd key bindings with - | Fail -> Fail - | Return opt -> Return (st0, opt) - end - end - end - -(** [betree_main::betree::Node::{5}::lookup] *) -and betree_node_lookup_back - (self : betree_node_t) (key : u64) (st : state) : - Tot (result betree_node_t) - (decreases (betree_node_lookup_decreases self key st)) - = - begin match self with - | BetreeNodeInternal node -> - begin match betree_load_internal_node_fwd node.betree_internal_id st with - | Fail -> Fail - | Return (st0, msgs) -> - begin match betree_node_lookup_first_message_for_key_fwd key msgs with - | Fail -> Fail - | Return pending -> - begin match pending with - | BetreeListCons p l -> - let (k, msg) = p in - if k <> key - then - begin match - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l) with - | Fail -> Fail - | Return _ -> - begin match betree_internal_lookup_in_children_back node key st0 - with - | Fail -> Fail - | Return node0 -> Return (BetreeNodeInternal node0) - end - end - else - begin match msg with - | BetreeMessageInsert v -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l) with - | Fail -> Fail - | Return _ -> Return (BetreeNodeInternal node) - end - | BetreeMessageDelete -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l) with - | Fail -> Fail - | Return _ -> Return (BetreeNodeInternal node) - end - | BetreeMessageUpsert ufs -> - begin match betree_internal_lookup_in_children_fwd node key st0 - with - | Fail -> Fail - | Return (st1, v) -> - begin match - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 with - | Fail -> Fail - | Return (st2, _) -> - begin match - betree_internal_lookup_in_children_back node key st0 with - | Fail -> Fail - | Return node0 -> - begin match - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 with - | Fail -> Fail - | Return pending0 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - pending0 with - | Fail -> Fail - | Return msgs0 -> - begin match - betree_store_internal_node_fwd - node0.betree_internal_id msgs0 st2 with - | Fail -> Fail - | Return (_, _) -> Return (BetreeNodeInternal node0) - end - end - end - end - end - end - end - | BetreeListNil -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - BetreeListNil with - | Fail -> Fail - | Return _ -> - begin match betree_internal_lookup_in_children_back node key st0 - with - | Fail -> Fail - | Return node0 -> Return (BetreeNodeInternal node0) - end - end - end - end - end - | BetreeNodeLeaf node -> - begin match betree_load_leaf_node_fwd node.betree_leaf_id st with - | Fail -> Fail - | Return (_, bindings) -> - begin match betree_node_lookup_in_bindings_fwd key bindings with - | Fail -> Fail - | Return _ -> Return (BetreeNodeLeaf node) - end - end - end - -(** [betree_main::betree::Internal::{4}::lookup_in_children] *) -and betree_internal_lookup_in_children_fwd - (self : betree_internal_t) (key : u64) (st : state) : - Tot (result (state & (option u64))) - (decreases (betree_internal_lookup_in_children_decreases self key st)) - = - if key < self.betree_internal_pivot - then - begin match betree_node_lookup_fwd self.betree_internal_left key st with - | Fail -> Fail - | Return (st0, opt) -> Return (st0, opt) - end - else - begin match betree_node_lookup_fwd self.betree_internal_right key st with - | Fail -> Fail - | Return (st0, opt) -> Return (st0, opt) - end - -(** [betree_main::betree::Internal::{4}::lookup_in_children] *) -and betree_internal_lookup_in_children_back - (self : betree_internal_t) (key : u64) (st : state) : - Tot (result betree_internal_t) - (decreases (betree_internal_lookup_in_children_decreases self key st)) - = - if key < self.betree_internal_pivot - then - begin match betree_node_lookup_back self.betree_internal_left key st with - | Fail -> Fail - | Return n -> - Return (Mkbetree_internal_t self.betree_internal_id - self.betree_internal_pivot n self.betree_internal_right) - end - else - begin match betree_node_lookup_back self.betree_internal_right key st with - | Fail -> Fail - | Return n -> - Return (Mkbetree_internal_t self.betree_internal_id - self.betree_internal_pivot self.betree_internal_left n) - end - -(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *) -let rec betree_node_lookup_mut_in_bindings_fwd - (key : u64) (bindings : betree_list_t (u64 & u64)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings)) - = - begin match bindings with - | BetreeListCons hd tl -> - let (i, i0) = hd in - if i >= key - then Return (BetreeListCons (i, i0) tl) - else - begin match betree_node_lookup_mut_in_bindings_fwd key tl with - | Fail -> Fail - | Return l -> Return l - end - | BetreeListNil -> Return BetreeListNil - end - -(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *) -let rec betree_node_lookup_mut_in_bindings_back - (key : u64) (bindings : betree_list_t (u64 & u64)) - (ret : betree_list_t (u64 & u64)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings)) - = - begin match bindings with - | BetreeListCons hd tl -> - let (i, i0) = hd in - if i >= key - then Return ret - else - begin match betree_node_lookup_mut_in_bindings_back key tl ret with - | Fail -> Fail - | Return tl0 -> Return (BetreeListCons (i, i0) tl0) - end - | BetreeListNil -> Return ret - end - -(** [betree_main::betree::Node::{5}::apply_to_leaf] *) -let betree_node_apply_to_leaf_fwd_back - (bindings : betree_list_t (u64 & u64)) (key : u64) - (new_msg : betree_message_t) : - result (betree_list_t (u64 & u64)) - = - begin match betree_node_lookup_mut_in_bindings_fwd key bindings with - | Fail -> Fail - | Return bindings0 -> - begin match betree_list_head_has_key_fwd u64 bindings0 key with - | Fail -> Fail - | Return b -> - if b - then - begin match betree_list_pop_front_fwd (u64 & u64) bindings0 with - | Fail -> Fail - | Return hd -> - begin match new_msg with - | BetreeMessageInsert v -> - begin match betree_list_pop_front_back (u64 & u64) bindings0 with - | Fail -> Fail - | Return bindings1 -> - begin match - betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) - with - | Fail -> Fail - | Return bindings2 -> - begin match - betree_node_lookup_mut_in_bindings_back key bindings - bindings2 with - | Fail -> Fail - | Return bindings3 -> Return bindings3 - end - end - end - | BetreeMessageDelete -> - begin match betree_list_pop_front_back (u64 & u64) bindings0 with - | Fail -> Fail - | Return bindings1 -> - begin match - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - with - | Fail -> Fail - | Return bindings2 -> Return bindings2 - end - end - | BetreeMessageUpsert s -> - let (_, i) = hd in - begin match betree_upsert_update_fwd (Some i) s with - | Fail -> Fail - | Return v -> - begin match betree_list_pop_front_back (u64 & u64) bindings0 with - | Fail -> Fail - | Return bindings1 -> - begin match - betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, - v) with - | Fail -> Fail - | Return bindings2 -> - begin match - betree_node_lookup_mut_in_bindings_back key bindings - bindings2 with - | Fail -> Fail - | Return bindings3 -> Return bindings3 - end - end - end - end - end - end - else - begin match new_msg with - | BetreeMessageInsert v -> - begin match - betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) with - | Fail -> Fail - | Return bindings1 -> - begin match - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - with - | Fail -> Fail - | Return bindings2 -> Return bindings2 - end - end - | BetreeMessageDelete -> - begin match - betree_node_lookup_mut_in_bindings_back key bindings bindings0 with - | Fail -> Fail - | Return bindings1 -> Return bindings1 - end - | BetreeMessageUpsert s -> - begin match betree_upsert_update_fwd None s with - | Fail -> Fail - | Return v -> - begin match - betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) - with - | Fail -> Fail - | Return bindings1 -> - begin match - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - with - | Fail -> Fail - | Return bindings2 -> Return bindings2 - end - end - end - end - end - end - -(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *) -let rec betree_node_apply_messages_to_leaf_fwd_back - (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 - | BetreeListCons new_msg new_msgs_tl -> - let (i, m) = new_msg in - begin match betree_node_apply_to_leaf_fwd_back bindings i m with - | Fail -> Fail - | Return bindings0 -> - begin match - betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl with - | Fail -> Fail - | Return bindings1 -> Return bindings1 - end - end - | BetreeListNil -> Return bindings - end - -(** [betree_main::betree::Node::{5}::filter_messages_for_key] *) -let rec betree_node_filter_messages_for_key_fwd_back - (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 - | BetreeListCons p l -> - let (k, m) = p in - if k = key - then - begin match - betree_list_pop_front_back (u64 & betree_message_t) (BetreeListCons (k, - m) l) with - | Fail -> Fail - | Return msgs0 -> - begin match betree_node_filter_messages_for_key_fwd_back key msgs0 with - | Fail -> Fail - | Return msgs1 -> Return msgs1 - end - end - else Return (BetreeListCons (k, m) l) - | BetreeListNil -> Return BetreeListNil - end - -(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *) -let rec betree_node_lookup_first_message_after_key_fwd - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_after_key_decreases key msgs)) - = - begin match msgs with - | BetreeListCons p next_msgs -> - let (k, m) = p in - if k = key - then - begin match betree_node_lookup_first_message_after_key_fwd key next_msgs - with - | Fail -> Fail - | Return l -> Return l - end - else Return (BetreeListCons (k, m) next_msgs) - | BetreeListNil -> Return BetreeListNil - end - -(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *) -let rec betree_node_lookup_first_message_after_key_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) - (ret : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_after_key_decreases key msgs)) - = - begin match msgs with - | BetreeListCons p next_msgs -> - let (k, m) = p in - if k = key - then - begin match - betree_node_lookup_first_message_after_key_back key next_msgs ret with - | Fail -> Fail - | Return next_msgs0 -> Return (BetreeListCons (k, m) next_msgs0) - end - else Return ret - | BetreeListNil -> Return ret - end - -(** [betree_main::betree::Node::{5}::apply_to_internal] *) -let betree_node_apply_to_internal_fwd_back - (msgs : betree_list_t (u64 & betree_message_t)) (key : u64) - (new_msg : betree_message_t) : - result (betree_list_t (u64 & betree_message_t)) - = - begin match betree_node_lookup_first_message_for_key_fwd key msgs with - | Fail -> Fail - | Return msgs0 -> - begin match betree_list_head_has_key_fwd betree_message_t msgs0 key with - | Fail -> Fail - | Return b -> - if b - then - begin match new_msg with - | BetreeMessageInsert i -> - begin match betree_node_filter_messages_for_key_fwd_back key msgs0 - with - | Fail -> Fail - | Return msgs1 -> - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 - (key, BetreeMessageInsert i) with - | Fail -> Fail - | Return msgs2 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs msgs2 - with - | Fail -> Fail - | Return msgs3 -> Return msgs3 - end - end - end - | BetreeMessageDelete -> - begin match betree_node_filter_messages_for_key_fwd_back key msgs0 - with - | Fail -> Fail - | Return msgs1 -> - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 - (key, BetreeMessageDelete) with - | Fail -> Fail - | Return msgs2 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs msgs2 - with - | Fail -> Fail - | Return msgs3 -> Return msgs3 - end - end - end - | BetreeMessageUpsert s -> - begin match betree_list_hd_fwd (u64 & betree_message_t) msgs0 with - | Fail -> Fail - | Return p -> - let (_, m) = p in - begin match m with - | BetreeMessageInsert prev -> - begin match betree_upsert_update_fwd (Some prev) s with - | Fail -> Fail - | Return v -> - begin match - betree_list_pop_front_back (u64 & betree_message_t) msgs0 - with - | Fail -> Fail - | Return msgs1 -> - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) - msgs1 (key, BetreeMessageInsert v) with - | Fail -> Fail - | Return msgs2 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - msgs2 with - | Fail -> Fail - | Return msgs3 -> Return msgs3 - end - end - end - end - | BetreeMessageDelete -> - begin match betree_upsert_update_fwd None s with - | Fail -> Fail - | Return v -> - begin match - betree_list_pop_front_back (u64 & betree_message_t) msgs0 - with - | Fail -> Fail - | Return msgs1 -> - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) - msgs1 (key, BetreeMessageInsert v) with - | Fail -> Fail - | Return msgs2 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - msgs2 with - | Fail -> Fail - | Return msgs3 -> Return msgs3 - end - end - end - end - | BetreeMessageUpsert ufs -> - begin match - betree_node_lookup_first_message_after_key_fwd key msgs0 with - | Fail -> Fail - | Return msgs1 -> - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) - msgs1 (key, BetreeMessageUpsert s) with - | Fail -> Fail - | Return msgs2 -> - begin match - betree_node_lookup_first_message_after_key_back key msgs0 - msgs2 with - | Fail -> Fail - | Return msgs3 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs - msgs3 with - | Fail -> Fail - | Return msgs4 -> Return msgs4 - end - end - end - end - end - end - end - else - begin match - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs0 (key, - new_msg) with - | Fail -> Fail - | Return msgs1 -> - begin match - betree_node_lookup_first_message_for_key_back key msgs msgs1 with - | Fail -> Fail - | Return msgs2 -> Return msgs2 - end - end - end - end - -(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *) -let rec betree_node_apply_messages_to_internal_fwd_back - (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 - | BetreeListCons new_msg new_msgs_tl -> - let (i, m) = new_msg in - begin match betree_node_apply_to_internal_fwd_back msgs i m with - | Fail -> Fail - | Return msgs0 -> - begin match - betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl with - | Fail -> Fail - | Return msgs1 -> Return msgs1 - end - end - | BetreeListNil -> Return msgs - end - -(** [betree_main::betree::Node::{5}::apply_messages] *) -let rec betree_node_apply_messages_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (state & unit)) - (decreases (betree_node_apply_messages_decreases self params node_id_cnt msgs - st)) - = - begin match self with - | BetreeNodeInternal node -> - begin match betree_load_internal_node_fwd node.betree_internal_id st with - | Fail -> Fail - | Return (st0, content) -> - begin match betree_node_apply_messages_to_internal_fwd_back content msgs - with - | Fail -> Fail - | Return content0 -> - begin match betree_list_len_fwd (u64 & betree_message_t) content0 with - | Fail -> Fail - | Return num_msgs -> - if num_msgs >= params.betree_params_min_flush_size - then - begin match - betree_internal_flush_fwd node params node_id_cnt content0 st0 - with - | Fail -> Fail - | Return (st1, content1) -> - begin match - betree_internal_flush_back node params node_id_cnt content0 st0 - with - | Fail -> Fail - | Return (node0, _) -> - begin match - betree_store_internal_node_fwd node0.betree_internal_id - content1 st1 with - | Fail -> Fail - | Return (st2, _) -> Return (st2, ()) - end - end - end - else - begin match - betree_store_internal_node_fwd node.betree_internal_id content0 - st0 with - | Fail -> Fail - | Return (st1, _) -> Return (st1, ()) - end - end - end - end - | BetreeNodeLeaf node -> - begin match betree_load_leaf_node_fwd node.betree_leaf_id st with - | Fail -> Fail - | Return (st0, content) -> - begin match betree_node_apply_messages_to_leaf_fwd_back content msgs with - | Fail -> Fail - | Return content0 -> - begin match betree_list_len_fwd (u64 & u64) content0 with - | Fail -> Fail - | Return len -> - begin match u64_mul 2 params.betree_params_split_size with - | Fail -> Fail - | Return i -> - if len >= i - then - begin match - betree_leaf_split_fwd node content0 params node_id_cnt st0 with - | Fail -> Fail - | Return (st1, _) -> - begin match - betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil - st1 with - | Fail -> Fail - | Return (st2, _) -> Return (st2, ()) - end - end - else - begin match - betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 - with - | Fail -> Fail - | Return (st1, _) -> Return (st1, ()) - end - end - end - end - end - end - -(** [betree_main::betree::Node::{5}::apply_messages] *) -and betree_node_apply_messages_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (betree_node_t & betree_node_id_counter_t)) - (decreases (betree_node_apply_messages_decreases self params node_id_cnt msgs - st)) - = - begin match self with - | BetreeNodeInternal node -> - begin match betree_load_internal_node_fwd node.betree_internal_id st with - | Fail -> Fail - | Return (st0, content) -> - begin match betree_node_apply_messages_to_internal_fwd_back content msgs - with - | Fail -> Fail - | Return content0 -> - begin match betree_list_len_fwd (u64 & betree_message_t) content0 with - | Fail -> Fail - | Return num_msgs -> - if num_msgs >= params.betree_params_min_flush_size - then - begin match - betree_internal_flush_fwd node params node_id_cnt content0 st0 - with - | Fail -> Fail - | Return (st1, content1) -> - begin match - betree_internal_flush_back node params node_id_cnt content0 st0 - with - | Fail -> Fail - | Return (node0, node_id_cnt0) -> - begin match - betree_store_internal_node_fwd node0.betree_internal_id - content1 st1 with - | Fail -> Fail - | Return (_, _) -> - Return (BetreeNodeInternal node0, node_id_cnt0) - end - end - end - else - begin match - betree_store_internal_node_fwd node.betree_internal_id content0 - st0 with - | Fail -> Fail - | Return (_, _) -> Return (BetreeNodeInternal node, node_id_cnt) - end - end - end - end - | BetreeNodeLeaf node -> - begin match betree_load_leaf_node_fwd node.betree_leaf_id st with - | Fail -> Fail - | Return (st0, content) -> - begin match betree_node_apply_messages_to_leaf_fwd_back content msgs with - | Fail -> Fail - | Return content0 -> - begin match betree_list_len_fwd (u64 & u64) content0 with - | Fail -> Fail - | Return len -> - begin match u64_mul 2 params.betree_params_split_size with - | Fail -> Fail - | Return i -> - if len >= i - then - begin match - betree_leaf_split_fwd node content0 params node_id_cnt st0 with - | Fail -> Fail - | Return (st1, new_node) -> - begin match - betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil - st1 with - | Fail -> Fail - | Return (_, _) -> - begin match - betree_leaf_split_back node content0 params node_id_cnt st0 - with - | Fail -> Fail - | Return node_id_cnt0 -> - Return (BetreeNodeInternal new_node, node_id_cnt0) - end - end - end - else - begin match - betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 - with - | Fail -> Fail - | Return (_, _) -> - Return (BetreeNodeLeaf (Mkbetree_leaf_t node.betree_leaf_id - len), node_id_cnt) - end - end - end - end - end - end - -(** [betree_main::betree::Internal::{4}::flush] *) -and betree_internal_flush_fwd - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (state & (betree_list_t (u64 & betree_message_t)))) - (decreases (betree_internal_flush_decreases self params node_id_cnt content - st)) - = - begin match - betree_list_partition_at_pivot_fwd betree_message_t content - self.betree_internal_pivot with - | Fail -> Fail - | Return p -> - let (msgs_left, msgs_right) = p in - begin match betree_list_len_fwd (u64 & betree_message_t) msgs_left with - | Fail -> Fail - | Return len_left -> - if len_left >= params.betree_params_min_flush_size - then - begin match - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st with - | Fail -> Fail - | Return (st0, _) -> - begin match - betree_node_apply_messages_back self.betree_internal_left params - node_id_cnt msgs_left st with - | Fail -> Fail - | Return (_, node_id_cnt0) -> - begin match betree_list_len_fwd (u64 & betree_message_t) msgs_right - with - | Fail -> Fail - | Return len_right -> - if len_right >= params.betree_params_min_flush_size - then - begin match - betree_node_apply_messages_fwd self.betree_internal_right - params node_id_cnt0 msgs_right st0 with - | Fail -> Fail - | Return (st1, _) -> - begin match - betree_node_apply_messages_back self.betree_internal_right - params node_id_cnt0 msgs_right st0 with - | Fail -> Fail - | Return (_, _) -> Return (st1, BetreeListNil) - end - end - else Return (st0, msgs_right) - end - end - end - else - begin match - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt msgs_right st with - | Fail -> Fail - | Return (st0, _) -> - begin match - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt msgs_right st with - | Fail -> Fail - | Return (_, _) -> Return (st0, msgs_left) - end - end - end - end - -(** [betree_main::betree::Internal::{4}::flush] *) -and betree_internal_flush_back - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (betree_internal_t & betree_node_id_counter_t)) - (decreases (betree_internal_flush_decreases self params node_id_cnt content - st)) - = - begin match - betree_list_partition_at_pivot_fwd betree_message_t content - self.betree_internal_pivot with - | Fail -> Fail - | Return p -> - let (msgs_left, msgs_right) = p in - begin match betree_list_len_fwd (u64 & betree_message_t) msgs_left with - | Fail -> Fail - | Return len_left -> - if len_left >= params.betree_params_min_flush_size - then - begin match - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st with - | Fail -> Fail - | Return (st0, _) -> - begin match - betree_node_apply_messages_back self.betree_internal_left params - node_id_cnt msgs_left st with - | Fail -> Fail - | Return (n, node_id_cnt0) -> - begin match betree_list_len_fwd (u64 & betree_message_t) msgs_right - with - | Fail -> Fail - | Return len_right -> - if len_right >= params.betree_params_min_flush_size - then - begin match - betree_node_apply_messages_back self.betree_internal_right - params node_id_cnt0 msgs_right st0 with - | Fail -> Fail - | Return (n0, node_id_cnt1) -> - Return (Mkbetree_internal_t self.betree_internal_id - self.betree_internal_pivot n n0, node_id_cnt1) - end - else - Return (Mkbetree_internal_t self.betree_internal_id - self.betree_internal_pivot n self.betree_internal_right, - node_id_cnt0) - end - end - end - else - begin match - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt msgs_right st with - | Fail -> Fail - | Return (n, node_id_cnt0) -> - Return (Mkbetree_internal_t self.betree_internal_id - self.betree_internal_pivot self.betree_internal_left n, - node_id_cnt0) - end - end - end - -(** [betree_main::betree::Node::{5}::apply] *) -let 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) : - result (state & unit) - = - let l = BetreeListNil in - begin match - betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons - (key, new_msg) l) st with - | Fail -> Fail - | Return (st0, _) -> - begin match - betree_node_apply_messages_back self params node_id_cnt (BetreeListCons - (key, new_msg) l) st with - | Fail -> Fail - | Return (_, _) -> Return (st0, ()) - end - end - -(** [betree_main::betree::Node::{5}::apply] *) -let 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) : - result (betree_node_t & betree_node_id_counter_t) - = - let l = BetreeListNil in - begin match - betree_node_apply_messages_back self params node_id_cnt (BetreeListCons - (key, new_msg) l) st with - | Fail -> Fail - | Return (self0, node_id_cnt0) -> Return (self0, node_id_cnt0) - end - -(** [betree_main::betree::BeTree::{6}::new] *) -let betree_be_tree_new_fwd - (min_flush_size : u64) (split_size : u64) (st : state) : - result (state & betree_be_tree_t) - = - begin match betree_node_id_counter_new_fwd with - | Fail -> Fail - | Return node_id_cnt -> - begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with - | Fail -> Fail - | Return id -> - begin match betree_store_leaf_node_fwd id BetreeListNil st with - | Fail -> Fail - | Return (st0, _) -> - begin match betree_node_id_counter_fresh_id_back node_id_cnt with - | Fail -> Fail - | Return node_id_cnt0 -> - Return (st0, Mkbetree_be_tree_t (Mkbetree_params_t min_flush_size - split_size) node_id_cnt0 (BetreeNodeLeaf (Mkbetree_leaf_t id 0))) - end - end - end - end - -(** [betree_main::betree::BeTree::{6}::apply] *) -let betree_be_tree_apply_fwd - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) : - result (state & unit) - = - begin match - betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st with - | Fail -> Fail - | Return (st0, _) -> - begin match - betree_node_apply_back self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st - with - | Fail -> Fail - | Return (_, _) -> Return (st0, ()) - end - end - -(** [betree_main::betree::BeTree::{6}::apply] *) -let betree_be_tree_apply_back - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) : - result betree_be_tree_t - = - begin match - betree_node_apply_back self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st with - | Fail -> Fail - | Return (n, nic) -> - Return (Mkbetree_be_tree_t self.betree_be_tree_params nic n) - end - -(** [betree_main::betree::BeTree::{6}::insert] *) -let betree_be_tree_insert_fwd - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : - result (state & unit) - = - begin match betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st - with - | Fail -> Fail - | Return (st0, _) -> - begin match - betree_be_tree_apply_back self key (BetreeMessageInsert value) st with - | Fail -> Fail - | Return _ -> Return (st0, ()) - end - end - -(** [betree_main::betree::BeTree::{6}::insert] *) -let betree_be_tree_insert_back - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : - result betree_be_tree_t - = - begin match betree_be_tree_apply_back self key (BetreeMessageInsert value) st - with - | Fail -> Fail - | Return self0 -> Return self0 - end - -(** [betree_main::betree::BeTree::{6}::delete] *) -let betree_be_tree_delete_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) = - begin match betree_be_tree_apply_fwd self key BetreeMessageDelete st with - | Fail -> Fail - | Return (st0, _) -> - begin match betree_be_tree_apply_back self key BetreeMessageDelete st with - | Fail -> Fail - | Return _ -> Return (st0, ()) - end - end - -(** [betree_main::betree::BeTree::{6}::delete] *) -let betree_be_tree_delete_back - (self : betree_be_tree_t) (key : u64) (st : state) : - result betree_be_tree_t - = - begin match betree_be_tree_apply_back self key BetreeMessageDelete st with - | Fail -> Fail - | Return self0 -> Return self0 - end - -(** [betree_main::betree::BeTree::{6}::upsert] *) -let betree_be_tree_upsert_fwd - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) - (st : state) : - result (state & unit) - = - begin match betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st - with - | Fail -> Fail - | Return (st0, _) -> - begin match betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st - with - | Fail -> Fail - | Return _ -> Return (st0, ()) - end - end - -(** [betree_main::betree::BeTree::{6}::upsert] *) -let betree_be_tree_upsert_back - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) - (st : state) : - result betree_be_tree_t - = - begin match betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st - with - | Fail -> Fail - | Return self0 -> Return self0 - end - -(** [betree_main::betree::BeTree::{6}::lookup] *) -let betree_be_tree_lookup_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : - result (state & (option u64)) - = - begin match betree_node_lookup_fwd self.betree_be_tree_root key st with - | Fail -> Fail - | Return (st0, opt) -> Return (st0, opt) - end - -(** [betree_main::betree::BeTree::{6}::lookup] *) -let betree_be_tree_lookup_back - (self : betree_be_tree_t) (key : u64) (st : state) : - result betree_be_tree_t - = - begin match betree_node_lookup_back self.betree_be_tree_root key st with - | Fail -> Fail - | Return n -> - Return (Mkbetree_be_tree_t self.betree_be_tree_params - self.betree_be_tree_node_id_cnt n) - end - -(** [betree_main::main] *) -let main_fwd : result unit = Return () - -(** Unit test for [betree_main::main] *) -let _ = assert_norm (main_fwd = Return ()) - diff --git a/tests/betree/BetreeMain.Opaque.fsti b/tests/betree/BetreeMain.Opaque.fsti deleted file mode 100644 index dc49601a..00000000 --- a/tests/betree/BetreeMain.Opaque.fsti +++ /dev/null @@ -1,30 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: opaque function definitions *) -module BetreeMain.Opaque -open Primitives -include BetreeMain.Types - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [betree_main::betree_utils::load_internal_node] *) -val betree_utils_load_internal_node_fwd - : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t))) - -(** [betree_main::betree_utils::store_internal_node] *) -val betree_utils_store_internal_node_fwd - : - u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state & - unit) - -(** [betree_main::betree_utils::load_leaf_node] *) -val betree_utils_load_leaf_node_fwd - : u64 -> state -> result (state & (betree_list_t (u64 & u64))) - -(** [betree_main::betree_utils::store_leaf_node] *) -val betree_utils_store_leaf_node_fwd - : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit) - -(** [core::option::Option::{0}::unwrap] *) -val core_option_option_unwrap_fwd - (t : Type0) : option t -> state -> result (state & t) - diff --git a/tests/betree/BetreeMain.Types.fsti b/tests/betree/BetreeMain.Types.fsti deleted file mode 100644 index c81e3302..00000000 --- a/tests/betree/BetreeMain.Types.fsti +++ /dev/null @@ -1,64 +0,0 @@ -(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) -(** [betree_main]: type definitions *) -module BetreeMain.Types -open Primitives - -#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" - -(** [betree_main::betree::List] *) -type betree_list_t (t : Type0) = -| BetreeListCons : t -> betree_list_t t -> betree_list_t t -| BetreeListNil : betree_list_t t - -(** [betree_main::betree::UpsertFunState] *) -type betree_upsert_fun_state_t = -| BetreeUpsertFunStateAdd : u64 -> betree_upsert_fun_state_t -| BetreeUpsertFunStateSub : u64 -> betree_upsert_fun_state_t - -(** [betree_main::betree::Message] *) -type betree_message_t = -| BetreeMessageInsert : u64 -> betree_message_t -| BetreeMessageDelete : betree_message_t -| BetreeMessageUpsert : betree_upsert_fun_state_t -> betree_message_t - -(** [betree_main::betree::Leaf] *) -type betree_leaf_t = { betree_leaf_id : u64; betree_leaf_size : u64; } - -(** [betree_main::betree::Node] *) -type betree_node_t = -| BetreeNodeInternal : betree_internal_t -> betree_node_t -| BetreeNodeLeaf : betree_leaf_t -> betree_node_t - -(** [betree_main::betree::Internal] *) -and 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::Params] *) -type betree_params_t = -{ - betree_params_min_flush_size : u64; betree_params_split_size : u64; -} - -(** [betree_main::betree::NodeIdCounter] *) -type betree_node_id_counter_t = { betree_node_id_counter_next_node_id : u64; } - -(** [betree_main::betree::BeTree] *) -type 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; -} - -(** [core::num::u64::{10}::MAX] *) -let core_num_u64_max_body : result u64 = Return 18446744073709551615 -let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body - -(** The state type used in the state-error monad *) -val state : Type0 - diff --git a/tests/betree/Makefile b/tests/betree/Makefile deleted file mode 100644 index a16b0edb..00000000 --- a/tests/betree/Makefile +++ /dev/null @@ -1,47 +0,0 @@ -INCLUDE_DIRS = . - -FSTAR_INCLUDES = $(addprefix --include ,$(INCLUDE_DIRS)) - -FSTAR_HINTS ?= --use_hints --use_hint_hashes --record_hints - -FSTAR_OPTIONS = $(FSTAR_HINTS) \ - --cache_checked_modules $(FSTAR_INCLUDES) --cmi \ - --warn_error '+241@247+285-274' \ - -FSTAR_NO_FLAGS = fstar.exe --already_cached 'Prims FStar LowStar Steel' --odir obj --cache_dir obj - -FSTAR = $(FSTAR_NO_FLAGS) $(FSTAR_OPTIONS) - -# The F* roots are used to compute the dependency graph, and generate the .depend file -FSTAR_ROOTS ?= $(wildcard *.fst *.fsti) - -# Build all the files -all: $(addprefix obj/,$(addsuffix .checked,$(FSTAR_ROOTS))) - -# This is the right way to ensure the .depend file always gets re-built. -ifeq (,$(filter %-in,$(MAKECMDGOALS))) -ifndef NODEPEND -ifndef MAKE_RESTARTS -.depend: .FORCE - $(FSTAR_NO_FLAGS) --dep full $(notdir $(FSTAR_ROOTS)) > $@ - -.PHONY: .FORCE -.FORCE: -endif -endif - -include .depend -endif - -# For the interactive mode -%.fst-in %.fsti-in: - @echo $(FSTAR_OPTIONS) - -# Generete the .checked files in batch mode -%.checked: - $(FSTAR) $(FSTAR_OPTIONS) $< && \ - touch -c $@ - -.PHONY: clean -clean: - rm -f obj/* diff --git a/tests/betree/Primitives.fst b/tests/betree/Primitives.fst deleted file mode 100644 index 96138e46..00000000 --- a/tests/betree/Primitives.fst +++ /dev/null @@ -1,287 +0,0 @@ -/// This file lists primitive and assumed functions and types -module Primitives -open FStar.Mul -open FStar.List.Tot - -#set-options "--z3rlimit 15 --fuel 0 --ifuel 1" - -(*** Utilities *) -val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) : - ls':list a{ - length ls' = length ls /\ - index ls' i == x - } -#push-options "--fuel 1" -let rec list_update #a ls i x = - match ls with - | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x -#pop-options - -(*** Result *) -type result (a : Type0) : Type0 = -| Return : v:a -> result a -| Fail : result a - -// Monadic bind and return. -// Re-definining those allows us to customize the result of the monadic notations -// like: `y <-- f x;` -let return (#a : Type0) (x:a) : result a = Return x -let bind (#a #b : Type0) (m : result a) (f : a -> result b) : result b = - match m with - | Return x -> f x - | Fail -> Fail - -// Monadic assert(...) -let massert (b:bool) : result unit = if b then Return () else Fail - -// Normalize and unwrap a successful result (used for globals). -let eval_global (#a : Type0) (x : result a{Return? (normalize_term x)}) : a = Return?.v x - -(*** Misc *) -type char = FStar.Char.char -type string = string - -let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x -let mem_replace_back (a : Type0) (x : a) (y : a) : a = y - -(*** Scalars *) -/// Rk.: most of the following code was at least partially generated - -let isize_min : int = -9223372036854775808 // TODO: should be opaque -let isize_max : int = 9223372036854775807 // TODO: should be opaque -let i8_min : int = -128 -let i8_max : int = 127 -let i16_min : int = -32768 -let i16_max : int = 32767 -let i32_min : int = -2147483648 -let i32_max : int = 2147483647 -let i64_min : int = -9223372036854775808 -let i64_max : int = 9223372036854775807 -let i128_min : int = -170141183460469231731687303715884105728 -let i128_max : int = 170141183460469231731687303715884105727 -let usize_min : int = 0 -let usize_max : int = 4294967295 // TODO: should be opaque -let u8_min : int = 0 -let u8_max : int = 255 -let u16_min : int = 0 -let u16_max : int = 65535 -let u32_min : int = 0 -let u32_max : int = 4294967295 -let u64_min : int = 0 -let u64_max : int = 18446744073709551615 -let u128_min : int = 0 -let u128_max : int = 340282366920938463463374607431768211455 - -type scalar_ty = -| Isize -| I8 -| I16 -| I32 -| I64 -| I128 -| Usize -| U8 -| U16 -| U32 -| U64 -| U128 - -let scalar_min (ty : scalar_ty) : int = - match ty with - | Isize -> isize_min - | I8 -> i8_min - | I16 -> i16_min - | I32 -> i32_min - | I64 -> i64_min - | I128 -> i128_min - | Usize -> usize_min - | U8 -> u8_min - | U16 -> u16_min - | U32 -> u32_min - | U64 -> u64_min - | U128 -> u128_min - -let scalar_max (ty : scalar_ty) : int = - match ty with - | Isize -> isize_max - | I8 -> i8_max - | I16 -> i16_max - | I32 -> i32_max - | I64 -> i64_max - | I128 -> i128_max - | Usize -> usize_max - | U8 -> u8_max - | U16 -> u16_max - | U32 -> u32_max - | U64 -> u64_max - | U128 -> u128_max - -type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty} - -let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) = - if scalar_min ty <= x && scalar_max ty >= x then Return x else Fail - -let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x) - -let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - if y <> 0 then mk_scalar ty (x / y) else Fail - -/// The remainder operation -let int_rem (x : int) (y : int{y <> 0}) : int = - if x >= 0 then (x % y) else -(x % y) - -(* Checking consistency with Rust *) -let _ = assert_norm(int_rem 1 2 = 1) -let _ = assert_norm(int_rem (-1) 2 = -1) -let _ = assert_norm(int_rem 1 (-2) = 1) -let _ = assert_norm(int_rem (-1) (-2) = -1) - -let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - if y <> 0 then mk_scalar ty (int_rem x y) else Fail - -let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - mk_scalar ty (x + y) - -let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - mk_scalar ty (x - y) - -let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = - mk_scalar ty (x * y) - -(** Cast an integer from a [src_ty] to a [tgt_ty] *) -// TODO: check the semantics of casts in Rust -let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) = - mk_scalar tgt_ty x - -/// The scalar types -type isize : eqtype = scalar Isize -type i8 : eqtype = scalar I8 -type i16 : eqtype = scalar I16 -type i32 : eqtype = scalar I32 -type i64 : eqtype = scalar I64 -type i128 : eqtype = scalar I128 -type usize : eqtype = scalar Usize -type u8 : eqtype = scalar U8 -type u16 : eqtype = scalar U16 -type u32 : eqtype = scalar U32 -type u64 : eqtype = scalar U64 -type u128 : eqtype = scalar U128 - -/// Negation -let isize_neg = scalar_neg #Isize -let i8_neg = scalar_neg #I8 -let i16_neg = scalar_neg #I16 -let i32_neg = scalar_neg #I32 -let i64_neg = scalar_neg #I64 -let i128_neg = scalar_neg #I128 - -/// Division -let isize_div = scalar_div #Isize -let i8_div = scalar_div #I8 -let i16_div = scalar_div #I16 -let i32_div = scalar_div #I32 -let i64_div = scalar_div #I64 -let i128_div = scalar_div #I128 -let usize_div = scalar_div #Usize -let u8_div = scalar_div #U8 -let u16_div = scalar_div #U16 -let u32_div = scalar_div #U32 -let u64_div = scalar_div #U64 -let u128_div = scalar_div #U128 - -/// Remainder -let isize_rem = scalar_rem #Isize -let i8_rem = scalar_rem #I8 -let i16_rem = scalar_rem #I16 -let i32_rem = scalar_rem #I32 -let i64_rem = scalar_rem #I64 -let i128_rem = scalar_rem #I128 -let usize_rem = scalar_rem #Usize -let u8_rem = scalar_rem #U8 -let u16_rem = scalar_rem #U16 -let u32_rem = scalar_rem #U32 -let u64_rem = scalar_rem #U64 -let u128_rem = scalar_rem #U128 - -/// Addition -let isize_add = scalar_add #Isize -let i8_add = scalar_add #I8 -let i16_add = scalar_add #I16 -let i32_add = scalar_add #I32 -let i64_add = scalar_add #I64 -let i128_add = scalar_add #I128 -let usize_add = scalar_add #Usize -let u8_add = scalar_add #U8 -let u16_add = scalar_add #U16 -let u32_add = scalar_add #U32 -let u64_add = scalar_add #U64 -let u128_add = scalar_add #U128 - -/// Substraction -let isize_sub = scalar_sub #Isize -let i8_sub = scalar_sub #I8 -let i16_sub = scalar_sub #I16 -let i32_sub = scalar_sub #I32 -let i64_sub = scalar_sub #I64 -let i128_sub = scalar_sub #I128 -let usize_sub = scalar_sub #Usize -let u8_sub = scalar_sub #U8 -let u16_sub = scalar_sub #U16 -let u32_sub = scalar_sub #U32 -let u64_sub = scalar_sub #U64 -let u128_sub = scalar_sub #U128 - -/// Multiplication -let isize_mul = scalar_mul #Isize -let i8_mul = scalar_mul #I8 -let i16_mul = scalar_mul #I16 -let i32_mul = scalar_mul #I32 -let i64_mul = scalar_mul #I64 -let i128_mul = scalar_mul #I128 -let usize_mul = scalar_mul #Usize -let u8_mul = scalar_mul #U8 -let u16_mul = scalar_mul #U16 -let u32_mul = scalar_mul #U32 -let u64_mul = scalar_mul #U64 -let u128_mul = scalar_mul #U128 - -(*** Vector *) -type vec (a : Type0) = v:list a{length v <= usize_max} - -let vec_new (a : Type0) : vec a = assert_norm(length #a [] == 0); [] -let vec_len (a : Type0) (v : vec a) : usize = length v - -// The **forward** function shouldn't be used -let vec_push_fwd (a : Type0) (v : vec a) (x : a) : unit = () -let vec_push_back (a : Type0) (v : vec a) (x : a) : - Pure (result (vec a)) - (requires True) - (ensures (fun res -> - match res with - | Fail -> True - | Return v' -> length v' = length v + 1)) = - if length v < usize_max then begin - (**) assert_norm(length [x] == 1); - (**) append_length v [x]; - (**) assert(length (append v [x]) = length v + 1); - Return (append v [x]) - end - else Fail - -// The **forward** function shouldn't be used -let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit = - if i < length v then Return () else Fail -let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) = - if i < length v then Return (list_update v i x) else Fail - -// The **backward** function shouldn't be used -let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a = - if i < length v then Return (index v i) else Fail -let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit = - if i < length v then Return () else Fail - -let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a = - if i < length v then Return (index v i) else Fail -let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) = - if i < length v then Return (list_update v i nx) else Fail - -- cgit v1.2.3