Library zoo_std.array__code
Require Import zoo.prelude.
Require Import zoo.language.typeclasses.
Require Import zoo.language.notations.
Require Import zoo.program_logic.assume.
Require Import zoo.program_logic.for_.
Require Import zoo.options.
Definition arrayู unsafe_alloc : val :=
๐ณ๐๐ป "sz" โ
๐ฎ๐น๐น๐ผ๐ฐ 0 "sz".
Definition arrayู alloc : val :=
๐ณ๐๐ป "sz" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_alloc "sz".
Definition arrayู create : val :=
๐ณ๐๐ป โฝ โ
arrayู unsafe_alloc 0.
Definition arrayู size : val :=
๐ณ๐๐ป "t" โ
๐๐ถ๐๐ฒ "t".
Definition arrayู unsafe_get : val :=
๐ณ๐๐ป "t" "i" โ
๐น๐ผ๐ฎ๐ฑ "t" "i".
Definition arrayู get : val :=
๐ณ๐๐ป "t" "i" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" < arrayู size "t") โฎ
arrayู unsafe_get "t" "i".
Definition arrayู unsafe_set : val :=
๐ณ๐๐ป "t" "i" "v" โ
๐๐๐ผ๐ฟ๐ฒ "t" "i" "v".
Definition arrayู set : val :=
๐ณ๐๐ป "t" "i" "v" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" < arrayู size "t") โฎ
arrayู unsafe_set "t" "i" "v".
Definition arrayู unsafe_swap : val :=
๐ณ๐๐ป "t" "i1" "i2" โ
๐น๐ฒ๐ "v1" = arrayู unsafe_get "t" "i1" ๐ถ๐ป
๐น๐ฒ๐ "v2" = arrayู unsafe_get "t" "i2" ๐ถ๐ป
arrayู unsafe_set "t" "i1" "v2" โฎ
arrayู unsafe_set "t" "i2" "v1".
Definition arrayู unsafe_fill_slice : val :=
๐ณ๐๐ป "t" "i" "n" "v" โ
๐ณ๐ผ๐ฟ "j" = 0 ๐๐ผ "n" ๐ฑ๐ผ
arrayู unsafe_set "t" ("i" + "j") "v"
๐ฑ๐ผ๐ป๐ฒ.
Definition arrayู fill_slice : val :=
๐ณ๐๐ป "t" "i" "n" "v" โ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_fill_slice "t" "i" "n" "v".
Definition arrayู fill : val :=
๐ณ๐๐ป "t" "v" โ
arrayู unsafe_fill_slice "t" 0 (arrayู size "t") "v".
Definition arrayู unsafe_make : val :=
๐ณ๐๐ป "sz" "v" โ
๐น๐ฒ๐ "t" = arrayู unsafe_alloc "sz" ๐ถ๐ป
arrayู fill "t" "v" โฎ
"t".
Definition arrayู make : val :=
๐ณ๐๐ป "sz" "v" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_make "sz" "v".
Definition arrayู foldli_aux : val :=
๐ฟ๐ฒ๐ฐ "foldli_aux" "fn" "t" "sz" "i" "acc" โ
๐ถ๐ณ "sz" โค "i" ๐๐ต๐ฒ๐ป (
"acc"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "v" = arrayู unsafe_get "t" "i" ๐ถ๐ป
"foldli_aux" "fn" "t" "sz" ("i" + 1) ("fn" "i" "acc" "v")
).
Definition arrayู foldli : val :=
๐ณ๐๐ป "fn" "acc" "t" โ
arrayู foldli_aux "fn" "t" (arrayู size "t") 0 "acc".
Definition arrayู foldl : val :=
๐ณ๐๐ป "fn" โ
arrayู foldli (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู foldri_aux : val :=
๐ฟ๐ฒ๐ฐ "foldri_aux" "fn" "t" "i" "acc" โ
๐ถ๐ณ "i" โค 0 ๐๐ต๐ฒ๐ป (
"acc"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "i" = "i" - 1 ๐ถ๐ป
๐น๐ฒ๐ "v" = arrayู unsafe_get "t" "i" ๐ถ๐ป
"foldri_aux" "fn" "t" "i" ("fn" "i" "v" "acc")
).
Definition arrayู foldri : val :=
๐ณ๐๐ป "fn" "t" "acc" โ
arrayู foldri_aux "fn" "t" (arrayู size "t") "acc".
Definition arrayู foldr : val :=
๐ณ๐๐ป "fn" โ
arrayู foldri (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู sum : val :=
๐ณ๐๐ป "t" โ
arrayู foldl (๐ณ๐๐ป "1" "2" โ "1" + "2") 0 "t".
Definition arrayู unsafe_iteri_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ณ๐ผ๐ฟ "k" = 0 ๐๐ผ "n" ๐ฑ๐ผ
"fn" "k" (arrayู unsafe_get "t" ("i" + "k"))
๐ฑ๐ผ๐ป๐ฒ.
Definition arrayู iteri_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_iteri_slice "fn" "t" "i" "n".
Definition arrayู unsafe_iter_slice : val :=
๐ณ๐๐ป "fn" โ
arrayู unsafe_iteri_slice (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู iter_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_iter_slice "fn" "t" "i" "n".
Definition arrayู iteri : val :=
๐ณ๐๐ป "fn" "t" โ
arrayู unsafe_iteri_slice "fn" "t" 0 (arrayู size "t").
Definition arrayู iter : val :=
๐ณ๐๐ป "fn" โ
arrayู iteri (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู unsafe_applyi_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
arrayู unsafe_iteri_slice
(๐ณ๐๐ป "k" "v" โ
arrayู unsafe_set "t" ("i" + "k") ("fn" "k" "v"))
"t"
"i"
"n".
Definition arrayู applyi_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_applyi_slice "fn" "t" "i" "n".
Definition arrayู unsafe_apply_slice : val :=
๐ณ๐๐ป "fn" โ
arrayู unsafe_applyi_slice (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู apply_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_apply_slice "fn" "t" "i" "n".
Definition arrayู applyi : val :=
๐ณ๐๐ป "fn" "t" โ
arrayู unsafe_applyi_slice "fn" "t" 0 (arrayู size "t").
Definition arrayู apply : val :=
๐ณ๐๐ป "fn" โ
arrayู applyi (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู unsafe_initi : val :=
๐ณ๐๐ป "sz" "fn" โ
๐น๐ฒ๐ "t" = arrayู unsafe_alloc "sz" ๐ถ๐ป
arrayู applyi (๐ณ๐๐ป "i" โฝ โ "fn" "i") "t" โฎ
"t".
Definition arrayู initi : val :=
๐ณ๐๐ป "sz" "fn" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_initi "sz" "fn".
Definition arrayู unsafe_init : val :=
๐ณ๐๐ป "sz" "fn" โ
arrayู unsafe_initi "sz" (๐ณ๐๐ป "_i" โ "fn" ()).
Definition arrayู init : val :=
๐ณ๐๐ป "sz" "fn" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_init "sz" "fn".
Definition arrayู mapi : val :=
๐ณ๐๐ป "fn" "t" โ
arrayู unsafe_initi
(arrayู size "t")
(๐ณ๐๐ป "i" โ "fn" "i" (arrayู unsafe_get "t" "i")).
Definition arrayู map : val :=
๐ณ๐๐ป "fn" โ
arrayู mapi (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู unsafe_copy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐ณ๐ผ๐ฟ "k" = 0 ๐๐ผ "n" ๐ฑ๐ผ
๐น๐ฒ๐ "v" = arrayู unsafe_get "t1" ("i1" + "k") ๐ถ๐ป
arrayู unsafe_set "t2" ("i2" + "k") "v"
๐ฑ๐ผ๐ป๐ฒ.
Definition arrayู copy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i1" + "n" โค "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i2" + "n" โค "sz2") โฎ
arrayู unsafe_copy_slice "t1" "i1" "t2" "i2" "n".
Definition arrayู unsafe_copy : val :=
๐ณ๐๐ป "t1" "t2" "i2" โ
arrayู unsafe_copy_slice "t1" 0 "t2" "i2" (arrayู size "t1").
Definition arrayู copy : val :=
๐ณ๐๐ป "t1" "t2" "i2" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i2" + arrayู size "t1" โค arrayู size "t2") โฎ
arrayู unsafe_copy "t1" "t2" "i2".
Definition arrayู unsafe_grow : val :=
๐ณ๐๐ป "t" "sz'" "v'" โ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐น๐ฒ๐ "t'" = arrayู unsafe_alloc "sz'" ๐ถ๐ป
arrayู unsafe_copy "t" "t'" 0 โฎ
arrayู unsafe_fill_slice "t'" "sz" ("sz'" - "sz") "v'" โฎ
"t'".
Definition arrayู grow : val :=
๐ณ๐๐ป "t" "sz'" "v'" โ
๐ฎ๐๐๐๐บ๐ฒ (arrayู size "t" โค "sz'") โฎ
arrayู unsafe_grow "t" "sz'" "v'".
Definition arrayู unsafe_sub : val :=
๐ณ๐๐ป "t" "i" "n" โ
๐น๐ฒ๐ "t'" = arrayู unsafe_alloc "n" ๐ถ๐ป
arrayู unsafe_copy_slice "t" "i" "t'" 0 "n" โฎ
"t'".
Definition arrayู sub : val :=
๐ณ๐๐ป "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค arrayู size "t") โฎ
arrayู unsafe_sub "t" "i" "n".
Definition arrayู unsafe_shrink : val :=
๐ณ๐๐ป "t" "sz'" โ
arrayู unsafe_sub "t" 0 "sz'".
Definition arrayู shrink : val :=
๐ณ๐๐ป "t" "sz'" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz'") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("sz'" โค arrayู size "t") โฎ
arrayู unsafe_shrink "t" "sz'".
Definition arrayู clone : val :=
๐ณ๐๐ป "t" โ
arrayู unsafe_shrink "t" (arrayู size "t").
Definition arrayู unsafe_cget : val :=
๐ณ๐๐ป "t" "i" โ
arrayู unsafe_get "t" ("i" ๐ฟ๐ฒ๐บ arrayู size "t").
Definition arrayู cget : val :=
๐ณ๐๐ป "t" "i" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 < arrayู size "t") โฎ
arrayู unsafe_cget "t" "i".
Definition arrayู unsafe_cset : val :=
๐ณ๐๐ป "t" "i" "v" โ
arrayู unsafe_set "t" ("i" ๐ฟ๐ฒ๐บ arrayู size "t") "v".
Definition arrayู cset : val :=
๐ณ๐๐ป "t" "i" "v" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 < arrayู size "t") โฎ
arrayู unsafe_cset "t" "i" "v".
Definition arrayู unsafe_ccopy_sliceโ : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐น๐ฒ๐ "i2" = "i2" ๐ฟ๐ฒ๐บ "sz2" ๐ถ๐ป
๐ถ๐ณ "i2" + "n" โค "sz2" ๐๐ต๐ฒ๐ป (
arrayู unsafe_copy_slice "t1" "i1" "t2" "i2" "n"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "n1" = "sz2" - "i2" ๐ถ๐ป
๐น๐ฒ๐ "n2" = "n" - "n1" ๐ถ๐ป
arrayู unsafe_copy_slice "t1" "i1" "t2" "i2" "n1" โฎ
arrayู unsafe_copy_slice "t1" ("i1" + "n1") "t2" 0 "n2"
).
Definition arrayู unsafe_ccopy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "i1" = "i1" ๐ฟ๐ฒ๐บ "sz1" ๐ถ๐ป
๐ถ๐ณ "i1" + "n" โค "sz1" ๐๐ต๐ฒ๐ป (
arrayู unsafe_ccopy_sliceโ "t1" "i1" "t2" "i2" "n"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "n1" = "sz1" - "i1" ๐ถ๐ป
๐น๐ฒ๐ "n2" = "n" - "n1" ๐ถ๐ป
arrayู unsafe_ccopy_sliceโ "t1" "i1" "t2" "i2" "n1" โฎ
arrayู unsafe_ccopy_sliceโ "t1" 0 "t2" ("i2" + "n1") "n2"
).
Definition arrayู ccopy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 < "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 < "sz2") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("n" โค "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("n" โค "sz2") โฎ
arrayู unsafe_ccopy_slice "t1" "i1" "t2" "i2" "n".
Definition arrayู unsafe_ccopy : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" โ
arrayู unsafe_ccopy_slice "t1" "i1" "t2" "i2" (arrayู size "t1").
Definition arrayู ccopy : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 < "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("sz1" โค "sz2") โฎ
arrayู unsafe_ccopy "t1" "i1" "t2" "i2".
Definition arrayู unsafe_cgrow_slice : val :=
๐ณ๐๐ป "t" "i" "n" "sz'" "v" โ
๐น๐ฒ๐ "t'" = arrayู unsafe_make "sz'" "v" ๐ถ๐ป
arrayู unsafe_ccopy_slice "t" "i" "t'" "i" "n" โฎ
"t'".
Definition arrayู unsafe_cgrow : val :=
๐ณ๐๐ป "t" "i" "sz'" "v" โ
arrayู unsafe_cgrow_slice "t" "i" (arrayู size "t") "sz'" "v".
Definition arrayู unsafe_cshrink_slice : val :=
๐ณ๐๐ป "t" "i" "sz'" โ
๐น๐ฒ๐ "t'" = arrayู unsafe_alloc "sz'" ๐ถ๐ป
arrayู unsafe_ccopy_slice "t" "i" "t'" "i" "sz'" โฎ
"t'".
Require Import zoo.language.typeclasses.
Require Import zoo.language.notations.
Require Import zoo.program_logic.assume.
Require Import zoo.program_logic.for_.
Require Import zoo.options.
Definition arrayู unsafe_alloc : val :=
๐ณ๐๐ป "sz" โ
๐ฎ๐น๐น๐ผ๐ฐ 0 "sz".
Definition arrayู alloc : val :=
๐ณ๐๐ป "sz" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_alloc "sz".
Definition arrayู create : val :=
๐ณ๐๐ป โฝ โ
arrayู unsafe_alloc 0.
Definition arrayู size : val :=
๐ณ๐๐ป "t" โ
๐๐ถ๐๐ฒ "t".
Definition arrayู unsafe_get : val :=
๐ณ๐๐ป "t" "i" โ
๐น๐ผ๐ฎ๐ฑ "t" "i".
Definition arrayู get : val :=
๐ณ๐๐ป "t" "i" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" < arrayู size "t") โฎ
arrayู unsafe_get "t" "i".
Definition arrayู unsafe_set : val :=
๐ณ๐๐ป "t" "i" "v" โ
๐๐๐ผ๐ฟ๐ฒ "t" "i" "v".
Definition arrayู set : val :=
๐ณ๐๐ป "t" "i" "v" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" < arrayู size "t") โฎ
arrayู unsafe_set "t" "i" "v".
Definition arrayู unsafe_swap : val :=
๐ณ๐๐ป "t" "i1" "i2" โ
๐น๐ฒ๐ "v1" = arrayู unsafe_get "t" "i1" ๐ถ๐ป
๐น๐ฒ๐ "v2" = arrayู unsafe_get "t" "i2" ๐ถ๐ป
arrayู unsafe_set "t" "i1" "v2" โฎ
arrayู unsafe_set "t" "i2" "v1".
Definition arrayู unsafe_fill_slice : val :=
๐ณ๐๐ป "t" "i" "n" "v" โ
๐ณ๐ผ๐ฟ "j" = 0 ๐๐ผ "n" ๐ฑ๐ผ
arrayู unsafe_set "t" ("i" + "j") "v"
๐ฑ๐ผ๐ป๐ฒ.
Definition arrayู fill_slice : val :=
๐ณ๐๐ป "t" "i" "n" "v" โ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_fill_slice "t" "i" "n" "v".
Definition arrayู fill : val :=
๐ณ๐๐ป "t" "v" โ
arrayู unsafe_fill_slice "t" 0 (arrayู size "t") "v".
Definition arrayู unsafe_make : val :=
๐ณ๐๐ป "sz" "v" โ
๐น๐ฒ๐ "t" = arrayู unsafe_alloc "sz" ๐ถ๐ป
arrayู fill "t" "v" โฎ
"t".
Definition arrayู make : val :=
๐ณ๐๐ป "sz" "v" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_make "sz" "v".
Definition arrayู foldli_aux : val :=
๐ฟ๐ฒ๐ฐ "foldli_aux" "fn" "t" "sz" "i" "acc" โ
๐ถ๐ณ "sz" โค "i" ๐๐ต๐ฒ๐ป (
"acc"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "v" = arrayู unsafe_get "t" "i" ๐ถ๐ป
"foldli_aux" "fn" "t" "sz" ("i" + 1) ("fn" "i" "acc" "v")
).
Definition arrayู foldli : val :=
๐ณ๐๐ป "fn" "acc" "t" โ
arrayู foldli_aux "fn" "t" (arrayู size "t") 0 "acc".
Definition arrayู foldl : val :=
๐ณ๐๐ป "fn" โ
arrayู foldli (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู foldri_aux : val :=
๐ฟ๐ฒ๐ฐ "foldri_aux" "fn" "t" "i" "acc" โ
๐ถ๐ณ "i" โค 0 ๐๐ต๐ฒ๐ป (
"acc"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "i" = "i" - 1 ๐ถ๐ป
๐น๐ฒ๐ "v" = arrayู unsafe_get "t" "i" ๐ถ๐ป
"foldri_aux" "fn" "t" "i" ("fn" "i" "v" "acc")
).
Definition arrayู foldri : val :=
๐ณ๐๐ป "fn" "t" "acc" โ
arrayู foldri_aux "fn" "t" (arrayู size "t") "acc".
Definition arrayู foldr : val :=
๐ณ๐๐ป "fn" โ
arrayู foldri (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู sum : val :=
๐ณ๐๐ป "t" โ
arrayู foldl (๐ณ๐๐ป "1" "2" โ "1" + "2") 0 "t".
Definition arrayู unsafe_iteri_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ณ๐ผ๐ฟ "k" = 0 ๐๐ผ "n" ๐ฑ๐ผ
"fn" "k" (arrayู unsafe_get "t" ("i" + "k"))
๐ฑ๐ผ๐ป๐ฒ.
Definition arrayู iteri_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_iteri_slice "fn" "t" "i" "n".
Definition arrayู unsafe_iter_slice : val :=
๐ณ๐๐ป "fn" โ
arrayู unsafe_iteri_slice (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู iter_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_iter_slice "fn" "t" "i" "n".
Definition arrayู iteri : val :=
๐ณ๐๐ป "fn" "t" โ
arrayู unsafe_iteri_slice "fn" "t" 0 (arrayู size "t").
Definition arrayู iter : val :=
๐ณ๐๐ป "fn" โ
arrayู iteri (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู unsafe_applyi_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
arrayู unsafe_iteri_slice
(๐ณ๐๐ป "k" "v" โ
arrayู unsafe_set "t" ("i" + "k") ("fn" "k" "v"))
"t"
"i"
"n".
Definition arrayู applyi_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_applyi_slice "fn" "t" "i" "n".
Definition arrayู unsafe_apply_slice : val :=
๐ณ๐๐ป "fn" โ
arrayู unsafe_applyi_slice (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู apply_slice : val :=
๐ณ๐๐ป "fn" "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ ("i" โค "sz") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค "sz") โฎ
arrayู unsafe_apply_slice "fn" "t" "i" "n".
Definition arrayู applyi : val :=
๐ณ๐๐ป "fn" "t" โ
arrayู unsafe_applyi_slice "fn" "t" 0 (arrayู size "t").
Definition arrayู apply : val :=
๐ณ๐๐ป "fn" โ
arrayู applyi (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู unsafe_initi : val :=
๐ณ๐๐ป "sz" "fn" โ
๐น๐ฒ๐ "t" = arrayู unsafe_alloc "sz" ๐ถ๐ป
arrayู applyi (๐ณ๐๐ป "i" โฝ โ "fn" "i") "t" โฎ
"t".
Definition arrayู initi : val :=
๐ณ๐๐ป "sz" "fn" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_initi "sz" "fn".
Definition arrayู unsafe_init : val :=
๐ณ๐๐ป "sz" "fn" โ
arrayู unsafe_initi "sz" (๐ณ๐๐ป "_i" โ "fn" ()).
Definition arrayู init : val :=
๐ณ๐๐ป "sz" "fn" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz") โฎ
arrayู unsafe_init "sz" "fn".
Definition arrayู mapi : val :=
๐ณ๐๐ป "fn" "t" โ
arrayู unsafe_initi
(arrayู size "t")
(๐ณ๐๐ป "i" โ "fn" "i" (arrayู unsafe_get "t" "i")).
Definition arrayู map : val :=
๐ณ๐๐ป "fn" โ
arrayู mapi (๐ณ๐๐ป "_i" โ "fn").
Definition arrayู unsafe_copy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐ณ๐ผ๐ฟ "k" = 0 ๐๐ผ "n" ๐ฑ๐ผ
๐น๐ฒ๐ "v" = arrayู unsafe_get "t1" ("i1" + "k") ๐ถ๐ป
arrayู unsafe_set "t2" ("i2" + "k") "v"
๐ฑ๐ผ๐ป๐ฒ.
Definition arrayู copy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i1" + "n" โค "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i2" + "n" โค "sz2") โฎ
arrayู unsafe_copy_slice "t1" "i1" "t2" "i2" "n".
Definition arrayู unsafe_copy : val :=
๐ณ๐๐ป "t1" "t2" "i2" โ
arrayู unsafe_copy_slice "t1" 0 "t2" "i2" (arrayู size "t1").
Definition arrayู copy : val :=
๐ณ๐๐ป "t1" "t2" "i2" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i2" + arrayู size "t1" โค arrayู size "t2") โฎ
arrayู unsafe_copy "t1" "t2" "i2".
Definition arrayู unsafe_grow : val :=
๐ณ๐๐ป "t" "sz'" "v'" โ
๐น๐ฒ๐ "sz" = arrayู size "t" ๐ถ๐ป
๐น๐ฒ๐ "t'" = arrayู unsafe_alloc "sz'" ๐ถ๐ป
arrayู unsafe_copy "t" "t'" 0 โฎ
arrayู unsafe_fill_slice "t'" "sz" ("sz'" - "sz") "v'" โฎ
"t'".
Definition arrayู grow : val :=
๐ณ๐๐ป "t" "sz'" "v'" โ
๐ฎ๐๐๐๐บ๐ฒ (arrayู size "t" โค "sz'") โฎ
arrayู unsafe_grow "t" "sz'" "v'".
Definition arrayู unsafe_sub : val :=
๐ณ๐๐ป "t" "i" "n" โ
๐น๐ฒ๐ "t'" = arrayู unsafe_alloc "n" ๐ถ๐ป
arrayู unsafe_copy_slice "t" "i" "t'" 0 "n" โฎ
"t'".
Definition arrayู sub : val :=
๐ณ๐๐ป "t" "i" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("i" + "n" โค arrayู size "t") โฎ
arrayู unsafe_sub "t" "i" "n".
Definition arrayู unsafe_shrink : val :=
๐ณ๐๐ป "t" "sz'" โ
arrayู unsafe_sub "t" 0 "sz'".
Definition arrayู shrink : val :=
๐ณ๐๐ป "t" "sz'" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "sz'") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("sz'" โค arrayู size "t") โฎ
arrayู unsafe_shrink "t" "sz'".
Definition arrayู clone : val :=
๐ณ๐๐ป "t" โ
arrayู unsafe_shrink "t" (arrayู size "t").
Definition arrayู unsafe_cget : val :=
๐ณ๐๐ป "t" "i" โ
arrayู unsafe_get "t" ("i" ๐ฟ๐ฒ๐บ arrayู size "t").
Definition arrayู cget : val :=
๐ณ๐๐ป "t" "i" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 < arrayู size "t") โฎ
arrayู unsafe_cget "t" "i".
Definition arrayู unsafe_cset : val :=
๐ณ๐๐ป "t" "i" "v" โ
arrayู unsafe_set "t" ("i" ๐ฟ๐ฒ๐บ arrayู size "t") "v".
Definition arrayู cset : val :=
๐ณ๐๐ป "t" "i" "v" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 < arrayู size "t") โฎ
arrayู unsafe_cset "t" "i" "v".
Definition arrayู unsafe_ccopy_sliceโ : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐น๐ฒ๐ "i2" = "i2" ๐ฟ๐ฒ๐บ "sz2" ๐ถ๐ป
๐ถ๐ณ "i2" + "n" โค "sz2" ๐๐ต๐ฒ๐ป (
arrayู unsafe_copy_slice "t1" "i1" "t2" "i2" "n"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "n1" = "sz2" - "i2" ๐ถ๐ป
๐น๐ฒ๐ "n2" = "n" - "n1" ๐ถ๐ป
arrayู unsafe_copy_slice "t1" "i1" "t2" "i2" "n1" โฎ
arrayู unsafe_copy_slice "t1" ("i1" + "n1") "t2" 0 "n2"
).
Definition arrayู unsafe_ccopy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "i1" = "i1" ๐ฟ๐ฒ๐บ "sz1" ๐ถ๐ป
๐ถ๐ณ "i1" + "n" โค "sz1" ๐๐ต๐ฒ๐ป (
arrayู unsafe_ccopy_sliceโ "t1" "i1" "t2" "i2" "n"
) ๐ฒ๐น๐๐ฒ (
๐น๐ฒ๐ "n1" = "sz1" - "i1" ๐ถ๐ป
๐น๐ฒ๐ "n2" = "n" - "n1" ๐ถ๐ป
arrayู unsafe_ccopy_sliceโ "t1" "i1" "t2" "i2" "n1" โฎ
arrayู unsafe_ccopy_sliceโ "t1" 0 "t2" ("i2" + "n1") "n2"
).
Definition arrayู ccopy_slice : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" "n" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "n") โฎ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 < "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 < "sz2") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("n" โค "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("n" โค "sz2") โฎ
arrayู unsafe_ccopy_slice "t1" "i1" "t2" "i2" "n".
Definition arrayู unsafe_ccopy : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" โ
arrayู unsafe_ccopy_slice "t1" "i1" "t2" "i2" (arrayู size "t1").
Definition arrayู ccopy : val :=
๐ณ๐๐ป "t1" "i1" "t2" "i2" โ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i1") โฎ
๐ฎ๐๐๐๐บ๐ฒ (0 โค "i2") โฎ
๐น๐ฒ๐ "sz1" = arrayู size "t1" ๐ถ๐ป
๐น๐ฒ๐ "sz2" = arrayู size "t2" ๐ถ๐ป
๐ฎ๐๐๐๐บ๐ฒ (0 < "sz1") โฎ
๐ฎ๐๐๐๐บ๐ฒ ("sz1" โค "sz2") โฎ
arrayู unsafe_ccopy "t1" "i1" "t2" "i2".
Definition arrayู unsafe_cgrow_slice : val :=
๐ณ๐๐ป "t" "i" "n" "sz'" "v" โ
๐น๐ฒ๐ "t'" = arrayู unsafe_make "sz'" "v" ๐ถ๐ป
arrayู unsafe_ccopy_slice "t" "i" "t'" "i" "n" โฎ
"t'".
Definition arrayู unsafe_cgrow : val :=
๐ณ๐๐ป "t" "i" "sz'" "v" โ
arrayู unsafe_cgrow_slice "t" "i" (arrayู size "t") "sz'" "v".
Definition arrayู unsafe_cshrink_slice : val :=
๐ณ๐๐ป "t" "i" "sz'" โ
๐น๐ฒ๐ "t'" = arrayู unsafe_alloc "sz'" ๐ถ๐ป
arrayู unsafe_ccopy_slice "t" "i" "t'" "i" "sz'" โฎ
"t'".