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authorSon Ho2023-12-22 18:56:49 +0100
committerSon Ho2023-12-22 18:56:49 +0100
commit632e2ddc0c5ed0c785b37fdc41394336e467f623 (patch)
treea55f88328e95311620bf1a512a4570cadd73ca0e
parent455ba366f9c8d07a1f1848ec0960b1f2d161e7cf (diff)
Update the library for Coq
Diffstat (limited to '')
-rw-r--r--backends/coq/Primitives.v116
1 files changed, 42 insertions, 74 deletions
diff --git a/backends/coq/Primitives.v b/backends/coq/Primitives.v
index 84280b96..c0056073 100644
--- a/backends/coq/Primitives.v
+++ b/backends/coq/Primitives.v
@@ -67,8 +67,7 @@ Definition string := Coq.Strings.String.string.
Definition char := Coq.Strings.Ascii.ascii.
Definition char_of_byte := Coq.Strings.Ascii.ascii_of_byte.
-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 .
+Definition core_mem_replace (a : Type) (x : a) (y : a) : a * (a -> a) := (x, fun x => x) .
Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
@@ -504,13 +503,15 @@ 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;
+ core_ops_index_IndexMut_index_mut :
+ Self ->
+ Idx ->
+ result (core_ops_index_IndexMut_indexInst.(core_ops_index_Index_Output) *
+ (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 {
@@ -524,13 +525,14 @@ 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;
+ core_ops_deref_DerefMut_deref_mut :
+ Self ->
+ result (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) *
+ (core_ops_deref_DerefMut_derefInst.(core_ops_deref_Deref_target) -> result Self));
}.
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;
@@ -543,8 +545,8 @@ 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.
+Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result (T * (T -> result T)) :=
+ Return (x, fun x => Return x).
(* Trait instance *)
Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
@@ -556,7 +558,6 @@ Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref
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;
|}.
@@ -639,16 +640,9 @@ Definition alloc_vec_Vec_bind {A B} (v: alloc_vec_Vec A) (f: list A -> result (l
| right _ => Fail_ Failure
end.
-(* The **forward** function shouldn't be used *)
-Definition alloc_vec_Vec_push_fwd (T: Type) (v: alloc_vec_Vec T) (x: T) : unit := tt.
-
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 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 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)
@@ -661,6 +655,14 @@ Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : u
(* Helper *)
Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
+Definition alloc_vec_Vec_index_mut_usize {T : Type} (v: alloc_vec_Vec T) (i: usize) :
+ result (T * (T -> result (alloc_vec_Vec T))) :=
+ match alloc_vec_Vec_index_usize v i with
+ | Return x =>
+ Return (x, alloc_vec_Vec_update_usize v i)
+ | Fail_ e => Fail_ e
+ end.
+
(* Trait declaration: [core::slice::index::private_slice_index::Sealed] *)
Definition core_slice_index_private_slice_index_Sealed (self : Type) := unit.
@@ -669,25 +671,23 @@ Record core_slice_index_SliceIndex (Self T : Type) := mk_core_slice_index_SliceI
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_mut :
+ Self -> T -> result (option core_slice_index_SliceIndex_Output * (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;
+ core_slice_index_SliceIndex_index_mut :
+ Self -> T -> result (core_slice_index_SliceIndex_Output * (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
@@ -704,11 +704,9 @@ Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Ra
(* [core::slice::index::Range::get_mut]: forward function *)
Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut_back :
- forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
+ forall (T : Type),
+ core_ops_range_Range usize -> slice T ->
+ result (option (slice T) * (option (slice T) -> result (slice T))).
(* [core::slice::index::Range::get_unchecked]: forward function *)
Definition core_slice_index_RangeUsize_get_unchecked
@@ -732,21 +730,14 @@ Axiom core_slice_index_RangeUsize_index :
(* [core::slice::index::Range::index_mut]: forward function *)
Axiom core_slice_index_RangeUsize_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_RangeUsize_index_mut_back :
- forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
+ forall (T : Type), core_ops_range_Range usize -> slice T -> result (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).
+ slice T -> Idx ->
+ result (inst.(core_slice_index_SliceIndex_Output) *
+ (inst.(core_slice_index_SliceIndex_Output) -> result (slice T))).
(* [core::array::[T; N]::index]: forward function *)
Axiom core_array_Array_index :
@@ -756,12 +747,9 @@ Axiom core_array_Array_index :
(* [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).
+ (a : array T N) (i : Idx),
+ result (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) *
+ (inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output) -> result (array T N))).
(* Trait implementation: [core::slice::index::private_slice_index::Range] *)
Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
@@ -774,12 +762,10 @@ Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
core_slice_index_SliceIndex_Output := slice T;
core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
- core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
- core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
|}.
(* Trait implementation: [core::slice::index::[T]] *)
@@ -796,7 +782,6 @@ Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
core_ops_index_IndexMut (slice T) Idx := {|
core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst 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]] *)
@@ -813,18 +798,14 @@ Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
core_ops_index_IndexMut (array T N) Idx := {|
core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst 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).
+Axiom core_slice_index_usize_get_mut :
+ forall (T : Type), usize -> slice T -> result (option T * (option T -> result (slice T))).
(* [core::slice::index::usize::get_unchecked]: forward function *)
Axiom core_slice_index_usize_get_unchecked :
@@ -838,11 +819,8 @@ Axiom core_slice_index_usize_get_unchecked_mut :
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).
+Axiom core_slice_index_usize_index_mut :
+ forall (T : Type), usize -> slice T -> result (T * (T -> result (slice T))).
(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
Definition core_slice_index_private_slice_index_SealedUsizeInst
@@ -855,12 +833,10 @@ Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
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 *)
@@ -869,12 +845,9 @@ Axiom alloc_vec_Vec_index : forall (T Idx : Type) (inst : core_slice_index_Slice
(* [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).
+ (Self : alloc_vec_Vec T) (i : Idx),
+ result (inst.(core_slice_index_SliceIndex_Output) *
+ (inst.(core_slice_index_SliceIndex_Output) -> result (alloc_vec_Vec T))).
(* Trait implementation: [alloc::vec::Vec] *)
Definition alloc_vec_Vec_coreopsindexIndexInst (T Idx : Type)
@@ -890,7 +863,6 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
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 *)
@@ -901,10 +873,6 @@ Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usiz
Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
- alloc_vec_Vec_index_usize v i.
-
-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_SliceIndexUsizeSliceTInst a) v i x =
- alloc_vec_Vec_update_usize v i x.
+ alloc_vec_Vec_index_mut_usize v i.
End Primitives.