diff options
Diffstat (limited to 'tests/hol4/hashmap')
| -rw-r--r-- | tests/hol4/hashmap/Holmakefile | 5 | ||||
| -rw-r--r-- | tests/hol4/hashmap/hashmap_FunsScript.sml | 567 | ||||
| -rw-r--r-- | tests/hol4/hashmap/hashmap_FunsTheory.sig | 550 | ||||
| -rw-r--r-- | tests/hol4/hashmap/hashmap_TypesScript.sml | 24 | ||||
| -rw-r--r-- | tests/hol4/hashmap/hashmap_TypesTheory.sig | 494 |
5 files changed, 1640 insertions, 0 deletions
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 |