diff options
Diffstat (limited to 'tests/coq/hashmap_on_disk/Primitives.v')
| -rw-r--r-- | tests/coq/hashmap_on_disk/Primitives.v | 419 |
1 files changed, 359 insertions, 60 deletions
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v index 71a2d9c3..85e38f01 100644 --- a/tests/coq/hashmap_on_disk/Primitives.v +++ b/tests/coq/hashmap_on_disk/Primitives.v @@ -63,13 +63,15 @@ Check (if true then Return (1 + 2) else Fail_ Failure)%global = 3. (*** Misc *) - Definition string := Coq.Strings.String.string. Definition char := Coq.Strings.Ascii.ascii. Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte. -Definition mem_replace_fwd (a : Type) (x : a) (y : a) : a := x . -Definition mem_replace_back (a : Type) (x : a) (y : a) : a := y . +Definition core_mem_replace (a : Type) (x : a) (y : a) : a := x . +Definition core_mem_replace_back (a : Type) (x : a) (y : a) : a := y . + +Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }. +Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }. (*** Scalars *) @@ -394,12 +396,89 @@ Notation "x s< y" := (scalar_ltb x y) (at level 80) : Primitives_scope. Notation "x s>= y" := (scalar_geb x y) (at level 80) : Primitives_scope. Notation "x s> y" := (scalar_gtb x y) (at level 80) : Primitives_scope. -(*** Range *) -Record range (T : Type) := mk_range { - start: T; - end_: T; +(** Constants *) +Definition core_u8_max := u8_max %u32. +Definition core_u16_max := u16_max %u32. +Definition core_u32_max := u32_max %u32. +Definition core_u64_max := u64_max %u64. +Definition core_u128_max := u64_max %u128. +Axiom core_usize_max : usize. (** TODO *) +Definition core_i8_max := i8_max %i32. +Definition core_i16_max := i16_max %i32. +Definition core_i32_max := i32_max %i32. +Definition core_i64_max := i64_max %i64. +Definition core_i128_max := i64_max %i128. +Axiom core_isize_max : isize. (** TODO *) + +(*** core::ops *) + +(* Trait declaration: [core::ops::index::Index] *) +Record core_ops_index_Index (Self Idx : Type) := mk_core_ops_index_Index { + core_ops_index_Index_Output : Type; + core_ops_index_Index_index : Self -> Idx -> result core_ops_index_Index_Output; +}. +Arguments mk_core_ops_index_Index {_ _}. +Arguments core_ops_index_Index_Output {_ _}. +Arguments core_ops_index_Index_index {_ _}. + +(* Trait declaration: [core::ops::index::IndexMut] *) +Record core_ops_index_IndexMut (Self Idx : Type) := mk_core_ops_index_IndexMut { + core_ops_index_IndexMut_indexInst : core_ops_index_Index Self Idx; + core_ops_index_IndexMut_index_mut : Self -> Idx -> result core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output); + core_ops_index_IndexMut_index_mut_back : Self -> Idx -> core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) -> result Self; +}. +Arguments mk_core_ops_index_IndexMut {_ _}. +Arguments core_ops_index_IndexMut_indexInst {_ _}. +Arguments core_ops_index_IndexMut_index_mut {_ _}. +Arguments core_ops_index_IndexMut_index_mut_back {_ _}. + +(* Trait declaration [core::ops::deref::Deref] *) +Record core_ops_deref_Deref (Self : Type) := mk_core_ops_deref_Deref { + core_ops_deref_Deref_target : Type; + core_ops_deref_Deref_deref : Self -> result core_ops_deref_Deref_target; +}. +Arguments mk_core_ops_deref_Deref {_}. +Arguments core_ops_deref_Deref_target {_}. +Arguments core_ops_deref_Deref_deref {_}. + +(* Trait declaration [core::ops::deref::DerefMut] *) +Record core_ops_deref_DerefMut (Self : Type) := mk_core_ops_deref_DerefMut { + core_ops_deref_DerefMut_derefInst : core_ops_deref_Deref Self; + core_ops_deref_DerefMut_deref_mut : Self -> result core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target); + core_ops_deref_DerefMut_deref_mut_back : Self -> core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self; }. -Arguments mk_range {_}. +Arguments mk_core_ops_deref_DerefMut {_}. +Arguments core_ops_deref_DerefMut_derefInst {_}. +Arguments core_ops_deref_DerefMut_deref_mut {_}. +Arguments core_ops_deref_DerefMut_deref_mut_back {_}. + +Record core_ops_range_Range (T : Type) := mk_core_ops_range_Range { + core_ops_range_Range_start : T; + core_ops_range_Range_end_ : T; +}. +Arguments mk_core_ops_range_Range {_}. +Arguments core_ops_range_Range_start {_}. +Arguments core_ops_range_Range_end_ {_}. + +(*** [alloc] *) + +Definition alloc_boxed_Box_deref (T : Type) (x : T) : result T := Return x. +Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x. +Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x. + +(* Trait instance *) +Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {| + core_ops_deref_Deref_target := Self; + core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self; +|}. + +(* Trait instance *) +Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {| + core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self; + core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self; + core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self; +|}. + (*** Arrays *) Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}. @@ -419,51 +498,50 @@ Qed. (* TODO: finish the definitions *) Axiom mk_array : forall (T : Type) (n : usize) (l : list T), array T n. -Axiom array_index_shared : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T. -Axiom array_index_mut_fwd : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T. -Axiom array_index_mut_back : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n). +(* For initialization *) +Axiom array_repeat : forall (T : Type) (n : usize) (x : T), array T n. + +Axiom array_index_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize), result T. +Axiom array_update_usize : forall (T : Type) (n : usize) (x : array T n) (i : usize) (nx : T), result (array T n). (*** Slice *) Definition slice T := { l: list T | Z.of_nat (length l) <= usize_max}. Axiom slice_len : forall (T : Type) (s : slice T), usize. -Axiom slice_index_shared : forall (T : Type) (x : slice T) (i : usize), result T. -Axiom slice_index_mut_fwd : forall (T : Type) (x : slice T) (i : usize), result T. -Axiom slice_index_mut_back : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T). +Axiom slice_index_usize : forall (T : Type) (x : slice T) (i : usize), result T. +Axiom slice_update_usize : forall (T : Type) (x : slice T) (i : usize) (nx : T), result (slice T). (*** Subslices *) -Axiom array_to_slice_shared : forall (T : Type) (n : usize) (x : array T n), result (slice T). -Axiom array_to_slice_mut_fwd : forall (T : Type) (n : usize) (x : array T n), result (slice T). -Axiom array_to_slice_mut_back : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n). +Axiom array_to_slice : forall (T : Type) (n : usize) (x : array T n), result (slice T). +Axiom array_from_slice : forall (T : Type) (n : usize) (x : array T n) (s : slice T), result (array T n). + +Axiom array_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize), result (slice T). +Axiom array_update_subslice: forall (T : Type) (n : usize) (x : array T n) (r : core_ops_range_Range usize) (ns : slice T), result (array T n). -Axiom array_subslice_shared: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T). -Axiom array_subslice_mut_fwd: forall (T : Type) (n : usize) (x : array T n) (r : range usize), result (slice T). -Axiom array_subslice_mut_back: forall (T : Type) (n : usize) (x : array T n) (r : range usize) (ns : slice T), result (array T n). -Axiom slice_subslice_shared: forall (T : Type) (x : slice T) (r : range usize), result (slice T). -Axiom slice_subslice_mut_fwd: forall (T : Type) (x : slice T) (r : range usize), result (slice T). -Axiom slice_subslice_mut_back: forall (T : Type) (x : slice T) (r : range usize) (ns : slice T), result (slice T). +Axiom slice_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize), result (slice T). +Axiom slice_update_subslice: forall (T : Type) (x : slice T) (r : core_ops_range_Range usize) (ns : slice T), result (slice T). (*** Vectors *) -Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }. +Definition alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }. -Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v. +Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig v. -Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)). +Definition alloc_vec_Vec_length {T: Type} (v: alloc_vec_Vec T) : Z := Z.of_nat (length (alloc_vec_Vec_to_list v)). -Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max). +Definition alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_usize_max). -Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max. +Lemma alloc_vec_Vec_len_in_usize {T} (v: alloc_vec_Vec T) : usize_min <= alloc_vec_Vec_length v <= usize_max. Proof. - unfold vec_length, usize_min. + unfold alloc_vec_Vec_length, usize_min. split. - lia. - apply (proj2_sig v). Qed. -Definition vec_len (T: Type) (v: vec T) : usize := - exist _ (vec_length v) (vec_len_in_usize v). +Definition alloc_vec_Vec_len (T: Type) (v: alloc_vec_Vec T) : usize := + exist _ (alloc_vec_Vec_length v) (alloc_vec_Vec_len_in_usize v). Fixpoint list_update {A} (l: list A) (n: nat) (a: A) : list A := @@ -474,50 +552,271 @@ Fixpoint list_update {A} (l: list A) (n: nat) (a: A) | S m => x :: (list_update t m a) end end. -Definition vec_bind {A B} (v: vec A) (f: list A -> result (list B)) : result (vec B) := - l <- f (vec_to_list v) ; +Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (list B)) : result (alloc_vec_Vec B) := + l <- f (alloc_vec_Vec_to_list v) ; match sumbool_of_bool (scalar_le_max Usize (Z.of_nat (length l))) with | left H => Return (exist _ l (scalar_le_max_valid _ _ H)) | right _ => Fail_ Failure end. (* The **forward** function shouldn't be used *) -Definition vec_push_fwd (T: Type) (v: vec T) (x: T) : unit := tt. +Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt. -Definition vec_push_back (T: Type) (v: vec T) (x: T) : result (vec T) := - vec_bind v (fun l => Return (l ++ [x])). +Definition alloc_vec_Vec_push (T: Type) (v: alloc_vec_Vec T) (x: T) : result (alloc_vec_Vec T) := + alloc_vec_Vec_bind v (fun l => Return (l ++ [x])). (* The **forward** function shouldn't be used *) -Definition vec_insert_fwd (T: Type) (v: vec T) (i: usize) (x: T) : result unit := - if to_Z i <? vec_length v then Return tt else Fail_ Failure. +Definition alloc_vec_Vec_insert_fwd (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result unit := + if to_Z i <? alloc_vec_Vec_length v then Return tt else Fail_ Failure. -Definition vec_insert_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) := - vec_bind v (fun l => +Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T) : result (alloc_vec_Vec T) := + alloc_vec_Vec_bind v (fun l => if to_Z i <? Z.of_nat (length l) then Return (list_update l (usize_to_nat i) x) else Fail_ Failure). -(* The **backward** function shouldn't be used *) -Definition vec_index_fwd (T: Type) (v: vec T) (i: usize) : result T := - match nth_error (vec_to_list v) (usize_to_nat i) with - | Some n => Return n - | None => Fail_ Failure - end. - -Definition vec_index_back (T: Type) (v: vec T) (i: usize) (x: T) : result unit := - if to_Z i <? vec_length v then Return tt else Fail_ Failure. - -(* The **backward** function shouldn't be used *) -Definition vec_index_mut_fwd (T: Type) (v: vec T) (i: usize) : result T := - match nth_error (vec_to_list v) (usize_to_nat i) with - | Some n => Return n - | None => Fail_ Failure +(* Helper *) +Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T. + +(* Helper *) +Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T). + +(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *) +Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit. + +(* Trait declaration: [core::slice::index::SliceIndex] *) +Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceIndex { + core_slice_index_SliceIndex_sealedInst : core_slice_index_private_slice_index_Sealed Self; + core_slice_index_SliceIndex_Output : Type; + core_slice_index_SliceIndex_get : Self -> T -> result (option core_slice_index_SliceIndex_Output); + core_slice_index_SliceIndex_get_mut : Self -> T -> result (option core_slice_index_SliceIndex_Output); + core_slice_index_SliceIndex_get_mut_back : Self -> T -> option core_slice_index_SliceIndex_Output -> result T; + core_slice_index_SliceIndex_get_unchecked : Self -> const_raw_ptr T -> result (const_raw_ptr core_slice_index_SliceIndex_Output); + core_slice_index_SliceIndex_get_unchecked_mut : Self -> mut_raw_ptr T -> result (mut_raw_ptr core_slice_index_SliceIndex_Output); + core_slice_index_SliceIndex_index : Self -> T -> result core_slice_index_SliceIndex_Output; + core_slice_index_SliceIndex_index_mut : Self -> T -> result core_slice_index_SliceIndex_Output; + core_slice_index_SliceIndex_index_mut_back : Self -> T -> core_slice_index_SliceIndex_Output -> result T; +}. +Arguments mk_core_slice_index_SliceIndex {_ _}. +Arguments core_slice_index_SliceIndex_sealedInst {_ _}. +Arguments core_slice_index_SliceIndex_Output {_ _}. +Arguments core_slice_index_SliceIndex_get {_ _}. +Arguments core_slice_index_SliceIndex_get_mut {_ _}. +Arguments core_slice_index_SliceIndex_get_mut_back {_ _}. +Arguments core_slice_index_SliceIndex_get_unchecked {_ _}. +Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}. +Arguments core_slice_index_SliceIndex_index {_ _}. +Arguments core_slice_index_SliceIndex_index_mut {_ _}. +Arguments core_slice_index_SliceIndex_index_mut_back {_ _}. + +(* [core::slice::index::[T]::index]: forward function *) +Definition core_slice_index_Slice_index + (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)) + (s : slice T) (i : Idx) : result inst.(core_slice_index_SliceIndex_Output) := + x <- inst.(core_slice_index_SliceIndex_get) i s; + match x with + | None => Fail_ Failure + | Some x => Return x end. -Definition vec_index_mut_back (T: Type) (v: vec T) (i: usize) (x: T) : result (vec T) := - vec_bind v (fun l => - if to_Z i <? Z.of_nat (length l) - then Return (list_update l (usize_to_nat i) x) - else Fail_ Failure). +(* [core::slice::index::Range:::get]: forward function *) +Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)). + +(* [core::slice::index::Range::get_mut]: forward function *) +Axiom core_slice_index_Range_get_mut : + forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)). + +(* [core::slice::index::Range::get_mut]: backward function 0 *) +Axiom core_slice_index_Range_get_mut_back : + forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T). + +(* [core::slice::index::Range::get_unchecked]: forward function *) +Definition core_slice_index_Range_get_unchecked + (T : Type) : + core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) := + (* Don't know what the model should be - for now we always fail to make + sure code which uses it fails *) + fun _ _ => Fail_ Failure. + +(* [core::slice::index::Range::get_unchecked_mut]: forward function *) +Definition core_slice_index_Range_get_unchecked_mut + (T : Type) : + core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) := + (* Don't know what the model should be - for now we always fail to make + sure code which uses it fails *) + fun _ _ => Fail_ Failure. + +(* [core::slice::index::Range::index]: forward function *) +Axiom core_slice_index_Range_index : + forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T). + +(* [core::slice::index::Range::index_mut]: forward function *) +Axiom core_slice_index_Range_index_mut : + forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T). + +(* [core::slice::index::Range::index_mut]: backward function 0 *) +Axiom core_slice_index_Range_index_mut_back : + forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T). + +(* [core::slice::index::[T]::index_mut]: forward function *) +Axiom core_slice_index_Slice_index_mut : + forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)), + slice T -> Idx -> result inst.(core_slice_index_SliceIndex_Output). + +(* [core::slice::index::[T]::index_mut]: backward function 0 *) +Axiom core_slice_index_Slice_index_mut_back : + forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)), + slice T -> Idx -> inst.(core_slice_index_SliceIndex_Output) -> result (slice T). + +(* [core::array::[T; N]::index]: forward function *) +Axiom core_array_Array_index : + forall (T Idx : Type) (N : usize) (inst : core_ops_index_Index (slice T) Idx) + (a : array T N) (i : Idx), result inst.(core_ops_index_Index_Output). + +(* [core::array::[T; N]::index_mut]: forward function *) +Axiom core_array_Array_index_mut : + forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx) + (a : array T N) (i : Idx), result inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output). + +(* [core::array::[T; N]::index_mut]: backward function 0 *) +Axiom core_array_Array_index_mut_back : + forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx) + (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N). + +(* Trait implementation: [core::slice::index::[T]] *) +Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type) + (inst : core_slice_index_SliceIndex Idx (slice T)) : + core_ops_index_Index (slice T) Idx := {| + core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output); + core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst; +|}. + +(* Trait implementation: [core::slice::index::private_slice_index::Range] *) +Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst + : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt. + +(* Trait implementation: [core::slice::index::Range] *) +Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) : + core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {| + core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst; + core_slice_index_SliceIndex_Output := slice T; + core_slice_index_SliceIndex_get := core_slice_index_Range_get T; + core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T; + core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T; + core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T; + core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T; + core_slice_index_SliceIndex_index := core_slice_index_Range_index T; + core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T; + core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T; +|}. + +(* Trait implementation: [core::slice::index::[T]] *) +Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type) + (inst : core_slice_index_SliceIndex Idx (slice T)) : + core_ops_index_IndexMut (slice T) Idx := {| + core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst; + core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst; + core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst; +|}. + +(* Trait implementation: [core::array::[T; N]] *) +Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize) + (inst : core_ops_index_Index (slice T) Idx) : + core_ops_index_Index (array T N) Idx := {| + core_ops_index_Index_Output := inst.(core_ops_index_Index_Output); + core_ops_index_Index_index := core_array_Array_index T Idx N inst; +|}. + +(* Trait implementation: [core::array::[T; N]] *) +Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize) + (inst : core_ops_index_IndexMut (slice T) Idx) : + core_ops_index_IndexMut (array T N) Idx := {| + core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst); + core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst; + core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst; +|}. + +(* [core::slice::index::usize::get]: forward function *) +Axiom core_slice_index_usize_get : forall (T : Type), usize -> slice T -> result (option T). + +(* [core::slice::index::usize::get_mut]: forward function *) +Axiom core_slice_index_usize_get_mut : forall (T : Type), usize -> slice T -> result (option T). + +(* [core::slice::index::usize::get_mut]: backward function 0 *) +Axiom core_slice_index_usize_get_mut_back : + forall (T : Type), usize -> slice T -> option T -> result (slice T). + +(* [core::slice::index::usize::get_unchecked]: forward function *) +Axiom core_slice_index_usize_get_unchecked : + forall (T : Type), usize -> const_raw_ptr (slice T) -> result (const_raw_ptr T). + +(* [core::slice::index::usize::get_unchecked_mut]: forward function *) +Axiom core_slice_index_usize_get_unchecked_mut : + forall (T : Type), usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr T). + +(* [core::slice::index::usize::index]: forward function *) +Axiom core_slice_index_usize_index : forall (T : Type), usize -> slice T -> result T. + +(* [core::slice::index::usize::index_mut]: forward function *) +Axiom core_slice_index_usize_index_mut : forall (T : Type), usize -> slice T -> result T. + +(* [core::slice::index::usize::index_mut]: backward function 0 *) +Axiom core_slice_index_usize_index_mut_back : + forall (T : Type), usize -> slice T -> T -> result (slice T). + +(* Trait implementation: [core::slice::index::private_slice_index::usize] *) +Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst + : core_slice_index_private_slice_index_Sealed usize := tt. + +(* Trait implementation: [core::slice::index::usize] *) +Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) : + core_slice_index_SliceIndex usize (slice T) := {| + core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst; + core_slice_index_SliceIndex_Output := T; + core_slice_index_SliceIndex_get := core_slice_index_usize_get T; + core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T; + core_slice_index_SliceIndex_get_mut_back := core_slice_index_usize_get_mut_back T; + core_slice_index_SliceIndex_get_unchecked := core_slice_index_usize_get_unchecked T; + core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_usize_get_unchecked_mut T; + core_slice_index_SliceIndex_index := core_slice_index_usize_index T; + core_slice_index_SliceIndex_index_mut := core_slice_index_usize_index_mut T; + core_slice_index_SliceIndex_index_mut_back := core_slice_index_usize_index_mut_back T; +|}. + +(* [alloc::vec::Vec::index]: forward function *) +Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)) + (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output). + +(* [alloc::vec::Vec::index_mut]: forward function *) +Axiom alloc_vec_Vec_index_mut : forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)) + (Self : alloc_vec_Vec T) (i : Idx), result inst.(core_slice_index_SliceIndex_Output). + +(* [alloc::vec::Vec::index_mut]: backward function 0 *) +Axiom alloc_vec_Vec_index_mut_back : + forall (T Idx : Type) (inst : core_slice_index_SliceIndex Idx (slice T)) + (Self : alloc_vec_Vec T) (i : Idx) (x : inst.(core_slice_index_SliceIndex_Output)), result (alloc_vec_Vec T). + +(* Trait implementation: [alloc::vec::Vec] *) +Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type) + (inst : core_slice_index_SliceIndex Idx (slice T)) : + core_ops_index_Index (alloc_vec_Vec T) Idx := {| + core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output); + core_ops_index_Index_index := alloc_vec_Vec_index T Idx inst; +|}. + +(* Trait implementation: [alloc::vec::Vec] *) +Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type) + (inst : core_slice_index_SliceIndex Idx (slice T)) : + core_ops_index_IndexMut (alloc_vec_Vec T) Idx := {| + core_ops_index_IndexMut_indexInst := alloc_vec_Vec_coreopsindexIndexInst T Idx inst; + core_ops_index_IndexMut_index_mut := alloc_vec_Vec_index_mut T Idx inst; + core_ops_index_IndexMut_index_mut_back := alloc_vec_Vec_index_mut_back T Idx inst; +|}. + +(*** Theorems *) + +Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a), + alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x = + alloc_vec_Vec_update_usize v i x. End Primitives. |