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-rw-r--r--tests/coq/demo/Demo.v48
-rw-r--r--tests/fstar/demo/Demo.fst45
-rw-r--r--tests/lean/Demo/Demo.lean47
-rw-r--r--tests/lean/Demo/Properties.lean16
4 files changed, 126 insertions, 30 deletions
diff --git a/tests/coq/demo/Demo.v b/tests/coq/demo/Demo.v
index ec7ca29d..48067c02 100644
--- a/tests/coq/demo/Demo.v
+++ b/tests/coq/demo/Demo.v
@@ -34,8 +34,14 @@ Definition use_mul2_add1 (x : u32) (y : u32) : result u32 :=
Definition incr (x : u32) : result u32 :=
u32_add x 1%u32.
+(** [demo::use_incr]:
+ Source: 'src/demo.rs', lines 25:0-25:17 *)
+Definition use_incr : result unit :=
+ i <- incr 0%u32; i1 <- incr i; _ <- incr i1; Return tt
+.
+
(** [demo::CList]
- Source: 'src/demo.rs', lines 27:0-27:17 *)
+ Source: 'src/demo.rs', lines 34:0-34:17 *)
Inductive CList_t (T : Type) :=
| CList_CCons : T -> CList_t T -> CList_t T
| CList_CNil : CList_t T
@@ -45,7 +51,7 @@ Arguments CList_CCons { _ }.
Arguments CList_CNil { _ }.
(** [demo::list_nth]:
- Source: 'src/demo.rs', lines 32:0-32:56 *)
+ Source: 'src/demo.rs', lines 39:0-39:56 *)
Fixpoint list_nth (T : Type) (n : nat) (l : CList_t T) (i : u32) : result T :=
match n with
| O => Fail_ OutOfFuel
@@ -61,7 +67,7 @@ Fixpoint list_nth (T : Type) (n : nat) (l : CList_t T) (i : u32) : result T :=
.
(** [demo::list_nth_mut]:
- Source: 'src/demo.rs', lines 47:0-47:68 *)
+ Source: 'src/demo.rs', lines 54:0-54:68 *)
Fixpoint list_nth_mut
(T : Type) (n : nat) (l : CList_t T) (i : u32) :
result (T * (T -> result (CList_t T)))
@@ -89,7 +95,7 @@ Fixpoint list_nth_mut
.
(** [demo::list_nth_mut1]: loop 0:
- Source: 'src/demo.rs', lines 62:0-71:1 *)
+ Source: 'src/demo.rs', lines 69:0-78:1 *)
Fixpoint list_nth_mut1_loop
(T : Type) (n : nat) (l : CList_t T) (i : u32) :
result (T * (T -> result (CList_t T)))
@@ -116,7 +122,7 @@ Fixpoint list_nth_mut1_loop
.
(** [demo::list_nth_mut1]:
- Source: 'src/demo.rs', lines 62:0-62:77 *)
+ Source: 'src/demo.rs', lines 69:0-69:77 *)
Definition list_nth_mut1
(T : Type) (n : nat) (l : CList_t T) (i : u32) :
result (T * (T -> result (CList_t T)))
@@ -125,7 +131,7 @@ Definition list_nth_mut1
.
(** [demo::i32_id]:
- Source: 'src/demo.rs', lines 73:0-73:28 *)
+ Source: 'src/demo.rs', lines 80:0-80:28 *)
Fixpoint i32_id (n : nat) (i : i32) : result i32 :=
match n with
| O => Fail_ OutOfFuel
@@ -136,8 +142,30 @@ Fixpoint i32_id (n : nat) (i : i32) : result i32 :=
end
.
+(** [demo::list_tail]:
+ Source: 'src/demo.rs', lines 88:0-88:64 *)
+Fixpoint list_tail
+ (T : Type) (n : nat) (l : CList_t T) :
+ result ((CList_t T) * (CList_t T -> result (CList_t T)))
+ :=
+ match n with
+ | O => Fail_ OutOfFuel
+ | S n1 =>
+ match l with
+ | CList_CCons t tl =>
+ p <- list_tail T n1 tl;
+ let (c, list_tail_back) := p in
+ let back_'a :=
+ fun (ret : CList_t T) =>
+ tl1 <- list_tail_back ret; Return (CList_CCons t tl1) in
+ Return (c, back_'a)
+ | CList_CNil => Return (CList_CNil, Return)
+ end
+ end
+.
+
(** Trait declaration: [demo::Counter]
- Source: 'src/demo.rs', lines 83:0-83:17 *)
+ Source: 'src/demo.rs', lines 97:0-97:17 *)
Record Counter_t (Self : Type) := mkCounter_t {
Counter_t_incr : Self -> result (usize * Self);
}.
@@ -146,19 +174,19 @@ Arguments mkCounter_t { _ }.
Arguments Counter_t_incr { _ }.
(** [demo::{(demo::Counter for usize)}::incr]:
- Source: 'src/demo.rs', lines 88:4-88:31 *)
+ Source: 'src/demo.rs', lines 102:4-102:31 *)
Definition counterUsize_incr (self : usize) : result (usize * usize) :=
self1 <- usize_add self 1%usize; Return (self, self1)
.
(** Trait implementation: [demo::{(demo::Counter for usize)}]
- Source: 'src/demo.rs', lines 87:0-87:22 *)
+ Source: 'src/demo.rs', lines 101:0-101:22 *)
Definition CounterUsize : Counter_t usize := {|
Counter_t_incr := counterUsize_incr;
|}.
(** [demo::use_counter]:
- Source: 'src/demo.rs', lines 95:0-95:59 *)
+ Source: 'src/demo.rs', lines 109:0-109:59 *)
Definition use_counter
(T : Type) (counterInst : Counter_t T) (cnt : T) : result (usize * T) :=
counterInst.(Counter_t_incr) cnt
diff --git a/tests/fstar/demo/Demo.fst b/tests/fstar/demo/Demo.fst
index d13d2ba3..5651b80f 100644
--- a/tests/fstar/demo/Demo.fst
+++ b/tests/fstar/demo/Demo.fst
@@ -28,14 +28,19 @@ let use_mul2_add1 (x : u32) (y : u32) : result u32 =
let incr (x : u32) : result u32 =
u32_add x 1
+(** [demo::use_incr]:
+ Source: 'src/demo.rs', lines 25:0-25:17 *)
+let use_incr : result unit =
+ let* i = incr 0 in let* i1 = incr i in let* _ = incr i1 in Return ()
+
(** [demo::CList]
- Source: 'src/demo.rs', lines 27:0-27:17 *)
+ Source: 'src/demo.rs', lines 34:0-34:17 *)
type cList_t (t : Type0) =
| CList_CCons : t -> cList_t t -> cList_t t
| CList_CNil : cList_t t
(** [demo::list_nth]:
- Source: 'src/demo.rs', lines 32:0-32:56 *)
+ Source: 'src/demo.rs', lines 39:0-39:56 *)
let rec list_nth (t : Type0) (n : nat) (l : cList_t t) (i : u32) : result t =
if is_zero n
then Fail OutOfFuel
@@ -48,7 +53,7 @@ let rec list_nth (t : Type0) (n : nat) (l : cList_t t) (i : u32) : result t =
end
(** [demo::list_nth_mut]:
- Source: 'src/demo.rs', lines 47:0-47:68 *)
+ Source: 'src/demo.rs', lines 54:0-54:68 *)
let rec list_nth_mut
(t : Type0) (n : nat) (l : cList_t t) (i : u32) :
result (t & (t -> result (cList_t t)))
@@ -74,7 +79,7 @@ let rec list_nth_mut
end
(** [demo::list_nth_mut1]: loop 0:
- Source: 'src/demo.rs', lines 62:0-71:1 *)
+ Source: 'src/demo.rs', lines 69:0-78:1 *)
let rec list_nth_mut1_loop
(t : Type0) (n : nat) (l : cList_t t) (i : u32) :
result (t & (t -> result (cList_t t)))
@@ -99,7 +104,7 @@ let rec list_nth_mut1_loop
end
(** [demo::list_nth_mut1]:
- Source: 'src/demo.rs', lines 62:0-62:77 *)
+ Source: 'src/demo.rs', lines 69:0-69:77 *)
let list_nth_mut1
(t : Type0) (n : nat) (l : cList_t t) (i : u32) :
result (t & (t -> result (cList_t t)))
@@ -107,7 +112,7 @@ let list_nth_mut1
let* (x, back_'a) = list_nth_mut1_loop t n l i in Return (x, back_'a)
(** [demo::i32_id]:
- Source: 'src/demo.rs', lines 73:0-73:28 *)
+ Source: 'src/demo.rs', lines 80:0-80:28 *)
let rec i32_id (n : nat) (i : i32) : result i32 =
if is_zero n
then Fail OutOfFuel
@@ -117,21 +122,41 @@ let rec i32_id (n : nat) (i : i32) : result i32 =
then Return 0
else let* i1 = i32_sub i 1 in let* i2 = i32_id n1 i1 in i32_add i2 1
+(** [demo::list_tail]:
+ Source: 'src/demo.rs', lines 88:0-88:64 *)
+let rec list_tail
+ (t : Type0) (n : nat) (l : cList_t t) :
+ result ((cList_t t) & (cList_t t -> result (cList_t t)))
+ =
+ if is_zero n
+ then Fail OutOfFuel
+ else
+ let n1 = decrease n in
+ begin match l with
+ | CList_CCons x tl ->
+ let* (c, list_tail_back) = list_tail t n1 tl in
+ let back_'a =
+ fun ret -> let* tl1 = list_tail_back ret in Return (CList_CCons x tl1)
+ in
+ Return (c, back_'a)
+ | CList_CNil -> Return (CList_CNil, Return)
+ end
+
(** Trait declaration: [demo::Counter]
- Source: 'src/demo.rs', lines 83:0-83:17 *)
+ Source: 'src/demo.rs', lines 97:0-97:17 *)
noeq type counter_t (self : Type0) = { incr : self -> result (usize & self); }
(** [demo::{(demo::Counter for usize)}::incr]:
- Source: 'src/demo.rs', lines 88:4-88:31 *)
+ Source: 'src/demo.rs', lines 102:4-102:31 *)
let counterUsize_incr (self : usize) : result (usize & usize) =
let* self1 = usize_add self 1 in Return (self, self1)
(** Trait implementation: [demo::{(demo::Counter for usize)}]
- Source: 'src/demo.rs', lines 87:0-87:22 *)
+ Source: 'src/demo.rs', lines 101:0-101:22 *)
let counterUsize : counter_t usize = { incr = counterUsize_incr; }
(** [demo::use_counter]:
- Source: 'src/demo.rs', lines 95:0-95:59 *)
+ Source: 'src/demo.rs', lines 109:0-109:59 *)
let use_counter
(t : Type0) (counterInst : counter_t t) (cnt : t) : result (usize & t) =
counterInst.incr cnt
diff --git a/tests/lean/Demo/Demo.lean b/tests/lean/Demo/Demo.lean
index 854b4853..f38b5cd3 100644
--- a/tests/lean/Demo/Demo.lean
+++ b/tests/lean/Demo/Demo.lean
@@ -36,14 +36,23 @@ def use_mul2_add1 (x : U32) (y : U32) : Result U32 :=
def incr (x : U32) : Result U32 :=
x + 1#u32
+/- [demo::use_incr]:
+ Source: 'src/demo.rs', lines 25:0-25:17 -/
+def use_incr : Result Unit :=
+ do
+ let i ← incr 0#u32
+ let i1 ← incr i
+ let _ ← incr i1
+ Result.ret ()
+
/- [demo::CList]
- Source: 'src/demo.rs', lines 27:0-27:17 -/
+ Source: 'src/demo.rs', lines 34:0-34:17 -/
inductive CList (T : Type) :=
| CCons : T → CList T → CList T
| CNil : CList T
/- [demo::list_nth]:
- Source: 'src/demo.rs', lines 32:0-32:56 -/
+ Source: 'src/demo.rs', lines 39:0-39:56 -/
divergent def list_nth (T : Type) (l : CList T) (i : U32) : Result T :=
match l with
| CList.CCons x tl =>
@@ -55,7 +64,7 @@ divergent def list_nth (T : Type) (l : CList T) (i : U32) : Result T :=
| CList.CNil => Result.fail .panic
/- [demo::list_nth_mut]:
- Source: 'src/demo.rs', lines 47:0-47:68 -/
+ Source: 'src/demo.rs', lines 54:0-54:68 -/
divergent def list_nth_mut
(T : Type) (l : CList T) (i : U32) :
Result (T × (T → Result (CList T)))
@@ -79,7 +88,7 @@ divergent def list_nth_mut
| CList.CNil => Result.fail .panic
/- [demo::list_nth_mut1]: loop 0:
- Source: 'src/demo.rs', lines 62:0-71:1 -/
+ Source: 'src/demo.rs', lines 69:0-78:1 -/
divergent def list_nth_mut1_loop
(T : Type) (l : CList T) (i : U32) :
Result (T × (T → Result (CList T)))
@@ -102,7 +111,7 @@ divergent def list_nth_mut1_loop
| CList.CNil => Result.fail .panic
/- [demo::list_nth_mut1]:
- Source: 'src/demo.rs', lines 62:0-62:77 -/
+ Source: 'src/demo.rs', lines 69:0-69:77 -/
def list_nth_mut1
(T : Type) (l : CList T) (i : U32) :
Result (T × (T → Result (CList T)))
@@ -112,7 +121,7 @@ def list_nth_mut1
Result.ret (t, back_'a)
/- [demo::i32_id]:
- Source: 'src/demo.rs', lines 73:0-73:28 -/
+ Source: 'src/demo.rs', lines 80:0-80:28 -/
divergent def i32_id (i : I32) : Result I32 :=
if i = 0#i32
then Result.ret 0#i32
@@ -121,26 +130,44 @@ divergent def i32_id (i : I32) : Result I32 :=
let i2 ← i32_id i1
i2 + 1#i32
+/- [demo::list_tail]:
+ Source: 'src/demo.rs', lines 88:0-88:64 -/
+divergent def list_tail
+ (T : Type) (l : CList T) :
+ Result ((CList T) × (CList T → Result (CList T)))
+ :=
+ match l with
+ | CList.CCons t tl =>
+ do
+ let (c, list_tail_back) ← list_tail T tl
+ let back_'a :=
+ fun ret =>
+ do
+ let tl1 ← list_tail_back ret
+ Result.ret (CList.CCons t tl1)
+ Result.ret (c, back_'a)
+ | CList.CNil => Result.ret (CList.CNil, Result.ret)
+
/- Trait declaration: [demo::Counter]
- Source: 'src/demo.rs', lines 83:0-83:17 -/
+ Source: 'src/demo.rs', lines 97:0-97:17 -/
structure Counter (Self : Type) where
incr : Self → Result (Usize × Self)
/- [demo::{(demo::Counter for usize)}::incr]:
- Source: 'src/demo.rs', lines 88:4-88:31 -/
+ Source: 'src/demo.rs', lines 102:4-102:31 -/
def CounterUsize.incr (self : Usize) : Result (Usize × Usize) :=
do
let self1 ← self + 1#usize
Result.ret (self, self1)
/- Trait implementation: [demo::{(demo::Counter for usize)}]
- Source: 'src/demo.rs', lines 87:0-87:22 -/
+ Source: 'src/demo.rs', lines 101:0-101:22 -/
def CounterUsize : Counter Usize := {
incr := CounterUsize.incr
}
/- [demo::use_counter]:
- Source: 'src/demo.rs', lines 95:0-95:59 -/
+ Source: 'src/demo.rs', lines 109:0-109:59 -/
def use_counter
(T : Type) (CounterInst : Counter T) (cnt : T) : Result (Usize × T) :=
CounterInst.incr cnt
diff --git a/tests/lean/Demo/Properties.lean b/tests/lean/Demo/Properties.lean
index cdec7332..e514ac3e 100644
--- a/tests/lean/Demo/Properties.lean
+++ b/tests/lean/Demo/Properties.lean
@@ -65,4 +65,20 @@ theorem i32_id_spec (x : I32) (h : 0 ≤ x.val) :
termination_by x.val.toNat
decreasing_by scalar_decr_tac
+theorem list_tail_spec {T : Type} [Inhabited T] (l : CList T) :
+ ∃ back, list_tail T l = ret (CList.CNil, back) ∧
+ ∀ tl', ∃ l', back tl' = ret l' ∧ l'.to_list = l.to_list ++ tl'.to_list := by
+ rw [list_tail]
+ match l with
+ | CNil =>
+ simp_all
+ | CCons hd tl =>
+ simp_all
+ progress as ⟨ back ⟩
+ simp
+ -- Proving the backward function
+ intro tl'
+ progress
+ simp_all
+
end demo
generated by cgit v1.2.3 (git 2.25.1) at 2024-12-31 19:58:32 +0000