diff options
Diffstat (limited to 'tests/hol4')
43 files changed, 13198 insertions, 0 deletions
diff --git a/tests/hol4/betree/Holmakefile b/tests/hol4/betree/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/betree/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/betree/betreeMain_FunsScript.sml b/tests/hol4/betree/betreeMain_FunsScript.sml new file mode 100644 index 00000000..df0c6a24 --- /dev/null +++ b/tests/hol4/betree/betreeMain_FunsScript.sml @@ -0,0 +1,1214 @@ +(** 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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 +’ + +(** [core::num::u64::{10}::MAX] *) +Definition core_num_u64_max_body_def: + core_num_u64_max_body : u64 result = Return (int_to_u64 18446744073709551615) +End +Definition core_num_u64_max_c_def: + core_num_u64_max_c : u64 = get_return_value core_num_u64_max_body +End + +val betree_upsert_update_fwd_def = Define ‘ + (** [betree_main::betree::upsert_update] *) + 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_num_u64_max_c prev0; + if u64_ge margin v then u64_add prev0 v else Return core_num_u64_max_c + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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_in_bindings_fwd_def] = DefineDiv ‘ + (** [betree_main::betree::Node::{5}::lookup_in_bindings] *) + 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_node_lookup_first_message_for_key_fwd_def] = DefineDiv ‘ + (** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *) + 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] *) + 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] *) + 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] *) + 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_fwd_def, betree_node_lookup_back_def, betree_internal_lookup_in_children_fwd_def, betree_internal_lookup_in_children_back_def] = DefineDiv ‘ + (** [betree_main::betree::Node::{5}::lookup] *) + (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] *) + (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)) + /\ + + (** [betree_main::betree::Internal::{4}::lookup_in_children] *) + (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] *) + 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) +’ + +val [betree_node_lookup_mut_in_bindings_fwd_def] = DefineDiv ‘ + (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *) + 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] *) + 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] *) + 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] *) + 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_node_filter_messages_for_key_fwd_back_def] = DefineDiv ‘ + (** [betree_main::betree::Node::{5}::filter_messages_for_key] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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_apply_messages_fwd_def, betree_node_apply_messages_back_def, betree_internal_flush_fwd_def, betree_internal_flush_back_def] = DefineDiv ‘ + (** [betree_main::betree::Node::{5}::apply_messages] *) + (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] *) + (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)) + /\ + + (** [betree_main::betree::Internal::{4}::flush] *) + (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] *) + 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 +’ + +val betree_node_apply_fwd_def = Define ‘ + (** [betree_main::betree::Node::{5}::apply] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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] *) + 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 new file mode 100644 index 00000000..6c249f70 --- /dev/null +++ b/tests/hol4/betree/betreeMain_FunsTheory.sig @@ -0,0 +1,1240 @@ +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 core_num_u64_max_body_def : thm + val core_num_u64_max_c_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_num_u64_max_c prev0; + if u64_ge margin v then u64_add prev0 v + else Return core_num_u64_max_c + od + | BetreeUpsertFunStateSub v' => + if u64_ge prev0 v' then u64_sub prev0 v' + else Return (int_to_u64 0) + + [core_num_u64_max_body_def] Definition + + ⊢ core_num_u64_max_body = Return (int_to_u64 18446744073709551615) + + [core_num_u64_max_c_def] Definition + + ⊢ core_num_u64_max_c = get_return_value core_num_u64_max_body + + [main_fwd_def] Definition + + ⊢ main_fwd = Return () + + +*) +end diff --git a/tests/hol4/betree/betreeMain_OpaqueScript.sml b/tests/hol4/betree/betreeMain_OpaqueScript.sml new file mode 100644 index 00000000..a6f0cf15 --- /dev/null +++ b/tests/hol4/betree/betreeMain_OpaqueScript.sml @@ -0,0 +1,26 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree_main]: opaque function definitions *) +open primitivesLib divDefLib +open betreeMain_TypesTheory + +val _ = new_theory "betreeMain_Opaque" + + +val _ = new_constant ("betree_utils_load_internal_node_fwd", + “:u64 -> state -> (state # (u64 # betree_message_t) betree_list_t) + result”) + +val _ = new_constant ("betree_utils_store_internal_node_fwd", + “:u64 -> (u64 # betree_message_t) betree_list_t -> state -> (state # unit) + result”) + +val _ = new_constant ("betree_utils_load_leaf_node_fwd", + “:u64 -> state -> (state # (u64 # u64) betree_list_t) result”) + +val _ = new_constant ("betree_utils_store_leaf_node_fwd", + “:u64 -> (u64 # u64) betree_list_t -> state -> (state # unit) result”) + +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 new file mode 100644 index 00000000..da7559a0 --- /dev/null +++ b/tests/hol4/betree/betreeMain_OpaqueTheory.sig @@ -0,0 +1,11 @@ +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 new file mode 100644 index 00000000..c43421c2 --- /dev/null +++ b/tests/hol4/betree/betreeMain_TypesScript.sml @@ -0,0 +1,76 @@ +(** 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::Node] *) + betree_node_t = + | BetreeNodeInternal betree_internal_t + | BetreeNodeLeaf betree_leaf_t + ; + + (** [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; + |> +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 new file mode 100644 index 00000000..5cbe4c6b --- /dev/null +++ b/tests/hol4/betree/betreeMain_TypesTheory.sig @@ -0,0 +1,1751 @@ +signature betreeMain_TypesTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val betree_be_tree_t_TY_DEF : 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_case_def : thm + val betree_leaf_t_TY_DEF : 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_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_node_t_size_def : thm + val betree_params_t_TY_DEF : 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 + val recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_def : thm + val recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_fupd_def : thm + val recordtype_betree_be_tree_t_seldef_betree_be_tree_params_def : thm + val recordtype_betree_be_tree_t_seldef_betree_be_tree_params_fupd_def : thm + val recordtype_betree_be_tree_t_seldef_betree_be_tree_root_def : thm + val recordtype_betree_be_tree_t_seldef_betree_be_tree_root_fupd_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_id_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_id_fupd_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_left_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_left_fupd_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_pivot_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_pivot_fupd_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_right_def : thm + val recordtype_betree_internal_t_seldef_betree_internal_right_fupd_def : thm + val recordtype_betree_leaf_t_seldef_betree_leaf_id_def : thm + val recordtype_betree_leaf_t_seldef_betree_leaf_id_fupd_def : thm + val recordtype_betree_leaf_t_seldef_betree_leaf_size_def : thm + val recordtype_betree_leaf_t_seldef_betree_leaf_size_fupd_def : thm + val recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_def : thm + val recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_fupd_def : thm + val recordtype_betree_params_t_seldef_betree_params_min_flush_size_def : thm + val recordtype_betree_params_t_seldef_betree_params_min_flush_size_fupd_def : thm + val recordtype_betree_params_t_seldef_betree_params_split_size_def : thm + val recordtype_betree_params_t_seldef_betree_params_split_size_fupd_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_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_node_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_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 + (λa1'. + ∀ $var$('betree_node_t') $var$('betree_internal_t'). + (∀a0'. + (∃a. a0' = + (λa. + ind_type$CONSTR 0 (ARB,ARB,ARB) + (ind_type$FCONS a (λn. ind_type$BOTTOM))) + a ∧ $var$('betree_internal_t') a) ∨ + (∃a. a0' = + (λa. + ind_type$CONSTR (SUC 0) (a,ARB,ARB) + (λn. ind_type$BOTTOM)) a) ⇒ + $var$('betree_node_t') a0') ∧ + (∀a1'. + (∃a0 a1 a2 a3. + a1' = + (λa0 a1 a2 a3. + ind_type$CONSTR (SUC (SUC 0)) (ARB,a0,a1) + (ind_type$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') a1') ⇒ + $var$('betree_internal_t') a1') rep + + [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_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_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_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 + (λa0'. + ∀ $var$('betree_node_t') $var$('betree_internal_t'). + (∀a0'. + (∃a. a0' = + (λa. + ind_type$CONSTR 0 (ARB,ARB,ARB) + (ind_type$FCONS a (λn. ind_type$BOTTOM))) + a ∧ $var$('betree_internal_t') a) ∨ + (∃a. a0' = + (λa. + ind_type$CONSTR (SUC 0) (a,ARB,ARB) + (λn. ind_type$BOTTOM)) a) ⇒ + $var$('betree_node_t') a0') ∧ + (∀a1'. + (∃a0 a1 a2 a3. + a1' = + (λa0 a1 a2 a3. + ind_type$CONSTR (SUC (SUC 0)) (ARB,a0,a1) + (ind_type$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') a1') ⇒ + $var$('betree_node_t') a0') 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_node_t_size_def] Definition + + ⊢ (∀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) ∧ + ∀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) + + [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_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 + + [recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_def] Definition + + ⊢ ∀b b0 b1. + (betree_be_tree_t b b0 b1).betree_be_tree_node_id_cnt = b0 + + [recordtype_betree_be_tree_t_seldef_betree_be_tree_node_id_cnt_fupd_def] 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 + + [recordtype_betree_be_tree_t_seldef_betree_be_tree_params_def] Definition + + ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_params = b + + [recordtype_betree_be_tree_t_seldef_betree_be_tree_params_fupd_def] 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 + + [recordtype_betree_be_tree_t_seldef_betree_be_tree_root_def] Definition + + ⊢ ∀b b0 b1. (betree_be_tree_t b b0 b1).betree_be_tree_root = b1 + + [recordtype_betree_be_tree_t_seldef_betree_be_tree_root_fupd_def] 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) + + [recordtype_betree_internal_t_seldef_betree_internal_id_def] Definition + + ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_id = u + + [recordtype_betree_internal_t_seldef_betree_internal_id_fupd_def] 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 + + [recordtype_betree_internal_t_seldef_betree_internal_left_def] Definition + + ⊢ ∀u u0 b b0. (betree_internal_t u u0 b b0).betree_internal_left = b + + [recordtype_betree_internal_t_seldef_betree_internal_left_fupd_def] 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 + + [recordtype_betree_internal_t_seldef_betree_internal_pivot_def] Definition + + ⊢ ∀u u0 b b0. + (betree_internal_t u u0 b b0).betree_internal_pivot = u0 + + [recordtype_betree_internal_t_seldef_betree_internal_pivot_fupd_def] 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 + + [recordtype_betree_internal_t_seldef_betree_internal_right_def] Definition + + ⊢ ∀u u0 b b0. + (betree_internal_t u u0 b b0).betree_internal_right = b0 + + [recordtype_betree_internal_t_seldef_betree_internal_right_fupd_def] 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) + + [recordtype_betree_leaf_t_seldef_betree_leaf_id_def] Definition + + ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_id = u + + [recordtype_betree_leaf_t_seldef_betree_leaf_id_fupd_def] Definition + + ⊢ ∀f u u0. + betree_leaf_t u u0 with betree_leaf_id updated_by f = + betree_leaf_t (f u) u0 + + [recordtype_betree_leaf_t_seldef_betree_leaf_size_def] Definition + + ⊢ ∀u u0. (betree_leaf_t u u0).betree_leaf_size = u0 + + [recordtype_betree_leaf_t_seldef_betree_leaf_size_fupd_def] Definition + + ⊢ ∀f u u0. + betree_leaf_t u u0 with betree_leaf_size updated_by f = + betree_leaf_t u (f u0) + + [recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_def] Definition + + ⊢ ∀u. (betree_node_id_counter_t u). + betree_node_id_counter_next_node_id = + u + + [recordtype_betree_node_id_counter_t_seldef_betree_node_id_counter_next_node_id_fupd_def] 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) + + [recordtype_betree_params_t_seldef_betree_params_min_flush_size_def] Definition + + ⊢ ∀u u0. (betree_params_t u u0).betree_params_min_flush_size = u + + [recordtype_betree_params_t_seldef_betree_params_min_flush_size_fupd_def] Definition + + ⊢ ∀f u u0. + betree_params_t u u0 with + betree_params_min_flush_size updated_by f = + betree_params_t (f u) u0 + + [recordtype_betree_params_t_seldef_betree_params_split_size_def] Definition + + ⊢ ∀u u0. (betree_params_t u u0).betree_params_split_size = u0 + + [recordtype_betree_params_t_seldef_betree_params_split_size_fupd_def] Definition + + ⊢ ∀f u u0. + betree_params_t u u0 with betree_params_split_size updated_by f = + betree_params_t u (f u0) + + [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. + (∀a. fn0 (BetreeNodeInternal a) = f0 a (fn1 a)) ∧ + (∀a. fn0 (BetreeNodeLeaf a) = f1 a) ∧ + ∀a0 a1 a2 a3. + fn1 (betree_internal_t a0 a1 a2 a3) = + f2 a0 a1 a2 a3 (fn0 a2) (fn0 a3) + + [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. P1 b ⇒ P0 (BetreeNodeInternal b)) ∧ + (∀b. P0 (BetreeNodeLeaf b)) ∧ + (∀b b0. P0 b ∧ P0 b0 ⇒ ∀u u0. P1 (betree_internal_t u0 u b b0)) ⇒ + (∀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. + (∀a. fn0 (BetreeNodeInternal a) = f0 a (fn1 a)) ∧ + (∀a. fn0 (BetreeNodeLeaf a) = f1 a) ∧ + ∀a0 a1 a2 a3. + fn1 (betree_internal_t a0 a1 a2 a3) = + f2 a0 a1 a2 a3 (fn0 a2) (fn0 a3) + + [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. P1 b ⇒ P0 (BetreeNodeInternal b)) ∧ + (∀b. P0 (BetreeNodeLeaf b)) ∧ + (∀b b0. P0 b ∧ P0 b0 ⇒ ∀u u0. P1 (betree_internal_t u0 u b b0)) ⇒ + (∀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_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_node_t] Theorem + + ⊢ DATATYPE + (betree_node_t BetreeNodeInternal BetreeNodeLeaf ∧ + record betree_internal_t betree_internal_id + betree_internal_pivot betree_internal_left + betree_internal_right) + + [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/hashmap/Holmakefile b/tests/hol4/hashmap/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/hashmap/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/hashmap/hashmap_FunsScript.sml b/tests/hol4/hashmap/hashmap_FunsScript.sml new file mode 100644 index 00000000..9ad497f5 --- /dev/null +++ b/tests/hol4/hashmap/hashmap_FunsScript.sml @@ -0,0 +1,567 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap]: function definitions *) +open primitivesLib divDefLib +open hashmap_TypesTheory + +val _ = new_theory "hashmap_Funs" + + +val hash_key_fwd_def = Define ‘ + (** [hashmap::hash_key] *) + hash_key_fwd (k : usize) : usize result = + Return k +’ + +val [hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::allocate_slots] *) + hash_map_allocate_slots_loop_fwd + (slots : 't list_t vec) (n : usize) : 't list_t vec result = + if usize_gt n (int_to_usize 0) + then ( + do + slots0 <- vec_push_back slots ListNil; + n0 <- usize_sub n (int_to_usize 1); + hash_map_allocate_slots_loop_fwd slots0 n0 + od) + else Return slots +’ + +val hash_map_allocate_slots_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::allocate_slots] *) + hash_map_allocate_slots_fwd + (slots : 't list_t vec) (n : usize) : 't list_t vec result = + hash_map_allocate_slots_loop_fwd slots n +’ + +val hash_map_new_with_capacity_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::new_with_capacity] *) + hash_map_new_with_capacity_fwd + (capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) : + 't hash_map_t result + = + let v = vec_new in + do + slots <- hash_map_allocate_slots_fwd v capacity; + i <- usize_mul capacity max_load_dividend; + i0 <- usize_div i max_load_divisor; + Return + (<| + hash_map_num_entries := (int_to_usize 0); + hash_map_max_load_factor := (max_load_dividend, max_load_divisor); + hash_map_max_load := i0; + hash_map_slots := slots + |>) + od +’ + +val hash_map_new_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::new] *) + hash_map_new_fwd : 't hash_map_t result = + hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4) + (int_to_usize 5) +’ + +val [hash_map_clear_loop_fwd_back_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::clear] *) + hash_map_clear_loop_fwd_back + (slots : 't list_t vec) (i : usize) : 't list_t vec result = + let i0 = vec_len slots in + if usize_lt i i0 + then ( + do + i1 <- usize_add i (int_to_usize 1); + slots0 <- vec_index_mut_back slots i ListNil; + hash_map_clear_loop_fwd_back slots0 i1 + od) + else Return slots +’ + +val hash_map_clear_fwd_back_def = Define ‘ + (** [hashmap::HashMap::{0}::clear] *) + hash_map_clear_fwd_back (self : 't hash_map_t) : 't hash_map_t result = + do + v <- hash_map_clear_loop_fwd_back self.hash_map_slots (int_to_usize 0); + Return + (self + with + <| + hash_map_num_entries := (int_to_usize 0); hash_map_slots := v + |>) + od +’ + +val hash_map_len_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::len] *) + hash_map_len_fwd (self : 't hash_map_t) : usize result = + Return self.hash_map_num_entries +’ + +val [hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::insert_in_list] *) + hash_map_insert_in_list_loop_fwd + (key : usize) (value : 't) (ls : 't list_t) : bool result = + (case ls of + | ListCons ckey cvalue tl => + if ckey = key + then Return F + else hash_map_insert_in_list_loop_fwd key value tl + | ListNil => Return T) +’ + +val hash_map_insert_in_list_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::insert_in_list] *) + hash_map_insert_in_list_fwd + (key : usize) (value : 't) (ls : 't list_t) : bool result = + hash_map_insert_in_list_loop_fwd key value ls +’ + +val [hash_map_insert_in_list_loop_back_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::insert_in_list] *) + hash_map_insert_in_list_loop_back + (key : usize) (value : 't) (ls : 't list_t) : 't list_t result = + (case ls of + | ListCons ckey cvalue tl => + if ckey = key + then Return (ListCons ckey value tl) + else ( + do + tl0 <- hash_map_insert_in_list_loop_back key value tl; + Return (ListCons ckey cvalue tl0) + od) + | ListNil => let l = ListNil in Return (ListCons key value l)) +’ + +val hash_map_insert_in_list_back_def = Define ‘ + (** [hashmap::HashMap::{0}::insert_in_list] *) + hash_map_insert_in_list_back + (key : usize) (value : 't) (ls : 't list_t) : 't list_t result = + hash_map_insert_in_list_loop_back key value ls +’ + +val hash_map_insert_no_resize_fwd_back_def = Define ‘ + (** [hashmap::HashMap::{0}::insert_no_resize] *) + hash_map_insert_no_resize_fwd_back + (self : 't hash_map_t) (key : usize) (value : 't) : 't hash_map_t result = + do + hash <- hash_key_fwd key; + let i = vec_len self.hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + inserted <- hash_map_insert_in_list_fwd key value l; + if inserted + then ( + do + i0 <- usize_add self.hash_map_num_entries (int_to_usize 1); + l0 <- hash_map_insert_in_list_back key value l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with <| hash_map_num_entries := i0; hash_map_slots := v |>) + od) + else ( + do + l0 <- hash_map_insert_in_list_back key value l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with <| hash_map_slots := v |>) + od) + od + od +’ + +(** [core::num::u32::{9}::MAX] *) +Definition core_num_u32_max_body_def: + core_num_u32_max_body : u32 result = Return (int_to_u32 4294967295) +End +Definition core_num_u32_max_c_def: + core_num_u32_max_c : u32 = get_return_value core_num_u32_max_body +End + +val [hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::move_elements_from_list] *) + hash_map_move_elements_from_list_loop_fwd_back + (ntable : 't hash_map_t) (ls : 't list_t) : 't hash_map_t result = + (case ls of + | ListCons k v tl => + do + ntable0 <- hash_map_insert_no_resize_fwd_back ntable k v; + hash_map_move_elements_from_list_loop_fwd_back ntable0 tl + od + | ListNil => Return ntable) +’ + +val hash_map_move_elements_from_list_fwd_back_def = Define ‘ + (** [hashmap::HashMap::{0}::move_elements_from_list] *) + hash_map_move_elements_from_list_fwd_back + (ntable : 't hash_map_t) (ls : 't list_t) : 't hash_map_t result = + hash_map_move_elements_from_list_loop_fwd_back ntable ls +’ + +val [hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::move_elements] *) + hash_map_move_elements_loop_fwd_back + (ntable : 't hash_map_t) (slots : 't list_t vec) (i : usize) : + ('t hash_map_t # 't list_t vec) result + = + let i0 = vec_len slots in + if usize_lt i i0 + then ( + do + l <- vec_index_mut_fwd slots i; + let ls = mem_replace_fwd l ListNil in + do + ntable0 <- hash_map_move_elements_from_list_fwd_back ntable ls; + i1 <- usize_add i (int_to_usize 1); + let l0 = mem_replace_back l ListNil in + do + slots0 <- vec_index_mut_back slots i l0; + hash_map_move_elements_loop_fwd_back ntable0 slots0 i1 + od + od + od) + else Return (ntable, slots) +’ + +val hash_map_move_elements_fwd_back_def = Define ‘ + (** [hashmap::HashMap::{0}::move_elements] *) + hash_map_move_elements_fwd_back + (ntable : 't hash_map_t) (slots : 't list_t vec) (i : usize) : + ('t hash_map_t # 't list_t vec) result + = + hash_map_move_elements_loop_fwd_back ntable slots i +’ + +val hash_map_try_resize_fwd_back_def = Define ‘ + (** [hashmap::HashMap::{0}::try_resize] *) + hash_map_try_resize_fwd_back (self : 't hash_map_t) : 't hash_map_t result = + do + max_usize <- mk_usize (u32_to_int core_num_u32_max_c); + let capacity = vec_len self.hash_map_slots in + do + n1 <- usize_div max_usize (int_to_usize 2); + let (i, i0) = self.hash_map_max_load_factor in + do + i1 <- usize_div n1 i; + if usize_le capacity i1 + then ( + do + i2 <- usize_mul capacity (int_to_usize 2); + ntable <- hash_map_new_with_capacity_fwd i2 i i0; + (ntable0, _) <- + hash_map_move_elements_fwd_back ntable self.hash_map_slots + (int_to_usize 0); + Return + (ntable0 + with + <| + hash_map_num_entries := self.hash_map_num_entries; + hash_map_max_load_factor := (i, i0) + |>) + od) + else Return (self with <| hash_map_max_load_factor := (i, i0) |>) + od + od + od +’ + +val hash_map_insert_fwd_back_def = Define ‘ + (** [hashmap::HashMap::{0}::insert] *) + hash_map_insert_fwd_back + (self : 't hash_map_t) (key : usize) (value : 't) : 't hash_map_t result = + do + self0 <- hash_map_insert_no_resize_fwd_back self key value; + i <- hash_map_len_fwd self0; + if usize_gt i self0.hash_map_max_load + then hash_map_try_resize_fwd_back self0 + else Return self0 + od +’ + +val [hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::contains_key_in_list] *) + hash_map_contains_key_in_list_loop_fwd + (key : usize) (ls : 't list_t) : bool result = + (case ls of + | ListCons ckey t tl => + if ckey = key + then Return T + else hash_map_contains_key_in_list_loop_fwd key tl + | ListNil => Return F) +’ + +val hash_map_contains_key_in_list_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::contains_key_in_list] *) + hash_map_contains_key_in_list_fwd + (key : usize) (ls : 't list_t) : bool result = + hash_map_contains_key_in_list_loop_fwd key ls +’ + +val hash_map_contains_key_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::contains_key] *) + hash_map_contains_key_fwd + (self : 't hash_map_t) (key : usize) : bool result = + do + hash <- hash_key_fwd key; + let i = vec_len self.hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hash_map_slots hash_mod; + hash_map_contains_key_in_list_fwd key l + od + od +’ + +val [hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::get_in_list] *) + hash_map_get_in_list_loop_fwd (key : usize) (ls : 't list_t) : 't result = + (case ls of + | ListCons ckey cvalue tl => + if ckey = key + then Return cvalue + else hash_map_get_in_list_loop_fwd key tl + | ListNil => Fail Failure) +’ + +val hash_map_get_in_list_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::get_in_list] *) + hash_map_get_in_list_fwd (key : usize) (ls : 't list_t) : 't result = + hash_map_get_in_list_loop_fwd key ls +’ + +val hash_map_get_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::get] *) + hash_map_get_fwd (self : 't hash_map_t) (key : usize) : 't result = + do + hash <- hash_key_fwd key; + let i = vec_len self.hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hash_map_slots hash_mod; + hash_map_get_in_list_fwd key l + od + od +’ + +val [hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::get_mut_in_list] *) + hash_map_get_mut_in_list_loop_fwd + (ls : 't list_t) (key : usize) : 't result = + (case ls of + | ListCons ckey cvalue tl => + if ckey = key + then Return cvalue + else hash_map_get_mut_in_list_loop_fwd tl key + | ListNil => Fail Failure) +’ + +val hash_map_get_mut_in_list_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::get_mut_in_list] *) + hash_map_get_mut_in_list_fwd (ls : 't list_t) (key : usize) : 't result = + hash_map_get_mut_in_list_loop_fwd ls key +’ + +val [hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::get_mut_in_list] *) + hash_map_get_mut_in_list_loop_back + (ls : 't list_t) (key : usize) (ret : 't) : 't list_t result = + (case ls of + | ListCons ckey cvalue tl => + if ckey = key + then Return (ListCons ckey ret tl) + else ( + do + tl0 <- hash_map_get_mut_in_list_loop_back tl key ret; + Return (ListCons ckey cvalue tl0) + od) + | ListNil => Fail Failure) +’ + +val hash_map_get_mut_in_list_back_def = Define ‘ + (** [hashmap::HashMap::{0}::get_mut_in_list] *) + hash_map_get_mut_in_list_back + (ls : 't list_t) (key : usize) (ret : 't) : 't list_t result = + hash_map_get_mut_in_list_loop_back ls key ret +’ + +val hash_map_get_mut_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::get_mut] *) + hash_map_get_mut_fwd (self : 't hash_map_t) (key : usize) : 't result = + do + hash <- hash_key_fwd key; + let i = vec_len self.hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + hash_map_get_mut_in_list_fwd l key + od + od +’ + +val hash_map_get_mut_back_def = Define ‘ + (** [hashmap::HashMap::{0}::get_mut] *) + hash_map_get_mut_back + (self : 't hash_map_t) (key : usize) (ret : 't) : 't hash_map_t result = + do + hash <- hash_key_fwd key; + let i = vec_len self.hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + l0 <- hash_map_get_mut_in_list_back l key ret; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with <| hash_map_slots := v |>) + od + od +’ + +val [hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::remove_from_list] *) + hash_map_remove_from_list_loop_fwd + (key : usize) (ls : 't list_t) : 't option result = + (case ls of + | ListCons ckey t tl => + if ckey = key + then + let mv_ls = mem_replace_fwd (ListCons ckey t tl) ListNil in + (case mv_ls of + | ListCons i cvalue tl0 => Return (SOME cvalue) + | ListNil => Fail Failure) + else hash_map_remove_from_list_loop_fwd key tl + | ListNil => Return NONE) +’ + +val hash_map_remove_from_list_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::remove_from_list] *) + hash_map_remove_from_list_fwd + (key : usize) (ls : 't list_t) : 't option result = + hash_map_remove_from_list_loop_fwd key ls +’ + +val [hash_map_remove_from_list_loop_back_def] = DefineDiv ‘ + (** [hashmap::HashMap::{0}::remove_from_list] *) + hash_map_remove_from_list_loop_back + (key : usize) (ls : 't list_t) : 't list_t result = + (case ls of + | ListCons ckey t tl => + if ckey = key + then + let mv_ls = mem_replace_fwd (ListCons ckey t tl) ListNil in + (case mv_ls of + | ListCons i cvalue tl0 => Return tl0 + | ListNil => Fail Failure) + else ( + do + tl0 <- hash_map_remove_from_list_loop_back key tl; + Return (ListCons ckey t tl0) + od) + | ListNil => Return ListNil) +’ + +val hash_map_remove_from_list_back_def = Define ‘ + (** [hashmap::HashMap::{0}::remove_from_list] *) + hash_map_remove_from_list_back + (key : usize) (ls : 't list_t) : 't list_t result = + hash_map_remove_from_list_loop_back key ls +’ + +val hash_map_remove_fwd_def = Define ‘ + (** [hashmap::HashMap::{0}::remove] *) + hash_map_remove_fwd (self : 't hash_map_t) (key : usize) : 't option result = + do + hash <- hash_key_fwd key; + let i = vec_len self.hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + x <- hash_map_remove_from_list_fwd key l; + (case x of + | NONE => Return NONE + | SOME x0 => + do + _ <- usize_sub self.hash_map_num_entries (int_to_usize 1); + Return (SOME x0) + od) + od + od +’ + +val hash_map_remove_back_def = Define ‘ + (** [hashmap::HashMap::{0}::remove] *) + hash_map_remove_back + (self : 't hash_map_t) (key : usize) : 't hash_map_t result = + do + hash <- hash_key_fwd key; + let i = vec_len self.hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + x <- hash_map_remove_from_list_fwd key l; + (case x of + | NONE => + do + l0 <- hash_map_remove_from_list_back key l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with <| hash_map_slots := v |>) + od + | SOME x0 => + do + i0 <- usize_sub self.hash_map_num_entries (int_to_usize 1); + l0 <- hash_map_remove_from_list_back key l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with <| hash_map_num_entries := i0; hash_map_slots := v |>) + od) + od + od +’ + +val test1_fwd_def = Define ‘ + (** [hashmap::test1] *) + test1_fwd : unit result = + do + hm <- hash_map_new_fwd; + hm0 <- hash_map_insert_fwd_back hm (int_to_usize 0) (int_to_u64 42); + hm1 <- hash_map_insert_fwd_back hm0 (int_to_usize 128) (int_to_u64 18); + hm2 <- hash_map_insert_fwd_back hm1 (int_to_usize 1024) (int_to_u64 138); + hm3 <- hash_map_insert_fwd_back hm2 (int_to_usize 1056) (int_to_u64 256); + i <- hash_map_get_fwd hm3 (int_to_usize 128); + if ~ (i = int_to_u64 18) + then Fail Failure + else ( + do + hm4 <- hash_map_get_mut_back hm3 (int_to_usize 1024) (int_to_u64 56); + i0 <- hash_map_get_fwd hm4 (int_to_usize 1024); + if ~ (i0 = int_to_u64 56) + then Fail Failure + else ( + do + x <- hash_map_remove_fwd hm4 (int_to_usize 1024); + (case x of + | NONE => Fail Failure + | SOME x0 => + if ~ (x0 = int_to_u64 56) + then Fail Failure + else ( + do + hm5 <- hash_map_remove_back hm4 (int_to_usize 1024); + i1 <- hash_map_get_fwd hm5 (int_to_usize 0); + if ~ (i1 = int_to_u64 42) + then Fail Failure + else ( + do + i2 <- hash_map_get_fwd hm5 (int_to_usize 128); + if ~ (i2 = int_to_u64 18) + then Fail Failure + else ( + do + i3 <- hash_map_get_fwd hm5 (int_to_usize 1056); + if ~ (i3 = int_to_u64 256) then Fail Failure else Return () + od) + od) + od)) + od) + od) + od +’ + +(** Unit test for [hashmap::test1] *) +val _ = assert_return (“test1_fwd”) + +val _ = export_theory () diff --git a/tests/hol4/hashmap/hashmap_FunsTheory.sig b/tests/hol4/hashmap/hashmap_FunsTheory.sig new file mode 100644 index 00000000..50482547 --- /dev/null +++ b/tests/hol4/hashmap/hashmap_FunsTheory.sig @@ -0,0 +1,550 @@ +signature hashmap_FunsTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val core_num_u32_max_body_def : thm + val core_num_u32_max_c_def : thm + val hash_key_fwd_def : thm + val hash_map_allocate_slots_fwd_def : thm + val hash_map_allocate_slots_loop_fwd_def : thm + val hash_map_clear_fwd_back_def : thm + val hash_map_clear_loop_fwd_back_def : thm + val hash_map_contains_key_fwd_def : thm + val hash_map_contains_key_in_list_fwd_def : thm + val hash_map_contains_key_in_list_loop_fwd_def : thm + val hash_map_get_fwd_def : thm + val hash_map_get_in_list_fwd_def : thm + val hash_map_get_in_list_loop_fwd_def : thm + val hash_map_get_mut_back_def : thm + val hash_map_get_mut_fwd_def : thm + val hash_map_get_mut_in_list_back_def : thm + val hash_map_get_mut_in_list_fwd_def : thm + val hash_map_get_mut_in_list_loop_back_def : thm + val hash_map_get_mut_in_list_loop_fwd_def : thm + val hash_map_insert_fwd_back_def : thm + val hash_map_insert_in_list_back_def : thm + val hash_map_insert_in_list_fwd_def : thm + val hash_map_insert_in_list_loop_back_def : thm + val hash_map_insert_in_list_loop_fwd_def : thm + val hash_map_insert_no_resize_fwd_back_def : thm + val hash_map_len_fwd_def : thm + val hash_map_move_elements_from_list_fwd_back_def : thm + val hash_map_move_elements_from_list_loop_fwd_back_def : thm + val hash_map_move_elements_fwd_back_def : thm + val hash_map_move_elements_loop_fwd_back_def : thm + val hash_map_new_fwd_def : thm + val hash_map_new_with_capacity_fwd_def : thm + val hash_map_remove_back_def : thm + val hash_map_remove_from_list_back_def : thm + val hash_map_remove_from_list_fwd_def : thm + val hash_map_remove_from_list_loop_back_def : thm + val hash_map_remove_from_list_loop_fwd_def : thm + val hash_map_remove_fwd_def : thm + val hash_map_try_resize_fwd_back_def : thm + val test1_fwd_def : thm + + val hashmap_Funs_grammars : type_grammar.grammar * term_grammar.grammar +(* + [hashmap_Types] Parent theory of "hashmap_Funs" + + [core_num_u32_max_body_def] Definition + + ⊢ core_num_u32_max_body = Return (int_to_u32 4294967295) + + [core_num_u32_max_c_def] Definition + + ⊢ core_num_u32_max_c = get_return_value core_num_u32_max_body + + [hash_key_fwd_def] Definition + + ⊢ ∀k. hash_key_fwd k = Return k + + [hash_map_allocate_slots_fwd_def] Definition + + ⊢ ∀slots n. + hash_map_allocate_slots_fwd slots n = + hash_map_allocate_slots_loop_fwd slots n + + [hash_map_allocate_slots_loop_fwd_def] Definition + + ⊢ ∀slots n. + hash_map_allocate_slots_loop_fwd slots n = + if usize_gt n (int_to_usize 0) then + do + slots0 <- vec_push_back slots ListNil; + n0 <- usize_sub n (int_to_usize 1); + hash_map_allocate_slots_loop_fwd slots0 n0 + od + else Return slots + + [hash_map_clear_fwd_back_def] Definition + + ⊢ ∀self. + hash_map_clear_fwd_back self = + do + v <- + hash_map_clear_loop_fwd_back self.hash_map_slots + (int_to_usize 0); + Return + (self with + <|hash_map_num_entries := int_to_usize 0; + hash_map_slots := v|>) + od + + [hash_map_clear_loop_fwd_back_def] Definition + + ⊢ ∀slots i. + hash_map_clear_loop_fwd_back slots i = + (let + i0 = vec_len slots + in + if usize_lt i i0 then + do + i1 <- usize_add i (int_to_usize 1); + slots0 <- vec_index_mut_back slots i ListNil; + hash_map_clear_loop_fwd_back slots0 i1 + od + else Return slots) + + [hash_map_contains_key_fwd_def] Definition + + ⊢ ∀self key. + hash_map_contains_key_fwd self key = + do + hash <- hash_key_fwd key; + i <<- vec_len self.hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hash_map_slots hash_mod; + hash_map_contains_key_in_list_fwd key l + od + + [hash_map_contains_key_in_list_fwd_def] Definition + + ⊢ ∀key ls. + hash_map_contains_key_in_list_fwd key ls = + hash_map_contains_key_in_list_loop_fwd key ls + + [hash_map_contains_key_in_list_loop_fwd_def] Definition + + ⊢ ∀key ls. + hash_map_contains_key_in_list_loop_fwd key ls = + case ls of + ListCons ckey t tl => + if ckey = key then Return T + else hash_map_contains_key_in_list_loop_fwd key tl + | ListNil => Return F + + [hash_map_get_fwd_def] Definition + + ⊢ ∀self key. + hash_map_get_fwd self key = + do + hash <- hash_key_fwd key; + i <<- vec_len self.hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hash_map_slots hash_mod; + hash_map_get_in_list_fwd key l + od + + [hash_map_get_in_list_fwd_def] Definition + + ⊢ ∀key ls. + hash_map_get_in_list_fwd key ls = + hash_map_get_in_list_loop_fwd key ls + + [hash_map_get_in_list_loop_fwd_def] Definition + + ⊢ ∀key ls. + hash_map_get_in_list_loop_fwd key ls = + case ls of + ListCons ckey cvalue tl => + if ckey = key then Return cvalue + else hash_map_get_in_list_loop_fwd key tl + | ListNil => Fail Failure + + [hash_map_get_mut_back_def] Definition + + ⊢ ∀self key ret. + hash_map_get_mut_back self key ret = + do + hash <- hash_key_fwd key; + i <<- vec_len self.hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + l0 <- hash_map_get_mut_in_list_back l key ret; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with hash_map_slots := v) + od + + [hash_map_get_mut_fwd_def] Definition + + ⊢ ∀self key. + hash_map_get_mut_fwd self key = + do + hash <- hash_key_fwd key; + i <<- vec_len self.hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + hash_map_get_mut_in_list_fwd l key + od + + [hash_map_get_mut_in_list_back_def] Definition + + ⊢ ∀ls key ret. + hash_map_get_mut_in_list_back ls key ret = + hash_map_get_mut_in_list_loop_back ls key ret + + [hash_map_get_mut_in_list_fwd_def] Definition + + ⊢ ∀ls key. + hash_map_get_mut_in_list_fwd ls key = + hash_map_get_mut_in_list_loop_fwd ls key + + [hash_map_get_mut_in_list_loop_back_def] Definition + + ⊢ ∀ls key ret. + hash_map_get_mut_in_list_loop_back ls key ret = + case ls of + ListCons ckey cvalue tl => + if ckey = key then Return (ListCons ckey ret tl) + else + do + tl0 <- hash_map_get_mut_in_list_loop_back tl key ret; + Return (ListCons ckey cvalue tl0) + od + | ListNil => Fail Failure + + [hash_map_get_mut_in_list_loop_fwd_def] Definition + + ⊢ ∀ls key. + hash_map_get_mut_in_list_loop_fwd ls key = + case ls of + ListCons ckey cvalue tl => + if ckey = key then Return cvalue + else hash_map_get_mut_in_list_loop_fwd tl key + | ListNil => Fail Failure + + [hash_map_insert_fwd_back_def] Definition + + ⊢ ∀self key value. + hash_map_insert_fwd_back self key value = + do + self0 <- hash_map_insert_no_resize_fwd_back self key value; + i <- hash_map_len_fwd self0; + if usize_gt i self0.hash_map_max_load then + hash_map_try_resize_fwd_back self0 + else Return self0 + od + + [hash_map_insert_in_list_back_def] Definition + + ⊢ ∀key value ls. + hash_map_insert_in_list_back key value ls = + hash_map_insert_in_list_loop_back key value ls + + [hash_map_insert_in_list_fwd_def] Definition + + ⊢ ∀key value ls. + hash_map_insert_in_list_fwd key value ls = + hash_map_insert_in_list_loop_fwd key value ls + + [hash_map_insert_in_list_loop_back_def] Definition + + ⊢ ∀key value ls. + hash_map_insert_in_list_loop_back key value ls = + case ls of + ListCons ckey cvalue tl => + if ckey = key then Return (ListCons ckey value tl) + else + do + tl0 <- hash_map_insert_in_list_loop_back key value tl; + Return (ListCons ckey cvalue tl0) + od + | ListNil => (let l = ListNil in Return (ListCons key value l)) + + [hash_map_insert_in_list_loop_fwd_def] Definition + + ⊢ ∀key value ls. + hash_map_insert_in_list_loop_fwd key value ls = + case ls of + ListCons ckey cvalue tl => + if ckey = key then Return F + else hash_map_insert_in_list_loop_fwd key value tl + | ListNil => Return T + + [hash_map_insert_no_resize_fwd_back_def] Definition + + ⊢ ∀self key value. + hash_map_insert_no_resize_fwd_back self key value = + do + hash <- hash_key_fwd key; + i <<- vec_len self.hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + inserted <- hash_map_insert_in_list_fwd key value l; + if inserted then + do + i0 <- usize_add self.hash_map_num_entries (int_to_usize 1); + l0 <- hash_map_insert_in_list_back key value l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return + (self with + <|hash_map_num_entries := i0; hash_map_slots := v|>) + od + else + do + l0 <- hash_map_insert_in_list_back key value l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with hash_map_slots := v) + od + od + + [hash_map_len_fwd_def] Definition + + ⊢ ∀self. hash_map_len_fwd self = Return self.hash_map_num_entries + + [hash_map_move_elements_from_list_fwd_back_def] Definition + + ⊢ ∀ntable ls. + hash_map_move_elements_from_list_fwd_back ntable ls = + hash_map_move_elements_from_list_loop_fwd_back ntable ls + + [hash_map_move_elements_from_list_loop_fwd_back_def] Definition + + ⊢ ∀ntable ls. + hash_map_move_elements_from_list_loop_fwd_back ntable ls = + case ls of + ListCons k v tl => + do + ntable0 <- hash_map_insert_no_resize_fwd_back ntable k v; + hash_map_move_elements_from_list_loop_fwd_back ntable0 tl + od + | ListNil => Return ntable + + [hash_map_move_elements_fwd_back_def] Definition + + ⊢ ∀ntable slots i. + hash_map_move_elements_fwd_back ntable slots i = + hash_map_move_elements_loop_fwd_back ntable slots i + + [hash_map_move_elements_loop_fwd_back_def] Definition + + ⊢ ∀ntable slots i. + hash_map_move_elements_loop_fwd_back ntable slots i = + (let + i0 = vec_len slots + in + if usize_lt i i0 then + do + l <- vec_index_mut_fwd slots i; + ls <<- mem_replace_fwd l ListNil; + ntable0 <- + hash_map_move_elements_from_list_fwd_back ntable ls; + i1 <- usize_add i (int_to_usize 1); + l0 <<- mem_replace_back l ListNil; + slots0 <- vec_index_mut_back slots i l0; + hash_map_move_elements_loop_fwd_back ntable0 slots0 i1 + od + else Return (ntable,slots)) + + [hash_map_new_fwd_def] Definition + + ⊢ hash_map_new_fwd = + hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4) + (int_to_usize 5) + + [hash_map_new_with_capacity_fwd_def] Definition + + ⊢ ∀capacity max_load_dividend max_load_divisor. + hash_map_new_with_capacity_fwd capacity max_load_dividend + max_load_divisor = + (let + v = vec_new + in + do + slots <- hash_map_allocate_slots_fwd v capacity; + i <- usize_mul capacity max_load_dividend; + i0 <- usize_div i max_load_divisor; + Return + <|hash_map_num_entries := int_to_usize 0; + hash_map_max_load_factor := + (max_load_dividend,max_load_divisor); + hash_map_max_load := i0; hash_map_slots := slots|> + od) + + [hash_map_remove_back_def] Definition + + ⊢ ∀self key. + hash_map_remove_back self key = + do + hash <- hash_key_fwd key; + i <<- vec_len self.hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + x <- hash_map_remove_from_list_fwd key l; + case x of + NONE => + do + l0 <- hash_map_remove_from_list_back key l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return (self with hash_map_slots := v) + od + | SOME x0 => + do + i0 <- usize_sub self.hash_map_num_entries (int_to_usize 1); + l0 <- hash_map_remove_from_list_back key l; + v <- vec_index_mut_back self.hash_map_slots hash_mod l0; + Return + (self with + <|hash_map_num_entries := i0; hash_map_slots := v|>) + od + od + + [hash_map_remove_from_list_back_def] Definition + + ⊢ ∀key ls. + hash_map_remove_from_list_back key ls = + hash_map_remove_from_list_loop_back key ls + + [hash_map_remove_from_list_fwd_def] Definition + + ⊢ ∀key ls. + hash_map_remove_from_list_fwd key ls = + hash_map_remove_from_list_loop_fwd key ls + + [hash_map_remove_from_list_loop_back_def] Definition + + ⊢ ∀key ls. + hash_map_remove_from_list_loop_back key ls = + case ls of + ListCons ckey t tl => + if ckey = key then + (let + mv_ls = mem_replace_fwd (ListCons ckey t tl) ListNil + in + case mv_ls of + ListCons i cvalue tl0 => Return tl0 + | ListNil => Fail Failure) + else + do + tl0 <- hash_map_remove_from_list_loop_back key tl; + Return (ListCons ckey t tl0) + od + | ListNil => Return ListNil + + [hash_map_remove_from_list_loop_fwd_def] Definition + + ⊢ ∀key ls. + hash_map_remove_from_list_loop_fwd key ls = + case ls of + ListCons ckey t tl => + if ckey = key then + (let + mv_ls = mem_replace_fwd (ListCons ckey t tl) ListNil + in + case mv_ls of + ListCons i cvalue tl0 => Return (SOME cvalue) + | ListNil => Fail Failure) + else hash_map_remove_from_list_loop_fwd key tl + | ListNil => Return NONE + + [hash_map_remove_fwd_def] Definition + + ⊢ ∀self key. + hash_map_remove_fwd self key = + do + hash <- hash_key_fwd key; + i <<- vec_len self.hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hash_map_slots hash_mod; + x <- hash_map_remove_from_list_fwd key l; + case x of + NONE => Return NONE + | SOME x0 => + monad_ignore_bind + (usize_sub self.hash_map_num_entries (int_to_usize 1)) + (Return (SOME x0)) + od + + [hash_map_try_resize_fwd_back_def] Definition + + ⊢ ∀self. + hash_map_try_resize_fwd_back self = + do + max_usize <- mk_usize (u32_to_int core_num_u32_max_c); + capacity <<- vec_len self.hash_map_slots; + n1 <- usize_div max_usize (int_to_usize 2); + (i,i0) <<- self.hash_map_max_load_factor; + i1 <- usize_div n1 i; + if usize_le capacity i1 then + do + i2 <- usize_mul capacity (int_to_usize 2); + ntable <- hash_map_new_with_capacity_fwd i2 i i0; + (ntable0,_) <- + hash_map_move_elements_fwd_back ntable + self.hash_map_slots (int_to_usize 0); + Return + (ntable0 with + <|hash_map_num_entries := self.hash_map_num_entries; + hash_map_max_load_factor := (i,i0)|>) + od + else Return (self with hash_map_max_load_factor := (i,i0)) + od + + [test1_fwd_def] Definition + + ⊢ test1_fwd = + do + hm <- hash_map_new_fwd; + hm0 <- + hash_map_insert_fwd_back hm (int_to_usize 0) (int_to_u64 42); + hm1 <- + hash_map_insert_fwd_back hm0 (int_to_usize 128) (int_to_u64 18); + hm2 <- + hash_map_insert_fwd_back hm1 (int_to_usize 1024) + (int_to_u64 138); + hm3 <- + hash_map_insert_fwd_back hm2 (int_to_usize 1056) + (int_to_u64 256); + i <- hash_map_get_fwd hm3 (int_to_usize 128); + if i ≠ int_to_u64 18 then Fail Failure + else + do + hm4 <- + hash_map_get_mut_back hm3 (int_to_usize 1024) + (int_to_u64 56); + i0 <- hash_map_get_fwd hm4 (int_to_usize 1024); + if i0 ≠ int_to_u64 56 then Fail Failure + else + do + x <- hash_map_remove_fwd hm4 (int_to_usize 1024); + case x of + NONE => Fail Failure + | SOME x0 => + if x0 ≠ int_to_u64 56 then Fail Failure + else + do + hm5 <- hash_map_remove_back hm4 (int_to_usize 1024); + i1 <- hash_map_get_fwd hm5 (int_to_usize 0); + if i1 ≠ int_to_u64 42 then Fail Failure + else + do + i2 <- hash_map_get_fwd hm5 (int_to_usize 128); + if i2 ≠ int_to_u64 18 then Fail Failure + else + do + i3 <- + hash_map_get_fwd hm5 (int_to_usize 1056); + if i3 ≠ int_to_u64 256 then Fail Failure + else Return () + od + od + od + od + od + od + + +*) +end diff --git a/tests/hol4/hashmap/hashmap_TypesScript.sml b/tests/hol4/hashmap/hashmap_TypesScript.sml new file mode 100644 index 00000000..a0865956 --- /dev/null +++ b/tests/hol4/hashmap/hashmap_TypesScript.sml @@ -0,0 +1,24 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap]: type definitions *) +open primitivesLib divDefLib + +val _ = new_theory "hashmap_Types" + + +Datatype: + (** [hashmap::List] *) + list_t = | ListCons usize 't list_t | ListNil +End + +Datatype: + (** [hashmap::HashMap] *) + hash_map_t = + <| + hash_map_num_entries : usize; + hash_map_max_load_factor : (usize # usize); + hash_map_max_load : usize; + hash_map_slots : 't list_t vec; + |> +End + +val _ = export_theory () diff --git a/tests/hol4/hashmap/hashmap_TypesTheory.sig b/tests/hol4/hashmap/hashmap_TypesTheory.sig new file mode 100644 index 00000000..4ad77ac5 --- /dev/null +++ b/tests/hol4/hashmap/hashmap_TypesTheory.sig @@ -0,0 +1,494 @@ +signature hashmap_TypesTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val hash_map_t_TY_DEF : thm + val hash_map_t_case_def : thm + val hash_map_t_size_def : thm + val list_t_TY_DEF : thm + val list_t_case_def : thm + val list_t_size_def : thm + val recordtype_hash_map_t_seldef_hash_map_max_load_def : thm + val recordtype_hash_map_t_seldef_hash_map_max_load_factor_def : thm + val recordtype_hash_map_t_seldef_hash_map_max_load_factor_fupd_def : thm + val recordtype_hash_map_t_seldef_hash_map_max_load_fupd_def : thm + val recordtype_hash_map_t_seldef_hash_map_num_entries_def : thm + val recordtype_hash_map_t_seldef_hash_map_num_entries_fupd_def : thm + val recordtype_hash_map_t_seldef_hash_map_slots_def : thm + val recordtype_hash_map_t_seldef_hash_map_slots_fupd_def : thm + + (* Theorems *) + val EXISTS_hash_map_t : thm + val FORALL_hash_map_t : thm + val datatype_hash_map_t : thm + val datatype_list_t : thm + val hash_map_t_11 : thm + val hash_map_t_Axiom : thm + val hash_map_t_accessors : thm + val hash_map_t_accfupds : thm + val hash_map_t_case_cong : thm + val hash_map_t_case_eq : thm + val hash_map_t_component_equality : thm + val hash_map_t_fn_updates : thm + val hash_map_t_fupdcanon : thm + val hash_map_t_fupdcanon_comp : thm + val hash_map_t_fupdfupds : thm + val hash_map_t_fupdfupds_comp : thm + val hash_map_t_induction : thm + val hash_map_t_literal_11 : thm + val hash_map_t_literal_nchotomy : thm + val hash_map_t_nchotomy : thm + val hash_map_t_updates_eq_literal : thm + val list_t_11 : thm + val list_t_Axiom : thm + val list_t_case_cong : thm + val list_t_case_eq : thm + val list_t_distinct : thm + val list_t_induction : thm + val list_t_nchotomy : thm + + val hashmap_Types_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "hashmap_Types" + + [hash_map_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('hash_map_t'). + (∀a0'. + (∃a0 a1 a2 a3. + a0' = + (λa0 a1 a2 a3. + ind_type$CONSTR 0 (a0,a1,a2,a3) + (λn. ind_type$BOTTOM)) a0 a1 a2 a3) ⇒ + $var$('hash_map_t') a0') ⇒ + $var$('hash_map_t') a0') rep + + [hash_map_t_case_def] Definition + + ⊢ ∀a0 a1 a2 a3 f. + hash_map_t_CASE (hash_map_t a0 a1 a2 a3) f = f a0 a1 a2 a3 + + [hash_map_t_size_def] Definition + + ⊢ ∀f a0 a1 a2 a3. + hash_map_t_size f (hash_map_t a0 a1 a2 a3) = + 1 + pair_size (λv. 0) (λv. 0) a1 + + [list_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('list_t'). + (∀a0'. + (∃a0 a1 a2. + a0' = + (λa0 a1 a2. + ind_type$CONSTR 0 (a0,a1) + (ind_type$FCONS a2 (λn. ind_type$BOTTOM))) + a0 a1 a2 ∧ $var$('list_t') a2) ∨ + a0' = + ind_type$CONSTR (SUC 0) (ARB,ARB) + (λn. ind_type$BOTTOM) ⇒ + $var$('list_t') a0') ⇒ + $var$('list_t') a0') rep + + [list_t_case_def] Definition + + ⊢ (∀a0 a1 a2 f v. list_t_CASE (ListCons a0 a1 a2) f v = f a0 a1 a2) ∧ + ∀f v. list_t_CASE ListNil f v = v + + [list_t_size_def] Definition + + ⊢ (∀f a0 a1 a2. + list_t_size f (ListCons a0 a1 a2) = + 1 + (f a1 + list_t_size f a2)) ∧ ∀f. list_t_size f ListNil = 0 + + [recordtype_hash_map_t_seldef_hash_map_max_load_def] Definition + + ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load = u0 + + [recordtype_hash_map_t_seldef_hash_map_max_load_factor_def] Definition + + ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load_factor = p + + [recordtype_hash_map_t_seldef_hash_map_max_load_factor_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hash_map_t u p u0 v with hash_map_max_load_factor updated_by f = + hash_map_t u (f p) u0 v + + [recordtype_hash_map_t_seldef_hash_map_max_load_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hash_map_t u p u0 v with hash_map_max_load updated_by f = + hash_map_t u p (f u0) v + + [recordtype_hash_map_t_seldef_hash_map_num_entries_def] Definition + + ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_num_entries = u + + [recordtype_hash_map_t_seldef_hash_map_num_entries_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hash_map_t u p u0 v with hash_map_num_entries updated_by f = + hash_map_t (f u) p u0 v + + [recordtype_hash_map_t_seldef_hash_map_slots_def] Definition + + ⊢ ∀u p u0 v. (hash_map_t u p u0 v).hash_map_slots = v + + [recordtype_hash_map_t_seldef_hash_map_slots_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hash_map_t u p u0 v with hash_map_slots updated_by f = + hash_map_t u p u0 (f v) + + [EXISTS_hash_map_t] Theorem + + ⊢ ∀P. (∃h. P h) ⇔ + ∃u0 p u v. + P + <|hash_map_num_entries := u0; + hash_map_max_load_factor := p; hash_map_max_load := u; + hash_map_slots := v|> + + [FORALL_hash_map_t] Theorem + + ⊢ ∀P. (∀h. P h) ⇔ + ∀u0 p u v. + P + <|hash_map_num_entries := u0; + hash_map_max_load_factor := p; hash_map_max_load := u; + hash_map_slots := v|> + + [datatype_hash_map_t] Theorem + + ⊢ DATATYPE + (record hash_map_t hash_map_num_entries hash_map_max_load_factor + hash_map_max_load hash_map_slots) + + [datatype_list_t] Theorem + + ⊢ DATATYPE (list_t ListCons ListNil) + + [hash_map_t_11] Theorem + + ⊢ ∀a0 a1 a2 a3 a0' a1' a2' a3'. + hash_map_t a0 a1 a2 a3 = hash_map_t a0' a1' a2' a3' ⇔ + a0 = a0' ∧ a1 = a1' ∧ a2 = a2' ∧ a3 = a3' + + [hash_map_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a0 a1 a2 a3. fn (hash_map_t a0 a1 a2 a3) = f a0 a1 a2 a3 + + [hash_map_t_accessors] Theorem + + ⊢ (∀u p u0 v. (hash_map_t u p u0 v).hash_map_num_entries = u) ∧ + (∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load_factor = p) ∧ + (∀u p u0 v. (hash_map_t u p u0 v).hash_map_max_load = u0) ∧ + ∀u p u0 v. (hash_map_t u p u0 v).hash_map_slots = v + + [hash_map_t_accfupds] Theorem + + ⊢ (∀h f. + (h with hash_map_max_load_factor updated_by f). + hash_map_num_entries = + h.hash_map_num_entries) ∧ + (∀h f. + (h with hash_map_max_load updated_by f).hash_map_num_entries = + h.hash_map_num_entries) ∧ + (∀h f. + (h with hash_map_slots updated_by f).hash_map_num_entries = + h.hash_map_num_entries) ∧ + (∀h f. + (h with hash_map_num_entries updated_by f). + hash_map_max_load_factor = + h.hash_map_max_load_factor) ∧ + (∀h f. + (h with hash_map_max_load updated_by f).hash_map_max_load_factor = + h.hash_map_max_load_factor) ∧ + (∀h f. + (h with hash_map_slots updated_by f).hash_map_max_load_factor = + h.hash_map_max_load_factor) ∧ + (∀h f. + (h with hash_map_num_entries updated_by f).hash_map_max_load = + h.hash_map_max_load) ∧ + (∀h f. + (h with hash_map_max_load_factor updated_by f).hash_map_max_load = + h.hash_map_max_load) ∧ + (∀h f. + (h with hash_map_slots updated_by f).hash_map_max_load = + h.hash_map_max_load) ∧ + (∀h f. + (h with hash_map_num_entries updated_by f).hash_map_slots = + h.hash_map_slots) ∧ + (∀h f. + (h with hash_map_max_load_factor updated_by f).hash_map_slots = + h.hash_map_slots) ∧ + (∀h f. + (h with hash_map_max_load updated_by f).hash_map_slots = + h.hash_map_slots) ∧ + (∀h f. + (h with hash_map_num_entries updated_by f).hash_map_num_entries = + f h.hash_map_num_entries) ∧ + (∀h f. + (h with hash_map_max_load_factor updated_by f). + hash_map_max_load_factor = + f h.hash_map_max_load_factor) ∧ + (∀h f. + (h with hash_map_max_load updated_by f).hash_map_max_load = + f h.hash_map_max_load) ∧ + ∀h f. + (h with hash_map_slots updated_by f).hash_map_slots = + f h.hash_map_slots + + [hash_map_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ + (∀a0 a1 a2 a3. + M' = hash_map_t a0 a1 a2 a3 ⇒ f a0 a1 a2 a3 = f' a0 a1 a2 a3) ⇒ + hash_map_t_CASE M f = hash_map_t_CASE M' f' + + [hash_map_t_case_eq] Theorem + + ⊢ hash_map_t_CASE x f = v ⇔ + ∃u p u0 v'. x = hash_map_t u p u0 v' ∧ f u p u0 v' = v + + [hash_map_t_component_equality] Theorem + + ⊢ ∀h1 h2. + h1 = h2 ⇔ + h1.hash_map_num_entries = h2.hash_map_num_entries ∧ + h1.hash_map_max_load_factor = h2.hash_map_max_load_factor ∧ + h1.hash_map_max_load = h2.hash_map_max_load ∧ + h1.hash_map_slots = h2.hash_map_slots + + [hash_map_t_fn_updates] Theorem + + ⊢ (∀f u p u0 v. + hash_map_t u p u0 v with hash_map_num_entries updated_by f = + hash_map_t (f u) p u0 v) ∧ + (∀f u p u0 v. + hash_map_t u p u0 v with hash_map_max_load_factor updated_by f = + hash_map_t u (f p) u0 v) ∧ + (∀f u p u0 v. + hash_map_t u p u0 v with hash_map_max_load updated_by f = + hash_map_t u p (f u0) v) ∧ + ∀f u p u0 v. + hash_map_t u p u0 v with hash_map_slots updated_by f = + hash_map_t u p u0 (f v) + + [hash_map_t_fupdcanon] Theorem + + ⊢ (∀h g f. + h with + <|hash_map_max_load_factor updated_by f; + hash_map_num_entries updated_by g|> = + h with + <|hash_map_num_entries updated_by g; + hash_map_max_load_factor updated_by f|>) ∧ + (∀h g f. + h with + <|hash_map_max_load updated_by f; + hash_map_num_entries updated_by g|> = + h with + <|hash_map_num_entries updated_by g; + hash_map_max_load updated_by f|>) ∧ + (∀h g f. + h with + <|hash_map_max_load updated_by f; + hash_map_max_load_factor updated_by g|> = + h with + <|hash_map_max_load_factor updated_by g; + hash_map_max_load updated_by f|>) ∧ + (∀h g f. + h with + <|hash_map_slots updated_by f; + hash_map_num_entries updated_by g|> = + h with + <|hash_map_num_entries updated_by g; + hash_map_slots updated_by f|>) ∧ + (∀h g f. + h with + <|hash_map_slots updated_by f; + hash_map_max_load_factor updated_by g|> = + h with + <|hash_map_max_load_factor updated_by g; + hash_map_slots updated_by f|>) ∧ + ∀h g f. + h with + <|hash_map_slots updated_by f; hash_map_max_load updated_by g|> = + h with + <|hash_map_max_load updated_by g; hash_map_slots updated_by f|> + + [hash_map_t_fupdcanon_comp] Theorem + + ⊢ ((∀g f. + hash_map_max_load_factor_fupd f ∘ hash_map_num_entries_fupd g = + hash_map_num_entries_fupd g ∘ hash_map_max_load_factor_fupd f) ∧ + ∀h g f. + hash_map_max_load_factor_fupd f ∘ hash_map_num_entries_fupd g ∘ + h = + hash_map_num_entries_fupd g ∘ hash_map_max_load_factor_fupd f ∘ + h) ∧ + ((∀g f. + hash_map_max_load_fupd f ∘ hash_map_num_entries_fupd g = + hash_map_num_entries_fupd g ∘ hash_map_max_load_fupd f) ∧ + ∀h g f. + hash_map_max_load_fupd f ∘ hash_map_num_entries_fupd g ∘ h = + hash_map_num_entries_fupd g ∘ hash_map_max_load_fupd f ∘ h) ∧ + ((∀g f. + hash_map_max_load_fupd f ∘ hash_map_max_load_factor_fupd g = + hash_map_max_load_factor_fupd g ∘ hash_map_max_load_fupd f) ∧ + ∀h g f. + hash_map_max_load_fupd f ∘ hash_map_max_load_factor_fupd g ∘ h = + hash_map_max_load_factor_fupd g ∘ hash_map_max_load_fupd f ∘ h) ∧ + ((∀g f. + hash_map_slots_fupd f ∘ hash_map_num_entries_fupd g = + hash_map_num_entries_fupd g ∘ hash_map_slots_fupd f) ∧ + ∀h g f. + hash_map_slots_fupd f ∘ hash_map_num_entries_fupd g ∘ h = + hash_map_num_entries_fupd g ∘ hash_map_slots_fupd f ∘ h) ∧ + ((∀g f. + hash_map_slots_fupd f ∘ hash_map_max_load_factor_fupd g = + hash_map_max_load_factor_fupd g ∘ hash_map_slots_fupd f) ∧ + ∀h g f. + hash_map_slots_fupd f ∘ hash_map_max_load_factor_fupd g ∘ h = + hash_map_max_load_factor_fupd g ∘ hash_map_slots_fupd f ∘ h) ∧ + (∀g f. + hash_map_slots_fupd f ∘ hash_map_max_load_fupd g = + hash_map_max_load_fupd g ∘ hash_map_slots_fupd f) ∧ + ∀h g f. + hash_map_slots_fupd f ∘ hash_map_max_load_fupd g ∘ h = + hash_map_max_load_fupd g ∘ hash_map_slots_fupd f ∘ h + + [hash_map_t_fupdfupds] Theorem + + ⊢ (∀h g f. + h with + <|hash_map_num_entries updated_by f; + hash_map_num_entries updated_by g|> = + h with hash_map_num_entries updated_by f ∘ g) ∧ + (∀h g f. + h with + <|hash_map_max_load_factor updated_by f; + hash_map_max_load_factor updated_by g|> = + h with hash_map_max_load_factor updated_by f ∘ g) ∧ + (∀h g f. + h with + <|hash_map_max_load updated_by f; + hash_map_max_load updated_by g|> = + h with hash_map_max_load updated_by f ∘ g) ∧ + ∀h g f. + h with + <|hash_map_slots updated_by f; hash_map_slots updated_by g|> = + h with hash_map_slots updated_by f ∘ g + + [hash_map_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. + hash_map_num_entries_fupd f ∘ hash_map_num_entries_fupd g = + hash_map_num_entries_fupd (f ∘ g)) ∧ + ∀h g f. + hash_map_num_entries_fupd f ∘ hash_map_num_entries_fupd g ∘ h = + hash_map_num_entries_fupd (f ∘ g) ∘ h) ∧ + ((∀g f. + hash_map_max_load_factor_fupd f ∘ + hash_map_max_load_factor_fupd g = + hash_map_max_load_factor_fupd (f ∘ g)) ∧ + ∀h g f. + hash_map_max_load_factor_fupd f ∘ + hash_map_max_load_factor_fupd g ∘ h = + hash_map_max_load_factor_fupd (f ∘ g) ∘ h) ∧ + ((∀g f. + hash_map_max_load_fupd f ∘ hash_map_max_load_fupd g = + hash_map_max_load_fupd (f ∘ g)) ∧ + ∀h g f. + hash_map_max_load_fupd f ∘ hash_map_max_load_fupd g ∘ h = + hash_map_max_load_fupd (f ∘ g) ∘ h) ∧ + (∀g f. + hash_map_slots_fupd f ∘ hash_map_slots_fupd g = + hash_map_slots_fupd (f ∘ g)) ∧ + ∀h g f. + hash_map_slots_fupd f ∘ hash_map_slots_fupd g ∘ h = + hash_map_slots_fupd (f ∘ g) ∘ h + + [hash_map_t_induction] Theorem + + ⊢ ∀P. (∀u p u0 v. P (hash_map_t u p u0 v)) ⇒ ∀h. P h + + [hash_map_t_literal_11] Theorem + + ⊢ ∀u01 p1 u1 v1 u02 p2 u2 v2. + <|hash_map_num_entries := u01; hash_map_max_load_factor := p1; + hash_map_max_load := u1; hash_map_slots := v1|> = + <|hash_map_num_entries := u02; hash_map_max_load_factor := p2; + hash_map_max_load := u2; hash_map_slots := v2|> ⇔ + u01 = u02 ∧ p1 = p2 ∧ u1 = u2 ∧ v1 = v2 + + [hash_map_t_literal_nchotomy] Theorem + + ⊢ ∀h. ∃u0 p u v. + h = + <|hash_map_num_entries := u0; hash_map_max_load_factor := p; + hash_map_max_load := u; hash_map_slots := v|> + + [hash_map_t_nchotomy] Theorem + + ⊢ ∀hh. ∃u p u0 v. hh = hash_map_t u p u0 v + + [hash_map_t_updates_eq_literal] Theorem + + ⊢ ∀h u0 p u v. + h with + <|hash_map_num_entries := u0; hash_map_max_load_factor := p; + hash_map_max_load := u; hash_map_slots := v|> = + <|hash_map_num_entries := u0; hash_map_max_load_factor := p; + hash_map_max_load := u; hash_map_slots := v|> + + [list_t_11] Theorem + + ⊢ ∀a0 a1 a2 a0' a1' a2'. + ListCons a0 a1 a2 = ListCons a0' a1' a2' ⇔ + a0 = a0' ∧ a1 = a1' ∧ a2 = a2' + + [list_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a0 a1 a2. fn (ListCons a0 a1 a2) = f0 a0 a1 a2 (fn a2)) ∧ + fn ListNil = f1 + + [list_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ + (∀a0 a1 a2. M' = ListCons a0 a1 a2 ⇒ f a0 a1 a2 = f' a0 a1 a2) ∧ + (M' = ListNil ⇒ v = v') ⇒ + list_t_CASE M f v = list_t_CASE M' f' v' + + [list_t_case_eq] Theorem + + ⊢ list_t_CASE x f v = v' ⇔ + (∃u t l. x = ListCons u t l ∧ f u t l = v') ∨ x = ListNil ∧ v = v' + + [list_t_distinct] Theorem + + ⊢ ∀a2 a1 a0. ListCons a0 a1 a2 ≠ ListNil + + [list_t_induction] Theorem + + ⊢ ∀P. (∀l. P l ⇒ ∀t u. P (ListCons u t l)) ∧ P ListNil ⇒ ∀l. P l + + [list_t_nchotomy] Theorem + + ⊢ ∀ll. (∃u t l. ll = ListCons u t l) ∨ ll = ListNil + + +*) +end diff --git a/tests/hol4/hashmap_on_disk/Holmakefile b/tests/hol4/hashmap_on_disk/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/hashmap_on_disk/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml new file mode 100644 index 00000000..5a8f7ff8 --- /dev/null +++ b/tests/hol4/hashmap_on_disk/hashmapMain_FunsScript.sml @@ -0,0 +1,646 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: function definitions *) +open primitivesLib divDefLib +open hashmapMain_TypesTheory hashmapMain_OpaqueTheory + +val _ = new_theory "hashmapMain_Funs" + + +val hashmap_hash_key_fwd_def = Define ‘ + (** [hashmap_main::hashmap::hash_key] *) + hashmap_hash_key_fwd (k : usize) : usize result = + Return k +’ + +val [hashmap_hash_map_allocate_slots_loop_fwd_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *) + hashmap_hash_map_allocate_slots_loop_fwd + (slots : 't hashmap_list_t vec) (n : usize) : + 't hashmap_list_t vec result + = + if usize_gt n (int_to_usize 0) + then ( + do + slots0 <- vec_push_back slots HashmapListNil; + n0 <- usize_sub n (int_to_usize 1); + hashmap_hash_map_allocate_slots_loop_fwd slots0 n0 + od) + else Return slots +’ + +val hashmap_hash_map_allocate_slots_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::allocate_slots] *) + hashmap_hash_map_allocate_slots_fwd + (slots : 't hashmap_list_t vec) (n : usize) : + 't hashmap_list_t vec result + = + hashmap_hash_map_allocate_slots_loop_fwd slots n +’ + +val hashmap_hash_map_new_with_capacity_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] *) + hashmap_hash_map_new_with_capacity_fwd + (capacity : usize) (max_load_dividend : usize) (max_load_divisor : usize) : + 't hashmap_hash_map_t result + = + let v = vec_new in + do + slots <- hashmap_hash_map_allocate_slots_fwd v capacity; + i <- usize_mul capacity max_load_dividend; + i0 <- usize_div i max_load_divisor; + Return + (<| + hashmap_hash_map_num_entries := (int_to_usize 0); + hashmap_hash_map_max_load_factor := + (max_load_dividend, max_load_divisor); + hashmap_hash_map_max_load := i0; + hashmap_hash_map_slots := slots + |>) + od +’ + +val hashmap_hash_map_new_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::new] *) + hashmap_hash_map_new_fwd : 't hashmap_hash_map_t result = + hashmap_hash_map_new_with_capacity_fwd (int_to_usize 32) (int_to_usize 4) + (int_to_usize 5) +’ + +val [hashmap_hash_map_clear_loop_fwd_back_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::clear] *) + hashmap_hash_map_clear_loop_fwd_back + (slots : 't hashmap_list_t vec) (i : usize) : + 't hashmap_list_t vec result + = + let i0 = vec_len slots in + if usize_lt i i0 + then ( + do + i1 <- usize_add i (int_to_usize 1); + slots0 <- vec_index_mut_back slots i HashmapListNil; + hashmap_hash_map_clear_loop_fwd_back slots0 i1 + od) + else Return slots +’ + +val hashmap_hash_map_clear_fwd_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::clear] *) + hashmap_hash_map_clear_fwd_back + (self : 't hashmap_hash_map_t) : 't hashmap_hash_map_t result = + do + v <- + hashmap_hash_map_clear_loop_fwd_back self.hashmap_hash_map_slots + (int_to_usize 0); + Return + (self + with + <| + hashmap_hash_map_num_entries := (int_to_usize 0); + hashmap_hash_map_slots := v + |>) + od +’ + +val hashmap_hash_map_len_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::len] *) + hashmap_hash_map_len_fwd (self : 't hashmap_hash_map_t) : usize result = + Return self.hashmap_hash_map_num_entries +’ + +val [hashmap_hash_map_insert_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *) + hashmap_hash_map_insert_in_list_loop_fwd + (key : usize) (value : 't) (ls : 't hashmap_list_t) : bool result = + (case ls of + | HashmapListCons ckey cvalue tl => + if ckey = key + then Return F + else hashmap_hash_map_insert_in_list_loop_fwd key value tl + | HashmapListNil => Return T) +’ + +val hashmap_hash_map_insert_in_list_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *) + hashmap_hash_map_insert_in_list_fwd + (key : usize) (value : 't) (ls : 't hashmap_list_t) : bool result = + hashmap_hash_map_insert_in_list_loop_fwd key value ls +’ + +val [hashmap_hash_map_insert_in_list_loop_back_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *) + hashmap_hash_map_insert_in_list_loop_back + (key : usize) (value : 't) (ls : 't hashmap_list_t) : + 't hashmap_list_t result + = + (case ls of + | HashmapListCons ckey cvalue tl => + if ckey = key + then Return (HashmapListCons ckey value tl) + else ( + do + tl0 <- hashmap_hash_map_insert_in_list_loop_back key value tl; + Return (HashmapListCons ckey cvalue tl0) + od) + | HashmapListNil => + let l = HashmapListNil in Return (HashmapListCons key value l)) +’ + +val hashmap_hash_map_insert_in_list_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::insert_in_list] *) + hashmap_hash_map_insert_in_list_back + (key : usize) (value : 't) (ls : 't hashmap_list_t) : + 't hashmap_list_t result + = + hashmap_hash_map_insert_in_list_loop_back key value ls +’ + +val hashmap_hash_map_insert_no_resize_fwd_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] *) + hashmap_hash_map_insert_no_resize_fwd_back + (self : 't hashmap_hash_map_t) (key : usize) (value : 't) : + 't hashmap_hash_map_t result + = + do + hash <- hashmap_hash_key_fwd key; + let i = vec_len self.hashmap_hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + inserted <- hashmap_hash_map_insert_in_list_fwd key value l; + if inserted + then ( + do + i0 <- usize_add self.hashmap_hash_map_num_entries (int_to_usize 1); + l0 <- hashmap_hash_map_insert_in_list_back key value l; + v <- vec_index_mut_back self.hashmap_hash_map_slots hash_mod l0; + Return + (self + with + <| + hashmap_hash_map_num_entries := i0; hashmap_hash_map_slots := v + |>) + od) + else ( + do + l0 <- hashmap_hash_map_insert_in_list_back key value l; + v <- vec_index_mut_back self.hashmap_hash_map_slots hash_mod l0; + Return (self with <| hashmap_hash_map_slots := v |>) + od) + od + od +’ + +(** [core::num::u32::{9}::MAX] *) +Definition core_num_u32_max_body_def: + core_num_u32_max_body : u32 result = Return (int_to_u32 4294967295) +End +Definition core_num_u32_max_c_def: + core_num_u32_max_c : u32 = get_return_value core_num_u32_max_body +End + +val [hashmap_hash_map_move_elements_from_list_loop_fwd_back_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *) + hashmap_hash_map_move_elements_from_list_loop_fwd_back + (ntable : 't hashmap_hash_map_t) (ls : 't hashmap_list_t) : + 't hashmap_hash_map_t result + = + (case ls of + | HashmapListCons k v tl => + do + ntable0 <- hashmap_hash_map_insert_no_resize_fwd_back ntable k v; + hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable0 tl + od + | HashmapListNil => Return ntable) +’ + +val hashmap_hash_map_move_elements_from_list_fwd_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] *) + hashmap_hash_map_move_elements_from_list_fwd_back + (ntable : 't hashmap_hash_map_t) (ls : 't hashmap_list_t) : + 't hashmap_hash_map_t result + = + hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable ls +’ + +val [hashmap_hash_map_move_elements_loop_fwd_back_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::move_elements] *) + hashmap_hash_map_move_elements_loop_fwd_back + (ntable : 't hashmap_hash_map_t) (slots : 't hashmap_list_t vec) + (i : usize) : + ('t hashmap_hash_map_t # 't hashmap_list_t vec) result + = + let i0 = vec_len slots in + if usize_lt i i0 + then ( + do + l <- vec_index_mut_fwd slots i; + let ls = mem_replace_fwd l HashmapListNil in + do + ntable0 <- hashmap_hash_map_move_elements_from_list_fwd_back ntable ls; + i1 <- usize_add i (int_to_usize 1); + let l0 = mem_replace_back l HashmapListNil in + do + slots0 <- vec_index_mut_back slots i l0; + hashmap_hash_map_move_elements_loop_fwd_back ntable0 slots0 i1 + od + od + od) + else Return (ntable, slots) +’ + +val hashmap_hash_map_move_elements_fwd_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::move_elements] *) + hashmap_hash_map_move_elements_fwd_back + (ntable : 't hashmap_hash_map_t) (slots : 't hashmap_list_t vec) + (i : usize) : + ('t hashmap_hash_map_t # 't hashmap_list_t vec) result + = + hashmap_hash_map_move_elements_loop_fwd_back ntable slots i +’ + +val hashmap_hash_map_try_resize_fwd_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::try_resize] *) + hashmap_hash_map_try_resize_fwd_back + (self : 't hashmap_hash_map_t) : 't hashmap_hash_map_t result = + do + max_usize <- mk_usize (u32_to_int core_num_u32_max_c); + let capacity = vec_len self.hashmap_hash_map_slots in + do + n1 <- usize_div max_usize (int_to_usize 2); + let (i, i0) = self.hashmap_hash_map_max_load_factor in + do + i1 <- usize_div n1 i; + if usize_le capacity i1 + then ( + do + i2 <- usize_mul capacity (int_to_usize 2); + ntable <- hashmap_hash_map_new_with_capacity_fwd i2 i i0; + (ntable0, _) <- + hashmap_hash_map_move_elements_fwd_back ntable + self.hashmap_hash_map_slots (int_to_usize 0); + Return + (ntable0 + with + <| + hashmap_hash_map_num_entries := self.hashmap_hash_map_num_entries; + hashmap_hash_map_max_load_factor := (i, i0) + |>) + od) + else Return (self with <| hashmap_hash_map_max_load_factor := (i, i0) |>) + od + od + od +’ + +val hashmap_hash_map_insert_fwd_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::insert] *) + hashmap_hash_map_insert_fwd_back + (self : 't hashmap_hash_map_t) (key : usize) (value : 't) : + 't hashmap_hash_map_t result + = + do + self0 <- hashmap_hash_map_insert_no_resize_fwd_back self key value; + i <- hashmap_hash_map_len_fwd self0; + if usize_gt i self0.hashmap_hash_map_max_load + then hashmap_hash_map_try_resize_fwd_back self0 + else Return self0 + od +’ + +val [hashmap_hash_map_contains_key_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *) + hashmap_hash_map_contains_key_in_list_loop_fwd + (key : usize) (ls : 't hashmap_list_t) : bool result = + (case ls of + | HashmapListCons ckey t tl => + if ckey = key + then Return T + else hashmap_hash_map_contains_key_in_list_loop_fwd key tl + | HashmapListNil => Return F) +’ + +val hashmap_hash_map_contains_key_in_list_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] *) + hashmap_hash_map_contains_key_in_list_fwd + (key : usize) (ls : 't hashmap_list_t) : bool result = + hashmap_hash_map_contains_key_in_list_loop_fwd key ls +’ + +val hashmap_hash_map_contains_key_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::contains_key] *) + hashmap_hash_map_contains_key_fwd + (self : 't hashmap_hash_map_t) (key : usize) : bool result = + do + hash <- hashmap_hash_key_fwd key; + let i = vec_len self.hashmap_hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hashmap_hash_map_slots hash_mod; + hashmap_hash_map_contains_key_in_list_fwd key l + od + od +’ + +val [hashmap_hash_map_get_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *) + hashmap_hash_map_get_in_list_loop_fwd + (key : usize) (ls : 't hashmap_list_t) : 't result = + (case ls of + | HashmapListCons ckey cvalue tl => + if ckey = key + then Return cvalue + else hashmap_hash_map_get_in_list_loop_fwd key tl + | HashmapListNil => Fail Failure) +’ + +val hashmap_hash_map_get_in_list_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_in_list] *) + hashmap_hash_map_get_in_list_fwd + (key : usize) (ls : 't hashmap_list_t) : 't result = + hashmap_hash_map_get_in_list_loop_fwd key ls +’ + +val hashmap_hash_map_get_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get] *) + hashmap_hash_map_get_fwd + (self : 't hashmap_hash_map_t) (key : usize) : 't result = + do + hash <- hashmap_hash_key_fwd key; + let i = vec_len self.hashmap_hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hashmap_hash_map_slots hash_mod; + hashmap_hash_map_get_in_list_fwd key l + od + od +’ + +val [hashmap_hash_map_get_mut_in_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *) + hashmap_hash_map_get_mut_in_list_loop_fwd + (ls : 't hashmap_list_t) (key : usize) : 't result = + (case ls of + | HashmapListCons ckey cvalue tl => + if ckey = key + then Return cvalue + else hashmap_hash_map_get_mut_in_list_loop_fwd tl key + | HashmapListNil => Fail Failure) +’ + +val hashmap_hash_map_get_mut_in_list_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *) + hashmap_hash_map_get_mut_in_list_fwd + (ls : 't hashmap_list_t) (key : usize) : 't result = + hashmap_hash_map_get_mut_in_list_loop_fwd ls key +’ + +val [hashmap_hash_map_get_mut_in_list_loop_back_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *) + hashmap_hash_map_get_mut_in_list_loop_back + (ls : 't hashmap_list_t) (key : usize) (ret : 't) : + 't hashmap_list_t result + = + (case ls of + | HashmapListCons ckey cvalue tl => + if ckey = key + then Return (HashmapListCons ckey ret tl) + else ( + do + tl0 <- hashmap_hash_map_get_mut_in_list_loop_back tl key ret; + Return (HashmapListCons ckey cvalue tl0) + od) + | HashmapListNil => Fail Failure) +’ + +val hashmap_hash_map_get_mut_in_list_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] *) + hashmap_hash_map_get_mut_in_list_back + (ls : 't hashmap_list_t) (key : usize) (ret : 't) : + 't hashmap_list_t result + = + hashmap_hash_map_get_mut_in_list_loop_back ls key ret +’ + +val hashmap_hash_map_get_mut_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_mut] *) + hashmap_hash_map_get_mut_fwd + (self : 't hashmap_hash_map_t) (key : usize) : 't result = + do + hash <- hashmap_hash_key_fwd key; + let i = vec_len self.hashmap_hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + hashmap_hash_map_get_mut_in_list_fwd l key + od + od +’ + +val hashmap_hash_map_get_mut_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::get_mut] *) + hashmap_hash_map_get_mut_back + (self : 't hashmap_hash_map_t) (key : usize) (ret : 't) : + 't hashmap_hash_map_t result + = + do + hash <- hashmap_hash_key_fwd key; + let i = vec_len self.hashmap_hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + l0 <- hashmap_hash_map_get_mut_in_list_back l key ret; + v <- vec_index_mut_back self.hashmap_hash_map_slots hash_mod l0; + Return (self with <| hashmap_hash_map_slots := v |>) + od + od +’ + +val [hashmap_hash_map_remove_from_list_loop_fwd_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *) + hashmap_hash_map_remove_from_list_loop_fwd + (key : usize) (ls : 't hashmap_list_t) : 't option result = + (case ls of + | HashmapListCons ckey t tl => + if ckey = key + then + let mv_ls = mem_replace_fwd (HashmapListCons ckey t tl) HashmapListNil + in + (case mv_ls of + | HashmapListCons i cvalue tl0 => Return (SOME cvalue) + | HashmapListNil => Fail Failure) + else hashmap_hash_map_remove_from_list_loop_fwd key tl + | HashmapListNil => Return NONE) +’ + +val hashmap_hash_map_remove_from_list_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *) + hashmap_hash_map_remove_from_list_fwd + (key : usize) (ls : 't hashmap_list_t) : 't option result = + hashmap_hash_map_remove_from_list_loop_fwd key ls +’ + +val [hashmap_hash_map_remove_from_list_loop_back_def] = DefineDiv ‘ + (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *) + hashmap_hash_map_remove_from_list_loop_back + (key : usize) (ls : 't hashmap_list_t) : 't hashmap_list_t result = + (case ls of + | HashmapListCons ckey t tl => + if ckey = key + then + let mv_ls = mem_replace_fwd (HashmapListCons ckey t tl) HashmapListNil + in + (case mv_ls of + | HashmapListCons i cvalue tl0 => Return tl0 + | HashmapListNil => Fail Failure) + else ( + do + tl0 <- hashmap_hash_map_remove_from_list_loop_back key tl; + Return (HashmapListCons ckey t tl0) + od) + | HashmapListNil => Return HashmapListNil) +’ + +val hashmap_hash_map_remove_from_list_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::remove_from_list] *) + hashmap_hash_map_remove_from_list_back + (key : usize) (ls : 't hashmap_list_t) : 't hashmap_list_t result = + hashmap_hash_map_remove_from_list_loop_back key ls +’ + +val hashmap_hash_map_remove_fwd_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::remove] *) + hashmap_hash_map_remove_fwd + (self : 't hashmap_hash_map_t) (key : usize) : 't option result = + do + hash <- hashmap_hash_key_fwd key; + let i = vec_len self.hashmap_hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + x <- hashmap_hash_map_remove_from_list_fwd key l; + (case x of + | NONE => Return NONE + | SOME x0 => + do + _ <- usize_sub self.hashmap_hash_map_num_entries (int_to_usize 1); + Return (SOME x0) + od) + od + od +’ + +val hashmap_hash_map_remove_back_def = Define ‘ + (** [hashmap_main::hashmap::HashMap::{0}::remove] *) + hashmap_hash_map_remove_back + (self : 't hashmap_hash_map_t) (key : usize) : + 't hashmap_hash_map_t result + = + do + hash <- hashmap_hash_key_fwd key; + let i = vec_len self.hashmap_hash_map_slots in + do + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + x <- hashmap_hash_map_remove_from_list_fwd key l; + (case x of + | NONE => + do + l0 <- hashmap_hash_map_remove_from_list_back key l; + v <- vec_index_mut_back self.hashmap_hash_map_slots hash_mod l0; + Return (self with <| hashmap_hash_map_slots := v |>) + od + | SOME x0 => + do + i0 <- usize_sub self.hashmap_hash_map_num_entries (int_to_usize 1); + l0 <- hashmap_hash_map_remove_from_list_back key l; + v <- vec_index_mut_back self.hashmap_hash_map_slots hash_mod l0; + Return + (self + with + <| + hashmap_hash_map_num_entries := i0; hashmap_hash_map_slots := v + |>) + od) + od + od +’ + +val hashmap_test1_fwd_def = Define ‘ + (** [hashmap_main::hashmap::test1] *) + hashmap_test1_fwd : unit result = + do + hm <- hashmap_hash_map_new_fwd; + hm0 <- + hashmap_hash_map_insert_fwd_back hm (int_to_usize 0) (int_to_u64 42); + hm1 <- + hashmap_hash_map_insert_fwd_back hm0 (int_to_usize 128) (int_to_u64 18); + hm2 <- + hashmap_hash_map_insert_fwd_back hm1 (int_to_usize 1024) (int_to_u64 138); + hm3 <- + hashmap_hash_map_insert_fwd_back hm2 (int_to_usize 1056) (int_to_u64 256); + i <- hashmap_hash_map_get_fwd hm3 (int_to_usize 128); + if ~ (i = int_to_u64 18) + then Fail Failure + else ( + do + hm4 <- + hashmap_hash_map_get_mut_back hm3 (int_to_usize 1024) (int_to_u64 56); + i0 <- hashmap_hash_map_get_fwd hm4 (int_to_usize 1024); + if ~ (i0 = int_to_u64 56) + then Fail Failure + else ( + do + x <- hashmap_hash_map_remove_fwd hm4 (int_to_usize 1024); + (case x of + | NONE => Fail Failure + | SOME x0 => + if ~ (x0 = int_to_u64 56) + then Fail Failure + else ( + do + hm5 <- hashmap_hash_map_remove_back hm4 (int_to_usize 1024); + i1 <- hashmap_hash_map_get_fwd hm5 (int_to_usize 0); + if ~ (i1 = int_to_u64 42) + then Fail Failure + else ( + do + i2 <- hashmap_hash_map_get_fwd hm5 (int_to_usize 128); + if ~ (i2 = int_to_u64 18) + then Fail Failure + else ( + do + i3 <- hashmap_hash_map_get_fwd hm5 (int_to_usize 1056); + if ~ (i3 = int_to_u64 256) then Fail Failure else Return () + od) + od) + od)) + od) + od) + od +’ + +(** Unit test for [hashmap_main::hashmap::test1] *) +val _ = assert_return (“hashmap_test1_fwd”) + +val insert_on_disk_fwd_def = Define ‘ + (** [hashmap_main::insert_on_disk] *) + insert_on_disk_fwd + (key : usize) (value : u64) (st : state) : (state # unit) result = + do + (st0, hm) <- hashmap_utils_deserialize_fwd st; + hm0 <- hashmap_hash_map_insert_fwd_back hm key value; + (st1, _) <- hashmap_utils_serialize_fwd hm0 st0; + Return (st1, ()) + od +’ + +val main_fwd_def = Define ‘ + (** [hashmap_main::main] *) + main_fwd : unit result = + Return () +’ + +(** Unit test for [hashmap_main::main] *) +val _ = assert_return (“main_fwd”) + +val _ = export_theory () diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_FunsTheory.sig b/tests/hol4/hashmap_on_disk/hashmapMain_FunsTheory.sig new file mode 100644 index 00000000..1d24cb26 --- /dev/null +++ b/tests/hol4/hashmap_on_disk/hashmapMain_FunsTheory.sig @@ -0,0 +1,608 @@ +signature hashmapMain_FunsTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val core_num_u32_max_body_def : thm + val core_num_u32_max_c_def : thm + val hashmap_hash_key_fwd_def : thm + val hashmap_hash_map_allocate_slots_fwd_def : thm + val hashmap_hash_map_allocate_slots_loop_fwd_def : thm + val hashmap_hash_map_clear_fwd_back_def : thm + val hashmap_hash_map_clear_loop_fwd_back_def : thm + val hashmap_hash_map_contains_key_fwd_def : thm + val hashmap_hash_map_contains_key_in_list_fwd_def : thm + val hashmap_hash_map_contains_key_in_list_loop_fwd_def : thm + val hashmap_hash_map_get_fwd_def : thm + val hashmap_hash_map_get_in_list_fwd_def : thm + val hashmap_hash_map_get_in_list_loop_fwd_def : thm + val hashmap_hash_map_get_mut_back_def : thm + val hashmap_hash_map_get_mut_fwd_def : thm + val hashmap_hash_map_get_mut_in_list_back_def : thm + val hashmap_hash_map_get_mut_in_list_fwd_def : thm + val hashmap_hash_map_get_mut_in_list_loop_back_def : thm + val hashmap_hash_map_get_mut_in_list_loop_fwd_def : thm + val hashmap_hash_map_insert_fwd_back_def : thm + val hashmap_hash_map_insert_in_list_back_def : thm + val hashmap_hash_map_insert_in_list_fwd_def : thm + val hashmap_hash_map_insert_in_list_loop_back_def : thm + val hashmap_hash_map_insert_in_list_loop_fwd_def : thm + val hashmap_hash_map_insert_no_resize_fwd_back_def : thm + val hashmap_hash_map_len_fwd_def : thm + val hashmap_hash_map_move_elements_from_list_fwd_back_def : thm + val hashmap_hash_map_move_elements_from_list_loop_fwd_back_def : thm + val hashmap_hash_map_move_elements_fwd_back_def : thm + val hashmap_hash_map_move_elements_loop_fwd_back_def : thm + val hashmap_hash_map_new_fwd_def : thm + val hashmap_hash_map_new_with_capacity_fwd_def : thm + val hashmap_hash_map_remove_back_def : thm + val hashmap_hash_map_remove_from_list_back_def : thm + val hashmap_hash_map_remove_from_list_fwd_def : thm + val hashmap_hash_map_remove_from_list_loop_back_def : thm + val hashmap_hash_map_remove_from_list_loop_fwd_def : thm + val hashmap_hash_map_remove_fwd_def : thm + val hashmap_hash_map_try_resize_fwd_back_def : thm + val hashmap_test1_fwd_def : thm + val insert_on_disk_fwd_def : thm + val main_fwd_def : thm + + val hashmapMain_Funs_grammars : type_grammar.grammar * term_grammar.grammar +(* + [hashmapMain_Opaque] Parent theory of "hashmapMain_Funs" + + [core_num_u32_max_body_def] Definition + + ⊢ core_num_u32_max_body = Return (int_to_u32 4294967295) + + [core_num_u32_max_c_def] Definition + + ⊢ core_num_u32_max_c = get_return_value core_num_u32_max_body + + [hashmap_hash_key_fwd_def] Definition + + ⊢ ∀k. hashmap_hash_key_fwd k = Return k + + [hashmap_hash_map_allocate_slots_fwd_def] Definition + + ⊢ ∀slots n. + hashmap_hash_map_allocate_slots_fwd slots n = + hashmap_hash_map_allocate_slots_loop_fwd slots n + + [hashmap_hash_map_allocate_slots_loop_fwd_def] Definition + + ⊢ ∀slots n. + hashmap_hash_map_allocate_slots_loop_fwd slots n = + if usize_gt n (int_to_usize 0) then + do + slots0 <- vec_push_back slots HashmapListNil; + n0 <- usize_sub n (int_to_usize 1); + hashmap_hash_map_allocate_slots_loop_fwd slots0 n0 + od + else Return slots + + [hashmap_hash_map_clear_fwd_back_def] Definition + + ⊢ ∀self. + hashmap_hash_map_clear_fwd_back self = + do + v <- + hashmap_hash_map_clear_loop_fwd_back + self.hashmap_hash_map_slots (int_to_usize 0); + Return + (self with + <|hashmap_hash_map_num_entries := int_to_usize 0; + hashmap_hash_map_slots := v|>) + od + + [hashmap_hash_map_clear_loop_fwd_back_def] Definition + + ⊢ ∀slots i. + hashmap_hash_map_clear_loop_fwd_back slots i = + (let + i0 = vec_len slots + in + if usize_lt i i0 then + do + i1 <- usize_add i (int_to_usize 1); + slots0 <- vec_index_mut_back slots i HashmapListNil; + hashmap_hash_map_clear_loop_fwd_back slots0 i1 + od + else Return slots) + + [hashmap_hash_map_contains_key_fwd_def] Definition + + ⊢ ∀self key. + hashmap_hash_map_contains_key_fwd self key = + do + hash <- hashmap_hash_key_fwd key; + i <<- vec_len self.hashmap_hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hashmap_hash_map_slots hash_mod; + hashmap_hash_map_contains_key_in_list_fwd key l + od + + [hashmap_hash_map_contains_key_in_list_fwd_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_contains_key_in_list_fwd key ls = + hashmap_hash_map_contains_key_in_list_loop_fwd key ls + + [hashmap_hash_map_contains_key_in_list_loop_fwd_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_contains_key_in_list_loop_fwd key ls = + case ls of + HashmapListCons ckey t tl => + if ckey = key then Return T + else hashmap_hash_map_contains_key_in_list_loop_fwd key tl + | HashmapListNil => Return F + + [hashmap_hash_map_get_fwd_def] Definition + + ⊢ ∀self key. + hashmap_hash_map_get_fwd self key = + do + hash <- hashmap_hash_key_fwd key; + i <<- vec_len self.hashmap_hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_fwd self.hashmap_hash_map_slots hash_mod; + hashmap_hash_map_get_in_list_fwd key l + od + + [hashmap_hash_map_get_in_list_fwd_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_get_in_list_fwd key ls = + hashmap_hash_map_get_in_list_loop_fwd key ls + + [hashmap_hash_map_get_in_list_loop_fwd_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_get_in_list_loop_fwd key ls = + case ls of + HashmapListCons ckey cvalue tl => + if ckey = key then Return cvalue + else hashmap_hash_map_get_in_list_loop_fwd key tl + | HashmapListNil => Fail Failure + + [hashmap_hash_map_get_mut_back_def] Definition + + ⊢ ∀self key ret. + hashmap_hash_map_get_mut_back self key ret = + do + hash <- hashmap_hash_key_fwd key; + i <<- vec_len self.hashmap_hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + l0 <- hashmap_hash_map_get_mut_in_list_back l key ret; + v <- vec_index_mut_back self.hashmap_hash_map_slots hash_mod l0; + Return (self with hashmap_hash_map_slots := v) + od + + [hashmap_hash_map_get_mut_fwd_def] Definition + + ⊢ ∀self key. + hashmap_hash_map_get_mut_fwd self key = + do + hash <- hashmap_hash_key_fwd key; + i <<- vec_len self.hashmap_hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + hashmap_hash_map_get_mut_in_list_fwd l key + od + + [hashmap_hash_map_get_mut_in_list_back_def] Definition + + ⊢ ∀ls key ret. + hashmap_hash_map_get_mut_in_list_back ls key ret = + hashmap_hash_map_get_mut_in_list_loop_back ls key ret + + [hashmap_hash_map_get_mut_in_list_fwd_def] Definition + + ⊢ ∀ls key. + hashmap_hash_map_get_mut_in_list_fwd ls key = + hashmap_hash_map_get_mut_in_list_loop_fwd ls key + + [hashmap_hash_map_get_mut_in_list_loop_back_def] Definition + + ⊢ ∀ls key ret. + hashmap_hash_map_get_mut_in_list_loop_back ls key ret = + case ls of + HashmapListCons ckey cvalue tl => + if ckey = key then Return (HashmapListCons ckey ret tl) + else + do + tl0 <- + hashmap_hash_map_get_mut_in_list_loop_back tl key ret; + Return (HashmapListCons ckey cvalue tl0) + od + | HashmapListNil => Fail Failure + + [hashmap_hash_map_get_mut_in_list_loop_fwd_def] Definition + + ⊢ ∀ls key. + hashmap_hash_map_get_mut_in_list_loop_fwd ls key = + case ls of + HashmapListCons ckey cvalue tl => + if ckey = key then Return cvalue + else hashmap_hash_map_get_mut_in_list_loop_fwd tl key + | HashmapListNil => Fail Failure + + [hashmap_hash_map_insert_fwd_back_def] Definition + + ⊢ ∀self key value. + hashmap_hash_map_insert_fwd_back self key value = + do + self0 <- + hashmap_hash_map_insert_no_resize_fwd_back self key value; + i <- hashmap_hash_map_len_fwd self0; + if usize_gt i self0.hashmap_hash_map_max_load then + hashmap_hash_map_try_resize_fwd_back self0 + else Return self0 + od + + [hashmap_hash_map_insert_in_list_back_def] Definition + + ⊢ ∀key value ls. + hashmap_hash_map_insert_in_list_back key value ls = + hashmap_hash_map_insert_in_list_loop_back key value ls + + [hashmap_hash_map_insert_in_list_fwd_def] Definition + + ⊢ ∀key value ls. + hashmap_hash_map_insert_in_list_fwd key value ls = + hashmap_hash_map_insert_in_list_loop_fwd key value ls + + [hashmap_hash_map_insert_in_list_loop_back_def] Definition + + ⊢ ∀key value ls. + hashmap_hash_map_insert_in_list_loop_back key value ls = + case ls of + HashmapListCons ckey cvalue tl => + if ckey = key then Return (HashmapListCons ckey value tl) + else + do + tl0 <- + hashmap_hash_map_insert_in_list_loop_back key value tl; + Return (HashmapListCons ckey cvalue tl0) + od + | HashmapListNil => + (let + l = HashmapListNil + in + Return (HashmapListCons key value l)) + + [hashmap_hash_map_insert_in_list_loop_fwd_def] Definition + + ⊢ ∀key value ls. + hashmap_hash_map_insert_in_list_loop_fwd key value ls = + case ls of + HashmapListCons ckey cvalue tl => + if ckey = key then Return F + else hashmap_hash_map_insert_in_list_loop_fwd key value tl + | HashmapListNil => Return T + + [hashmap_hash_map_insert_no_resize_fwd_back_def] Definition + + ⊢ ∀self key value. + hashmap_hash_map_insert_no_resize_fwd_back self key value = + do + hash <- hashmap_hash_key_fwd key; + i <<- vec_len self.hashmap_hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + inserted <- hashmap_hash_map_insert_in_list_fwd key value l; + if inserted then + do + i0 <- + usize_add self.hashmap_hash_map_num_entries + (int_to_usize 1); + l0 <- hashmap_hash_map_insert_in_list_back key value l; + v <- + vec_index_mut_back self.hashmap_hash_map_slots hash_mod + l0; + Return + (self with + <|hashmap_hash_map_num_entries := i0; + hashmap_hash_map_slots := v|>) + od + else + do + l0 <- hashmap_hash_map_insert_in_list_back key value l; + v <- + vec_index_mut_back self.hashmap_hash_map_slots hash_mod + l0; + Return (self with hashmap_hash_map_slots := v) + od + od + + [hashmap_hash_map_len_fwd_def] Definition + + ⊢ ∀self. + hashmap_hash_map_len_fwd self = + Return self.hashmap_hash_map_num_entries + + [hashmap_hash_map_move_elements_from_list_fwd_back_def] Definition + + ⊢ ∀ntable ls. + hashmap_hash_map_move_elements_from_list_fwd_back ntable ls = + hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable ls + + [hashmap_hash_map_move_elements_from_list_loop_fwd_back_def] Definition + + ⊢ ∀ntable ls. + hashmap_hash_map_move_elements_from_list_loop_fwd_back ntable ls = + case ls of + HashmapListCons k v tl => + do + ntable0 <- + hashmap_hash_map_insert_no_resize_fwd_back ntable k v; + hashmap_hash_map_move_elements_from_list_loop_fwd_back + ntable0 tl + od + | HashmapListNil => Return ntable + + [hashmap_hash_map_move_elements_fwd_back_def] Definition + + ⊢ ∀ntable slots i. + hashmap_hash_map_move_elements_fwd_back ntable slots i = + hashmap_hash_map_move_elements_loop_fwd_back ntable slots i + + [hashmap_hash_map_move_elements_loop_fwd_back_def] Definition + + ⊢ ∀ntable slots i. + hashmap_hash_map_move_elements_loop_fwd_back ntable slots i = + (let + i0 = vec_len slots + in + if usize_lt i i0 then + do + l <- vec_index_mut_fwd slots i; + ls <<- mem_replace_fwd l HashmapListNil; + ntable0 <- + hashmap_hash_map_move_elements_from_list_fwd_back ntable + ls; + i1 <- usize_add i (int_to_usize 1); + l0 <<- mem_replace_back l HashmapListNil; + slots0 <- vec_index_mut_back slots i l0; + hashmap_hash_map_move_elements_loop_fwd_back ntable0 + slots0 i1 + od + else Return (ntable,slots)) + + [hashmap_hash_map_new_fwd_def] Definition + + ⊢ hashmap_hash_map_new_fwd = + hashmap_hash_map_new_with_capacity_fwd (int_to_usize 32) + (int_to_usize 4) (int_to_usize 5) + + [hashmap_hash_map_new_with_capacity_fwd_def] Definition + + ⊢ ∀capacity max_load_dividend max_load_divisor. + hashmap_hash_map_new_with_capacity_fwd capacity max_load_dividend + max_load_divisor = + (let + v = vec_new + in + do + slots <- hashmap_hash_map_allocate_slots_fwd v capacity; + i <- usize_mul capacity max_load_dividend; + i0 <- usize_div i max_load_divisor; + Return + <|hashmap_hash_map_num_entries := int_to_usize 0; + hashmap_hash_map_max_load_factor := + (max_load_dividend,max_load_divisor); + hashmap_hash_map_max_load := i0; + hashmap_hash_map_slots := slots|> + od) + + [hashmap_hash_map_remove_back_def] Definition + + ⊢ ∀self key. + hashmap_hash_map_remove_back self key = + do + hash <- hashmap_hash_key_fwd key; + i <<- vec_len self.hashmap_hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + x <- hashmap_hash_map_remove_from_list_fwd key l; + case x of + NONE => + do + l0 <- hashmap_hash_map_remove_from_list_back key l; + v <- + vec_index_mut_back self.hashmap_hash_map_slots hash_mod + l0; + Return (self with hashmap_hash_map_slots := v) + od + | SOME x0 => + do + i0 <- + usize_sub self.hashmap_hash_map_num_entries + (int_to_usize 1); + l0 <- hashmap_hash_map_remove_from_list_back key l; + v <- + vec_index_mut_back self.hashmap_hash_map_slots hash_mod + l0; + Return + (self with + <|hashmap_hash_map_num_entries := i0; + hashmap_hash_map_slots := v|>) + od + od + + [hashmap_hash_map_remove_from_list_back_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_remove_from_list_back key ls = + hashmap_hash_map_remove_from_list_loop_back key ls + + [hashmap_hash_map_remove_from_list_fwd_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_remove_from_list_fwd key ls = + hashmap_hash_map_remove_from_list_loop_fwd key ls + + [hashmap_hash_map_remove_from_list_loop_back_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_remove_from_list_loop_back key ls = + case ls of + HashmapListCons ckey t tl => + if ckey = key then + (let + mv_ls = + mem_replace_fwd (HashmapListCons ckey t tl) + HashmapListNil + in + case mv_ls of + HashmapListCons i cvalue tl0 => Return tl0 + | HashmapListNil => Fail Failure) + else + do + tl0 <- hashmap_hash_map_remove_from_list_loop_back key tl; + Return (HashmapListCons ckey t tl0) + od + | HashmapListNil => Return HashmapListNil + + [hashmap_hash_map_remove_from_list_loop_fwd_def] Definition + + ⊢ ∀key ls. + hashmap_hash_map_remove_from_list_loop_fwd key ls = + case ls of + HashmapListCons ckey t tl => + if ckey = key then + (let + mv_ls = + mem_replace_fwd (HashmapListCons ckey t tl) + HashmapListNil + in + case mv_ls of + HashmapListCons i cvalue tl0 => Return (SOME cvalue) + | HashmapListNil => Fail Failure) + else hashmap_hash_map_remove_from_list_loop_fwd key tl + | HashmapListNil => Return NONE + + [hashmap_hash_map_remove_fwd_def] Definition + + ⊢ ∀self key. + hashmap_hash_map_remove_fwd self key = + do + hash <- hashmap_hash_key_fwd key; + i <<- vec_len self.hashmap_hash_map_slots; + hash_mod <- usize_rem hash i; + l <- vec_index_mut_fwd self.hashmap_hash_map_slots hash_mod; + x <- hashmap_hash_map_remove_from_list_fwd key l; + case x of + NONE => Return NONE + | SOME x0 => + monad_ignore_bind + (usize_sub self.hashmap_hash_map_num_entries + (int_to_usize 1)) (Return (SOME x0)) + od + + [hashmap_hash_map_try_resize_fwd_back_def] Definition + + ⊢ ∀self. + hashmap_hash_map_try_resize_fwd_back self = + do + max_usize <- mk_usize (u32_to_int core_num_u32_max_c); + capacity <<- vec_len self.hashmap_hash_map_slots; + n1 <- usize_div max_usize (int_to_usize 2); + (i,i0) <<- self.hashmap_hash_map_max_load_factor; + i1 <- usize_div n1 i; + if usize_le capacity i1 then + do + i2 <- usize_mul capacity (int_to_usize 2); + ntable <- hashmap_hash_map_new_with_capacity_fwd i2 i i0; + (ntable0,_) <- + hashmap_hash_map_move_elements_fwd_back ntable + self.hashmap_hash_map_slots (int_to_usize 0); + Return + (ntable0 with + <|hashmap_hash_map_num_entries := + self.hashmap_hash_map_num_entries; + hashmap_hash_map_max_load_factor := (i,i0)|>) + od + else + Return (self with hashmap_hash_map_max_load_factor := (i,i0)) + od + + [hashmap_test1_fwd_def] Definition + + ⊢ hashmap_test1_fwd = + do + hm <- hashmap_hash_map_new_fwd; + hm0 <- + hashmap_hash_map_insert_fwd_back hm (int_to_usize 0) + (int_to_u64 42); + hm1 <- + hashmap_hash_map_insert_fwd_back hm0 (int_to_usize 128) + (int_to_u64 18); + hm2 <- + hashmap_hash_map_insert_fwd_back hm1 (int_to_usize 1024) + (int_to_u64 138); + hm3 <- + hashmap_hash_map_insert_fwd_back hm2 (int_to_usize 1056) + (int_to_u64 256); + i <- hashmap_hash_map_get_fwd hm3 (int_to_usize 128); + if i ≠ int_to_u64 18 then Fail Failure + else + do + hm4 <- + hashmap_hash_map_get_mut_back hm3 (int_to_usize 1024) + (int_to_u64 56); + i0 <- hashmap_hash_map_get_fwd hm4 (int_to_usize 1024); + if i0 ≠ int_to_u64 56 then Fail Failure + else + do + x <- hashmap_hash_map_remove_fwd hm4 (int_to_usize 1024); + case x of + NONE => Fail Failure + | SOME x0 => + if x0 ≠ int_to_u64 56 then Fail Failure + else + do + hm5 <- + hashmap_hash_map_remove_back hm4 + (int_to_usize 1024); + i1 <- hashmap_hash_map_get_fwd hm5 (int_to_usize 0); + if i1 ≠ int_to_u64 42 then Fail Failure + else + do + i2 <- + hashmap_hash_map_get_fwd hm5 + (int_to_usize 128); + if i2 ≠ int_to_u64 18 then Fail Failure + else + do + i3 <- + hashmap_hash_map_get_fwd hm5 + (int_to_usize 1056); + if i3 ≠ int_to_u64 256 then Fail Failure + else Return () + od + od + od + od + od + od + + [insert_on_disk_fwd_def] Definition + + ⊢ ∀key value st. + insert_on_disk_fwd key value st = + do + (st0,hm) <- hashmap_utils_deserialize_fwd st; + hm0 <- hashmap_hash_map_insert_fwd_back hm key value; + (st1,_) <- hashmap_utils_serialize_fwd hm0 st0; + Return (st1,()) + od + + [main_fwd_def] Definition + + ⊢ main_fwd = Return () + + +*) +end diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml new file mode 100644 index 00000000..5f6bcbb4 --- /dev/null +++ b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueScript.sml @@ -0,0 +1,15 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: opaque function definitions *) +open primitivesLib divDefLib +open hashmapMain_TypesTheory + +val _ = new_theory "hashmapMain_Opaque" + + +val _ = new_constant ("hashmap_utils_deserialize_fwd", + “:state -> (state # u64 hashmap_hash_map_t) result”) + +val _ = new_constant ("hashmap_utils_serialize_fwd", + “:u64 hashmap_hash_map_t -> state -> (state # unit) result”) + +val _ = export_theory () diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueTheory.sig b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueTheory.sig new file mode 100644 index 00000000..f7373609 --- /dev/null +++ b/tests/hol4/hashmap_on_disk/hashmapMain_OpaqueTheory.sig @@ -0,0 +1,11 @@ +signature hashmapMain_OpaqueTheory = +sig + type thm = Thm.thm + + val hashmapMain_Opaque_grammars : type_grammar.grammar * term_grammar.grammar +(* + [hashmapMain_Types] Parent theory of "hashmapMain_Opaque" + + +*) +end diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_TypesScript.sml b/tests/hol4/hashmap_on_disk/hashmapMain_TypesScript.sml new file mode 100644 index 00000000..3f8ca9b9 --- /dev/null +++ b/tests/hol4/hashmap_on_disk/hashmapMain_TypesScript.sml @@ -0,0 +1,27 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [hashmap_main]: type definitions *) +open primitivesLib divDefLib + +val _ = new_theory "hashmapMain_Types" + + +Datatype: + (** [hashmap_main::hashmap::List] *) + hashmap_list_t = | HashmapListCons usize 't hashmap_list_t | HashmapListNil +End + +Datatype: + (** [hashmap_main::hashmap::HashMap] *) + hashmap_hash_map_t = + <| + hashmap_hash_map_num_entries : usize; + hashmap_hash_map_max_load_factor : (usize # usize); + hashmap_hash_map_max_load : usize; + hashmap_hash_map_slots : 't hashmap_list_t vec; + |> +End + +(** The state type used in the state-error monad *) +val _ = new_type ("state", 0) + +val _ = export_theory () diff --git a/tests/hol4/hashmap_on_disk/hashmapMain_TypesTheory.sig b/tests/hol4/hashmap_on_disk/hashmapMain_TypesTheory.sig new file mode 100644 index 00000000..bea7eb76 --- /dev/null +++ b/tests/hol4/hashmap_on_disk/hashmapMain_TypesTheory.sig @@ -0,0 +1,568 @@ +signature hashmapMain_TypesTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val hashmap_hash_map_t_TY_DEF : thm + val hashmap_hash_map_t_case_def : thm + val hashmap_hash_map_t_size_def : thm + val hashmap_list_t_TY_DEF : thm + val hashmap_list_t_case_def : thm + val hashmap_list_t_size_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_fupd_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_fupd_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_fupd_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_def : thm + val recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_fupd_def : thm + + (* Theorems *) + val EXISTS_hashmap_hash_map_t : thm + val FORALL_hashmap_hash_map_t : thm + val datatype_hashmap_hash_map_t : thm + val datatype_hashmap_list_t : thm + val hashmap_hash_map_t_11 : thm + val hashmap_hash_map_t_Axiom : thm + val hashmap_hash_map_t_accessors : thm + val hashmap_hash_map_t_accfupds : thm + val hashmap_hash_map_t_case_cong : thm + val hashmap_hash_map_t_case_eq : thm + val hashmap_hash_map_t_component_equality : thm + val hashmap_hash_map_t_fn_updates : thm + val hashmap_hash_map_t_fupdcanon : thm + val hashmap_hash_map_t_fupdcanon_comp : thm + val hashmap_hash_map_t_fupdfupds : thm + val hashmap_hash_map_t_fupdfupds_comp : thm + val hashmap_hash_map_t_induction : thm + val hashmap_hash_map_t_literal_11 : thm + val hashmap_hash_map_t_literal_nchotomy : thm + val hashmap_hash_map_t_nchotomy : thm + val hashmap_hash_map_t_updates_eq_literal : thm + val hashmap_list_t_11 : thm + val hashmap_list_t_Axiom : thm + val hashmap_list_t_case_cong : thm + val hashmap_list_t_case_eq : thm + val hashmap_list_t_distinct : thm + val hashmap_list_t_induction : thm + val hashmap_list_t_nchotomy : thm + + val hashmapMain_Types_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "hashmapMain_Types" + + [hashmap_hash_map_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('hashmap_hash_map_t'). + (∀a0'. + (∃a0 a1 a2 a3. + a0' = + (λa0 a1 a2 a3. + ind_type$CONSTR 0 (a0,a1,a2,a3) + (λn. ind_type$BOTTOM)) a0 a1 a2 a3) ⇒ + $var$('hashmap_hash_map_t') a0') ⇒ + $var$('hashmap_hash_map_t') a0') rep + + [hashmap_hash_map_t_case_def] Definition + + ⊢ ∀a0 a1 a2 a3 f. + hashmap_hash_map_t_CASE (hashmap_hash_map_t a0 a1 a2 a3) f = + f a0 a1 a2 a3 + + [hashmap_hash_map_t_size_def] Definition + + ⊢ ∀f a0 a1 a2 a3. + hashmap_hash_map_t_size f (hashmap_hash_map_t a0 a1 a2 a3) = + 1 + pair_size (λv. 0) (λv. 0) a1 + + [hashmap_list_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('hashmap_list_t'). + (∀a0'. + (∃a0 a1 a2. + a0' = + (λa0 a1 a2. + ind_type$CONSTR 0 (a0,a1) + (ind_type$FCONS a2 (λn. ind_type$BOTTOM))) + a0 a1 a2 ∧ $var$('hashmap_list_t') a2) ∨ + a0' = + ind_type$CONSTR (SUC 0) (ARB,ARB) + (λn. ind_type$BOTTOM) ⇒ + $var$('hashmap_list_t') a0') ⇒ + $var$('hashmap_list_t') a0') rep + + [hashmap_list_t_case_def] Definition + + ⊢ (∀a0 a1 a2 f v. + hashmap_list_t_CASE (HashmapListCons a0 a1 a2) f v = f a0 a1 a2) ∧ + ∀f v. hashmap_list_t_CASE HashmapListNil f v = v + + [hashmap_list_t_size_def] Definition + + ⊢ (∀f a0 a1 a2. + hashmap_list_t_size f (HashmapListCons a0 a1 a2) = + 1 + (f a1 + hashmap_list_t_size f a2)) ∧ + ∀f. hashmap_list_t_size f HashmapListNil = 0 + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_def] Definition + + ⊢ ∀u p u0 v. + (hashmap_hash_map_t u p u0 v).hashmap_hash_map_max_load = u0 + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_def] Definition + + ⊢ ∀u p u0 v. + (hashmap_hash_map_t u p u0 v).hashmap_hash_map_max_load_factor = + p + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_factor_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_max_load_factor updated_by f = + hashmap_hash_map_t u (f p) u0 v + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_max_load_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_max_load updated_by f = + hashmap_hash_map_t u p (f u0) v + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_def] Definition + + ⊢ ∀u p u0 v. + (hashmap_hash_map_t u p u0 v).hashmap_hash_map_num_entries = u + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_num_entries_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_num_entries updated_by f = + hashmap_hash_map_t (f u) p u0 v + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_def] Definition + + ⊢ ∀u p u0 v. (hashmap_hash_map_t u p u0 v).hashmap_hash_map_slots = v + + [recordtype_hashmap_hash_map_t_seldef_hashmap_hash_map_slots_fupd_def] Definition + + ⊢ ∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_slots updated_by f = + hashmap_hash_map_t u p u0 (f v) + + [EXISTS_hashmap_hash_map_t] Theorem + + ⊢ ∀P. (∃h. P h) ⇔ + ∃u0 p u v. + P + <|hashmap_hash_map_num_entries := u0; + hashmap_hash_map_max_load_factor := p; + hashmap_hash_map_max_load := u; + hashmap_hash_map_slots := v|> + + [FORALL_hashmap_hash_map_t] Theorem + + ⊢ ∀P. (∀h. P h) ⇔ + ∀u0 p u v. + P + <|hashmap_hash_map_num_entries := u0; + hashmap_hash_map_max_load_factor := p; + hashmap_hash_map_max_load := u; + hashmap_hash_map_slots := v|> + + [datatype_hashmap_hash_map_t] Theorem + + ⊢ DATATYPE + (record hashmap_hash_map_t hashmap_hash_map_num_entries + hashmap_hash_map_max_load_factor hashmap_hash_map_max_load + hashmap_hash_map_slots) + + [datatype_hashmap_list_t] Theorem + + ⊢ DATATYPE (hashmap_list_t HashmapListCons HashmapListNil) + + [hashmap_hash_map_t_11] Theorem + + ⊢ ∀a0 a1 a2 a3 a0' a1' a2' a3'. + hashmap_hash_map_t a0 a1 a2 a3 = + hashmap_hash_map_t a0' a1' a2' a3' ⇔ + a0 = a0' ∧ a1 = a1' ∧ a2 = a2' ∧ a3 = a3' + + [hashmap_hash_map_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a0 a1 a2 a3. + fn (hashmap_hash_map_t a0 a1 a2 a3) = f a0 a1 a2 a3 + + [hashmap_hash_map_t_accessors] Theorem + + ⊢ (∀u p u0 v. + (hashmap_hash_map_t u p u0 v).hashmap_hash_map_num_entries = u) ∧ + (∀u p u0 v. + (hashmap_hash_map_t u p u0 v).hashmap_hash_map_max_load_factor = + p) ∧ + (∀u p u0 v. + (hashmap_hash_map_t u p u0 v).hashmap_hash_map_max_load = u0) ∧ + ∀u p u0 v. (hashmap_hash_map_t u p u0 v).hashmap_hash_map_slots = v + + [hashmap_hash_map_t_accfupds] Theorem + + ⊢ (∀h f. + (h with hashmap_hash_map_max_load_factor updated_by f). + hashmap_hash_map_num_entries = + h.hashmap_hash_map_num_entries) ∧ + (∀h f. + (h with hashmap_hash_map_max_load updated_by f). + hashmap_hash_map_num_entries = + h.hashmap_hash_map_num_entries) ∧ + (∀h f. + (h with hashmap_hash_map_slots updated_by f). + hashmap_hash_map_num_entries = + h.hashmap_hash_map_num_entries) ∧ + (∀h f. + (h with hashmap_hash_map_num_entries updated_by f). + hashmap_hash_map_max_load_factor = + h.hashmap_hash_map_max_load_factor) ∧ + (∀h f. + (h with hashmap_hash_map_max_load updated_by f). + hashmap_hash_map_max_load_factor = + h.hashmap_hash_map_max_load_factor) ∧ + (∀h f. + (h with hashmap_hash_map_slots updated_by f). + hashmap_hash_map_max_load_factor = + h.hashmap_hash_map_max_load_factor) ∧ + (∀h f. + (h with hashmap_hash_map_num_entries updated_by f). + hashmap_hash_map_max_load = + h.hashmap_hash_map_max_load) ∧ + (∀h f. + (h with hashmap_hash_map_max_load_factor updated_by f). + hashmap_hash_map_max_load = + h.hashmap_hash_map_max_load) ∧ + (∀h f. + (h with hashmap_hash_map_slots updated_by f). + hashmap_hash_map_max_load = + h.hashmap_hash_map_max_load) ∧ + (∀h f. + (h with hashmap_hash_map_num_entries updated_by f). + hashmap_hash_map_slots = + h.hashmap_hash_map_slots) ∧ + (∀h f. + (h with hashmap_hash_map_max_load_factor updated_by f). + hashmap_hash_map_slots = + h.hashmap_hash_map_slots) ∧ + (∀h f. + (h with hashmap_hash_map_max_load updated_by f). + hashmap_hash_map_slots = + h.hashmap_hash_map_slots) ∧ + (∀h f. + (h with hashmap_hash_map_num_entries updated_by f). + hashmap_hash_map_num_entries = + f h.hashmap_hash_map_num_entries) ∧ + (∀h f. + (h with hashmap_hash_map_max_load_factor updated_by f). + hashmap_hash_map_max_load_factor = + f h.hashmap_hash_map_max_load_factor) ∧ + (∀h f. + (h with hashmap_hash_map_max_load updated_by f). + hashmap_hash_map_max_load = + f h.hashmap_hash_map_max_load) ∧ + ∀h f. + (h with hashmap_hash_map_slots updated_by f). + hashmap_hash_map_slots = + f h.hashmap_hash_map_slots + + [hashmap_hash_map_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ + (∀a0 a1 a2 a3. + M' = hashmap_hash_map_t a0 a1 a2 a3 ⇒ + f a0 a1 a2 a3 = f' a0 a1 a2 a3) ⇒ + hashmap_hash_map_t_CASE M f = hashmap_hash_map_t_CASE M' f' + + [hashmap_hash_map_t_case_eq] Theorem + + ⊢ hashmap_hash_map_t_CASE x f = v ⇔ + ∃u p u0 v'. x = hashmap_hash_map_t u p u0 v' ∧ f u p u0 v' = v + + [hashmap_hash_map_t_component_equality] Theorem + + ⊢ ∀h1 h2. + h1 = h2 ⇔ + h1.hashmap_hash_map_num_entries = h2.hashmap_hash_map_num_entries ∧ + h1.hashmap_hash_map_max_load_factor = + h2.hashmap_hash_map_max_load_factor ∧ + h1.hashmap_hash_map_max_load = h2.hashmap_hash_map_max_load ∧ + h1.hashmap_hash_map_slots = h2.hashmap_hash_map_slots + + [hashmap_hash_map_t_fn_updates] Theorem + + ⊢ (∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_num_entries updated_by f = + hashmap_hash_map_t (f u) p u0 v) ∧ + (∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_max_load_factor updated_by f = + hashmap_hash_map_t u (f p) u0 v) ∧ + (∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_max_load updated_by f = + hashmap_hash_map_t u p (f u0) v) ∧ + ∀f u p u0 v. + hashmap_hash_map_t u p u0 v with + hashmap_hash_map_slots updated_by f = + hashmap_hash_map_t u p u0 (f v) + + [hashmap_hash_map_t_fupdcanon] Theorem + + ⊢ (∀h g f. + h with + <|hashmap_hash_map_max_load_factor updated_by f; + hashmap_hash_map_num_entries updated_by g|> = + h with + <|hashmap_hash_map_num_entries updated_by g; + hashmap_hash_map_max_load_factor updated_by f|>) ∧ + (∀h g f. + h with + <|hashmap_hash_map_max_load updated_by f; + hashmap_hash_map_num_entries updated_by g|> = + h with + <|hashmap_hash_map_num_entries updated_by g; + hashmap_hash_map_max_load updated_by f|>) ∧ + (∀h g f. + h with + <|hashmap_hash_map_max_load updated_by f; + hashmap_hash_map_max_load_factor updated_by g|> = + h with + <|hashmap_hash_map_max_load_factor updated_by g; + hashmap_hash_map_max_load updated_by f|>) ∧ + (∀h g f. + h with + <|hashmap_hash_map_slots updated_by f; + hashmap_hash_map_num_entries updated_by g|> = + h with + <|hashmap_hash_map_num_entries updated_by g; + hashmap_hash_map_slots updated_by f|>) ∧ + (∀h g f. + h with + <|hashmap_hash_map_slots updated_by f; + hashmap_hash_map_max_load_factor updated_by g|> = + h with + <|hashmap_hash_map_max_load_factor updated_by g; + hashmap_hash_map_slots updated_by f|>) ∧ + ∀h g f. + h with + <|hashmap_hash_map_slots updated_by f; + hashmap_hash_map_max_load updated_by g|> = + h with + <|hashmap_hash_map_max_load updated_by g; + hashmap_hash_map_slots updated_by f|> + + [hashmap_hash_map_t_fupdcanon_comp] Theorem + + ⊢ ((∀g f. + hashmap_hash_map_max_load_factor_fupd f ∘ + hashmap_hash_map_num_entries_fupd g = + hashmap_hash_map_num_entries_fupd g ∘ + hashmap_hash_map_max_load_factor_fupd f) ∧ + ∀h g f. + hashmap_hash_map_max_load_factor_fupd f ∘ + hashmap_hash_map_num_entries_fupd g ∘ h = + hashmap_hash_map_num_entries_fupd g ∘ + hashmap_hash_map_max_load_factor_fupd f ∘ h) ∧ + ((∀g f. + hashmap_hash_map_max_load_fupd f ∘ + hashmap_hash_map_num_entries_fupd g = + hashmap_hash_map_num_entries_fupd g ∘ + hashmap_hash_map_max_load_fupd f) ∧ + ∀h g f. + hashmap_hash_map_max_load_fupd f ∘ + hashmap_hash_map_num_entries_fupd g ∘ h = + hashmap_hash_map_num_entries_fupd g ∘ + hashmap_hash_map_max_load_fupd f ∘ h) ∧ + ((∀g f. + hashmap_hash_map_max_load_fupd f ∘ + hashmap_hash_map_max_load_factor_fupd g = + hashmap_hash_map_max_load_factor_fupd g ∘ + hashmap_hash_map_max_load_fupd f) ∧ + ∀h g f. + hashmap_hash_map_max_load_fupd f ∘ + hashmap_hash_map_max_load_factor_fupd g ∘ h = + hashmap_hash_map_max_load_factor_fupd g ∘ + hashmap_hash_map_max_load_fupd f ∘ h) ∧ + ((∀g f. + hashmap_hash_map_slots_fupd f ∘ + hashmap_hash_map_num_entries_fupd g = + hashmap_hash_map_num_entries_fupd g ∘ + hashmap_hash_map_slots_fupd f) ∧ + ∀h g f. + hashmap_hash_map_slots_fupd f ∘ + hashmap_hash_map_num_entries_fupd g ∘ h = + hashmap_hash_map_num_entries_fupd g ∘ + hashmap_hash_map_slots_fupd f ∘ h) ∧ + ((∀g f. + hashmap_hash_map_slots_fupd f ∘ + hashmap_hash_map_max_load_factor_fupd g = + hashmap_hash_map_max_load_factor_fupd g ∘ + hashmap_hash_map_slots_fupd f) ∧ + ∀h g f. + hashmap_hash_map_slots_fupd f ∘ + hashmap_hash_map_max_load_factor_fupd g ∘ h = + hashmap_hash_map_max_load_factor_fupd g ∘ + hashmap_hash_map_slots_fupd f ∘ h) ∧ + (∀g f. + hashmap_hash_map_slots_fupd f ∘ hashmap_hash_map_max_load_fupd g = + hashmap_hash_map_max_load_fupd g ∘ hashmap_hash_map_slots_fupd f) ∧ + ∀h g f. + hashmap_hash_map_slots_fupd f ∘ + hashmap_hash_map_max_load_fupd g ∘ h = + hashmap_hash_map_max_load_fupd g ∘ + hashmap_hash_map_slots_fupd f ∘ h + + [hashmap_hash_map_t_fupdfupds] Theorem + + ⊢ (∀h g f. + h with + <|hashmap_hash_map_num_entries updated_by f; + hashmap_hash_map_num_entries updated_by g|> = + h with hashmap_hash_map_num_entries updated_by f ∘ g) ∧ + (∀h g f. + h with + <|hashmap_hash_map_max_load_factor updated_by f; + hashmap_hash_map_max_load_factor updated_by g|> = + h with hashmap_hash_map_max_load_factor updated_by f ∘ g) ∧ + (∀h g f. + h with + <|hashmap_hash_map_max_load updated_by f; + hashmap_hash_map_max_load updated_by g|> = + h with hashmap_hash_map_max_load updated_by f ∘ g) ∧ + ∀h g f. + h with + <|hashmap_hash_map_slots updated_by f; + hashmap_hash_map_slots updated_by g|> = + h with hashmap_hash_map_slots updated_by f ∘ g + + [hashmap_hash_map_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. + hashmap_hash_map_num_entries_fupd f ∘ + hashmap_hash_map_num_entries_fupd g = + hashmap_hash_map_num_entries_fupd (f ∘ g)) ∧ + ∀h g f. + hashmap_hash_map_num_entries_fupd f ∘ + hashmap_hash_map_num_entries_fupd g ∘ h = + hashmap_hash_map_num_entries_fupd (f ∘ g) ∘ h) ∧ + ((∀g f. + hashmap_hash_map_max_load_factor_fupd f ∘ + hashmap_hash_map_max_load_factor_fupd g = + hashmap_hash_map_max_load_factor_fupd (f ∘ g)) ∧ + ∀h g f. + hashmap_hash_map_max_load_factor_fupd f ∘ + hashmap_hash_map_max_load_factor_fupd g ∘ h = + hashmap_hash_map_max_load_factor_fupd (f ∘ g) ∘ h) ∧ + ((∀g f. + hashmap_hash_map_max_load_fupd f ∘ + hashmap_hash_map_max_load_fupd g = + hashmap_hash_map_max_load_fupd (f ∘ g)) ∧ + ∀h g f. + hashmap_hash_map_max_load_fupd f ∘ + hashmap_hash_map_max_load_fupd g ∘ h = + hashmap_hash_map_max_load_fupd (f ∘ g) ∘ h) ∧ + (∀g f. + hashmap_hash_map_slots_fupd f ∘ hashmap_hash_map_slots_fupd g = + hashmap_hash_map_slots_fupd (f ∘ g)) ∧ + ∀h g f. + hashmap_hash_map_slots_fupd f ∘ hashmap_hash_map_slots_fupd g ∘ h = + hashmap_hash_map_slots_fupd (f ∘ g) ∘ h + + [hashmap_hash_map_t_induction] Theorem + + ⊢ ∀P. (∀u p u0 v. P (hashmap_hash_map_t u p u0 v)) ⇒ ∀h. P h + + [hashmap_hash_map_t_literal_11] Theorem + + ⊢ ∀u01 p1 u1 v1 u02 p2 u2 v2. + <|hashmap_hash_map_num_entries := u01; + hashmap_hash_map_max_load_factor := p1; + hashmap_hash_map_max_load := u1; hashmap_hash_map_slots := v1|> = + <|hashmap_hash_map_num_entries := u02; + hashmap_hash_map_max_load_factor := p2; + hashmap_hash_map_max_load := u2; hashmap_hash_map_slots := v2|> ⇔ + u01 = u02 ∧ p1 = p2 ∧ u1 = u2 ∧ v1 = v2 + + [hashmap_hash_map_t_literal_nchotomy] Theorem + + ⊢ ∀h. ∃u0 p u v. + h = + <|hashmap_hash_map_num_entries := u0; + hashmap_hash_map_max_load_factor := p; + hashmap_hash_map_max_load := u; hashmap_hash_map_slots := v|> + + [hashmap_hash_map_t_nchotomy] Theorem + + ⊢ ∀hh. ∃u p u0 v. hh = hashmap_hash_map_t u p u0 v + + [hashmap_hash_map_t_updates_eq_literal] Theorem + + ⊢ ∀h u0 p u v. + h with + <|hashmap_hash_map_num_entries := u0; + hashmap_hash_map_max_load_factor := p; + hashmap_hash_map_max_load := u; hashmap_hash_map_slots := v|> = + <|hashmap_hash_map_num_entries := u0; + hashmap_hash_map_max_load_factor := p; + hashmap_hash_map_max_load := u; hashmap_hash_map_slots := v|> + + [hashmap_list_t_11] Theorem + + ⊢ ∀a0 a1 a2 a0' a1' a2'. + HashmapListCons a0 a1 a2 = HashmapListCons a0' a1' a2' ⇔ + a0 = a0' ∧ a1 = a1' ∧ a2 = a2' + + [hashmap_list_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a0 a1 a2. fn (HashmapListCons a0 a1 a2) = f0 a0 a1 a2 (fn a2)) ∧ + fn HashmapListNil = f1 + + [hashmap_list_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ + (∀a0 a1 a2. + M' = HashmapListCons a0 a1 a2 ⇒ f a0 a1 a2 = f' a0 a1 a2) ∧ + (M' = HashmapListNil ⇒ v = v') ⇒ + hashmap_list_t_CASE M f v = hashmap_list_t_CASE M' f' v' + + [hashmap_list_t_case_eq] Theorem + + ⊢ hashmap_list_t_CASE x f v = v' ⇔ + (∃u t h. x = HashmapListCons u t h ∧ f u t h = v') ∨ + x = HashmapListNil ∧ v = v' + + [hashmap_list_t_distinct] Theorem + + ⊢ ∀a2 a1 a0. HashmapListCons a0 a1 a2 ≠ HashmapListNil + + [hashmap_list_t_induction] Theorem + + ⊢ ∀P. (∀h. P h ⇒ ∀t u. P (HashmapListCons u t h)) ∧ P HashmapListNil ⇒ + ∀h. P h + + [hashmap_list_t_nchotomy] Theorem + + ⊢ ∀hh. (∃u t h. hh = HashmapListCons u t h) ∨ hh = HashmapListNil + + +*) +end diff --git a/tests/hol4/misc-constants/Holmakefile b/tests/hol4/misc-constants/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/misc-constants/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/misc-constants/constantsScript.sml b/tests/hol4/misc-constants/constantsScript.sml new file mode 100644 index 00000000..324d553d --- /dev/null +++ b/tests/hol4/misc-constants/constantsScript.sml @@ -0,0 +1,225 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [constants] *) +open primitivesLib divDefLib + +val _ = new_theory "constants" + + +(** [constants::X0] *) +Definition x0_body_def: + x0_body : u32 result = Return (int_to_u32 0) +End +Definition x0_c_def: + x0_c : u32 = get_return_value x0_body +End + +(** [core::num::u32::{9}::MAX] *) +Definition core_num_u32_max_body_def: + core_num_u32_max_body : u32 result = Return (int_to_u32 4294967295) +End +Definition core_num_u32_max_c_def: + core_num_u32_max_c : u32 = get_return_value core_num_u32_max_body +End + +(** [constants::X1] *) +Definition x1_body_def: + x1_body : u32 result = Return core_num_u32_max_c +End +Definition x1_c_def: + x1_c : u32 = get_return_value x1_body +End + +(** [constants::X2] *) +Definition x2_body_def: + x2_body : u32 result = Return (int_to_u32 3) +End +Definition x2_c_def: + x2_c : u32 = get_return_value x2_body +End + +val incr_fwd_def = Define ‘ + (** [constants::incr] *) + incr_fwd (n : u32) : u32 result = + u32_add n (int_to_u32 1) +’ + +(** [constants::X3] *) +Definition x3_body_def: + x3_body : u32 result = incr_fwd (int_to_u32 32) +End +Definition x3_c_def: + x3_c : u32 = get_return_value x3_body +End + +val mk_pair0_fwd_def = Define ‘ + (** [constants::mk_pair0] *) + mk_pair0_fwd (x : u32) (y : u32) : (u32 # u32) result = + Return (x, y) +’ + +Datatype: + (** [constants::Pair] *) + pair_t = <| pair_x : 't1; pair_y : 't2; |> +End + +val mk_pair1_fwd_def = Define ‘ + (** [constants::mk_pair1] *) + mk_pair1_fwd (x : u32) (y : u32) : (u32, u32) pair_t result = + Return (<| pair_x := x; pair_y := y |>) +’ + +(** [constants::P0] *) +Definition p0_body_def: + p0_body : (u32 # u32) result = mk_pair0_fwd (int_to_u32 0) (int_to_u32 1) +End +Definition p0_c_def: + p0_c : (u32 # u32) = get_return_value p0_body +End + +(** [constants::P1] *) +Definition p1_body_def: + p1_body : (u32, u32) pair_t result = + mk_pair1_fwd (int_to_u32 0) (int_to_u32 1) +End +Definition p1_c_def: + p1_c : (u32, u32) pair_t = get_return_value p1_body +End + +(** [constants::P2] *) +Definition p2_body_def: + p2_body : (u32 # u32) result = Return (int_to_u32 0, int_to_u32 1) +End +Definition p2_c_def: + p2_c : (u32 # u32) = get_return_value p2_body +End + +(** [constants::P3] *) +Definition p3_body_def: + p3_body : (u32, u32) pair_t result = + Return (<| pair_x := (int_to_u32 0); pair_y := (int_to_u32 1) |>) +End +Definition p3_c_def: + p3_c : (u32, u32) pair_t = get_return_value p3_body +End + +Datatype: + (** [constants::Wrap] *) + wrap_t = <| wrap_val : 't; |> +End + +val wrap_new_fwd_def = Define ‘ + (** [constants::Wrap::{0}::new] *) + wrap_new_fwd (val : 't) : 't wrap_t result = + Return (<| wrap_val := val |>) +’ + +(** [constants::Y] *) +Definition y_body_def: + y_body : i32 wrap_t result = wrap_new_fwd (int_to_i32 2) +End +Definition y_c_def: + y_c : i32 wrap_t = get_return_value y_body +End + +val unwrap_y_fwd_def = Define ‘ + (** [constants::unwrap_y] *) + unwrap_y_fwd : i32 result = + Return y_c.wrap_val +’ + +(** [constants::YVAL] *) +Definition yval_body_def: + yval_body : i32 result = unwrap_y_fwd +End +Definition yval_c_def: + yval_c : i32 = get_return_value yval_body +End + +(** [constants::get_z1::Z1] *) +Definition get_z1_z1_body_def: + get_z1_z1_body : i32 result = Return (int_to_i32 3) +End +Definition get_z1_z1_c_def: + get_z1_z1_c : i32 = get_return_value get_z1_z1_body +End + +val get_z1_fwd_def = Define ‘ + (** [constants::get_z1] *) + get_z1_fwd : i32 result = + Return get_z1_z1_c +’ + +val add_fwd_def = Define ‘ + (** [constants::add] *) + add_fwd (a : i32) (b : i32) : i32 result = + i32_add a b +’ + +(** [constants::Q1] *) +Definition q1_body_def: + q1_body : i32 result = Return (int_to_i32 5) +End +Definition q1_c_def: + q1_c : i32 = get_return_value q1_body +End + +(** [constants::Q2] *) +Definition q2_body_def: + q2_body : i32 result = Return q1_c +End +Definition q2_c_def: + q2_c : i32 = get_return_value q2_body +End + +(** [constants::Q3] *) +Definition q3_body_def: + q3_body : i32 result = add_fwd q2_c (int_to_i32 3) +End +Definition q3_c_def: + q3_c : i32 = get_return_value q3_body +End + +val get_z2_fwd_def = Define ‘ + (** [constants::get_z2] *) + get_z2_fwd : i32 result = + do + i <- get_z1_fwd; + i0 <- add_fwd i q3_c; + add_fwd q1_c i0 + od +’ + +(** [constants::S1] *) +Definition s1_body_def: + s1_body : u32 result = Return (int_to_u32 6) +End +Definition s1_c_def: + s1_c : u32 = get_return_value s1_body +End + +(** [constants::S2] *) +Definition s2_body_def: + s2_body : u32 result = incr_fwd s1_c +End +Definition s2_c_def: + s2_c : u32 = get_return_value s2_body +End + +(** [constants::S3] *) +Definition s3_body_def: + s3_body : (u32, u32) pair_t result = Return p3_c +End +Definition s3_c_def: + s3_c : (u32, u32) pair_t = get_return_value s3_body +End + +(** [constants::S4] *) +Definition s4_body_def: + s4_body : (u32, u32) pair_t result = + mk_pair1_fwd (int_to_u32 7) (int_to_u32 8) +End +Definition s4_c_def: + s4_c : (u32, u32) pair_t = get_return_value s4_body +End + +val _ = export_theory () diff --git a/tests/hol4/misc-constants/constantsTheory.sig b/tests/hol4/misc-constants/constantsTheory.sig new file mode 100644 index 00000000..6148221f --- /dev/null +++ b/tests/hol4/misc-constants/constantsTheory.sig @@ -0,0 +1,548 @@ +signature constantsTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val add_fwd_def : thm + val core_num_u32_max_body_def : thm + val core_num_u32_max_c_def : thm + val get_z1_fwd_def : thm + val get_z1_z1_body_def : thm + val get_z1_z1_c_def : thm + val get_z2_fwd_def : thm + val incr_fwd_def : thm + val mk_pair0_fwd_def : thm + val mk_pair1_fwd_def : thm + val p0_body_def : thm + val p0_c_def : thm + val p1_body_def : thm + val p1_c_def : thm + val p2_body_def : thm + val p2_c_def : thm + val p3_body_def : thm + val p3_c_def : thm + val pair_t_TY_DEF : thm + val pair_t_case_def : thm + val pair_t_size_def : thm + val q1_body_def : thm + val q1_c_def : thm + val q2_body_def : thm + val q2_c_def : thm + val q3_body_def : thm + val q3_c_def : thm + val recordtype_pair_t_seldef_pair_x_def : thm + val recordtype_pair_t_seldef_pair_x_fupd_def : thm + val recordtype_pair_t_seldef_pair_y_def : thm + val recordtype_pair_t_seldef_pair_y_fupd_def : thm + val recordtype_wrap_t_seldef_wrap_val_def : thm + val recordtype_wrap_t_seldef_wrap_val_fupd_def : thm + val s1_body_def : thm + val s1_c_def : thm + val s2_body_def : thm + val s2_c_def : thm + val s3_body_def : thm + val s3_c_def : thm + val s4_body_def : thm + val s4_c_def : thm + val unwrap_y_fwd_def : thm + val wrap_new_fwd_def : thm + val wrap_t_TY_DEF : thm + val wrap_t_case_def : thm + val wrap_t_size_def : thm + val x0_body_def : thm + val x0_c_def : thm + val x1_body_def : thm + val x1_c_def : thm + val x2_body_def : thm + val x2_c_def : thm + val x3_body_def : thm + val x3_c_def : thm + val y_body_def : thm + val y_c_def : thm + val yval_body_def : thm + val yval_c_def : thm + + (* Theorems *) + val EXISTS_pair_t : thm + val EXISTS_wrap_t : thm + val FORALL_pair_t : thm + val FORALL_wrap_t : thm + val datatype_pair_t : thm + val datatype_wrap_t : thm + val pair_t_11 : thm + val pair_t_Axiom : thm + val pair_t_accessors : thm + val pair_t_accfupds : thm + val pair_t_case_cong : thm + val pair_t_case_eq : thm + val pair_t_component_equality : thm + val pair_t_fn_updates : thm + val pair_t_fupdcanon : thm + val pair_t_fupdcanon_comp : thm + val pair_t_fupdfupds : thm + val pair_t_fupdfupds_comp : thm + val pair_t_induction : thm + val pair_t_literal_11 : thm + val pair_t_literal_nchotomy : thm + val pair_t_nchotomy : thm + val pair_t_updates_eq_literal : thm + val wrap_t_11 : thm + val wrap_t_Axiom : thm + val wrap_t_accessors : thm + val wrap_t_accfupds : thm + val wrap_t_case_cong : thm + val wrap_t_case_eq : thm + val wrap_t_component_equality : thm + val wrap_t_fn_updates : thm + val wrap_t_fupdfupds : thm + val wrap_t_fupdfupds_comp : thm + val wrap_t_induction : thm + val wrap_t_literal_11 : thm + val wrap_t_literal_nchotomy : thm + val wrap_t_nchotomy : thm + val wrap_t_updates_eq_literal : thm + + val constants_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "constants" + + [add_fwd_def] Definition + + ⊢ ∀a b. add_fwd a b = i32_add a b + + [core_num_u32_max_body_def] Definition + + ⊢ core_num_u32_max_body = Return (int_to_u32 4294967295) + + [core_num_u32_max_c_def] Definition + + ⊢ core_num_u32_max_c = get_return_value core_num_u32_max_body + + [get_z1_fwd_def] Definition + + ⊢ get_z1_fwd = Return get_z1_z1_c + + [get_z1_z1_body_def] Definition + + ⊢ get_z1_z1_body = Return (int_to_i32 3) + + [get_z1_z1_c_def] Definition + + ⊢ get_z1_z1_c = get_return_value get_z1_z1_body + + [get_z2_fwd_def] Definition + + ⊢ get_z2_fwd = + do i <- get_z1_fwd; i0 <- add_fwd i q3_c; add_fwd q1_c i0 od + + [incr_fwd_def] Definition + + ⊢ ∀n. incr_fwd n = u32_add n (int_to_u32 1) + + [mk_pair0_fwd_def] Definition + + ⊢ ∀x y. mk_pair0_fwd x y = Return (x,y) + + [mk_pair1_fwd_def] Definition + + ⊢ ∀x y. mk_pair1_fwd x y = Return <|pair_x := x; pair_y := y|> + + [p0_body_def] Definition + + ⊢ p0_body = mk_pair0_fwd (int_to_u32 0) (int_to_u32 1) + + [p0_c_def] Definition + + ⊢ p0_c = get_return_value p0_body + + [p1_body_def] Definition + + ⊢ p1_body = mk_pair1_fwd (int_to_u32 0) (int_to_u32 1) + + [p1_c_def] Definition + + ⊢ p1_c = get_return_value p1_body + + [p2_body_def] Definition + + ⊢ p2_body = Return (int_to_u32 0,int_to_u32 1) + + [p2_c_def] Definition + + ⊢ p2_c = get_return_value p2_body + + [p3_body_def] Definition + + ⊢ p3_body = Return <|pair_x := int_to_u32 0; pair_y := int_to_u32 1|> + + [p3_c_def] Definition + + ⊢ p3_c = get_return_value p3_body + + [pair_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('pair_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 (a0,a1) + (λn. ind_type$BOTTOM)) a0 a1) ⇒ + $var$('pair_t') a0') ⇒ + $var$('pair_t') a0') rep + + [pair_t_case_def] Definition + + ⊢ ∀a0 a1 f. pair_t_CASE (pair_t a0 a1) f = f a0 a1 + + [pair_t_size_def] Definition + + ⊢ ∀f f1 a0 a1. pair_t_size f f1 (pair_t a0 a1) = 1 + (f a0 + f1 a1) + + [q1_body_def] Definition + + ⊢ q1_body = Return (int_to_i32 5) + + [q1_c_def] Definition + + ⊢ q1_c = get_return_value q1_body + + [q2_body_def] Definition + + ⊢ q2_body = Return q1_c + + [q2_c_def] Definition + + ⊢ q2_c = get_return_value q2_body + + [q3_body_def] Definition + + ⊢ q3_body = add_fwd q2_c (int_to_i32 3) + + [q3_c_def] Definition + + ⊢ q3_c = get_return_value q3_body + + [recordtype_pair_t_seldef_pair_x_def] Definition + + ⊢ ∀t t0. (pair_t t t0).pair_x = t + + [recordtype_pair_t_seldef_pair_x_fupd_def] Definition + + ⊢ ∀f t t0. pair_t t t0 with pair_x updated_by f = pair_t (f t) t0 + + [recordtype_pair_t_seldef_pair_y_def] Definition + + ⊢ ∀t t0. (pair_t t t0).pair_y = t0 + + [recordtype_pair_t_seldef_pair_y_fupd_def] Definition + + ⊢ ∀f t t0. pair_t t t0 with pair_y updated_by f = pair_t t (f t0) + + [recordtype_wrap_t_seldef_wrap_val_def] Definition + + ⊢ ∀t. (wrap_t t).wrap_val = t + + [recordtype_wrap_t_seldef_wrap_val_fupd_def] Definition + + ⊢ ∀f t. wrap_t t with wrap_val updated_by f = wrap_t (f t) + + [s1_body_def] Definition + + ⊢ s1_body = Return (int_to_u32 6) + + [s1_c_def] Definition + + ⊢ s1_c = get_return_value s1_body + + [s2_body_def] Definition + + ⊢ s2_body = incr_fwd s1_c + + [s2_c_def] Definition + + ⊢ s2_c = get_return_value s2_body + + [s3_body_def] Definition + + ⊢ s3_body = Return p3_c + + [s3_c_def] Definition + + ⊢ s3_c = get_return_value s3_body + + [s4_body_def] Definition + + ⊢ s4_body = mk_pair1_fwd (int_to_u32 7) (int_to_u32 8) + + [s4_c_def] Definition + + ⊢ s4_c = get_return_value s4_body + + [unwrap_y_fwd_def] Definition + + ⊢ unwrap_y_fwd = Return y_c.wrap_val + + [wrap_new_fwd_def] Definition + + ⊢ ∀val. wrap_new_fwd val = Return <|wrap_val := val|> + + [wrap_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('wrap_t'). + (∀a0. + (∃a. a0 = + (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) + a) ⇒ + $var$('wrap_t') a0) ⇒ + $var$('wrap_t') a0) rep + + [wrap_t_case_def] Definition + + ⊢ ∀a f. wrap_t_CASE (wrap_t a) f = f a + + [wrap_t_size_def] Definition + + ⊢ ∀f a. wrap_t_size f (wrap_t a) = 1 + f a + + [x0_body_def] Definition + + ⊢ x0_body = Return (int_to_u32 0) + + [x0_c_def] Definition + + ⊢ x0_c = get_return_value x0_body + + [x1_body_def] Definition + + ⊢ x1_body = Return core_num_u32_max_c + + [x1_c_def] Definition + + ⊢ x1_c = get_return_value x1_body + + [x2_body_def] Definition + + ⊢ x2_body = Return (int_to_u32 3) + + [x2_c_def] Definition + + ⊢ x2_c = get_return_value x2_body + + [x3_body_def] Definition + + ⊢ x3_body = incr_fwd (int_to_u32 32) + + [x3_c_def] Definition + + ⊢ x3_c = get_return_value x3_body + + [y_body_def] Definition + + ⊢ y_body = wrap_new_fwd (int_to_i32 2) + + [y_c_def] Definition + + ⊢ y_c = get_return_value y_body + + [yval_body_def] Definition + + ⊢ yval_body = unwrap_y_fwd + + [yval_c_def] Definition + + ⊢ yval_c = get_return_value yval_body + + [EXISTS_pair_t] Theorem + + ⊢ ∀P. (∃p. P p) ⇔ ∃t0 t. P <|pair_x := t0; pair_y := t|> + + [EXISTS_wrap_t] Theorem + + ⊢ ∀P. (∃w. P w) ⇔ ∃u. P <|wrap_val := u|> + + [FORALL_pair_t] Theorem + + ⊢ ∀P. (∀p. P p) ⇔ ∀t0 t. P <|pair_x := t0; pair_y := t|> + + [FORALL_wrap_t] Theorem + + ⊢ ∀P. (∀w. P w) ⇔ ∀u. P <|wrap_val := u|> + + [datatype_pair_t] Theorem + + ⊢ DATATYPE (record pair_t pair_x pair_y) + + [datatype_wrap_t] Theorem + + ⊢ DATATYPE (record wrap_t wrap_val) + + [pair_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. pair_t a0 a1 = pair_t a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [pair_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a0 a1. fn (pair_t a0 a1) = f a0 a1 + + [pair_t_accessors] Theorem + + ⊢ (∀t t0. (pair_t t t0).pair_x = t) ∧ + ∀t t0. (pair_t t t0).pair_y = t0 + + [pair_t_accfupds] Theorem + + ⊢ (∀p f. (p with pair_y updated_by f).pair_x = p.pair_x) ∧ + (∀p f. (p with pair_x updated_by f).pair_y = p.pair_y) ∧ + (∀p f. (p with pair_x updated_by f).pair_x = f p.pair_x) ∧ + ∀p f. (p with pair_y updated_by f).pair_y = f p.pair_y + + [pair_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a0 a1. M' = pair_t a0 a1 ⇒ f a0 a1 = f' a0 a1) ⇒ + pair_t_CASE M f = pair_t_CASE M' f' + + [pair_t_case_eq] Theorem + + ⊢ pair_t_CASE x f = v ⇔ ∃t t0. x = pair_t t t0 ∧ f t t0 = v + + [pair_t_component_equality] Theorem + + ⊢ ∀p1 p2. p1 = p2 ⇔ p1.pair_x = p2.pair_x ∧ p1.pair_y = p2.pair_y + + [pair_t_fn_updates] Theorem + + ⊢ (∀f t t0. pair_t t t0 with pair_x updated_by f = pair_t (f t) t0) ∧ + ∀f t t0. pair_t t t0 with pair_y updated_by f = pair_t t (f t0) + + [pair_t_fupdcanon] Theorem + + ⊢ ∀p g f. + p with <|pair_y updated_by f; pair_x updated_by g|> = + p with <|pair_x updated_by g; pair_y updated_by f|> + + [pair_t_fupdcanon_comp] Theorem + + ⊢ (∀g f. + pair_y_fupd f ∘ pair_x_fupd g = pair_x_fupd g ∘ pair_y_fupd f) ∧ + ∀h g f. + pair_y_fupd f ∘ pair_x_fupd g ∘ h = + pair_x_fupd g ∘ pair_y_fupd f ∘ h + + [pair_t_fupdfupds] Theorem + + ⊢ (∀p g f. + p with <|pair_x updated_by f; pair_x updated_by g|> = + p with pair_x updated_by f ∘ g) ∧ + ∀p g f. + p with <|pair_y updated_by f; pair_y updated_by g|> = + p with pair_y updated_by f ∘ g + + [pair_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. pair_x_fupd f ∘ pair_x_fupd g = pair_x_fupd (f ∘ g)) ∧ + ∀h g f. + pair_x_fupd f ∘ pair_x_fupd g ∘ h = pair_x_fupd (f ∘ g) ∘ h) ∧ + (∀g f. pair_y_fupd f ∘ pair_y_fupd g = pair_y_fupd (f ∘ g)) ∧ + ∀h g f. pair_y_fupd f ∘ pair_y_fupd g ∘ h = pair_y_fupd (f ∘ g) ∘ h + + [pair_t_induction] Theorem + + ⊢ ∀P. (∀t t0. P (pair_t t t0)) ⇒ ∀p. P p + + [pair_t_literal_11] Theorem + + ⊢ ∀t01 t1 t02 t2. + <|pair_x := t01; pair_y := t1|> = <|pair_x := t02; pair_y := t2|> ⇔ + t01 = t02 ∧ t1 = t2 + + [pair_t_literal_nchotomy] Theorem + + ⊢ ∀p. ∃t0 t. p = <|pair_x := t0; pair_y := t|> + + [pair_t_nchotomy] Theorem + + ⊢ ∀pp. ∃t t0. pp = pair_t t t0 + + [pair_t_updates_eq_literal] Theorem + + ⊢ ∀p t0 t. + p with <|pair_x := t0; pair_y := t|> = + <|pair_x := t0; pair_y := t|> + + [wrap_t_11] Theorem + + ⊢ ∀a a'. wrap_t a = wrap_t a' ⇔ a = a' + + [wrap_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a. fn (wrap_t a) = f a + + [wrap_t_accessors] Theorem + + ⊢ ∀t. (wrap_t t).wrap_val = t + + [wrap_t_accfupds] Theorem + + ⊢ ∀w f. (w with wrap_val updated_by f).wrap_val = f w.wrap_val + + [wrap_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a. M' = wrap_t a ⇒ f a = f' a) ⇒ + wrap_t_CASE M f = wrap_t_CASE M' f' + + [wrap_t_case_eq] Theorem + + ⊢ wrap_t_CASE x f = v ⇔ ∃t. x = wrap_t t ∧ f t = v + + [wrap_t_component_equality] Theorem + + ⊢ ∀w1 w2. w1 = w2 ⇔ w1.wrap_val = w2.wrap_val + + [wrap_t_fn_updates] Theorem + + ⊢ ∀f t. wrap_t t with wrap_val updated_by f = wrap_t (f t) + + [wrap_t_fupdfupds] Theorem + + ⊢ ∀w g f. + w with <|wrap_val updated_by f; wrap_val updated_by g|> = + w with wrap_val updated_by f ∘ g + + [wrap_t_fupdfupds_comp] Theorem + + ⊢ (∀g f. wrap_val_fupd f ∘ wrap_val_fupd g = wrap_val_fupd (f ∘ g)) ∧ + ∀h g f. + wrap_val_fupd f ∘ wrap_val_fupd g ∘ h = wrap_val_fupd (f ∘ g) ∘ h + + [wrap_t_induction] Theorem + + ⊢ ∀P. (∀t. P (wrap_t t)) ⇒ ∀w. P w + + [wrap_t_literal_11] Theorem + + ⊢ ∀u1 u2. <|wrap_val := u1|> = <|wrap_val := u2|> ⇔ u1 = u2 + + [wrap_t_literal_nchotomy] Theorem + + ⊢ ∀w. ∃u. w = <|wrap_val := u|> + + [wrap_t_nchotomy] Theorem + + ⊢ ∀ww. ∃t. ww = wrap_t t + + [wrap_t_updates_eq_literal] Theorem + + ⊢ ∀w u. w with wrap_val := u = <|wrap_val := u|> + + +*) +end diff --git a/tests/hol4/misc-external/Holmakefile b/tests/hol4/misc-external/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/misc-external/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/misc-external/external_FunsScript.sml b/tests/hol4/misc-external/external_FunsScript.sml new file mode 100644 index 00000000..8172bc1c --- /dev/null +++ b/tests/hol4/misc-external/external_FunsScript.sml @@ -0,0 +1,108 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [external]: function definitions *) +open primitivesLib divDefLib +open external_TypesTheory external_OpaqueTheory + +val _ = new_theory "external_Funs" + + +val swap_fwd_def = Define ‘ + (** [external::swap] *) + swap_fwd (x : 't) (y : 't) (st : state) : (state # unit) result = + do + (st0, _) <- core_mem_swap_fwd x y st; + (st1, _) <- core_mem_swap_back0 x y st st0; + (st2, _) <- core_mem_swap_back1 x y st st1; + Return (st2, ()) + od +’ + +val swap_back_def = Define ‘ + (** [external::swap] *) + swap_back + (x : 't) (y : 't) (st : state) (st0 : state) : (state # ('t # 't)) result = + do + (st1, _) <- core_mem_swap_fwd x y st; + (st2, x0) <- core_mem_swap_back0 x y st st1; + (_, y0) <- core_mem_swap_back1 x y st st2; + Return (st0, (x0, y0)) + od +’ + +val test_new_non_zero_u32_fwd_def = Define ‘ + (** [external::test_new_non_zero_u32] *) + test_new_non_zero_u32_fwd + (x : u32) (st : state) : (state # core_num_nonzero_non_zero_u32_t) result = + do + (st0, opt) <- core_num_nonzero_non_zero_u32_new_fwd x st; + core_option_option_unwrap_fwd opt st0 + od +’ + +val test_vec_fwd_def = Define ‘ + (** [external::test_vec] *) + test_vec_fwd : unit result = + let v = vec_new in do + _ <- vec_push_back v (int_to_u32 0); + Return () + od +’ + +(** Unit test for [external::test_vec] *) +val _ = assert_return (“test_vec_fwd”) + +val custom_swap_fwd_def = Define ‘ + (** [external::custom_swap] *) + custom_swap_fwd (x : 't) (y : 't) (st : state) : (state # 't) result = + do + (st0, _) <- core_mem_swap_fwd x y st; + (st1, x0) <- core_mem_swap_back0 x y st st0; + (st2, _) <- core_mem_swap_back1 x y st st1; + Return (st2, x0) + od +’ + +val custom_swap_back_def = Define ‘ + (** [external::custom_swap] *) + custom_swap_back + (x : 't) (y : 't) (st : state) (ret : 't) (st0 : state) : + (state # ('t # 't)) result + = + do + (st1, _) <- core_mem_swap_fwd x y st; + (st2, _) <- core_mem_swap_back0 x y st st1; + (_, y0) <- core_mem_swap_back1 x y st st2; + Return (st0, (ret, y0)) + od +’ + +val test_custom_swap_fwd_def = Define ‘ + (** [external::test_custom_swap] *) + test_custom_swap_fwd + (x : u32) (y : u32) (st : state) : (state # unit) result = + do + (st0, _) <- custom_swap_fwd x y st; + Return (st0, ()) + od +’ + +val test_custom_swap_back_def = Define ‘ + (** [external::test_custom_swap] *) + test_custom_swap_back + (x : u32) (y : u32) (st : state) (st0 : state) : + (state # (u32 # u32)) result + = + custom_swap_back x y st (int_to_u32 1) st0 +’ + +val test_swap_non_zero_fwd_def = Define ‘ + (** [external::test_swap_non_zero] *) + test_swap_non_zero_fwd (x : u32) (st : state) : (state # u32) result = + do + (st0, _) <- swap_fwd x (int_to_u32 0) st; + (st1, (x0, _)) <- swap_back x (int_to_u32 0) st st0; + if x0 = int_to_u32 0 then Fail Failure else Return (st1, x0) + od +’ + +val _ = export_theory () diff --git a/tests/hol4/misc-external/external_FunsTheory.sig b/tests/hol4/misc-external/external_FunsTheory.sig new file mode 100644 index 00000000..490f9d06 --- /dev/null +++ b/tests/hol4/misc-external/external_FunsTheory.sig @@ -0,0 +1,105 @@ +signature external_FunsTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val custom_swap_back_def : thm + val custom_swap_fwd_def : thm + val swap_back_def : thm + val swap_fwd_def : thm + val test_custom_swap_back_def : thm + val test_custom_swap_fwd_def : thm + val test_new_non_zero_u32_fwd_def : thm + val test_swap_non_zero_fwd_def : thm + val test_vec_fwd_def : thm + + val external_Funs_grammars : type_grammar.grammar * term_grammar.grammar +(* + [external_Opaque] Parent theory of "external_Funs" + + [custom_swap_back_def] Definition + + ⊢ ∀x y st ret st0. + custom_swap_back x y st ret st0 = + do + (st1,_) <- core_mem_swap_fwd x y st; + (st2,_) <- core_mem_swap_back0 x y st st1; + (_,y0) <- core_mem_swap_back1 x y st st2; + Return (st0,ret,y0) + od + + [custom_swap_fwd_def] Definition + + ⊢ ∀x y st. + custom_swap_fwd x y st = + do + (st0,_) <- core_mem_swap_fwd x y st; + (st1,x0) <- core_mem_swap_back0 x y st st0; + (st2,_) <- core_mem_swap_back1 x y st st1; + Return (st2,x0) + od + + [swap_back_def] Definition + + ⊢ ∀x y st st0. + swap_back x y st st0 = + do + (st1,_) <- core_mem_swap_fwd x y st; + (st2,x0) <- core_mem_swap_back0 x y st st1; + (_,y0) <- core_mem_swap_back1 x y st st2; + Return (st0,x0,y0) + od + + [swap_fwd_def] Definition + + ⊢ ∀x y st. + swap_fwd x y st = + do + (st0,_) <- core_mem_swap_fwd x y st; + (st1,_) <- core_mem_swap_back0 x y st st0; + (st2,_) <- core_mem_swap_back1 x y st st1; + Return (st2,()) + od + + [test_custom_swap_back_def] Definition + + ⊢ ∀x y st st0. + test_custom_swap_back x y st st0 = + custom_swap_back x y st (int_to_u32 1) st0 + + [test_custom_swap_fwd_def] Definition + + ⊢ ∀x y st. + test_custom_swap_fwd x y st = + do (st0,_) <- custom_swap_fwd x y st; Return (st0,()) od + + [test_new_non_zero_u32_fwd_def] Definition + + ⊢ ∀x st. + test_new_non_zero_u32_fwd x st = + do + (st0,opt) <- core_num_nonzero_non_zero_u32_new_fwd x st; + core_option_option_unwrap_fwd opt st0 + od + + [test_swap_non_zero_fwd_def] Definition + + ⊢ ∀x st. + test_swap_non_zero_fwd x st = + do + (st0,_) <- swap_fwd x (int_to_u32 0) st; + (st1,x0,_) <- swap_back x (int_to_u32 0) st st0; + if x0 = int_to_u32 0 then Fail Failure else Return (st1,x0) + od + + [test_vec_fwd_def] Definition + + ⊢ test_vec_fwd = + (let + v = vec_new + in + monad_ignore_bind (vec_push_back v (int_to_u32 0)) (Return ())) + + +*) +end diff --git a/tests/hol4/misc-external/external_OpaqueScript.sml b/tests/hol4/misc-external/external_OpaqueScript.sml new file mode 100644 index 00000000..e2fd281d --- /dev/null +++ b/tests/hol4/misc-external/external_OpaqueScript.sml @@ -0,0 +1,25 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [external]: opaque function definitions *) +open primitivesLib divDefLib +open external_TypesTheory + +val _ = new_theory "external_Opaque" + + +val _ = new_constant ("core_mem_swap_fwd", + “:'t -> 't -> state -> (state # unit) result”) + +val _ = new_constant ("core_mem_swap_back0", + “:'t -> 't -> state -> state -> (state # 't) result”) + +val _ = new_constant ("core_mem_swap_back1", + “:'t -> 't -> state -> state -> (state # 't) result”) + +val _ = new_constant ("core_num_nonzero_non_zero_u32_new_fwd", + “:u32 -> state -> (state # core_num_nonzero_non_zero_u32_t option) + result”) + +val _ = new_constant ("core_option_option_unwrap_fwd", + “:'t option -> state -> (state # 't) result”) + +val _ = export_theory () diff --git a/tests/hol4/misc-external/external_OpaqueTheory.sig b/tests/hol4/misc-external/external_OpaqueTheory.sig new file mode 100644 index 00000000..7cd7a08c --- /dev/null +++ b/tests/hol4/misc-external/external_OpaqueTheory.sig @@ -0,0 +1,11 @@ +signature external_OpaqueTheory = +sig + type thm = Thm.thm + + val external_Opaque_grammars : type_grammar.grammar * term_grammar.grammar +(* + [external_Types] Parent theory of "external_Opaque" + + +*) +end diff --git a/tests/hol4/misc-external/external_TypesScript.sml b/tests/hol4/misc-external/external_TypesScript.sml new file mode 100644 index 00000000..d290c3f6 --- /dev/null +++ b/tests/hol4/misc-external/external_TypesScript.sml @@ -0,0 +1,13 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [external]: type definitions *) +open primitivesLib divDefLib + +val _ = new_theory "external_Types" + + +val _ = new_type ("core_num_nonzero_non_zero_u32_t", 0) + +(** The state type used in the state-error monad *) +val _ = new_type ("state", 0) + +val _ = export_theory () diff --git a/tests/hol4/misc-external/external_TypesTheory.sig b/tests/hol4/misc-external/external_TypesTheory.sig new file mode 100644 index 00000000..17e2e8e3 --- /dev/null +++ b/tests/hol4/misc-external/external_TypesTheory.sig @@ -0,0 +1,11 @@ +signature external_TypesTheory = +sig + type thm = Thm.thm + + val external_Types_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "external_Types" + + +*) +end diff --git a/tests/hol4/misc-loops/Holmakefile b/tests/hol4/misc-loops/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/misc-loops/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/misc-loops/loops_FunsScript.sml b/tests/hol4/misc-loops/loops_FunsScript.sml new file mode 100644 index 00000000..f0ef036b --- /dev/null +++ b/tests/hol4/misc-loops/loops_FunsScript.sml @@ -0,0 +1,753 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [loops]: function definitions *) +open primitivesLib divDefLib +open loops_TypesTheory + +val _ = new_theory "loops_Funs" + + +val [sum_loop_fwd_def] = DefineDiv ‘ + (** [loops::sum] *) + sum_loop_fwd (max : u32) (i : u32) (s : u32) : u32 result = + if u32_lt i max + then ( + do + s0 <- u32_add s i; + i0 <- u32_add i (int_to_u32 1); + sum_loop_fwd max i0 s0 + od) + else u32_mul s (int_to_u32 2) +’ + +val sum_fwd_def = Define ‘ + (** [loops::sum] *) + sum_fwd (max : u32) : u32 result = + sum_loop_fwd max (int_to_u32 0) (int_to_u32 0) +’ + +val [sum_with_mut_borrows_loop_fwd_def] = DefineDiv ‘ + (** [loops::sum_with_mut_borrows] *) + sum_with_mut_borrows_loop_fwd + (max : u32) (mi : u32) (ms : u32) : u32 result = + if u32_lt mi max + then ( + do + ms0 <- u32_add ms mi; + mi0 <- u32_add mi (int_to_u32 1); + sum_with_mut_borrows_loop_fwd max mi0 ms0 + od) + else u32_mul ms (int_to_u32 2) +’ + +val sum_with_mut_borrows_fwd_def = Define ‘ + (** [loops::sum_with_mut_borrows] *) + sum_with_mut_borrows_fwd (max : u32) : u32 result = + sum_with_mut_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0) +’ + +val [sum_with_shared_borrows_loop_fwd_def] = DefineDiv ‘ + (** [loops::sum_with_shared_borrows] *) + sum_with_shared_borrows_loop_fwd + (max : u32) (i : u32) (s : u32) : u32 result = + if u32_lt i max + then ( + do + i0 <- u32_add i (int_to_u32 1); + s0 <- u32_add s i0; + sum_with_shared_borrows_loop_fwd max i0 s0 + od) + else u32_mul s (int_to_u32 2) +’ + +val sum_with_shared_borrows_fwd_def = Define ‘ + (** [loops::sum_with_shared_borrows] *) + sum_with_shared_borrows_fwd (max : u32) : u32 result = + sum_with_shared_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0) +’ + +val [clear_loop_fwd_back_def] = DefineDiv ‘ + (** [loops::clear] *) + clear_loop_fwd_back (v : u32 vec) (i : usize) : u32 vec result = + let i0 = vec_len v in + if usize_lt i i0 + then ( + do + i1 <- usize_add i (int_to_usize 1); + v0 <- vec_index_mut_back v i (int_to_u32 0); + clear_loop_fwd_back v0 i1 + od) + else Return v +’ + +val clear_fwd_back_def = Define ‘ + (** [loops::clear] *) + clear_fwd_back (v : u32 vec) : u32 vec result = + clear_loop_fwd_back v (int_to_usize 0) +’ + +val [list_mem_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_mem] *) + list_mem_loop_fwd (x : u32) (ls : u32 list_t) : bool result = + (case ls of + | ListCons y tl => if y = x then Return T else list_mem_loop_fwd x tl + | ListNil => Return F) +’ + +val list_mem_fwd_def = Define ‘ + (** [loops::list_mem] *) + list_mem_fwd (x : u32) (ls : u32 list_t) : bool result = + list_mem_loop_fwd x ls +’ + +val [list_nth_mut_loop_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop] *) + list_nth_mut_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result = + (case ls of + | ListCons x tl => + if i = int_to_u32 0 + then Return x + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_loop_fwd tl i0 + od) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_fwd_def = Define ‘ + (** [loops::list_nth_mut_loop] *) + list_nth_mut_loop_fwd (ls : 't list_t) (i : u32) : 't result = + list_nth_mut_loop_loop_fwd ls i +’ + +val [list_nth_mut_loop_loop_back_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop] *) + list_nth_mut_loop_loop_back + (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result = + (case ls of + | ListCons x tl => + if i = int_to_u32 0 + then Return (ListCons ret tl) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_loop_loop_back tl i0 ret; + Return (ListCons x tl0) + od) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_back_def = Define ‘ + (** [loops::list_nth_mut_loop] *) + list_nth_mut_loop_back + (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result = + list_nth_mut_loop_loop_back ls i ret +’ + +val [list_nth_shared_loop_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_shared_loop] *) + list_nth_shared_loop_loop_fwd (ls : 't list_t) (i : u32) : 't result = + (case ls of + | ListCons x tl => + if i = int_to_u32 0 + then Return x + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_loop_fwd tl i0 + od) + | ListNil => Fail Failure) +’ + +val list_nth_shared_loop_fwd_def = Define ‘ + (** [loops::list_nth_shared_loop] *) + list_nth_shared_loop_fwd (ls : 't list_t) (i : u32) : 't result = + list_nth_shared_loop_loop_fwd ls i +’ + +val [get_elem_mut_loop_fwd_def] = DefineDiv ‘ + (** [loops::get_elem_mut] *) + get_elem_mut_loop_fwd (x : usize) (ls : usize list_t) : usize result = + (case ls of + | ListCons y tl => if y = x then Return y else get_elem_mut_loop_fwd x tl + | ListNil => Fail Failure) +’ + +val get_elem_mut_fwd_def = Define ‘ + (** [loops::get_elem_mut] *) + get_elem_mut_fwd (slots : usize list_t vec) (x : usize) : usize result = + do + l <- vec_index_mut_fwd slots (int_to_usize 0); + get_elem_mut_loop_fwd x l + od +’ + +val [get_elem_mut_loop_back_def] = DefineDiv ‘ + (** [loops::get_elem_mut] *) + get_elem_mut_loop_back + (x : usize) (ls : usize list_t) (ret : usize) : usize list_t result = + (case ls of + | ListCons y tl => + if y = x + then Return (ListCons ret tl) + else ( + do + tl0 <- get_elem_mut_loop_back x tl ret; + Return (ListCons y tl0) + od) + | ListNil => Fail Failure) +’ + +val get_elem_mut_back_def = Define ‘ + (** [loops::get_elem_mut] *) + get_elem_mut_back + (slots : usize list_t vec) (x : usize) (ret : usize) : + usize list_t vec result + = + do + l <- vec_index_mut_fwd slots (int_to_usize 0); + l0 <- get_elem_mut_loop_back x l ret; + vec_index_mut_back slots (int_to_usize 0) l0 + od +’ + +val [get_elem_shared_loop_fwd_def] = DefineDiv ‘ + (** [loops::get_elem_shared] *) + get_elem_shared_loop_fwd (x : usize) (ls : usize list_t) : usize result = + (case ls of + | ListCons y tl => + if y = x then Return y else get_elem_shared_loop_fwd x tl + | ListNil => Fail Failure) +’ + +val get_elem_shared_fwd_def = Define ‘ + (** [loops::get_elem_shared] *) + get_elem_shared_fwd (slots : usize list_t vec) (x : usize) : usize result = + do + l <- vec_index_fwd slots (int_to_usize 0); + get_elem_shared_loop_fwd x l + od +’ + +val id_mut_fwd_def = Define ‘ + (** [loops::id_mut] *) + id_mut_fwd (ls : 't list_t) : 't list_t result = + Return ls +’ + +val id_mut_back_def = Define ‘ + (** [loops::id_mut] *) + id_mut_back (ls : 't list_t) (ret : 't list_t) : 't list_t result = + Return ret +’ + +val id_shared_fwd_def = Define ‘ + (** [loops::id_shared] *) + id_shared_fwd (ls : 't list_t) : 't list_t result = + Return ls +’ + +val [list_nth_mut_loop_with_id_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop_with_id] *) + list_nth_mut_loop_with_id_loop_fwd (i : u32) (ls : 't list_t) : 't result = + (case ls of + | ListCons x tl => + if i = int_to_u32 0 + then Return x + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_with_id_loop_fwd i0 tl + od) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_with_id_fwd_def = Define ‘ + (** [loops::list_nth_mut_loop_with_id] *) + list_nth_mut_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result = + do + ls0 <- id_mut_fwd ls; + list_nth_mut_loop_with_id_loop_fwd i ls0 + od +’ + +val [list_nth_mut_loop_with_id_loop_back_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop_with_id] *) + list_nth_mut_loop_with_id_loop_back + (i : u32) (ls : 't list_t) (ret : 't) : 't list_t result = + (case ls of + | ListCons x tl => + if i = int_to_u32 0 + then Return (ListCons ret tl) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_loop_with_id_loop_back i0 tl ret; + Return (ListCons x tl0) + od) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_with_id_back_def = Define ‘ + (** [loops::list_nth_mut_loop_with_id] *) + list_nth_mut_loop_with_id_back + (ls : 't list_t) (i : u32) (ret : 't) : 't list_t result = + do + ls0 <- id_mut_fwd ls; + l <- list_nth_mut_loop_with_id_loop_back i ls0 ret; + id_mut_back ls l + od +’ + +val [list_nth_shared_loop_with_id_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_shared_loop_with_id] *) + list_nth_shared_loop_with_id_loop_fwd + (i : u32) (ls : 't list_t) : 't result = + (case ls of + | ListCons x tl => + if i = int_to_u32 0 + then Return x + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_with_id_loop_fwd i0 tl + od) + | ListNil => Fail Failure) +’ + +val list_nth_shared_loop_with_id_fwd_def = Define ‘ + (** [loops::list_nth_shared_loop_with_id] *) + list_nth_shared_loop_with_id_fwd (ls : 't list_t) (i : u32) : 't result = + do + ls0 <- id_shared_fwd ls; + list_nth_shared_loop_with_id_loop_fwd i ls0 + od +’ + +val [list_nth_mut_loop_pair_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop_pair] *) + list_nth_mut_loop_pair_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_pair_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_pair_fwd_def = Define ‘ + (** [loops::list_nth_mut_loop_pair] *) + list_nth_mut_loop_pair_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_mut_loop_pair_loop_fwd ls0 ls1 i +’ + +val [list_nth_mut_loop_pair_loop_back'a_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop_pair] *) + list_nth_mut_loop_pair_loop_back'a + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (ListCons ret tl0) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl00 <- list_nth_mut_loop_pair_loop_back'a tl0 tl1 i0 ret; + Return (ListCons x0 tl00) + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_pair_back'a_def = Define ‘ + (** [loops::list_nth_mut_loop_pair] *) + list_nth_mut_loop_pair_back'a + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret +’ + +val [list_nth_mut_loop_pair_loop_back'b_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop_pair] *) + list_nth_mut_loop_pair_loop_back'b + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (ListCons ret tl1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl10 <- list_nth_mut_loop_pair_loop_back'b tl0 tl1 i0 ret; + Return (ListCons x1 tl10) + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_pair_back'b_def = Define ‘ + (** [loops::list_nth_mut_loop_pair] *) + list_nth_mut_loop_pair_back'b + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret +’ + +val [list_nth_shared_loop_pair_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_shared_loop_pair] *) + list_nth_shared_loop_pair_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_pair_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_shared_loop_pair_fwd_def = Define ‘ + (** [loops::list_nth_shared_loop_pair] *) + list_nth_shared_loop_pair_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_shared_loop_pair_loop_fwd ls0 ls1 i +’ + +val [list_nth_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop_pair_merge] *) + list_nth_mut_loop_pair_merge_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_pair_merge_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_pair_merge_fwd_def = Define ‘ + (** [loops::list_nth_mut_loop_pair_merge] *) + list_nth_mut_loop_pair_merge_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i +’ + +val [list_nth_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘ + (** [loops::list_nth_mut_loop_pair_merge] *) + list_nth_mut_loop_pair_merge_loop_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) : + ('t list_t # 't list_t) result + = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then let (t, t0) = ret in Return (ListCons t tl0, ListCons t0 tl1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + (tl00, tl10) <- + list_nth_mut_loop_pair_merge_loop_back tl0 tl1 i0 ret; + Return (ListCons x0 tl00, ListCons x1 tl10) + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_loop_pair_merge_back_def = Define ‘ + (** [loops::list_nth_mut_loop_pair_merge] *) + list_nth_mut_loop_pair_merge_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : ('t # 't)) : + ('t list_t # 't list_t) result + = + list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret +’ + +val [list_nth_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_shared_loop_pair_merge] *) + list_nth_shared_loop_pair_merge_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_pair_merge_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_shared_loop_pair_merge_fwd_def = Define ‘ + (** [loops::list_nth_shared_loop_pair_merge] *) + list_nth_shared_loop_pair_merge_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i +’ + +val [list_nth_mut_shared_loop_pair_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_mut_shared_loop_pair] *) + list_nth_mut_shared_loop_pair_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_shared_loop_pair_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_shared_loop_pair_fwd_def = Define ‘ + (** [loops::list_nth_mut_shared_loop_pair] *) + list_nth_mut_shared_loop_pair_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i +’ + +val [list_nth_mut_shared_loop_pair_loop_back_def] = DefineDiv ‘ + (** [loops::list_nth_mut_shared_loop_pair] *) + list_nth_mut_shared_loop_pair_loop_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (ListCons ret tl0) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl00 <- list_nth_mut_shared_loop_pair_loop_back tl0 tl1 i0 ret; + Return (ListCons x0 tl00) + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_shared_loop_pair_back_def = Define ‘ + (** [loops::list_nth_mut_shared_loop_pair] *) + list_nth_mut_shared_loop_pair_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret +’ + +val [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_mut_shared_loop_pair_merge] *) + list_nth_mut_shared_loop_pair_merge_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_shared_loop_pair_merge_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_shared_loop_pair_merge_fwd_def = Define ‘ + (** [loops::list_nth_mut_shared_loop_pair_merge] *) + list_nth_mut_shared_loop_pair_merge_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i +’ + +val [list_nth_mut_shared_loop_pair_merge_loop_back_def] = DefineDiv ‘ + (** [loops::list_nth_mut_shared_loop_pair_merge] *) + list_nth_mut_shared_loop_pair_merge_loop_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (ListCons ret tl0) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl00 <- list_nth_mut_shared_loop_pair_merge_loop_back tl0 tl1 i0 ret; + Return (ListCons x0 tl00) + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_mut_shared_loop_pair_merge_back_def = Define ‘ + (** [loops::list_nth_mut_shared_loop_pair_merge] *) + list_nth_mut_shared_loop_pair_merge_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret +’ + +val [list_nth_shared_mut_loop_pair_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_shared_mut_loop_pair] *) + list_nth_shared_mut_loop_pair_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_mut_loop_pair_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_shared_mut_loop_pair_fwd_def = Define ‘ + (** [loops::list_nth_shared_mut_loop_pair] *) + list_nth_shared_mut_loop_pair_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i +’ + +val [list_nth_shared_mut_loop_pair_loop_back_def] = DefineDiv ‘ + (** [loops::list_nth_shared_mut_loop_pair] *) + list_nth_shared_mut_loop_pair_loop_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (ListCons ret tl1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl10 <- list_nth_shared_mut_loop_pair_loop_back tl0 tl1 i0 ret; + Return (ListCons x1 tl10) + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_shared_mut_loop_pair_back_def = Define ‘ + (** [loops::list_nth_shared_mut_loop_pair] *) + list_nth_shared_mut_loop_pair_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret +’ + +val [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] = DefineDiv ‘ + (** [loops::list_nth_shared_mut_loop_pair_merge] *) + list_nth_shared_mut_loop_pair_merge_loop_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (x0, x1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_mut_loop_pair_merge_loop_fwd tl0 tl1 i0 + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_shared_mut_loop_pair_merge_fwd_def = Define ‘ + (** [loops::list_nth_shared_mut_loop_pair_merge] *) + list_nth_shared_mut_loop_pair_merge_fwd + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) : ('t # 't) result = + list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i +’ + +val [list_nth_shared_mut_loop_pair_merge_loop_back_def] = DefineDiv ‘ + (** [loops::list_nth_shared_mut_loop_pair_merge] *) + list_nth_shared_mut_loop_pair_merge_loop_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + (case ls0 of + | ListCons x0 tl0 => + (case ls1 of + | ListCons x1 tl1 => + if i = int_to_u32 0 + then Return (ListCons ret tl1) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl10 <- list_nth_shared_mut_loop_pair_merge_loop_back tl0 tl1 i0 ret; + Return (ListCons x1 tl10) + od) + | ListNil => Fail Failure) + | ListNil => Fail Failure) +’ + +val list_nth_shared_mut_loop_pair_merge_back_def = Define ‘ + (** [loops::list_nth_shared_mut_loop_pair_merge] *) + list_nth_shared_mut_loop_pair_merge_back + (ls0 : 't list_t) (ls1 : 't list_t) (i : u32) (ret : 't) : + 't list_t result + = + list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret +’ + +val _ = export_theory () diff --git a/tests/hol4/misc-loops/loops_FunsTheory.sig b/tests/hol4/misc-loops/loops_FunsTheory.sig new file mode 100644 index 00000000..63fe56c9 --- /dev/null +++ b/tests/hol4/misc-loops/loops_FunsTheory.sig @@ -0,0 +1,731 @@ +signature loops_FunsTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val clear_fwd_back_def : thm + val clear_loop_fwd_back_def : thm + val get_elem_mut_back_def : thm + val get_elem_mut_fwd_def : thm + val get_elem_mut_loop_back_def : thm + val get_elem_mut_loop_fwd_def : thm + val get_elem_shared_fwd_def : thm + val get_elem_shared_loop_fwd_def : thm + val id_mut_back_def : thm + val id_mut_fwd_def : thm + val id_shared_fwd_def : thm + val list_mem_fwd_def : thm + val list_mem_loop_fwd_def : thm + val list_nth_mut_loop_back_def : thm + val list_nth_mut_loop_fwd_def : thm + val list_nth_mut_loop_loop_back_def : thm + val list_nth_mut_loop_loop_fwd_def : thm + val list_nth_mut_loop_pair_back'a_def : thm + val list_nth_mut_loop_pair_back'b_def : thm + val list_nth_mut_loop_pair_fwd_def : thm + val list_nth_mut_loop_pair_loop_back'a_def : thm + val list_nth_mut_loop_pair_loop_back'b_def : thm + val list_nth_mut_loop_pair_loop_fwd_def : thm + val list_nth_mut_loop_pair_merge_back_def : thm + val list_nth_mut_loop_pair_merge_fwd_def : thm + val list_nth_mut_loop_pair_merge_loop_back_def : thm + val list_nth_mut_loop_pair_merge_loop_fwd_def : thm + val list_nth_mut_loop_with_id_back_def : thm + val list_nth_mut_loop_with_id_fwd_def : thm + val list_nth_mut_loop_with_id_loop_back_def : thm + val list_nth_mut_loop_with_id_loop_fwd_def : thm + val list_nth_mut_shared_loop_pair_back_def : thm + val list_nth_mut_shared_loop_pair_fwd_def : thm + val list_nth_mut_shared_loop_pair_loop_back_def : thm + val list_nth_mut_shared_loop_pair_loop_fwd_def : thm + val list_nth_mut_shared_loop_pair_merge_back_def : thm + val list_nth_mut_shared_loop_pair_merge_fwd_def : thm + val list_nth_mut_shared_loop_pair_merge_loop_back_def : thm + val list_nth_mut_shared_loop_pair_merge_loop_fwd_def : thm + val list_nth_shared_loop_fwd_def : thm + val list_nth_shared_loop_loop_fwd_def : thm + val list_nth_shared_loop_pair_fwd_def : thm + val list_nth_shared_loop_pair_loop_fwd_def : thm + val list_nth_shared_loop_pair_merge_fwd_def : thm + val list_nth_shared_loop_pair_merge_loop_fwd_def : thm + val list_nth_shared_loop_with_id_fwd_def : thm + val list_nth_shared_loop_with_id_loop_fwd_def : thm + val list_nth_shared_mut_loop_pair_back_def : thm + val list_nth_shared_mut_loop_pair_fwd_def : thm + val list_nth_shared_mut_loop_pair_loop_back_def : thm + val list_nth_shared_mut_loop_pair_loop_fwd_def : thm + val list_nth_shared_mut_loop_pair_merge_back_def : thm + val list_nth_shared_mut_loop_pair_merge_fwd_def : thm + val list_nth_shared_mut_loop_pair_merge_loop_back_def : thm + val list_nth_shared_mut_loop_pair_merge_loop_fwd_def : thm + val sum_fwd_def : thm + val sum_loop_fwd_def : thm + val sum_with_mut_borrows_fwd_def : thm + val sum_with_mut_borrows_loop_fwd_def : thm + val sum_with_shared_borrows_fwd_def : thm + val sum_with_shared_borrows_loop_fwd_def : thm + + val loops_Funs_grammars : type_grammar.grammar * term_grammar.grammar +(* + [loops_Types] Parent theory of "loops_Funs" + + [clear_fwd_back_def] Definition + + ⊢ ∀v. clear_fwd_back v = clear_loop_fwd_back v (int_to_usize 0) + + [clear_loop_fwd_back_def] Definition + + ⊢ ∀v i. + clear_loop_fwd_back v i = + (let + i0 = vec_len v + in + if usize_lt i i0 then + do + i1 <- usize_add i (int_to_usize 1); + v0 <- vec_index_mut_back v i (int_to_u32 0); + clear_loop_fwd_back v0 i1 + od + else Return v) + + [get_elem_mut_back_def] Definition + + ⊢ ∀slots x ret. + get_elem_mut_back slots x ret = + do + l <- vec_index_mut_fwd slots (int_to_usize 0); + l0 <- get_elem_mut_loop_back x l ret; + vec_index_mut_back slots (int_to_usize 0) l0 + od + + [get_elem_mut_fwd_def] Definition + + ⊢ ∀slots x. + get_elem_mut_fwd slots x = + do + l <- vec_index_mut_fwd slots (int_to_usize 0); + get_elem_mut_loop_fwd x l + od + + [get_elem_mut_loop_back_def] Definition + + ⊢ ∀x ls ret. + get_elem_mut_loop_back x ls ret = + case ls of + ListCons y tl => + if y = x then Return (ListCons ret tl) + else + do + tl0 <- get_elem_mut_loop_back x tl ret; + Return (ListCons y tl0) + od + | ListNil => Fail Failure + + [get_elem_mut_loop_fwd_def] Definition + + ⊢ ∀x ls. + get_elem_mut_loop_fwd x ls = + case ls of + ListCons y tl => + if y = x then Return y else get_elem_mut_loop_fwd x tl + | ListNil => Fail Failure + + [get_elem_shared_fwd_def] Definition + + ⊢ ∀slots x. + get_elem_shared_fwd slots x = + do + l <- vec_index_fwd slots (int_to_usize 0); + get_elem_shared_loop_fwd x l + od + + [get_elem_shared_loop_fwd_def] Definition + + ⊢ ∀x ls. + get_elem_shared_loop_fwd x ls = + case ls of + ListCons y tl => + if y = x then Return y else get_elem_shared_loop_fwd x tl + | ListNil => Fail Failure + + [id_mut_back_def] Definition + + ⊢ ∀ls ret. id_mut_back ls ret = Return ret + + [id_mut_fwd_def] Definition + + ⊢ ∀ls. id_mut_fwd ls = Return ls + + [id_shared_fwd_def] Definition + + ⊢ ∀ls. id_shared_fwd ls = Return ls + + [list_mem_fwd_def] Definition + + ⊢ ∀x ls. list_mem_fwd x ls = list_mem_loop_fwd x ls + + [list_mem_loop_fwd_def] Definition + + ⊢ ∀x ls. + list_mem_loop_fwd x ls = + case ls of + ListCons y tl => + if y = x then Return T else list_mem_loop_fwd x tl + | ListNil => Return F + + [list_nth_mut_loop_back_def] Definition + + ⊢ ∀ls i ret. + list_nth_mut_loop_back ls i ret = + list_nth_mut_loop_loop_back ls i ret + + [list_nth_mut_loop_fwd_def] Definition + + ⊢ ∀ls i. list_nth_mut_loop_fwd ls i = list_nth_mut_loop_loop_fwd ls i + + [list_nth_mut_loop_loop_back_def] Definition + + ⊢ ∀ls i ret. + list_nth_mut_loop_loop_back ls i ret = + case ls of + ListCons x tl => + if i = int_to_u32 0 then Return (ListCons ret tl) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_loop_loop_back tl i0 ret; + Return (ListCons x tl0) + od + | ListNil => Fail Failure + + [list_nth_mut_loop_loop_fwd_def] Definition + + ⊢ ∀ls i. + list_nth_mut_loop_loop_fwd ls i = + case ls of + ListCons x tl => + if i = int_to_u32 0 then Return x + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_loop_fwd tl i0 + od + | ListNil => Fail Failure + + [list_nth_mut_loop_pair_back'a_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_loop_pair_back'a ls0 ls1 i ret = + list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret + + [list_nth_mut_loop_pair_back'b_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_loop_pair_back'b ls0 ls1 i ret = + list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret + + [list_nth_mut_loop_pair_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_loop_pair_fwd ls0 ls1 i = + list_nth_mut_loop_pair_loop_fwd ls0 ls1 i + + [list_nth_mut_loop_pair_loop_back'a_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (ListCons ret tl0) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl00 <- + list_nth_mut_loop_pair_loop_back'a tl0 tl1 i0 ret; + Return (ListCons x0 tl00) + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_loop_pair_loop_back'b_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (ListCons ret tl1) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl10 <- + list_nth_mut_loop_pair_loop_back'b tl0 tl1 i0 ret; + Return (ListCons x1 tl10) + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_loop_pair_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_loop_pair_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_pair_loop_fwd tl0 tl1 i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_loop_pair_merge_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_loop_pair_merge_back ls0 ls1 i ret = + list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret + + [list_nth_mut_loop_pair_merge_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_loop_pair_merge_fwd ls0 ls1 i = + list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i + + [list_nth_mut_loop_pair_merge_loop_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then + (let + (t,t0) = ret + in + Return (ListCons t tl0,ListCons t0 tl1)) + else + do + i0 <- u32_sub i (int_to_u32 1); + (tl00,tl10) <- + list_nth_mut_loop_pair_merge_loop_back tl0 tl1 i0 + ret; + Return (ListCons x0 tl00,ListCons x1 tl10) + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_loop_pair_merge_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_pair_merge_loop_fwd tl0 tl1 i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_loop_with_id_back_def] Definition + + ⊢ ∀ls i ret. + list_nth_mut_loop_with_id_back ls i ret = + do + ls0 <- id_mut_fwd ls; + l <- list_nth_mut_loop_with_id_loop_back i ls0 ret; + id_mut_back ls l + od + + [list_nth_mut_loop_with_id_fwd_def] Definition + + ⊢ ∀ls i. + list_nth_mut_loop_with_id_fwd ls i = + do + ls0 <- id_mut_fwd ls; + list_nth_mut_loop_with_id_loop_fwd i ls0 + od + + [list_nth_mut_loop_with_id_loop_back_def] Definition + + ⊢ ∀i ls ret. + list_nth_mut_loop_with_id_loop_back i ls ret = + case ls of + ListCons x tl => + if i = int_to_u32 0 then Return (ListCons ret tl) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_loop_with_id_loop_back i0 tl ret; + Return (ListCons x tl0) + od + | ListNil => Fail Failure + + [list_nth_mut_loop_with_id_loop_fwd_def] Definition + + ⊢ ∀i ls. + list_nth_mut_loop_with_id_loop_fwd i ls = + case ls of + ListCons x tl => + if i = int_to_u32 0 then Return x + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_loop_with_id_loop_fwd i0 tl + od + | ListNil => Fail Failure + + [list_nth_mut_shared_loop_pair_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_shared_loop_pair_back ls0 ls1 i ret = + list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret + + [list_nth_mut_shared_loop_pair_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_shared_loop_pair_fwd ls0 ls1 i = + list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i + + [list_nth_mut_shared_loop_pair_loop_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (ListCons ret tl0) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl00 <- + list_nth_mut_shared_loop_pair_loop_back tl0 tl1 i0 + ret; + Return (ListCons x0 tl00) + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_shared_loop_pair_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_shared_loop_pair_loop_fwd tl0 tl1 i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_shared_loop_pair_merge_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_shared_loop_pair_merge_back ls0 ls1 i ret = + list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret + + [list_nth_mut_shared_loop_pair_merge_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_shared_loop_pair_merge_fwd ls0 ls1 i = + list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i + + [list_nth_mut_shared_loop_pair_merge_loop_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (ListCons ret tl0) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl00 <- + list_nth_mut_shared_loop_pair_merge_loop_back tl0 + tl1 i0 ret; + Return (ListCons x0 tl00) + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_shared_loop_pair_merge_loop_fwd tl0 tl1 + i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_shared_loop_fwd_def] Definition + + ⊢ ∀ls i. + list_nth_shared_loop_fwd ls i = + list_nth_shared_loop_loop_fwd ls i + + [list_nth_shared_loop_loop_fwd_def] Definition + + ⊢ ∀ls i. + list_nth_shared_loop_loop_fwd ls i = + case ls of + ListCons x tl => + if i = int_to_u32 0 then Return x + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_loop_fwd tl i0 + od + | ListNil => Fail Failure + + [list_nth_shared_loop_pair_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_loop_pair_fwd ls0 ls1 i = + list_nth_shared_loop_pair_loop_fwd ls0 ls1 i + + [list_nth_shared_loop_pair_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_loop_pair_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_pair_loop_fwd tl0 tl1 i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_shared_loop_pair_merge_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_loop_pair_merge_fwd ls0 ls1 i = + list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i + + [list_nth_shared_loop_pair_merge_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_pair_merge_loop_fwd tl0 tl1 i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_shared_loop_with_id_fwd_def] Definition + + ⊢ ∀ls i. + list_nth_shared_loop_with_id_fwd ls i = + do + ls0 <- id_shared_fwd ls; + list_nth_shared_loop_with_id_loop_fwd i ls0 + od + + [list_nth_shared_loop_with_id_loop_fwd_def] Definition + + ⊢ ∀i ls. + list_nth_shared_loop_with_id_loop_fwd i ls = + case ls of + ListCons x tl => + if i = int_to_u32 0 then Return x + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_loop_with_id_loop_fwd i0 tl + od + | ListNil => Fail Failure + + [list_nth_shared_mut_loop_pair_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_shared_mut_loop_pair_back ls0 ls1 i ret = + list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret + + [list_nth_shared_mut_loop_pair_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_mut_loop_pair_fwd ls0 ls1 i = + list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i + + [list_nth_shared_mut_loop_pair_loop_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (ListCons ret tl1) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl10 <- + list_nth_shared_mut_loop_pair_loop_back tl0 tl1 i0 + ret; + Return (ListCons x1 tl10) + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_shared_mut_loop_pair_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_mut_loop_pair_loop_fwd tl0 tl1 i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_shared_mut_loop_pair_merge_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_shared_mut_loop_pair_merge_back ls0 ls1 i ret = + list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret + + [list_nth_shared_mut_loop_pair_merge_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_mut_loop_pair_merge_fwd ls0 ls1 i = + list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i + + [list_nth_shared_mut_loop_pair_merge_loop_back_def] Definition + + ⊢ ∀ls0 ls1 i ret. + list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (ListCons ret tl1) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl10 <- + list_nth_shared_mut_loop_pair_merge_loop_back tl0 + tl1 i0 ret; + Return (ListCons x1 tl10) + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] Definition + + ⊢ ∀ls0 ls1 i. + list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i = + case ls0 of + ListCons x0 tl0 => + (case ls1 of + ListCons x1 tl1 => + if i = int_to_u32 0 then Return (x0,x1) + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_mut_loop_pair_merge_loop_fwd tl0 tl1 + i0 + od + | ListNil => Fail Failure) + | ListNil => Fail Failure + + [sum_fwd_def] Definition + + ⊢ ∀max. sum_fwd max = sum_loop_fwd max (int_to_u32 0) (int_to_u32 0) + + [sum_loop_fwd_def] Definition + + ⊢ ∀max i s. + sum_loop_fwd max i s = + if u32_lt i max then + do + s0 <- u32_add s i; + i0 <- u32_add i (int_to_u32 1); + sum_loop_fwd max i0 s0 + od + else u32_mul s (int_to_u32 2) + + [sum_with_mut_borrows_fwd_def] Definition + + ⊢ ∀max. + sum_with_mut_borrows_fwd max = + sum_with_mut_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0) + + [sum_with_mut_borrows_loop_fwd_def] Definition + + ⊢ ∀max mi ms. + sum_with_mut_borrows_loop_fwd max mi ms = + if u32_lt mi max then + do + ms0 <- u32_add ms mi; + mi0 <- u32_add mi (int_to_u32 1); + sum_with_mut_borrows_loop_fwd max mi0 ms0 + od + else u32_mul ms (int_to_u32 2) + + [sum_with_shared_borrows_fwd_def] Definition + + ⊢ ∀max. + sum_with_shared_borrows_fwd max = + sum_with_shared_borrows_loop_fwd max (int_to_u32 0) + (int_to_u32 0) + + [sum_with_shared_borrows_loop_fwd_def] Definition + + ⊢ ∀max i s. + sum_with_shared_borrows_loop_fwd max i s = + if u32_lt i max then + do + i0 <- u32_add i (int_to_u32 1); + s0 <- u32_add s i0; + sum_with_shared_borrows_loop_fwd max i0 s0 + od + else u32_mul s (int_to_u32 2) + + +*) +end diff --git a/tests/hol4/misc-loops/loops_TypesScript.sml b/tests/hol4/misc-loops/loops_TypesScript.sml new file mode 100644 index 00000000..e3e5b8d1 --- /dev/null +++ b/tests/hol4/misc-loops/loops_TypesScript.sml @@ -0,0 +1,13 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [loops]: type definitions *) +open primitivesLib divDefLib + +val _ = new_theory "loops_Types" + + +Datatype: + (** [loops::List] *) + list_t = | ListCons 't list_t | ListNil +End + +val _ = export_theory () diff --git a/tests/hol4/misc-loops/loops_TypesTheory.sig b/tests/hol4/misc-loops/loops_TypesTheory.sig new file mode 100644 index 00000000..c3e638d8 --- /dev/null +++ b/tests/hol4/misc-loops/loops_TypesTheory.sig @@ -0,0 +1,94 @@ +signature loops_TypesTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val list_t_TY_DEF : thm + val list_t_case_def : thm + val list_t_size_def : thm + + (* Theorems *) + val datatype_list_t : thm + val list_t_11 : thm + val list_t_Axiom : thm + val list_t_case_cong : thm + val list_t_case_eq : thm + val list_t_distinct : thm + val list_t_induction : thm + val list_t_nchotomy : thm + + val loops_Types_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "loops_Types" + + [list_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('list_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 a0 + (ind_type$FCONS a1 (λn. ind_type$BOTTOM))) + a0 a1 ∧ $var$('list_t') a1) ∨ + a0' = + ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ + $var$('list_t') a0') ⇒ + $var$('list_t') a0') rep + + [list_t_case_def] Definition + + ⊢ (∀a0 a1 f v. list_t_CASE (ListCons a0 a1) f v = f a0 a1) ∧ + ∀f v. list_t_CASE ListNil f v = v + + [list_t_size_def] Definition + + ⊢ (∀f a0 a1. + list_t_size f (ListCons a0 a1) = 1 + (f a0 + list_t_size f a1)) ∧ + ∀f. list_t_size f ListNil = 0 + + [datatype_list_t] Theorem + + ⊢ DATATYPE (list_t ListCons ListNil) + + [list_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + ListCons a0 a1 = ListCons a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [list_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a0 a1. fn (ListCons a0 a1) = f0 a0 a1 (fn a1)) ∧ + fn ListNil = f1 + + [list_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ (∀a0 a1. M' = ListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ + (M' = ListNil ⇒ v = v') ⇒ + list_t_CASE M f v = list_t_CASE M' f' v' + + [list_t_case_eq] Theorem + + ⊢ list_t_CASE x f v = v' ⇔ + (∃t l. x = ListCons t l ∧ f t l = v') ∨ x = ListNil ∧ v = v' + + [list_t_distinct] Theorem + + ⊢ ∀a1 a0. ListCons a0 a1 ≠ ListNil + + [list_t_induction] Theorem + + ⊢ ∀P. (∀l. P l ⇒ ∀t. P (ListCons t l)) ∧ P ListNil ⇒ ∀l. P l + + [list_t_nchotomy] Theorem + + ⊢ ∀ll. (∃t l. ll = ListCons t l) ∨ ll = ListNil + + +*) +end diff --git a/tests/hol4/misc-no_nested_borrows/Holmakefile b/tests/hol4/misc-no_nested_borrows/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/misc-no_nested_borrows/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml new file mode 100644 index 00000000..c8b106cd --- /dev/null +++ b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsScript.sml @@ -0,0 +1,590 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [no_nested_borrows] *) +open primitivesLib divDefLib + +val _ = new_theory "noNestedBorrows" + + +Datatype: + (** [no_nested_borrows::Pair] *) + pair_t = <| pair_x : 't1; pair_y : 't2; |> +End + +Datatype: + (** [no_nested_borrows::List] *) + list_t = | ListCons 't list_t | ListNil +End + +Datatype: + (** [no_nested_borrows::One] *) + one_t = | OneOne 't1 +End + +Datatype: + (** [no_nested_borrows::EmptyEnum] *) + empty_enum_t = | EmptyEnumEmpty +End + +Datatype: + (** [no_nested_borrows::Enum] *) + enum_t = | EnumVariant1 | EnumVariant2 +End + +Type empty_struct_t = “: unit” + +Datatype: + (** [no_nested_borrows::Sum] *) + sum_t = | SumLeft 't1 | SumRight 't2 +End + +val neg_test_fwd_def = Define ‘ + (** [no_nested_borrows::neg_test] *) + neg_test_fwd (x : i32) : i32 result = + i32_neg x +’ + +val add_test_fwd_def = Define ‘ + (** [no_nested_borrows::add_test] *) + add_test_fwd (x : u32) (y : u32) : u32 result = + u32_add x y +’ + +val subs_test_fwd_def = Define ‘ + (** [no_nested_borrows::subs_test] *) + subs_test_fwd (x : u32) (y : u32) : u32 result = + u32_sub x y +’ + +val div_test_fwd_def = Define ‘ + (** [no_nested_borrows::div_test] *) + div_test_fwd (x : u32) (y : u32) : u32 result = + u32_div x y +’ + +val div_test1_fwd_def = Define ‘ + (** [no_nested_borrows::div_test1] *) + div_test1_fwd (x : u32) : u32 result = + u32_div x (int_to_u32 2) +’ + +val rem_test_fwd_def = Define ‘ + (** [no_nested_borrows::rem_test] *) + rem_test_fwd (x : u32) (y : u32) : u32 result = + u32_rem x y +’ + +val cast_test_fwd_def = Define ‘ + (** [no_nested_borrows::cast_test] *) + cast_test_fwd (x : u32) : i32 result = + mk_i32 (u32_to_int x) +’ + +val test2_fwd_def = Define ‘ + (** [no_nested_borrows::test2] *) + test2_fwd : unit result = + do + _ <- u32_add (int_to_u32 23) (int_to_u32 44); + Return () + od +’ + +(** Unit test for [no_nested_borrows::test2] *) +val _ = assert_return (“test2_fwd”) + +val get_max_fwd_def = Define ‘ + (** [no_nested_borrows::get_max] *) + get_max_fwd (x : u32) (y : u32) : u32 result = + if u32_ge x y then Return x else Return y +’ + +val test3_fwd_def = Define ‘ + (** [no_nested_borrows::test3] *) + test3_fwd : unit result = + do + x <- get_max_fwd (int_to_u32 4) (int_to_u32 3); + y <- get_max_fwd (int_to_u32 10) (int_to_u32 11); + z <- u32_add x y; + if ~ (z = int_to_u32 15) then Fail Failure else Return () + od +’ + +(** Unit test for [no_nested_borrows::test3] *) +val _ = assert_return (“test3_fwd”) + +val test_neg1_fwd_def = Define ‘ + (** [no_nested_borrows::test_neg1] *) + test_neg1_fwd : unit result = + do + y <- i32_neg (int_to_i32 3); + if ~ (y = int_to_i32 (-3)) then Fail Failure else Return () + od +’ + +(** Unit test for [no_nested_borrows::test_neg1] *) +val _ = assert_return (“test_neg1_fwd”) + +val refs_test1_fwd_def = Define ‘ + (** [no_nested_borrows::refs_test1] *) + refs_test1_fwd : unit result = + if ~ (int_to_i32 1 = int_to_i32 1) then Fail Failure else Return () +’ + +(** Unit test for [no_nested_borrows::refs_test1] *) +val _ = assert_return (“refs_test1_fwd”) + +val refs_test2_fwd_def = Define ‘ + (** [no_nested_borrows::refs_test2] *) + refs_test2_fwd : unit result = + if ~ (int_to_i32 2 = int_to_i32 2) + then Fail Failure + else + if ~ (int_to_i32 0 = int_to_i32 0) + then Fail Failure + else + if ~ (int_to_i32 2 = int_to_i32 2) + then Fail Failure + else + if ~ (int_to_i32 2 = int_to_i32 2) then Fail Failure else Return () +’ + +(** Unit test for [no_nested_borrows::refs_test2] *) +val _ = assert_return (“refs_test2_fwd”) + +val test_list1_fwd_def = Define ‘ + (** [no_nested_borrows::test_list1] *) + test_list1_fwd : unit result = + Return () +’ + +(** Unit test for [no_nested_borrows::test_list1] *) +val _ = assert_return (“test_list1_fwd”) + +val test_box1_fwd_def = Define ‘ + (** [no_nested_borrows::test_box1] *) + test_box1_fwd : unit result = + let b = int_to_i32 1 in + let x = b in + if ~ (x = int_to_i32 1) then Fail Failure else Return () +’ + +(** Unit test for [no_nested_borrows::test_box1] *) +val _ = assert_return (“test_box1_fwd”) + +val copy_int_fwd_def = Define ‘ + (** [no_nested_borrows::copy_int] *) + copy_int_fwd (x : i32) : i32 result = + Return x +’ + +val test_unreachable_fwd_def = Define ‘ + (** [no_nested_borrows::test_unreachable] *) + test_unreachable_fwd (b : bool) : unit result = + if b then Fail Failure else Return () +’ + +val test_panic_fwd_def = Define ‘ + (** [no_nested_borrows::test_panic] *) + test_panic_fwd (b : bool) : unit result = + if b then Fail Failure else Return () +’ + +val test_copy_int_fwd_def = Define ‘ + (** [no_nested_borrows::test_copy_int] *) + test_copy_int_fwd : unit result = + do + y <- copy_int_fwd (int_to_i32 0); + if ~ (int_to_i32 0 = y) then Fail Failure else Return () + od +’ + +(** Unit test for [no_nested_borrows::test_copy_int] *) +val _ = assert_return (“test_copy_int_fwd”) + +val is_cons_fwd_def = Define ‘ + (** [no_nested_borrows::is_cons] *) + is_cons_fwd (l : 't list_t) : bool result = + (case l of | ListCons t l0 => Return T | ListNil => Return F) +’ + +val test_is_cons_fwd_def = Define ‘ + (** [no_nested_borrows::test_is_cons] *) + test_is_cons_fwd : unit result = + let l = ListNil in + do + b <- is_cons_fwd (ListCons (int_to_i32 0) l); + if ~ b then Fail Failure else Return () + od +’ + +(** Unit test for [no_nested_borrows::test_is_cons] *) +val _ = assert_return (“test_is_cons_fwd”) + +val split_list_fwd_def = Define ‘ + (** [no_nested_borrows::split_list] *) + split_list_fwd (l : 't list_t) : ('t # 't list_t) result = + (case l of | ListCons hd tl => Return (hd, tl) | ListNil => Fail Failure) +’ + +val test_split_list_fwd_def = Define ‘ + (** [no_nested_borrows::test_split_list] *) + test_split_list_fwd : unit result = + let l = ListNil in + do + p <- split_list_fwd (ListCons (int_to_i32 0) l); + let (hd, _) = p in + if ~ (hd = int_to_i32 0) then Fail Failure else Return () + od +’ + +(** Unit test for [no_nested_borrows::test_split_list] *) +val _ = assert_return (“test_split_list_fwd”) + +val choose_fwd_def = Define ‘ + (** [no_nested_borrows::choose] *) + choose_fwd (b : bool) (x : 't) (y : 't) : 't result = + if b then Return x else Return y +’ + +val choose_back_def = Define ‘ + (** [no_nested_borrows::choose] *) + choose_back (b : bool) (x : 't) (y : 't) (ret : 't) : ('t # 't) result = + if b then Return (ret, y) else Return (x, ret) +’ + +val choose_test_fwd_def = Define ‘ + (** [no_nested_borrows::choose_test] *) + choose_test_fwd : unit result = + do + z <- choose_fwd T (int_to_i32 0) (int_to_i32 0); + z0 <- i32_add z (int_to_i32 1); + if ~ (z0 = int_to_i32 1) + then Fail Failure + else ( + do + (x, y) <- choose_back T (int_to_i32 0) (int_to_i32 0) z0; + if ~ (x = int_to_i32 1) + then Fail Failure + else if ~ (y = int_to_i32 0) then Fail Failure else Return () + od) + od +’ + +(** Unit test for [no_nested_borrows::choose_test] *) +val _ = assert_return (“choose_test_fwd”) + +val test_char_fwd_def = Define ‘ + (** [no_nested_borrows::test_char] *) + test_char_fwd : char result = + Return #"a" +’ + +Datatype: + (** [no_nested_borrows::NodeElem] *) + node_elem_t = | NodeElemCons tree_t node_elem_t | NodeElemNil ; + + (** [no_nested_borrows::Tree] *) + tree_t = | TreeLeaf 't | TreeNode 't node_elem_t tree_t +End + +val [list_length_fwd_def] = DefineDiv ‘ + (** [no_nested_borrows::list_length] *) + list_length_fwd (l : 't list_t) : u32 result = + (case l of + | ListCons t l1 => do + i <- list_length_fwd l1; + u32_add (int_to_u32 1) i + od + | ListNil => Return (int_to_u32 0)) +’ + +val [list_nth_shared_fwd_def] = DefineDiv ‘ + (** [no_nested_borrows::list_nth_shared] *) + list_nth_shared_fwd (l : 't list_t) (i : u32) : 't result = + (case l of + | ListCons x tl => + if i = int_to_u32 0 + then Return x + else (do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_fwd tl i0 + od) + | ListNil => Fail Failure) +’ + +val [list_nth_mut_fwd_def] = DefineDiv ‘ + (** [no_nested_borrows::list_nth_mut] *) + list_nth_mut_fwd (l : 't list_t) (i : u32) : 't result = + (case l of + | ListCons x tl => + if i = int_to_u32 0 + then Return x + else (do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_fwd tl i0 + od) + | ListNil => Fail Failure) +’ + +val [list_nth_mut_back_def] = DefineDiv ‘ + (** [no_nested_borrows::list_nth_mut] *) + list_nth_mut_back (l : 't list_t) (i : u32) (ret : 't) : 't list_t result = + (case l of + | ListCons x tl => + if i = int_to_u32 0 + then Return (ListCons ret tl) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_back tl i0 ret; + Return (ListCons x tl0) + od) + | ListNil => Fail Failure) +’ + +val [list_rev_aux_fwd_def] = DefineDiv ‘ + (** [no_nested_borrows::list_rev_aux] *) + list_rev_aux_fwd (li : 't list_t) (lo : 't list_t) : 't list_t result = + (case li of + | ListCons hd tl => list_rev_aux_fwd tl (ListCons hd lo) + | ListNil => Return lo) +’ + +val list_rev_fwd_back_def = Define ‘ + (** [no_nested_borrows::list_rev] *) + list_rev_fwd_back (l : 't list_t) : 't list_t result = + let li = mem_replace_fwd l ListNil in list_rev_aux_fwd li ListNil +’ + +val test_list_functions_fwd_def = Define ‘ + (** [no_nested_borrows::test_list_functions] *) + test_list_functions_fwd : unit result = + let l = ListNil in + let l0 = ListCons (int_to_i32 2) l in + let l1 = ListCons (int_to_i32 1) l0 in + do + i <- list_length_fwd (ListCons (int_to_i32 0) l1); + if ~ (i = int_to_u32 3) + then Fail Failure + else ( + do + i0 <- list_nth_shared_fwd (ListCons (int_to_i32 0) l1) (int_to_u32 0); + if ~ (i0 = int_to_i32 0) + then Fail Failure + else ( + do + i1 <- list_nth_shared_fwd (ListCons (int_to_i32 0) l1) (int_to_u32 1); + if ~ (i1 = int_to_i32 1) + then Fail Failure + else ( + do + i2 <- + list_nth_shared_fwd (ListCons (int_to_i32 0) l1) (int_to_u32 2); + if ~ (i2 = int_to_i32 2) + then Fail Failure + else ( + do + ls <- + list_nth_mut_back (ListCons (int_to_i32 0) l1) (int_to_u32 1) + (int_to_i32 3); + i3 <- list_nth_shared_fwd ls (int_to_u32 0); + if ~ (i3 = int_to_i32 0) + then Fail Failure + else ( + do + i4 <- list_nth_shared_fwd ls (int_to_u32 1); + if ~ (i4 = int_to_i32 3) + then Fail Failure + else ( + do + i5 <- list_nth_shared_fwd ls (int_to_u32 2); + if ~ (i5 = int_to_i32 2) then Fail Failure else Return () + od) + od) + od) + od) + od) + od) + od +’ + +(** Unit test for [no_nested_borrows::test_list_functions] *) +val _ = assert_return (“test_list_functions_fwd”) + +val id_mut_pair1_fwd_def = Define ‘ + (** [no_nested_borrows::id_mut_pair1] *) + id_mut_pair1_fwd (x : 't1) (y : 't2) : ('t1 # 't2) result = + Return (x, y) +’ + +val id_mut_pair1_back_def = Define ‘ + (** [no_nested_borrows::id_mut_pair1] *) + id_mut_pair1_back + (x : 't1) (y : 't2) (ret : ('t1 # 't2)) : ('t1 # 't2) result = + let (t, t0) = ret in Return (t, t0) +’ + +val id_mut_pair2_fwd_def = Define ‘ + (** [no_nested_borrows::id_mut_pair2] *) + id_mut_pair2_fwd (p : ('t1 # 't2)) : ('t1 # 't2) result = + let (t, t0) = p in Return (t, t0) +’ + +val id_mut_pair2_back_def = Define ‘ + (** [no_nested_borrows::id_mut_pair2] *) + id_mut_pair2_back + (p : ('t1 # 't2)) (ret : ('t1 # 't2)) : ('t1 # 't2) result = + let (t, t0) = ret in Return (t, t0) +’ + +val id_mut_pair3_fwd_def = Define ‘ + (** [no_nested_borrows::id_mut_pair3] *) + id_mut_pair3_fwd (x : 't1) (y : 't2) : ('t1 # 't2) result = + Return (x, y) +’ + +val id_mut_pair3_back'a_def = Define ‘ + (** [no_nested_borrows::id_mut_pair3] *) + id_mut_pair3_back'a (x : 't1) (y : 't2) (ret : 't1) : 't1 result = + Return ret +’ + +val id_mut_pair3_back'b_def = Define ‘ + (** [no_nested_borrows::id_mut_pair3] *) + id_mut_pair3_back'b (x : 't1) (y : 't2) (ret : 't2) : 't2 result = + Return ret +’ + +val id_mut_pair4_fwd_def = Define ‘ + (** [no_nested_borrows::id_mut_pair4] *) + id_mut_pair4_fwd (p : ('t1 # 't2)) : ('t1 # 't2) result = + let (t, t0) = p in Return (t, t0) +’ + +val id_mut_pair4_back'a_def = Define ‘ + (** [no_nested_borrows::id_mut_pair4] *) + id_mut_pair4_back'a (p : ('t1 # 't2)) (ret : 't1) : 't1 result = + Return ret +’ + +val id_mut_pair4_back'b_def = Define ‘ + (** [no_nested_borrows::id_mut_pair4] *) + id_mut_pair4_back'b (p : ('t1 # 't2)) (ret : 't2) : 't2 result = + Return ret +’ + +Datatype: + (** [no_nested_borrows::StructWithTuple] *) + struct_with_tuple_t = <| struct_with_tuple_p : ('t1 # 't2); |> +End + +val new_tuple1_fwd_def = Define ‘ + (** [no_nested_borrows::new_tuple1] *) + new_tuple1_fwd : (u32, u32) struct_with_tuple_t result = + Return (<| struct_with_tuple_p := (int_to_u32 1, int_to_u32 2) |>) +’ + +val new_tuple2_fwd_def = Define ‘ + (** [no_nested_borrows::new_tuple2] *) + new_tuple2_fwd : (i16, i16) struct_with_tuple_t result = + Return (<| struct_with_tuple_p := (int_to_i16 1, int_to_i16 2) |>) +’ + +val new_tuple3_fwd_def = Define ‘ + (** [no_nested_borrows::new_tuple3] *) + new_tuple3_fwd : (u64, i64) struct_with_tuple_t result = + Return (<| struct_with_tuple_p := (int_to_u64 1, int_to_i64 2) |>) +’ + +Datatype: + (** [no_nested_borrows::StructWithPair] *) + struct_with_pair_t = <| struct_with_pair_p : ('t1, 't2) pair_t; |> +End + +val new_pair1_fwd_def = Define ‘ + (** [no_nested_borrows::new_pair1] *) + new_pair1_fwd : (u32, u32) struct_with_pair_t result = + Return + (<| + struct_with_pair_p := + (<| pair_x := (int_to_u32 1); pair_y := (int_to_u32 2) |>) + |>) +’ + +val test_constants_fwd_def = Define ‘ + (** [no_nested_borrows::test_constants] *) + test_constants_fwd : unit result = + do + swt <- new_tuple1_fwd; + let (i, _) = swt.struct_with_tuple_p in + if ~ (i = int_to_u32 1) + then Fail Failure + else ( + do + swt0 <- new_tuple2_fwd; + let (i0, _) = swt0.struct_with_tuple_p in + if ~ (i0 = int_to_i16 1) + then Fail Failure + else ( + do + swt1 <- new_tuple3_fwd; + let (i1, _) = swt1.struct_with_tuple_p in + if ~ (i1 = int_to_u64 1) + then Fail Failure + else ( + do + swp <- new_pair1_fwd; + if ~ (swp.struct_with_pair_p.pair_x = int_to_u32 1) + then Fail Failure + else Return () + od) + od) + od) + od +’ + +(** Unit test for [no_nested_borrows::test_constants] *) +val _ = assert_return (“test_constants_fwd”) + +val test_weird_borrows1_fwd_def = Define ‘ + (** [no_nested_borrows::test_weird_borrows1] *) + test_weird_borrows1_fwd : unit result = + Return () +’ + +(** Unit test for [no_nested_borrows::test_weird_borrows1] *) +val _ = assert_return (“test_weird_borrows1_fwd”) + +val test_mem_replace_fwd_back_def = Define ‘ + (** [no_nested_borrows::test_mem_replace] *) + test_mem_replace_fwd_back (px : u32) : u32 result = + let y = mem_replace_fwd px (int_to_u32 1) in + if ~ (y = int_to_u32 0) then Fail Failure else Return (int_to_u32 2) +’ + +val test_shared_borrow_bool1_fwd_def = Define ‘ + (** [no_nested_borrows::test_shared_borrow_bool1] *) + test_shared_borrow_bool1_fwd (b : bool) : u32 result = + if b then Return (int_to_u32 0) else Return (int_to_u32 1) +’ + +val test_shared_borrow_bool2_fwd_def = Define ‘ + (** [no_nested_borrows::test_shared_borrow_bool2] *) + test_shared_borrow_bool2_fwd : u32 result = + Return (int_to_u32 0) +’ + +val test_shared_borrow_enum1_fwd_def = Define ‘ + (** [no_nested_borrows::test_shared_borrow_enum1] *) + test_shared_borrow_enum1_fwd (l : u32 list_t) : u32 result = + (case l of + | ListCons i l0 => Return (int_to_u32 1) + | ListNil => Return (int_to_u32 0)) +’ + +val test_shared_borrow_enum2_fwd_def = Define ‘ + (** [no_nested_borrows::test_shared_borrow_enum2] *) + test_shared_borrow_enum2_fwd : u32 result = + Return (int_to_u32 0) +’ + +val _ = export_theory () diff --git a/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig new file mode 100644 index 00000000..82c842be --- /dev/null +++ b/tests/hol4/misc-no_nested_borrows/noNestedBorrowsTheory.sig @@ -0,0 +1,1596 @@ +signature noNestedBorrowsTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val add_test_fwd_def : thm + val cast_test_fwd_def : thm + val choose_back_def : thm + val choose_fwd_def : thm + val choose_test_fwd_def : thm + val copy_int_fwd_def : thm + val div_test1_fwd_def : thm + val div_test_fwd_def : thm + val empty_enum_t_BIJ : thm + val empty_enum_t_CASE : thm + val empty_enum_t_TY_DEF : thm + val empty_enum_t_size_def : thm + val enum_t_BIJ : thm + val enum_t_CASE : thm + val enum_t_TY_DEF : thm + val enum_t_size_def : thm + val get_max_fwd_def : thm + val id_mut_pair1_back_def : thm + val id_mut_pair1_fwd_def : thm + val id_mut_pair2_back_def : thm + val id_mut_pair2_fwd_def : thm + val id_mut_pair3_back'a_def : thm + val id_mut_pair3_back'b_def : thm + val id_mut_pair3_fwd_def : thm + val id_mut_pair4_back'a_def : thm + val id_mut_pair4_back'b_def : thm + val id_mut_pair4_fwd_def : thm + val is_cons_fwd_def : thm + val list_length_fwd_def : thm + val list_nth_mut_back_def : thm + val list_nth_mut_fwd_def : thm + val list_nth_shared_fwd_def : thm + val list_rev_aux_fwd_def : thm + val list_rev_fwd_back_def : thm + val list_t_TY_DEF : thm + val list_t_case_def : thm + val list_t_size_def : thm + val neg_test_fwd_def : thm + val new_pair1_fwd_def : thm + val new_tuple1_fwd_def : thm + val new_tuple2_fwd_def : thm + val new_tuple3_fwd_def : thm + val node_elem_t_TY_DEF : thm + val node_elem_t_case_def : thm + val node_elem_t_size_def : thm + val one_t_TY_DEF : thm + val one_t_case_def : thm + val one_t_size_def : thm + val pair_t_TY_DEF : thm + val pair_t_case_def : thm + val pair_t_size_def : thm + val recordtype_pair_t_seldef_pair_x_def : thm + val recordtype_pair_t_seldef_pair_x_fupd_def : thm + val recordtype_pair_t_seldef_pair_y_def : thm + val recordtype_pair_t_seldef_pair_y_fupd_def : thm + val recordtype_struct_with_pair_t_seldef_struct_with_pair_p_def : thm + val recordtype_struct_with_pair_t_seldef_struct_with_pair_p_fupd_def : thm + val recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_def : thm + val recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_fupd_def : thm + val refs_test1_fwd_def : thm + val refs_test2_fwd_def : thm + val rem_test_fwd_def : thm + val split_list_fwd_def : thm + val struct_with_pair_t_TY_DEF : thm + val struct_with_pair_t_case_def : thm + val struct_with_pair_t_size_def : thm + val struct_with_tuple_t_TY_DEF : thm + val struct_with_tuple_t_case_def : thm + val struct_with_tuple_t_size_def : thm + val subs_test_fwd_def : thm + val sum_t_TY_DEF : thm + val sum_t_case_def : thm + val sum_t_size_def : thm + val test2_fwd_def : thm + val test3_fwd_def : thm + val test_box1_fwd_def : thm + val test_char_fwd_def : thm + val test_constants_fwd_def : thm + val test_copy_int_fwd_def : thm + val test_is_cons_fwd_def : thm + val test_list1_fwd_def : thm + val test_list_functions_fwd_def : thm + val test_mem_replace_fwd_back_def : thm + val test_neg1_fwd_def : thm + val test_panic_fwd_def : thm + val test_shared_borrow_bool1_fwd_def : thm + val test_shared_borrow_bool2_fwd_def : thm + val test_shared_borrow_enum1_fwd_def : thm + val test_shared_borrow_enum2_fwd_def : thm + val test_split_list_fwd_def : thm + val test_unreachable_fwd_def : thm + val test_weird_borrows1_fwd_def : thm + val tree_t_TY_DEF : thm + val tree_t_case_def : thm + + (* Theorems *) + val EXISTS_pair_t : thm + val EXISTS_struct_with_pair_t : thm + val EXISTS_struct_with_tuple_t : thm + val FORALL_pair_t : thm + val FORALL_struct_with_pair_t : thm + val FORALL_struct_with_tuple_t : thm + val datatype_empty_enum_t : thm + val datatype_enum_t : thm + val datatype_list_t : thm + val datatype_node_elem_t : thm + val datatype_one_t : thm + val datatype_pair_t : thm + val datatype_struct_with_pair_t : thm + val datatype_struct_with_tuple_t : thm + val datatype_sum_t : thm + val empty_enum_t2num_11 : thm + val empty_enum_t2num_ONTO : thm + val empty_enum_t2num_num2empty_enum_t : thm + val empty_enum_t2num_thm : thm + val empty_enum_t_Axiom : thm + val empty_enum_t_EQ_empty_enum_t : thm + val empty_enum_t_case_cong : thm + val empty_enum_t_case_def : thm + val empty_enum_t_case_eq : thm + val empty_enum_t_induction : thm + val empty_enum_t_nchotomy : thm + val enum_t2num_11 : thm + val enum_t2num_ONTO : thm + val enum_t2num_num2enum_t : thm + val enum_t2num_thm : thm + val enum_t_Axiom : thm + val enum_t_EQ_enum_t : thm + val enum_t_case_cong : thm + val enum_t_case_def : thm + val enum_t_case_eq : thm + val enum_t_distinct : thm + val enum_t_induction : thm + val enum_t_nchotomy : thm + val list_t_11 : thm + val list_t_Axiom : thm + val list_t_case_cong : thm + val list_t_case_eq : thm + val list_t_distinct : thm + val list_t_induction : thm + val list_t_nchotomy : thm + val node_elem_t_11 : thm + val node_elem_t_Axiom : thm + val node_elem_t_case_cong : thm + val node_elem_t_case_eq : thm + val node_elem_t_distinct : thm + val node_elem_t_induction : thm + val node_elem_t_nchotomy : thm + val num2empty_enum_t_11 : thm + val num2empty_enum_t_ONTO : thm + val num2empty_enum_t_empty_enum_t2num : thm + val num2empty_enum_t_thm : thm + val num2enum_t_11 : thm + val num2enum_t_ONTO : thm + val num2enum_t_enum_t2num : thm + val num2enum_t_thm : thm + val one_t_11 : thm + val one_t_Axiom : thm + val one_t_case_cong : thm + val one_t_case_eq : thm + val one_t_induction : thm + val one_t_nchotomy : thm + val pair_t_11 : thm + val pair_t_Axiom : thm + val pair_t_accessors : thm + val pair_t_accfupds : thm + val pair_t_case_cong : thm + val pair_t_case_eq : thm + val pair_t_component_equality : thm + val pair_t_fn_updates : thm + val pair_t_fupdcanon : thm + val pair_t_fupdcanon_comp : thm + val pair_t_fupdfupds : thm + val pair_t_fupdfupds_comp : thm + val pair_t_induction : thm + val pair_t_literal_11 : thm + val pair_t_literal_nchotomy : thm + val pair_t_nchotomy : thm + val pair_t_updates_eq_literal : thm + val struct_with_pair_t_11 : thm + val struct_with_pair_t_Axiom : thm + val struct_with_pair_t_accessors : thm + val struct_with_pair_t_accfupds : thm + val struct_with_pair_t_case_cong : thm + val struct_with_pair_t_case_eq : thm + val struct_with_pair_t_component_equality : thm + val struct_with_pair_t_fn_updates : thm + val struct_with_pair_t_fupdfupds : thm + val struct_with_pair_t_fupdfupds_comp : thm + val struct_with_pair_t_induction : thm + val struct_with_pair_t_literal_11 : thm + val struct_with_pair_t_literal_nchotomy : thm + val struct_with_pair_t_nchotomy : thm + val struct_with_pair_t_updates_eq_literal : thm + val struct_with_tuple_t_11 : thm + val struct_with_tuple_t_Axiom : thm + val struct_with_tuple_t_accessors : thm + val struct_with_tuple_t_accfupds : thm + val struct_with_tuple_t_case_cong : thm + val struct_with_tuple_t_case_eq : thm + val struct_with_tuple_t_component_equality : thm + val struct_with_tuple_t_fn_updates : thm + val struct_with_tuple_t_fupdfupds : thm + val struct_with_tuple_t_fupdfupds_comp : thm + val struct_with_tuple_t_induction : thm + val struct_with_tuple_t_literal_11 : thm + val struct_with_tuple_t_literal_nchotomy : thm + val struct_with_tuple_t_nchotomy : thm + val struct_with_tuple_t_updates_eq_literal : thm + val sum_t_11 : thm + val sum_t_Axiom : thm + val sum_t_case_cong : thm + val sum_t_case_eq : thm + val sum_t_distinct : thm + val sum_t_induction : thm + val sum_t_nchotomy : thm + val tree_t_11 : thm + val tree_t_Axiom : thm + val tree_t_case_cong : thm + val tree_t_case_eq : thm + val tree_t_distinct : thm + val tree_t_induction : thm + val tree_t_nchotomy : thm + + val noNestedBorrows_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "noNestedBorrows" + + [add_test_fwd_def] Definition + + ⊢ ∀x y. add_test_fwd x y = u32_add x y + + [cast_test_fwd_def] Definition + + ⊢ ∀x. cast_test_fwd x = mk_i32 (u32_to_int x) + + [choose_back_def] Definition + + ⊢ ∀b x y ret. + choose_back b x y ret = + if b then Return (ret,y) else Return (x,ret) + + [choose_fwd_def] Definition + + ⊢ ∀b x y. choose_fwd b x y = if b then Return x else Return y + + [choose_test_fwd_def] Definition + + ⊢ choose_test_fwd = + do + z <- choose_fwd T (int_to_i32 0) (int_to_i32 0); + z0 <- i32_add z (int_to_i32 1); + if z0 ≠ int_to_i32 1 then Fail Failure + else + do + (x,y) <- choose_back T (int_to_i32 0) (int_to_i32 0) z0; + if x ≠ int_to_i32 1 then Fail Failure + else if y ≠ int_to_i32 0 then Fail Failure + else Return () + od + od + + [copy_int_fwd_def] Definition + + ⊢ ∀x. copy_int_fwd x = Return x + + [div_test1_fwd_def] Definition + + ⊢ ∀x. div_test1_fwd x = u32_div x (int_to_u32 2) + + [div_test_fwd_def] Definition + + ⊢ ∀x y. div_test_fwd x y = u32_div x y + + [empty_enum_t_BIJ] Definition + + ⊢ (∀a. num2empty_enum_t (empty_enum_t2num a) = a) ∧ + ∀r. (λn. n < 1) r ⇔ empty_enum_t2num (num2empty_enum_t r) = r + + [empty_enum_t_CASE] Definition + + ⊢ ∀x v0. + (case x of EmptyEnumEmpty => v0) = (λm. v0) (empty_enum_t2num x) + + [empty_enum_t_TY_DEF] Definition + + ⊢ ∃rep. TYPE_DEFINITION (λn. n < 1) rep + + [empty_enum_t_size_def] Definition + + ⊢ ∀x. empty_enum_t_size x = 0 + + [enum_t_BIJ] Definition + + ⊢ (∀a. num2enum_t (enum_t2num a) = a) ∧ + ∀r. (λn. n < 2) r ⇔ enum_t2num (num2enum_t r) = r + + [enum_t_CASE] Definition + + ⊢ ∀x v0 v1. + (case x of EnumVariant1 => v0 | EnumVariant2 => v1) = + (λm. if m = 0 then v0 else v1) (enum_t2num x) + + [enum_t_TY_DEF] Definition + + ⊢ ∃rep. TYPE_DEFINITION (λn. n < 2) rep + + [enum_t_size_def] Definition + + ⊢ ∀x. enum_t_size x = 0 + + [get_max_fwd_def] Definition + + ⊢ ∀x y. get_max_fwd x y = if u32_ge x y then Return x else Return y + + [id_mut_pair1_back_def] Definition + + ⊢ ∀x y ret. + id_mut_pair1_back x y ret = (let (t,t0) = ret in Return (t,t0)) + + [id_mut_pair1_fwd_def] Definition + + ⊢ ∀x y. id_mut_pair1_fwd x y = Return (x,y) + + [id_mut_pair2_back_def] Definition + + ⊢ ∀p ret. + id_mut_pair2_back p ret = (let (t,t0) = ret in Return (t,t0)) + + [id_mut_pair2_fwd_def] Definition + + ⊢ ∀p. id_mut_pair2_fwd p = (let (t,t0) = p in Return (t,t0)) + + [id_mut_pair3_back'a_def] Definition + + ⊢ ∀x y ret. id_mut_pair3_back'a x y ret = Return ret + + [id_mut_pair3_back'b_def] Definition + + ⊢ ∀x y ret. id_mut_pair3_back'b x y ret = Return ret + + [id_mut_pair3_fwd_def] Definition + + ⊢ ∀x y. id_mut_pair3_fwd x y = Return (x,y) + + [id_mut_pair4_back'a_def] Definition + + ⊢ ∀p ret. id_mut_pair4_back'a p ret = Return ret + + [id_mut_pair4_back'b_def] Definition + + ⊢ ∀p ret. id_mut_pair4_back'b p ret = Return ret + + [id_mut_pair4_fwd_def] Definition + + ⊢ ∀p. id_mut_pair4_fwd p = (let (t,t0) = p in Return (t,t0)) + + [is_cons_fwd_def] Definition + + ⊢ ∀l. is_cons_fwd l = + case l of ListCons t l0 => Return T | ListNil => Return F + + [list_length_fwd_def] Definition + + ⊢ ∀l. list_length_fwd l = + case l of + ListCons t l1 => + do i <- list_length_fwd l1; u32_add (int_to_u32 1) i od + | ListNil => Return (int_to_u32 0) + + [list_nth_mut_back_def] Definition + + ⊢ ∀l i ret. + list_nth_mut_back l i ret = + case l of + ListCons x tl => + if i = int_to_u32 0 then Return (ListCons ret tl) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_back tl i0 ret; + Return (ListCons x tl0) + od + | ListNil => Fail Failure + + [list_nth_mut_fwd_def] Definition + + ⊢ ∀l i. + list_nth_mut_fwd l i = + case l of + ListCons x tl => + if i = int_to_u32 0 then Return x + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_fwd tl i0 + od + | ListNil => Fail Failure + + [list_nth_shared_fwd_def] Definition + + ⊢ ∀l i. + list_nth_shared_fwd l i = + case l of + ListCons x tl => + if i = int_to_u32 0 then Return x + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_shared_fwd tl i0 + od + | ListNil => Fail Failure + + [list_rev_aux_fwd_def] Definition + + ⊢ ∀li lo. + list_rev_aux_fwd li lo = + case li of + ListCons hd tl => list_rev_aux_fwd tl (ListCons hd lo) + | ListNil => Return lo + + [list_rev_fwd_back_def] Definition + + ⊢ ∀l. list_rev_fwd_back l = + (let + li = mem_replace_fwd l ListNil + in + list_rev_aux_fwd li ListNil) + + [list_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('list_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 a0 + (ind_type$FCONS a1 (λn. ind_type$BOTTOM))) + a0 a1 ∧ $var$('list_t') a1) ∨ + a0' = + ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ + $var$('list_t') a0') ⇒ + $var$('list_t') a0') rep + + [list_t_case_def] Definition + + ⊢ (∀a0 a1 f v. list_t_CASE (ListCons a0 a1) f v = f a0 a1) ∧ + ∀f v. list_t_CASE ListNil f v = v + + [list_t_size_def] Definition + + ⊢ (∀f a0 a1. + list_t_size f (ListCons a0 a1) = 1 + (f a0 + list_t_size f a1)) ∧ + ∀f. list_t_size f ListNil = 0 + + [neg_test_fwd_def] Definition + + ⊢ ∀x. neg_test_fwd x = i32_neg x + + [new_pair1_fwd_def] Definition + + ⊢ new_pair1_fwd = + Return + <|struct_with_pair_p := + <|pair_x := int_to_u32 1; pair_y := int_to_u32 2|> |> + + [new_tuple1_fwd_def] Definition + + ⊢ new_tuple1_fwd = + Return <|struct_with_tuple_p := (int_to_u32 1,int_to_u32 2)|> + + [new_tuple2_fwd_def] Definition + + ⊢ new_tuple2_fwd = + Return <|struct_with_tuple_p := (int_to_i16 1,int_to_i16 2)|> + + [new_tuple3_fwd_def] Definition + + ⊢ new_tuple3_fwd = + Return <|struct_with_tuple_p := (int_to_u64 1,int_to_i64 2)|> + + [node_elem_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('node_elem_t') $var$('tree_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 ARB + (ind_type$FCONS a0 + (ind_type$FCONS a1 (λn. ind_type$BOTTOM)))) + a0 a1 ∧ $var$('tree_t') a0 ∧ + $var$('node_elem_t') a1) ∨ + a0' = + ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ + $var$('node_elem_t') a0') ∧ + (∀a1'. + (∃a. a1' = + (λa. + ind_type$CONSTR (SUC (SUC 0)) a + (λn. ind_type$BOTTOM)) a) ∨ + (∃a0 a1 a2. + a1' = + (λa0 a1 a2. + ind_type$CONSTR (SUC (SUC (SUC 0))) a0 + (ind_type$FCONS a1 + (ind_type$FCONS a2 (λn. ind_type$BOTTOM)))) + a0 a1 a2 ∧ $var$('node_elem_t') a1 ∧ + $var$('tree_t') a2) ⇒ + $var$('tree_t') a1') ⇒ + $var$('node_elem_t') a0') rep + + [node_elem_t_case_def] Definition + + ⊢ (∀a0 a1 f v. node_elem_t_CASE (NodeElemCons a0 a1) f v = f a0 a1) ∧ + ∀f v. node_elem_t_CASE NodeElemNil f v = v + + [node_elem_t_size_def] Definition + + ⊢ (∀f a0 a1. + node_elem_t_size f (NodeElemCons a0 a1) = + 1 + (tree_t_size f a0 + node_elem_t_size f a1)) ∧ + (∀f. node_elem_t_size f NodeElemNil = 0) ∧ + (∀f a. tree_t_size f (TreeLeaf a) = 1 + f a) ∧ + ∀f a0 a1 a2. + tree_t_size f (TreeNode a0 a1 a2) = + 1 + (f a0 + (node_elem_t_size f a1 + tree_t_size f a2)) + + [one_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('one_t'). + (∀a0. + (∃a. a0 = + (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) + a) ⇒ + $var$('one_t') a0) ⇒ + $var$('one_t') a0) rep + + [one_t_case_def] Definition + + ⊢ ∀a f. one_t_CASE (OneOne a) f = f a + + [one_t_size_def] Definition + + ⊢ ∀f a. one_t_size f (OneOne a) = 1 + f a + + [pair_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('pair_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 (a0,a1) + (λn. ind_type$BOTTOM)) a0 a1) ⇒ + $var$('pair_t') a0') ⇒ + $var$('pair_t') a0') rep + + [pair_t_case_def] Definition + + ⊢ ∀a0 a1 f. pair_t_CASE (pair_t a0 a1) f = f a0 a1 + + [pair_t_size_def] Definition + + ⊢ ∀f f1 a0 a1. pair_t_size f f1 (pair_t a0 a1) = 1 + (f a0 + f1 a1) + + [recordtype_pair_t_seldef_pair_x_def] Definition + + ⊢ ∀t t0. (pair_t t t0).pair_x = t + + [recordtype_pair_t_seldef_pair_x_fupd_def] Definition + + ⊢ ∀f t t0. pair_t t t0 with pair_x updated_by f = pair_t (f t) t0 + + [recordtype_pair_t_seldef_pair_y_def] Definition + + ⊢ ∀t t0. (pair_t t t0).pair_y = t0 + + [recordtype_pair_t_seldef_pair_y_fupd_def] Definition + + ⊢ ∀f t t0. pair_t t t0 with pair_y updated_by f = pair_t t (f t0) + + [recordtype_struct_with_pair_t_seldef_struct_with_pair_p_def] Definition + + ⊢ ∀p. (struct_with_pair_t p).struct_with_pair_p = p + + [recordtype_struct_with_pair_t_seldef_struct_with_pair_p_fupd_def] Definition + + ⊢ ∀f p. + struct_with_pair_t p with struct_with_pair_p updated_by f = + struct_with_pair_t (f p) + + [recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_def] Definition + + ⊢ ∀p. (struct_with_tuple_t p).struct_with_tuple_p = p + + [recordtype_struct_with_tuple_t_seldef_struct_with_tuple_p_fupd_def] Definition + + ⊢ ∀f p. + struct_with_tuple_t p with struct_with_tuple_p updated_by f = + struct_with_tuple_t (f p) + + [refs_test1_fwd_def] Definition + + ⊢ refs_test1_fwd = + if int_to_i32 1 ≠ int_to_i32 1 then Fail Failure else Return () + + [refs_test2_fwd_def] Definition + + ⊢ refs_test2_fwd = + if int_to_i32 2 ≠ int_to_i32 2 then Fail Failure + else if int_to_i32 0 ≠ int_to_i32 0 then Fail Failure + else if int_to_i32 2 ≠ int_to_i32 2 then Fail Failure + else if int_to_i32 2 ≠ int_to_i32 2 then Fail Failure + else Return () + + [rem_test_fwd_def] Definition + + ⊢ ∀x y. rem_test_fwd x y = u32_rem x y + + [split_list_fwd_def] Definition + + ⊢ ∀l. split_list_fwd l = + case l of + ListCons hd tl => Return (hd,tl) + | ListNil => Fail Failure + + [struct_with_pair_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('struct_with_pair_t'). + (∀a0. + (∃a. a0 = + (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) + a) ⇒ + $var$('struct_with_pair_t') a0) ⇒ + $var$('struct_with_pair_t') a0) rep + + [struct_with_pair_t_case_def] Definition + + ⊢ ∀a f. struct_with_pair_t_CASE (struct_with_pair_t a) f = f a + + [struct_with_pair_t_size_def] Definition + + ⊢ ∀f f1 a. + struct_with_pair_t_size f f1 (struct_with_pair_t a) = + 1 + pair_t_size f f1 a + + [struct_with_tuple_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('struct_with_tuple_t'). + (∀a0. + (∃a. a0 = + (λa. ind_type$CONSTR 0 a (λn. ind_type$BOTTOM)) + a) ⇒ + $var$('struct_with_tuple_t') a0) ⇒ + $var$('struct_with_tuple_t') a0) rep + + [struct_with_tuple_t_case_def] Definition + + ⊢ ∀a f. struct_with_tuple_t_CASE (struct_with_tuple_t a) f = f a + + [struct_with_tuple_t_size_def] Definition + + ⊢ ∀f f1 a. + struct_with_tuple_t_size f f1 (struct_with_tuple_t a) = + 1 + pair_size f f1 a + + [subs_test_fwd_def] Definition + + ⊢ ∀x y. subs_test_fwd x y = u32_sub x y + + [sum_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0. + ∀ $var$('sum_t'). + (∀a0. + (∃a. a0 = + (λa. + ind_type$CONSTR 0 (a,ARB) + (λn. ind_type$BOTTOM)) a) ∨ + (∃a. a0 = + (λa. + ind_type$CONSTR (SUC 0) (ARB,a) + (λn. ind_type$BOTTOM)) a) ⇒ + $var$('sum_t') a0) ⇒ + $var$('sum_t') a0) rep + + [sum_t_case_def] Definition + + ⊢ (∀a f f1. sum_t_CASE (SumLeft a) f f1 = f a) ∧ + ∀a f f1. sum_t_CASE (SumRight a) f f1 = f1 a + + [sum_t_size_def] Definition + + ⊢ (∀f f1 a. sum_t_size f f1 (SumLeft a) = 1 + f a) ∧ + ∀f f1 a. sum_t_size f f1 (SumRight a) = 1 + f1 a + + [test2_fwd_def] Definition + + ⊢ test2_fwd = + monad_ignore_bind (u32_add (int_to_u32 23) (int_to_u32 44)) + (Return ()) + + [test3_fwd_def] Definition + + ⊢ test3_fwd = + do + x <- get_max_fwd (int_to_u32 4) (int_to_u32 3); + y <- get_max_fwd (int_to_u32 10) (int_to_u32 11); + z <- u32_add x y; + if z ≠ int_to_u32 15 then Fail Failure else Return () + od + + [test_box1_fwd_def] Definition + + ⊢ test_box1_fwd = + (let + b = int_to_i32 1; + x = b + in + if x ≠ int_to_i32 1 then Fail Failure else Return ()) + + [test_char_fwd_def] Definition + + ⊢ test_char_fwd = Return #"a" + + [test_constants_fwd_def] Definition + + ⊢ test_constants_fwd = + do + swt <- new_tuple1_fwd; + (i,_) <<- swt.struct_with_tuple_p; + if i ≠ int_to_u32 1 then Fail Failure + else + do + swt0 <- new_tuple2_fwd; + (i0,_) <<- swt0.struct_with_tuple_p; + if i0 ≠ int_to_i16 1 then Fail Failure + else + do + swt1 <- new_tuple3_fwd; + (i1,_) <<- swt1.struct_with_tuple_p; + if i1 ≠ int_to_u64 1 then Fail Failure + else + do + swp <- new_pair1_fwd; + if swp.struct_with_pair_p.pair_x ≠ int_to_u32 1 then + Fail Failure + else Return () + od + od + od + od + + [test_copy_int_fwd_def] Definition + + ⊢ test_copy_int_fwd = + do + y <- copy_int_fwd (int_to_i32 0); + if int_to_i32 0 ≠ y then Fail Failure else Return () + od + + [test_is_cons_fwd_def] Definition + + ⊢ test_is_cons_fwd = + (let + l = ListNil + in + do + b <- is_cons_fwd (ListCons (int_to_i32 0) l); + if ¬b then Fail Failure else Return () + od) + + [test_list1_fwd_def] Definition + + ⊢ test_list1_fwd = Return () + + [test_list_functions_fwd_def] Definition + + ⊢ test_list_functions_fwd = + (let + l = ListNil; + l0 = ListCons (int_to_i32 2) l; + l1 = ListCons (int_to_i32 1) l0 + in + do + i <- list_length_fwd (ListCons (int_to_i32 0) l1); + if i ≠ int_to_u32 3 then Fail Failure + else + do + i0 <- + list_nth_shared_fwd (ListCons (int_to_i32 0) l1) + (int_to_u32 0); + if i0 ≠ int_to_i32 0 then Fail Failure + else + do + i1 <- + list_nth_shared_fwd (ListCons (int_to_i32 0) l1) + (int_to_u32 1); + if i1 ≠ int_to_i32 1 then Fail Failure + else + do + i2 <- + list_nth_shared_fwd (ListCons (int_to_i32 0) l1) + (int_to_u32 2); + if i2 ≠ int_to_i32 2 then Fail Failure + else + do + ls <- + list_nth_mut_back + (ListCons (int_to_i32 0) l1) + (int_to_u32 1) (int_to_i32 3); + i3 <- list_nth_shared_fwd ls (int_to_u32 0); + if i3 ≠ int_to_i32 0 then Fail Failure + else + do + i4 <- + list_nth_shared_fwd ls (int_to_u32 1); + if i4 ≠ int_to_i32 3 then Fail Failure + else + do + i5 <- + list_nth_shared_fwd ls + (int_to_u32 2); + if i5 ≠ int_to_i32 2 then Fail Failure + else Return () + od + od + od + od + od + od + od) + + [test_mem_replace_fwd_back_def] Definition + + ⊢ ∀px. + test_mem_replace_fwd_back px = + (let + y = mem_replace_fwd px (int_to_u32 1) + in + if y ≠ int_to_u32 0 then Fail Failure + else Return (int_to_u32 2)) + + [test_neg1_fwd_def] Definition + + ⊢ test_neg1_fwd = + do + y <- i32_neg (int_to_i32 3); + if y ≠ int_to_i32 (-3) then Fail Failure else Return () + od + + [test_panic_fwd_def] Definition + + ⊢ ∀b. test_panic_fwd b = if b then Fail Failure else Return () + + [test_shared_borrow_bool1_fwd_def] Definition + + ⊢ ∀b. test_shared_borrow_bool1_fwd b = + if b then Return (int_to_u32 0) else Return (int_to_u32 1) + + [test_shared_borrow_bool2_fwd_def] Definition + + ⊢ test_shared_borrow_bool2_fwd = Return (int_to_u32 0) + + [test_shared_borrow_enum1_fwd_def] Definition + + ⊢ ∀l. test_shared_borrow_enum1_fwd l = + case l of + ListCons i l0 => Return (int_to_u32 1) + | ListNil => Return (int_to_u32 0) + + [test_shared_borrow_enum2_fwd_def] Definition + + ⊢ test_shared_borrow_enum2_fwd = Return (int_to_u32 0) + + [test_split_list_fwd_def] Definition + + ⊢ test_split_list_fwd = + (let + l = ListNil + in + do + p <- split_list_fwd (ListCons (int_to_i32 0) l); + (hd,_) <<- p; + if hd ≠ int_to_i32 0 then Fail Failure else Return () + od) + + [test_unreachable_fwd_def] Definition + + ⊢ ∀b. test_unreachable_fwd b = if b then Fail Failure else Return () + + [test_weird_borrows1_fwd_def] Definition + + ⊢ test_weird_borrows1_fwd = Return () + + [tree_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa1'. + ∀ $var$('node_elem_t') $var$('tree_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 ARB + (ind_type$FCONS a0 + (ind_type$FCONS a1 (λn. ind_type$BOTTOM)))) + a0 a1 ∧ $var$('tree_t') a0 ∧ + $var$('node_elem_t') a1) ∨ + a0' = + ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ + $var$('node_elem_t') a0') ∧ + (∀a1'. + (∃a. a1' = + (λa. + ind_type$CONSTR (SUC (SUC 0)) a + (λn. ind_type$BOTTOM)) a) ∨ + (∃a0 a1 a2. + a1' = + (λa0 a1 a2. + ind_type$CONSTR (SUC (SUC (SUC 0))) a0 + (ind_type$FCONS a1 + (ind_type$FCONS a2 (λn. ind_type$BOTTOM)))) + a0 a1 a2 ∧ $var$('node_elem_t') a1 ∧ + $var$('tree_t') a2) ⇒ + $var$('tree_t') a1') ⇒ + $var$('tree_t') a1') rep + + [tree_t_case_def] Definition + + ⊢ (∀a f f1. tree_t_CASE (TreeLeaf a) f f1 = f a) ∧ + ∀a0 a1 a2 f f1. tree_t_CASE (TreeNode a0 a1 a2) f f1 = f1 a0 a1 a2 + + [EXISTS_pair_t] Theorem + + ⊢ ∀P. (∃p. P p) ⇔ ∃t0 t. P <|pair_x := t0; pair_y := t|> + + [EXISTS_struct_with_pair_t] Theorem + + ⊢ ∀P. (∃s. P s) ⇔ ∃p. P <|struct_with_pair_p := p|> + + [EXISTS_struct_with_tuple_t] Theorem + + ⊢ ∀P. (∃s. P s) ⇔ ∃p. P <|struct_with_tuple_p := p|> + + [FORALL_pair_t] Theorem + + ⊢ ∀P. (∀p. P p) ⇔ ∀t0 t. P <|pair_x := t0; pair_y := t|> + + [FORALL_struct_with_pair_t] Theorem + + ⊢ ∀P. (∀s. P s) ⇔ ∀p. P <|struct_with_pair_p := p|> + + [FORALL_struct_with_tuple_t] Theorem + + ⊢ ∀P. (∀s. P s) ⇔ ∀p. P <|struct_with_tuple_p := p|> + + [datatype_empty_enum_t] Theorem + + ⊢ DATATYPE (empty_enum_t EmptyEnumEmpty) + + [datatype_enum_t] Theorem + + ⊢ DATATYPE (enum_t EnumVariant1 EnumVariant2) + + [datatype_list_t] Theorem + + ⊢ DATATYPE (list_t ListCons ListNil) + + [datatype_node_elem_t] Theorem + + ⊢ DATATYPE + (node_elem_t NodeElemCons NodeElemNil ∧ tree_t TreeLeaf TreeNode) + + [datatype_one_t] Theorem + + ⊢ DATATYPE (one_t OneOne) + + [datatype_pair_t] Theorem + + ⊢ DATATYPE (record pair_t pair_x pair_y) + + [datatype_struct_with_pair_t] Theorem + + ⊢ DATATYPE (record struct_with_pair_t struct_with_pair_p) + + [datatype_struct_with_tuple_t] Theorem + + ⊢ DATATYPE (record struct_with_tuple_t struct_with_tuple_p) + + [datatype_sum_t] Theorem + + ⊢ DATATYPE (sum_t SumLeft SumRight) + + [empty_enum_t2num_11] Theorem + + ⊢ ∀a a'. empty_enum_t2num a = empty_enum_t2num a' ⇔ a = a' + + [empty_enum_t2num_ONTO] Theorem + + ⊢ ∀r. r < 1 ⇔ ∃a. r = empty_enum_t2num a + + [empty_enum_t2num_num2empty_enum_t] Theorem + + ⊢ ∀r. r < 1 ⇔ empty_enum_t2num (num2empty_enum_t r) = r + + [empty_enum_t2num_thm] Theorem + + ⊢ empty_enum_t2num EmptyEnumEmpty = 0 + + [empty_enum_t_Axiom] Theorem + + ⊢ ∀x0. ∃f. f EmptyEnumEmpty = x0 + + [empty_enum_t_EQ_empty_enum_t] Theorem + + ⊢ ∀a a'. a = a' ⇔ empty_enum_t2num a = empty_enum_t2num a' + + [empty_enum_t_case_cong] Theorem + + ⊢ ∀M M' v0. + M = M' ∧ (M' = EmptyEnumEmpty ⇒ v0 = v0') ⇒ + (case M of EmptyEnumEmpty => v0) = + case M' of EmptyEnumEmpty => v0' + + [empty_enum_t_case_def] Theorem + + ⊢ ∀v0. (case EmptyEnumEmpty of EmptyEnumEmpty => v0) = v0 + + [empty_enum_t_case_eq] Theorem + + ⊢ (case x of EmptyEnumEmpty => v0) = v ⇔ x = EmptyEnumEmpty ∧ v0 = v + + [empty_enum_t_induction] Theorem + + ⊢ ∀P. P EmptyEnumEmpty ⇒ ∀a. P a + + [empty_enum_t_nchotomy] Theorem + + ⊢ ∀a. a = EmptyEnumEmpty + + [enum_t2num_11] Theorem + + ⊢ ∀a a'. enum_t2num a = enum_t2num a' ⇔ a = a' + + [enum_t2num_ONTO] Theorem + + ⊢ ∀r. r < 2 ⇔ ∃a. r = enum_t2num a + + [enum_t2num_num2enum_t] Theorem + + ⊢ ∀r. r < 2 ⇔ enum_t2num (num2enum_t r) = r + + [enum_t2num_thm] Theorem + + ⊢ enum_t2num EnumVariant1 = 0 ∧ enum_t2num EnumVariant2 = 1 + + [enum_t_Axiom] Theorem + + ⊢ ∀x0 x1. ∃f. f EnumVariant1 = x0 ∧ f EnumVariant2 = x1 + + [enum_t_EQ_enum_t] Theorem + + ⊢ ∀a a'. a = a' ⇔ enum_t2num a = enum_t2num a' + + [enum_t_case_cong] Theorem + + ⊢ ∀M M' v0 v1. + M = M' ∧ (M' = EnumVariant1 ⇒ v0 = v0') ∧ + (M' = EnumVariant2 ⇒ v1 = v1') ⇒ + (case M of EnumVariant1 => v0 | EnumVariant2 => v1) = + case M' of EnumVariant1 => v0' | EnumVariant2 => v1' + + [enum_t_case_def] Theorem + + ⊢ (∀v0 v1. + (case EnumVariant1 of EnumVariant1 => v0 | EnumVariant2 => v1) = + v0) ∧ + ∀v0 v1. + (case EnumVariant2 of EnumVariant1 => v0 | EnumVariant2 => v1) = + v1 + + [enum_t_case_eq] Theorem + + ⊢ (case x of EnumVariant1 => v0 | EnumVariant2 => v1) = v ⇔ + x = EnumVariant1 ∧ v0 = v ∨ x = EnumVariant2 ∧ v1 = v + + [enum_t_distinct] Theorem + + ⊢ EnumVariant1 ≠ EnumVariant2 + + [enum_t_induction] Theorem + + ⊢ ∀P. P EnumVariant1 ∧ P EnumVariant2 ⇒ ∀a. P a + + [enum_t_nchotomy] Theorem + + ⊢ ∀a. a = EnumVariant1 ∨ a = EnumVariant2 + + [list_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + ListCons a0 a1 = ListCons a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [list_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a0 a1. fn (ListCons a0 a1) = f0 a0 a1 (fn a1)) ∧ + fn ListNil = f1 + + [list_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ (∀a0 a1. M' = ListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ + (M' = ListNil ⇒ v = v') ⇒ + list_t_CASE M f v = list_t_CASE M' f' v' + + [list_t_case_eq] Theorem + + ⊢ list_t_CASE x f v = v' ⇔ + (∃t l. x = ListCons t l ∧ f t l = v') ∨ x = ListNil ∧ v = v' + + [list_t_distinct] Theorem + + ⊢ ∀a1 a0. ListCons a0 a1 ≠ ListNil + + [list_t_induction] Theorem + + ⊢ ∀P. (∀l. P l ⇒ ∀t. P (ListCons t l)) ∧ P ListNil ⇒ ∀l. P l + + [list_t_nchotomy] Theorem + + ⊢ ∀ll. (∃t l. ll = ListCons t l) ∨ ll = ListNil + + [node_elem_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + NodeElemCons a0 a1 = NodeElemCons a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [node_elem_t_Axiom] Theorem + + ⊢ ∀f0 f1 f2 f3. ∃fn0 fn1. + (∀a0 a1. fn0 (NodeElemCons a0 a1) = f0 a0 a1 (fn1 a0) (fn0 a1)) ∧ + fn0 NodeElemNil = f1 ∧ (∀a. fn1 (TreeLeaf a) = f2 a) ∧ + ∀a0 a1 a2. + fn1 (TreeNode a0 a1 a2) = f3 a0 a1 a2 (fn0 a1) (fn1 a2) + + [node_elem_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ (∀a0 a1. M' = NodeElemCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ + (M' = NodeElemNil ⇒ v = v') ⇒ + node_elem_t_CASE M f v = node_elem_t_CASE M' f' v' + + [node_elem_t_case_eq] Theorem + + ⊢ node_elem_t_CASE x f v = v' ⇔ + (∃t n. x = NodeElemCons t n ∧ f t n = v') ∨ + x = NodeElemNil ∧ v = v' + + [node_elem_t_distinct] Theorem + + ⊢ ∀a1 a0. NodeElemCons a0 a1 ≠ NodeElemNil + + [node_elem_t_induction] Theorem + + ⊢ ∀P0 P1. + (∀t n. P1 t ∧ P0 n ⇒ P0 (NodeElemCons t n)) ∧ P0 NodeElemNil ∧ + (∀t. P1 (TreeLeaf t)) ∧ + (∀n t. P0 n ∧ P1 t ⇒ ∀t0. P1 (TreeNode t0 n t)) ⇒ + (∀n. P0 n) ∧ ∀t. P1 t + + [node_elem_t_nchotomy] Theorem + + ⊢ ∀nn. (∃t n. nn = NodeElemCons t n) ∨ nn = NodeElemNil + + [num2empty_enum_t_11] Theorem + + ⊢ ∀r r'. + r < 1 ⇒ + r' < 1 ⇒ + (num2empty_enum_t r = num2empty_enum_t r' ⇔ r = r') + + [num2empty_enum_t_ONTO] Theorem + + ⊢ ∀a. ∃r. a = num2empty_enum_t r ∧ r < 1 + + [num2empty_enum_t_empty_enum_t2num] Theorem + + ⊢ ∀a. num2empty_enum_t (empty_enum_t2num a) = a + + [num2empty_enum_t_thm] Theorem + + ⊢ num2empty_enum_t 0 = EmptyEnumEmpty + + [num2enum_t_11] Theorem + + ⊢ ∀r r'. r < 2 ⇒ r' < 2 ⇒ (num2enum_t r = num2enum_t r' ⇔ r = r') + + [num2enum_t_ONTO] Theorem + + ⊢ ∀a. ∃r. a = num2enum_t r ∧ r < 2 + + [num2enum_t_enum_t2num] Theorem + + ⊢ ∀a. num2enum_t (enum_t2num a) = a + + [num2enum_t_thm] Theorem + + ⊢ num2enum_t 0 = EnumVariant1 ∧ num2enum_t 1 = EnumVariant2 + + [one_t_11] Theorem + + ⊢ ∀a a'. OneOne a = OneOne a' ⇔ a = a' + + [one_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a. fn (OneOne a) = f a + + [one_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a. M' = OneOne a ⇒ f a = f' a) ⇒ + one_t_CASE M f = one_t_CASE M' f' + + [one_t_case_eq] Theorem + + ⊢ one_t_CASE x f = v ⇔ ∃t. x = OneOne t ∧ f t = v + + [one_t_induction] Theorem + + ⊢ ∀P. (∀t. P (OneOne t)) ⇒ ∀ $o. P $o + + [one_t_nchotomy] Theorem + + ⊢ ∀oo. ∃t. oo = OneOne t + + [pair_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. pair_t a0 a1 = pair_t a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [pair_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a0 a1. fn (pair_t a0 a1) = f a0 a1 + + [pair_t_accessors] Theorem + + ⊢ (∀t t0. (pair_t t t0).pair_x = t) ∧ + ∀t t0. (pair_t t t0).pair_y = t0 + + [pair_t_accfupds] Theorem + + ⊢ (∀p f. (p with pair_y updated_by f).pair_x = p.pair_x) ∧ + (∀p f. (p with pair_x updated_by f).pair_y = p.pair_y) ∧ + (∀p f. (p with pair_x updated_by f).pair_x = f p.pair_x) ∧ + ∀p f. (p with pair_y updated_by f).pair_y = f p.pair_y + + [pair_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a0 a1. M' = pair_t a0 a1 ⇒ f a0 a1 = f' a0 a1) ⇒ + pair_t_CASE M f = pair_t_CASE M' f' + + [pair_t_case_eq] Theorem + + ⊢ pair_t_CASE x f = v ⇔ ∃t t0. x = pair_t t t0 ∧ f t t0 = v + + [pair_t_component_equality] Theorem + + ⊢ ∀p1 p2. p1 = p2 ⇔ p1.pair_x = p2.pair_x ∧ p1.pair_y = p2.pair_y + + [pair_t_fn_updates] Theorem + + ⊢ (∀f t t0. pair_t t t0 with pair_x updated_by f = pair_t (f t) t0) ∧ + ∀f t t0. pair_t t t0 with pair_y updated_by f = pair_t t (f t0) + + [pair_t_fupdcanon] Theorem + + ⊢ ∀p g f. + p with <|pair_y updated_by f; pair_x updated_by g|> = + p with <|pair_x updated_by g; pair_y updated_by f|> + + [pair_t_fupdcanon_comp] Theorem + + ⊢ (∀g f. + pair_y_fupd f ∘ pair_x_fupd g = pair_x_fupd g ∘ pair_y_fupd f) ∧ + ∀h g f. + pair_y_fupd f ∘ pair_x_fupd g ∘ h = + pair_x_fupd g ∘ pair_y_fupd f ∘ h + + [pair_t_fupdfupds] Theorem + + ⊢ (∀p g f. + p with <|pair_x updated_by f; pair_x updated_by g|> = + p with pair_x updated_by f ∘ g) ∧ + ∀p g f. + p with <|pair_y updated_by f; pair_y updated_by g|> = + p with pair_y updated_by f ∘ g + + [pair_t_fupdfupds_comp] Theorem + + ⊢ ((∀g f. pair_x_fupd f ∘ pair_x_fupd g = pair_x_fupd (f ∘ g)) ∧ + ∀h g f. + pair_x_fupd f ∘ pair_x_fupd g ∘ h = pair_x_fupd (f ∘ g) ∘ h) ∧ + (∀g f. pair_y_fupd f ∘ pair_y_fupd g = pair_y_fupd (f ∘ g)) ∧ + ∀h g f. pair_y_fupd f ∘ pair_y_fupd g ∘ h = pair_y_fupd (f ∘ g) ∘ h + + [pair_t_induction] Theorem + + ⊢ ∀P. (∀t t0. P (pair_t t t0)) ⇒ ∀p. P p + + [pair_t_literal_11] Theorem + + ⊢ ∀t01 t1 t02 t2. + <|pair_x := t01; pair_y := t1|> = <|pair_x := t02; pair_y := t2|> ⇔ + t01 = t02 ∧ t1 = t2 + + [pair_t_literal_nchotomy] Theorem + + ⊢ ∀p. ∃t0 t. p = <|pair_x := t0; pair_y := t|> + + [pair_t_nchotomy] Theorem + + ⊢ ∀pp. ∃t t0. pp = pair_t t t0 + + [pair_t_updates_eq_literal] Theorem + + ⊢ ∀p t0 t. + p with <|pair_x := t0; pair_y := t|> = + <|pair_x := t0; pair_y := t|> + + [struct_with_pair_t_11] Theorem + + ⊢ ∀a a'. struct_with_pair_t a = struct_with_pair_t a' ⇔ a = a' + + [struct_with_pair_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a. fn (struct_with_pair_t a) = f a + + [struct_with_pair_t_accessors] Theorem + + ⊢ ∀p. (struct_with_pair_t p).struct_with_pair_p = p + + [struct_with_pair_t_accfupds] Theorem + + ⊢ ∀s f. + (s with struct_with_pair_p updated_by f).struct_with_pair_p = + f s.struct_with_pair_p + + [struct_with_pair_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a. M' = struct_with_pair_t a ⇒ f a = f' a) ⇒ + struct_with_pair_t_CASE M f = struct_with_pair_t_CASE M' f' + + [struct_with_pair_t_case_eq] Theorem + + ⊢ struct_with_pair_t_CASE x f = v ⇔ + ∃p. x = struct_with_pair_t p ∧ f p = v + + [struct_with_pair_t_component_equality] Theorem + + ⊢ ∀s1 s2. s1 = s2 ⇔ s1.struct_with_pair_p = s2.struct_with_pair_p + + [struct_with_pair_t_fn_updates] Theorem + + ⊢ ∀f p. + struct_with_pair_t p with struct_with_pair_p updated_by f = + struct_with_pair_t (f p) + + [struct_with_pair_t_fupdfupds] Theorem + + ⊢ ∀s g f. + s with + <|struct_with_pair_p updated_by f; + struct_with_pair_p updated_by g|> = + s with struct_with_pair_p updated_by f ∘ g + + [struct_with_pair_t_fupdfupds_comp] Theorem + + ⊢ (∀g f. + struct_with_pair_p_fupd f ∘ struct_with_pair_p_fupd g = + struct_with_pair_p_fupd (f ∘ g)) ∧ + ∀h g f. + struct_with_pair_p_fupd f ∘ struct_with_pair_p_fupd g ∘ h = + struct_with_pair_p_fupd (f ∘ g) ∘ h + + [struct_with_pair_t_induction] Theorem + + ⊢ ∀P. (∀p. P (struct_with_pair_t p)) ⇒ ∀s. P s + + [struct_with_pair_t_literal_11] Theorem + + ⊢ ∀p1 p2. + <|struct_with_pair_p := p1|> = <|struct_with_pair_p := p2|> ⇔ + p1 = p2 + + [struct_with_pair_t_literal_nchotomy] Theorem + + ⊢ ∀s. ∃p. s = <|struct_with_pair_p := p|> + + [struct_with_pair_t_nchotomy] Theorem + + ⊢ ∀ss. ∃p. ss = struct_with_pair_t p + + [struct_with_pair_t_updates_eq_literal] Theorem + + ⊢ ∀s p. s with struct_with_pair_p := p = <|struct_with_pair_p := p|> + + [struct_with_tuple_t_11] Theorem + + ⊢ ∀a a'. struct_with_tuple_t a = struct_with_tuple_t a' ⇔ a = a' + + [struct_with_tuple_t_Axiom] Theorem + + ⊢ ∀f. ∃fn. ∀a. fn (struct_with_tuple_t a) = f a + + [struct_with_tuple_t_accessors] Theorem + + ⊢ ∀p. (struct_with_tuple_t p).struct_with_tuple_p = p + + [struct_with_tuple_t_accfupds] Theorem + + ⊢ ∀s f. + (s with struct_with_tuple_p updated_by f).struct_with_tuple_p = + f s.struct_with_tuple_p + + [struct_with_tuple_t_case_cong] Theorem + + ⊢ ∀M M' f. + M = M' ∧ (∀a. M' = struct_with_tuple_t a ⇒ f a = f' a) ⇒ + struct_with_tuple_t_CASE M f = struct_with_tuple_t_CASE M' f' + + [struct_with_tuple_t_case_eq] Theorem + + ⊢ struct_with_tuple_t_CASE x f = v ⇔ + ∃p. x = struct_with_tuple_t p ∧ f p = v + + [struct_with_tuple_t_component_equality] Theorem + + ⊢ ∀s1 s2. s1 = s2 ⇔ s1.struct_with_tuple_p = s2.struct_with_tuple_p + + [struct_with_tuple_t_fn_updates] Theorem + + ⊢ ∀f p. + struct_with_tuple_t p with struct_with_tuple_p updated_by f = + struct_with_tuple_t (f p) + + [struct_with_tuple_t_fupdfupds] Theorem + + ⊢ ∀s g f. + s with + <|struct_with_tuple_p updated_by f; + struct_with_tuple_p updated_by g|> = + s with struct_with_tuple_p updated_by f ∘ g + + [struct_with_tuple_t_fupdfupds_comp] Theorem + + ⊢ (∀g f. + struct_with_tuple_p_fupd f ∘ struct_with_tuple_p_fupd g = + struct_with_tuple_p_fupd (f ∘ g)) ∧ + ∀h g f. + struct_with_tuple_p_fupd f ∘ struct_with_tuple_p_fupd g ∘ h = + struct_with_tuple_p_fupd (f ∘ g) ∘ h + + [struct_with_tuple_t_induction] Theorem + + ⊢ ∀P. (∀p. P (struct_with_tuple_t p)) ⇒ ∀s. P s + + [struct_with_tuple_t_literal_11] Theorem + + ⊢ ∀p1 p2. + <|struct_with_tuple_p := p1|> = <|struct_with_tuple_p := p2|> ⇔ + p1 = p2 + + [struct_with_tuple_t_literal_nchotomy] Theorem + + ⊢ ∀s. ∃p. s = <|struct_with_tuple_p := p|> + + [struct_with_tuple_t_nchotomy] Theorem + + ⊢ ∀ss. ∃p. ss = struct_with_tuple_t p + + [struct_with_tuple_t_updates_eq_literal] Theorem + + ⊢ ∀s p. + s with struct_with_tuple_p := p = <|struct_with_tuple_p := p|> + + [sum_t_11] Theorem + + ⊢ (∀a a'. SumLeft a = SumLeft a' ⇔ a = a') ∧ + ∀a a'. SumRight a = SumRight a' ⇔ a = a' + + [sum_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a. fn (SumLeft a) = f0 a) ∧ ∀a. fn (SumRight a) = f1 a + + [sum_t_case_cong] Theorem + + ⊢ ∀M M' f f1. + M = M' ∧ (∀a. M' = SumLeft a ⇒ f a = f' a) ∧ + (∀a. M' = SumRight a ⇒ f1 a = f1' a) ⇒ + sum_t_CASE M f f1 = sum_t_CASE M' f' f1' + + [sum_t_case_eq] Theorem + + ⊢ sum_t_CASE x f f1 = v ⇔ + (∃t. x = SumLeft t ∧ f t = v) ∨ ∃t. x = SumRight t ∧ f1 t = v + + [sum_t_distinct] Theorem + + ⊢ ∀a' a. SumLeft a ≠ SumRight a' + + [sum_t_induction] Theorem + + ⊢ ∀P. (∀t. P (SumLeft t)) ∧ (∀t. P (SumRight t)) ⇒ ∀s. P s + + [sum_t_nchotomy] Theorem + + ⊢ ∀ss. (∃t. ss = SumLeft t) ∨ ∃t. ss = SumRight t + + [tree_t_11] Theorem + + ⊢ (∀a a'. TreeLeaf a = TreeLeaf a' ⇔ a = a') ∧ + ∀a0 a1 a2 a0' a1' a2'. + TreeNode a0 a1 a2 = TreeNode a0' a1' a2' ⇔ + a0 = a0' ∧ a1 = a1' ∧ a2 = a2' + + [tree_t_Axiom] Theorem + + ⊢ ∀f0 f1 f2 f3. ∃fn0 fn1. + (∀a0 a1. fn0 (NodeElemCons a0 a1) = f0 a0 a1 (fn1 a0) (fn0 a1)) ∧ + fn0 NodeElemNil = f1 ∧ (∀a. fn1 (TreeLeaf a) = f2 a) ∧ + ∀a0 a1 a2. + fn1 (TreeNode a0 a1 a2) = f3 a0 a1 a2 (fn0 a1) (fn1 a2) + + [tree_t_case_cong] Theorem + + ⊢ ∀M M' f f1. + M = M' ∧ (∀a. M' = TreeLeaf a ⇒ f a = f' a) ∧ + (∀a0 a1 a2. M' = TreeNode a0 a1 a2 ⇒ f1 a0 a1 a2 = f1' a0 a1 a2) ⇒ + tree_t_CASE M f f1 = tree_t_CASE M' f' f1' + + [tree_t_case_eq] Theorem + + ⊢ tree_t_CASE x f f1 = v ⇔ + (∃t. x = TreeLeaf t ∧ f t = v) ∨ + ∃t0 n t. x = TreeNode t0 n t ∧ f1 t0 n t = v + + [tree_t_distinct] Theorem + + ⊢ ∀a2 a1 a0 a. TreeLeaf a ≠ TreeNode a0 a1 a2 + + [tree_t_induction] Theorem + + ⊢ ∀P0 P1. + (∀t n. P1 t ∧ P0 n ⇒ P0 (NodeElemCons t n)) ∧ P0 NodeElemNil ∧ + (∀t. P1 (TreeLeaf t)) ∧ + (∀n t. P0 n ∧ P1 t ⇒ ∀t0. P1 (TreeNode t0 n t)) ⇒ + (∀n. P0 n) ∧ ∀t. P1 t + + [tree_t_nchotomy] Theorem + + ⊢ ∀tt. (∃t. tt = TreeLeaf t) ∨ ∃t0 n t. tt = TreeNode t0 n t + + +*) +end diff --git a/tests/hol4/misc-paper/Holmakefile b/tests/hol4/misc-paper/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/misc-paper/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/misc-paper/paperScript.sml b/tests/hol4/misc-paper/paperScript.sml new file mode 100644 index 00000000..4d6e99ba --- /dev/null +++ b/tests/hol4/misc-paper/paperScript.sml @@ -0,0 +1,135 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [paper] *) +open primitivesLib divDefLib + +val _ = new_theory "paper" + + +val ref_incr_fwd_back_def = Define ‘ + (** [paper::ref_incr] *) + ref_incr_fwd_back (x : i32) : i32 result = + i32_add x (int_to_i32 1) +’ + +val test_incr_fwd_def = Define ‘ + (** [paper::test_incr] *) + test_incr_fwd : unit result = + do + x <- ref_incr_fwd_back (int_to_i32 0); + if ~ (x = int_to_i32 1) then Fail Failure else Return () + od +’ + +(** Unit test for [paper::test_incr] *) +val _ = assert_return (“test_incr_fwd”) + +val choose_fwd_def = Define ‘ + (** [paper::choose] *) + choose_fwd (b : bool) (x : 't) (y : 't) : 't result = + if b then Return x else Return y +’ + +val choose_back_def = Define ‘ + (** [paper::choose] *) + choose_back (b : bool) (x : 't) (y : 't) (ret : 't) : ('t # 't) result = + if b then Return (ret, y) else Return (x, ret) +’ + +val test_choose_fwd_def = Define ‘ + (** [paper::test_choose] *) + test_choose_fwd : unit result = + do + z <- choose_fwd T (int_to_i32 0) (int_to_i32 0); + z0 <- i32_add z (int_to_i32 1); + if ~ (z0 = int_to_i32 1) + then Fail Failure + else ( + do + (x, y) <- choose_back T (int_to_i32 0) (int_to_i32 0) z0; + if ~ (x = int_to_i32 1) + then Fail Failure + else if ~ (y = int_to_i32 0) then Fail Failure else Return () + od) + od +’ + +(** Unit test for [paper::test_choose] *) +val _ = assert_return (“test_choose_fwd”) + +Datatype: + (** [paper::List] *) + list_t = | ListCons 't list_t | ListNil +End + +val [list_nth_mut_fwd_def] = DefineDiv ‘ + (** [paper::list_nth_mut] *) + list_nth_mut_fwd (l : 't list_t) (i : u32) : 't result = + (case l of + | ListCons x tl => + if i = int_to_u32 0 + then Return x + else (do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_fwd tl i0 + od) + | ListNil => Fail Failure) +’ + +val [list_nth_mut_back_def] = DefineDiv ‘ + (** [paper::list_nth_mut] *) + list_nth_mut_back (l : 't list_t) (i : u32) (ret : 't) : 't list_t result = + (case l of + | ListCons x tl => + if i = int_to_u32 0 + then Return (ListCons ret tl) + else ( + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_back tl i0 ret; + Return (ListCons x tl0) + od) + | ListNil => Fail Failure) +’ + +val [sum_fwd_def] = DefineDiv ‘ + (** [paper::sum] *) + sum_fwd (l : i32 list_t) : i32 result = + (case l of + | ListCons x tl => do + i <- sum_fwd tl; + i32_add x i + od + | ListNil => Return (int_to_i32 0)) +’ + +val test_nth_fwd_def = Define ‘ + (** [paper::test_nth] *) + test_nth_fwd : unit result = + let l = ListNil in + let l0 = ListCons (int_to_i32 3) l in + let l1 = ListCons (int_to_i32 2) l0 in + do + x <- list_nth_mut_fwd (ListCons (int_to_i32 1) l1) (int_to_u32 2); + x0 <- i32_add x (int_to_i32 1); + l2 <- list_nth_mut_back (ListCons (int_to_i32 1) l1) (int_to_u32 2) x0; + i <- sum_fwd l2; + if ~ (i = int_to_i32 7) then Fail Failure else Return () + od +’ + +(** Unit test for [paper::test_nth] *) +val _ = assert_return (“test_nth_fwd”) + +val call_choose_fwd_def = Define ‘ + (** [paper::call_choose] *) + call_choose_fwd (p : (u32 # u32)) : u32 result = + let (px, py) = p in + do + pz <- choose_fwd T px py; + pz0 <- u32_add pz (int_to_u32 1); + (px0, _) <- choose_back T px py pz0; + Return px0 + od +’ + +val _ = export_theory () diff --git a/tests/hol4/misc-paper/paperTheory.sig b/tests/hol4/misc-paper/paperTheory.sig new file mode 100644 index 00000000..2da80da1 --- /dev/null +++ b/tests/hol4/misc-paper/paperTheory.sig @@ -0,0 +1,210 @@ +signature paperTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val call_choose_fwd_def : thm + val choose_back_def : thm + val choose_fwd_def : thm + val list_nth_mut_back_def : thm + val list_nth_mut_fwd_def : thm + val list_t_TY_DEF : thm + val list_t_case_def : thm + val list_t_size_def : thm + val ref_incr_fwd_back_def : thm + val sum_fwd_def : thm + val test_choose_fwd_def : thm + val test_incr_fwd_def : thm + val test_nth_fwd_def : thm + + (* Theorems *) + val datatype_list_t : thm + val list_t_11 : thm + val list_t_Axiom : thm + val list_t_case_cong : thm + val list_t_case_eq : thm + val list_t_distinct : thm + val list_t_induction : thm + val list_t_nchotomy : thm + + val paper_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "paper" + + [call_choose_fwd_def] Definition + + ⊢ ∀p. call_choose_fwd p = + (let + (px,py) = p + in + do + pz <- choose_fwd T px py; + pz0 <- u32_add pz (int_to_u32 1); + (px0,_) <- choose_back T px py pz0; + Return px0 + od) + + [choose_back_def] Definition + + ⊢ ∀b x y ret. + choose_back b x y ret = + if b then Return (ret,y) else Return (x,ret) + + [choose_fwd_def] Definition + + ⊢ ∀b x y. choose_fwd b x y = if b then Return x else Return y + + [list_nth_mut_back_def] Definition + + ⊢ ∀l i ret. + list_nth_mut_back l i ret = + case l of + ListCons x tl => + if i = int_to_u32 0 then Return (ListCons ret tl) + else + do + i0 <- u32_sub i (int_to_u32 1); + tl0 <- list_nth_mut_back tl i0 ret; + Return (ListCons x tl0) + od + | ListNil => Fail Failure + + [list_nth_mut_fwd_def] Definition + + ⊢ ∀l i. + list_nth_mut_fwd l i = + case l of + ListCons x tl => + if i = int_to_u32 0 then Return x + else + do + i0 <- u32_sub i (int_to_u32 1); + list_nth_mut_fwd tl i0 + od + | ListNil => Fail Failure + + [list_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('list_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 a0 + (ind_type$FCONS a1 (λn. ind_type$BOTTOM))) + a0 a1 ∧ $var$('list_t') a1) ∨ + a0' = + ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ + $var$('list_t') a0') ⇒ + $var$('list_t') a0') rep + + [list_t_case_def] Definition + + ⊢ (∀a0 a1 f v. list_t_CASE (ListCons a0 a1) f v = f a0 a1) ∧ + ∀f v. list_t_CASE ListNil f v = v + + [list_t_size_def] Definition + + ⊢ (∀f a0 a1. + list_t_size f (ListCons a0 a1) = 1 + (f a0 + list_t_size f a1)) ∧ + ∀f. list_t_size f ListNil = 0 + + [ref_incr_fwd_back_def] Definition + + ⊢ ∀x. ref_incr_fwd_back x = i32_add x (int_to_i32 1) + + [sum_fwd_def] Definition + + ⊢ ∀l. sum_fwd l = + case l of + ListCons x tl => do i <- sum_fwd tl; i32_add x i od + | ListNil => Return (int_to_i32 0) + + [test_choose_fwd_def] Definition + + ⊢ test_choose_fwd = + do + z <- choose_fwd T (int_to_i32 0) (int_to_i32 0); + z0 <- i32_add z (int_to_i32 1); + if z0 ≠ int_to_i32 1 then Fail Failure + else + do + (x,y) <- choose_back T (int_to_i32 0) (int_to_i32 0) z0; + if x ≠ int_to_i32 1 then Fail Failure + else if y ≠ int_to_i32 0 then Fail Failure + else Return () + od + od + + [test_incr_fwd_def] Definition + + ⊢ test_incr_fwd = + do + x <- ref_incr_fwd_back (int_to_i32 0); + if x ≠ int_to_i32 1 then Fail Failure else Return () + od + + [test_nth_fwd_def] Definition + + ⊢ test_nth_fwd = + (let + l = ListNil; + l0 = ListCons (int_to_i32 3) l; + l1 = ListCons (int_to_i32 2) l0 + in + do + x <- + list_nth_mut_fwd (ListCons (int_to_i32 1) l1) (int_to_u32 2); + x0 <- i32_add x (int_to_i32 1); + l2 <- + list_nth_mut_back (ListCons (int_to_i32 1) l1) + (int_to_u32 2) x0; + i <- sum_fwd l2; + if i ≠ int_to_i32 7 then Fail Failure else Return () + od) + + [datatype_list_t] Theorem + + ⊢ DATATYPE (list_t ListCons ListNil) + + [list_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + ListCons a0 a1 = ListCons a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [list_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a0 a1. fn (ListCons a0 a1) = f0 a0 a1 (fn a1)) ∧ + fn ListNil = f1 + + [list_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ (∀a0 a1. M' = ListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ + (M' = ListNil ⇒ v = v') ⇒ + list_t_CASE M f v = list_t_CASE M' f' v' + + [list_t_case_eq] Theorem + + ⊢ list_t_CASE x f v = v' ⇔ + (∃t l. x = ListCons t l ∧ f t l = v') ∨ x = ListNil ∧ v = v' + + [list_t_distinct] Theorem + + ⊢ ∀a1 a0. ListCons a0 a1 ≠ ListNil + + [list_t_induction] Theorem + + ⊢ ∀P. (∀l. P l ⇒ ∀t. P (ListCons t l)) ∧ P ListNil ⇒ ∀l. P l + + [list_t_nchotomy] Theorem + + ⊢ ∀ll. (∃t l. ll = ListCons t l) ∨ ll = ListNil + + +*) +end diff --git a/tests/hol4/misc-polonius_list/Holmakefile b/tests/hol4/misc-polonius_list/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/misc-polonius_list/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/misc-polonius_list/poloniusListScript.sml b/tests/hol4/misc-polonius_list/poloniusListScript.sml new file mode 100644 index 00000000..dd631169 --- /dev/null +++ b/tests/hol4/misc-polonius_list/poloniusListScript.sml @@ -0,0 +1,37 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [polonius_list] *) +open primitivesLib divDefLib + +val _ = new_theory "poloniusList" + + +Datatype: + (** [polonius_list::List] *) + list_t = | ListCons 't list_t | ListNil +End + +val [get_list_at_x_fwd_def] = DefineDiv ‘ + (** [polonius_list::get_list_at_x] *) + get_list_at_x_fwd (ls : u32 list_t) (x : u32) : u32 list_t result = + (case ls of + | ListCons hd tl => + if hd = x then Return (ListCons hd tl) else get_list_at_x_fwd tl x + | ListNil => Return ListNil) +’ + +val [get_list_at_x_back_def] = DefineDiv ‘ + (** [polonius_list::get_list_at_x] *) + get_list_at_x_back + (ls : u32 list_t) (x : u32) (ret : u32 list_t) : u32 list_t result = + (case ls of + | ListCons hd tl => + if hd = x + then Return ret + else (do + tl0 <- get_list_at_x_back tl x ret; + Return (ListCons hd tl0) + od) + | ListNil => Return ret) +’ + +val _ = export_theory () diff --git a/tests/hol4/misc-polonius_list/poloniusListTheory.sig b/tests/hol4/misc-polonius_list/poloniusListTheory.sig new file mode 100644 index 00000000..41f21df7 --- /dev/null +++ b/tests/hol4/misc-polonius_list/poloniusListTheory.sig @@ -0,0 +1,120 @@ +signature poloniusListTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val get_list_at_x_back_def : thm + val get_list_at_x_fwd_def : thm + val list_t_TY_DEF : thm + val list_t_case_def : thm + val list_t_size_def : thm + + (* Theorems *) + val datatype_list_t : thm + val list_t_11 : thm + val list_t_Axiom : thm + val list_t_case_cong : thm + val list_t_case_eq : thm + val list_t_distinct : thm + val list_t_induction : thm + val list_t_nchotomy : thm + + val poloniusList_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "poloniusList" + + [get_list_at_x_back_def] Definition + + ⊢ ∀ls x ret. + get_list_at_x_back ls x ret = + case ls of + ListCons hd tl => + if hd = x then Return ret + else + do + tl0 <- get_list_at_x_back tl x ret; + Return (ListCons hd tl0) + od + | ListNil => Return ret + + [get_list_at_x_fwd_def] Definition + + ⊢ ∀ls x. + get_list_at_x_fwd ls x = + case ls of + ListCons hd tl => + if hd = x then Return (ListCons hd tl) + else get_list_at_x_fwd tl x + | ListNil => Return ListNil + + [list_t_TY_DEF] Definition + + ⊢ ∃rep. + TYPE_DEFINITION + (λa0'. + ∀ $var$('list_t'). + (∀a0'. + (∃a0 a1. + a0' = + (λa0 a1. + ind_type$CONSTR 0 a0 + (ind_type$FCONS a1 (λn. ind_type$BOTTOM))) + a0 a1 ∧ $var$('list_t') a1) ∨ + a0' = + ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ + $var$('list_t') a0') ⇒ + $var$('list_t') a0') rep + + [list_t_case_def] Definition + + ⊢ (∀a0 a1 f v. list_t_CASE (ListCons a0 a1) f v = f a0 a1) ∧ + ∀f v. list_t_CASE ListNil f v = v + + [list_t_size_def] Definition + + ⊢ (∀f a0 a1. + list_t_size f (ListCons a0 a1) = 1 + (f a0 + list_t_size f a1)) ∧ + ∀f. list_t_size f ListNil = 0 + + [datatype_list_t] Theorem + + ⊢ DATATYPE (list_t ListCons ListNil) + + [list_t_11] Theorem + + ⊢ ∀a0 a1 a0' a1'. + ListCons a0 a1 = ListCons a0' a1' ⇔ a0 = a0' ∧ a1 = a1' + + [list_t_Axiom] Theorem + + ⊢ ∀f0 f1. ∃fn. + (∀a0 a1. fn (ListCons a0 a1) = f0 a0 a1 (fn a1)) ∧ + fn ListNil = f1 + + [list_t_case_cong] Theorem + + ⊢ ∀M M' f v. + M = M' ∧ (∀a0 a1. M' = ListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ + (M' = ListNil ⇒ v = v') ⇒ + list_t_CASE M f v = list_t_CASE M' f' v' + + [list_t_case_eq] Theorem + + ⊢ list_t_CASE x f v = v' ⇔ + (∃t l. x = ListCons t l ∧ f t l = v') ∨ x = ListNil ∧ v = v' + + [list_t_distinct] Theorem + + ⊢ ∀a1 a0. ListCons a0 a1 ≠ ListNil + + [list_t_induction] Theorem + + ⊢ ∀P. (∀l. P l ⇒ ∀t. P (ListCons t l)) ∧ P ListNil ⇒ ∀l. P l + + [list_t_nchotomy] Theorem + + ⊢ ∀ll. (∃t l. ll = ListCons t l) ∨ ll = ListNil + + +*) +end |