Merge pull request #68 from AeneasVerif/son/update_lean

Update Lean to v4.6.0-rc1

4 files changed, 1448 insertions, 0 deletions

diff --git a/tests/coq/arrays/Arrays.v b/tests/coq/arrays/Arrays.v
new file mode 100644
index 00000000..3a6fb02f
--- /dev/null
+++ b/tests/coq/arrays/Arrays.v
@@ -0,0 +1,519 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [arrays] *)
+Require Import Primitives.
+Import Primitives.
+Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
+Local Open Scope Primitives_scope.
+Module Arrays.
+
+(** [arrays::AB]
+    Source: 'src/arrays.rs', lines 3:0-3:11 *)
+Inductive AB_t := | AB_A : AB_t | AB_B : AB_t.
+
+(** [arrays::incr]:
+    Source: 'src/arrays.rs', lines 8:0-8:24 *)
+Definition incr (x : u32) : result u32 :=
+  u32_add x 1%u32.
+
+(** [arrays::array_to_shared_slice_]:
+    Source: 'src/arrays.rs', lines 16:0-16:53 *)
+Definition array_to_shared_slice_
+  (T : Type) (s : array T 32%usize) : result (slice T) :=
+  array_to_slice T 32%usize s
+.
+
+(** [arrays::array_to_mut_slice_]:
+    Source: 'src/arrays.rs', lines 21:0-21:58 *)
+Definition array_to_mut_slice_
+  (T : Type) (s : array T 32%usize) :
+  result ((slice T) * (slice T -> result (array T 32%usize)))
+  :=
+  p <- array_to_slice_mut T 32%usize s;
+  let (s1, to_slice_mut_back) := p in
+  Return (s1, to_slice_mut_back)
+.
+
+(** [arrays::array_len]:
+    Source: 'src/arrays.rs', lines 25:0-25:40 *)
+Definition array_len (T : Type) (s : array T 32%usize) : result usize :=
+  s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i
+.
+
+(** [arrays::shared_array_len]:
+    Source: 'src/arrays.rs', lines 29:0-29:48 *)
+Definition shared_array_len (T : Type) (s : array T 32%usize) : result usize :=
+  s1 <- array_to_slice T 32%usize s; let i := slice_len T s1 in Return i
+.
+
+(** [arrays::shared_slice_len]:
+    Source: 'src/arrays.rs', lines 33:0-33:44 *)
+Definition shared_slice_len (T : Type) (s : slice T) : result usize :=
+  let i := slice_len T s in Return i
+.
+
+(** [arrays::index_array_shared]:
+    Source: 'src/arrays.rs', lines 37:0-37:57 *)
+Definition index_array_shared
+  (T : Type) (s : array T 32%usize) (i : usize) : result T :=
+  array_index_usize T 32%usize s i
+.
+
+(** [arrays::index_array_u32]:
+    Source: 'src/arrays.rs', lines 44:0-44:53 *)
+Definition index_array_u32 (s : array u32 32%usize) (i : usize) : result u32 :=
+  array_index_usize u32 32%usize s i
+.
+
+(** [arrays::index_array_copy]:
+    Source: 'src/arrays.rs', lines 48:0-48:45 *)
+Definition index_array_copy (x : array u32 32%usize) : result u32 :=
+  array_index_usize u32 32%usize x 0%usize
+.
+
+(** [arrays::index_mut_array]:
+    Source: 'src/arrays.rs', lines 52:0-52:62 *)
+Definition index_mut_array
+  (T : Type) (s : array T 32%usize) (i : usize) :
+  result (T * (T -> result (array T 32%usize)))
+  :=
+  p <- array_index_mut_usize T 32%usize s i;
+  let (t, index_mut_back) := p in
+  Return (t, index_mut_back)
+.
+
+(** [arrays::index_slice]:
+    Source: 'src/arrays.rs', lines 56:0-56:46 *)
+Definition index_slice (T : Type) (s : slice T) (i : usize) : result T :=
+  slice_index_usize T s i
+.
+
+(** [arrays::index_mut_slice]:
+    Source: 'src/arrays.rs', lines 60:0-60:58 *)
+Definition index_mut_slice
+  (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T)))
+  :=
+  p <- slice_index_mut_usize T s i;
+  let (t, index_mut_back) := p in
+  Return (t, index_mut_back)
+.
+
+(** [arrays::slice_subslice_shared_]:
+    Source: 'src/arrays.rs', lines 64:0-64:70 *)
+Definition slice_subslice_shared_
+  (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
+  core_slice_index_Slice_index u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [arrays::slice_subslice_mut_]:
+    Source: 'src/arrays.rs', lines 68:0-68:75 *)
+Definition slice_subslice_mut_
+  (x : slice u32) (y : usize) (z : usize) :
+  result ((slice u32) * (slice u32 -> result (slice u32)))
+  :=
+  p <-
+    core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
+      {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |};
+  let (s, index_mut_back) := p in
+  Return (s, index_mut_back)
+.
+
+(** [arrays::array_to_slice_shared_]:
+    Source: 'src/arrays.rs', lines 72:0-72:54 *)
+Definition array_to_slice_shared_
+  (x : array u32 32%usize) : result (slice u32) :=
+  array_to_slice u32 32%usize x
+.
+
+(** [arrays::array_to_slice_mut_]:
+    Source: 'src/arrays.rs', lines 76:0-76:59 *)
+Definition array_to_slice_mut_
+  (x : array u32 32%usize) :
+  result ((slice u32) * (slice u32 -> result (array u32 32%usize)))
+  :=
+  p <- array_to_slice_mut u32 32%usize x;
+  let (s, to_slice_mut_back) := p in
+  Return (s, to_slice_mut_back)
+.
+
+(** [arrays::array_subslice_shared_]:
+    Source: 'src/arrays.rs', lines 80:0-80:74 *)
+Definition array_subslice_shared_
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
+    (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [arrays::array_subslice_mut_]:
+    Source: 'src/arrays.rs', lines 84:0-84:79 *)
+Definition array_subslice_mut_
+  (x : array u32 32%usize) (y : usize) (z : usize) :
+  result ((slice u32) * (slice u32 -> result (array u32 32%usize)))
+  :=
+  p <-
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 32%usize
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+      {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |};
+  let (s, index_mut_back) := p in
+  Return (s, index_mut_back)
+.
+
+(** [arrays::index_slice_0]:
+    Source: 'src/arrays.rs', lines 88:0-88:38 *)
+Definition index_slice_0 (T : Type) (s : slice T) : result T :=
+  slice_index_usize T s 0%usize
+.
+
+(** [arrays::index_array_0]:
+    Source: 'src/arrays.rs', lines 92:0-92:42 *)
+Definition index_array_0 (T : Type) (s : array T 32%usize) : result T :=
+  array_index_usize T 32%usize s 0%usize
+.
+
+(** [arrays::index_index_array]:
+    Source: 'src/arrays.rs', lines 103:0-103:71 *)
+Definition index_index_array
+  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
+  result u32
+  :=
+  a <- array_index_usize (array u32 32%usize) 32%usize s i;
+  array_index_usize u32 32%usize a j
+.
+
+(** [arrays::update_update_array]:
+    Source: 'src/arrays.rs', lines 114:0-114:70 *)
+Definition update_update_array
+  (s : array (array u32 32%usize) 32%usize) (i : usize) (j : usize) :
+  result unit
+  :=
+  p <- array_index_mut_usize (array u32 32%usize) 32%usize s i;
+  let (a, index_mut_back) := p in
+  p1 <- array_index_mut_usize u32 32%usize a j;
+  let (_, index_mut_back1) := p1 in
+  a1 <- index_mut_back1 0%u32;
+  _ <- index_mut_back a1;
+  Return tt
+.
+
+(** [arrays::array_local_deep_copy]:
+    Source: 'src/arrays.rs', lines 118:0-118:43 *)
+Definition array_local_deep_copy (x : array u32 32%usize) : result unit :=
+  Return tt
+.
+
+(** [arrays::take_array]:
+    Source: 'src/arrays.rs', lines 122:0-122:30 *)
+Definition take_array (a : array u32 2%usize) : result unit :=
+  Return tt.
+
+(** [arrays::take_array_borrow]:
+    Source: 'src/arrays.rs', lines 123:0-123:38 *)
+Definition take_array_borrow (a : array u32 2%usize) : result unit :=
+  Return tt
+.
+
+(** [arrays::take_slice]:
+    Source: 'src/arrays.rs', lines 124:0-124:28 *)
+Definition take_slice (s : slice u32) : result unit :=
+  Return tt.
+
+(** [arrays::take_mut_slice]:
+    Source: 'src/arrays.rs', lines 125:0-125:36 *)
+Definition take_mut_slice (s : slice u32) : result (slice u32) :=
+  Return s.
+
+(** [arrays::const_array]:
+    Source: 'src/arrays.rs', lines 127:0-127:32 *)
+Definition const_array : result (array u32 2%usize) :=
+  Return (mk_array u32 2%usize [ 0%u32; 0%u32 ])
+.
+
+(** [arrays::const_slice]:
+    Source: 'src/arrays.rs', lines 131:0-131:20 *)
+Definition const_slice : result unit :=
+  _ <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  Return tt
+.
+
+(** [arrays::take_all]:
+    Source: 'src/arrays.rs', lines 141:0-141:17 *)
+Definition take_all : result unit :=
+  _ <- take_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_slice s;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s1, to_slice_mut_back) := p in
+  s2 <- take_mut_slice s1;
+  _ <- to_slice_mut_back s2;
+  Return tt
+.
+
+(** [arrays::index_array]:
+    Source: 'src/arrays.rs', lines 155:0-155:38 *)
+Definition index_array (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [arrays::index_array_borrow]:
+    Source: 'src/arrays.rs', lines 158:0-158:46 *)
+Definition index_array_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [arrays::index_slice_u32_0]:
+    Source: 'src/arrays.rs', lines 162:0-162:42 *)
+Definition index_slice_u32_0 (x : slice u32) : result u32 :=
+  slice_index_usize u32 x 0%usize
+.
+
+(** [arrays::index_mut_slice_u32_0]:
+    Source: 'src/arrays.rs', lines 166:0-166:50 *)
+Definition index_mut_slice_u32_0
+  (x : slice u32) : result (u32 * (slice u32)) :=
+  i <- slice_index_usize u32 x 0%usize; Return (i, x)
+.
+
+(** [arrays::index_all]:
+    Source: 'src/arrays.rs', lines 170:0-170:25 *)
+Definition index_all : result u32 :=
+  i <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i1 <- index_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i2 <- u32_add i i1;
+  i3 <- index_array_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i4 <- u32_add i2 i3;
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i5 <- index_slice_u32_0 s;
+  i6 <- u32_add i4 i5;
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s1, to_slice_mut_back) := p in
+  p1 <- index_mut_slice_u32_0 s1;
+  let (i7, s2) := p1 in
+  i8 <- u32_add i6 i7;
+  _ <- to_slice_mut_back s2;
+  Return i8
+.
+
+(** [arrays::update_array]:
+    Source: 'src/arrays.rs', lines 184:0-184:36 *)
+Definition update_array (x : array u32 2%usize) : result unit :=
+  p <- array_index_mut_usize u32 2%usize x 0%usize;
+  let (_, index_mut_back) := p in
+  _ <- index_mut_back 1%u32;
+  Return tt
+.
+
+(** [arrays::update_array_mut_borrow]:
+    Source: 'src/arrays.rs', lines 187:0-187:48 *)
+Definition update_array_mut_borrow
+  (x : array u32 2%usize) : result (array u32 2%usize) :=
+  p <- array_index_mut_usize u32 2%usize x 0%usize;
+  let (_, index_mut_back) := p in
+  index_mut_back 1%u32
+.
+
+(** [arrays::update_mut_slice]:
+    Source: 'src/arrays.rs', lines 190:0-190:38 *)
+Definition update_mut_slice (x : slice u32) : result (slice u32) :=
+  p <- slice_index_mut_usize u32 x 0%usize;
+  let (_, index_mut_back) := p in
+  index_mut_back 1%u32
+.
+
+(** [arrays::update_all]:
+    Source: 'src/arrays.rs', lines 194:0-194:19 *)
+Definition update_all : result unit :=
+  _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- update_array (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  a <- update_array_mut_borrow (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  p <- array_to_slice_mut u32 2%usize a;
+  let (s, to_slice_mut_back) := p in
+  s1 <- update_mut_slice s;
+  _ <- to_slice_mut_back s1;
+  Return tt
+.
+
+(** [arrays::range_all]:
+    Source: 'src/arrays.rs', lines 205:0-205:18 *)
+Definition range_all : result unit :=
+  p <-
+    core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
+      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ])
+      {|
+        core_ops_range_Range_start := 1%usize;
+        core_ops_range_Range_end_ := 3%usize
+      |};
+  let (s, index_mut_back) := p in
+  s1 <- update_mut_slice s;
+  _ <- index_mut_back s1;
+  Return tt
+.
+
+(** [arrays::deref_array_borrow]:
+    Source: 'src/arrays.rs', lines 214:0-214:46 *)
+Definition deref_array_borrow (x : array u32 2%usize) : result u32 :=
+  array_index_usize u32 2%usize x 0%usize
+.
+
+(** [arrays::deref_array_mut_borrow]:
+    Source: 'src/arrays.rs', lines 219:0-219:54 *)
+Definition deref_array_mut_borrow
+  (x : array u32 2%usize) : result (u32 * (array u32 2%usize)) :=
+  i <- array_index_usize u32 2%usize x 0%usize; Return (i, x)
+.
+
+(** [arrays::take_array_t]:
+    Source: 'src/arrays.rs', lines 227:0-227:31 *)
+Definition take_array_t (a : array AB_t 2%usize) : result unit :=
+  Return tt.
+
+(** [arrays::non_copyable_array]:
+    Source: 'src/arrays.rs', lines 229:0-229:27 *)
+Definition non_copyable_array : result unit :=
+  _ <- take_array_t (mk_array AB_t 2%usize [ AB_A; AB_B ]); Return tt
+.
+
+(** [arrays::sum]: loop 0:
+    Source: 'src/arrays.rs', lines 242:0-250:1 *)
+Fixpoint sum_loop
+  (n : nat) (s : slice u32) (sum1 : u32) (i : usize) : result u32 :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    let i1 := slice_len u32 s in
+    if i s< i1
+    then (
+      i2 <- slice_index_usize u32 s i;
+      sum3 <- u32_add sum1 i2;
+      i3 <- usize_add i 1%usize;
+      sum_loop n1 s sum3 i3)
+    else Return sum1
+  end
+.
+
+(** [arrays::sum]:
+    Source: 'src/arrays.rs', lines 242:0-242:28 *)
+Definition sum (n : nat) (s : slice u32) : result u32 :=
+  sum_loop n s 0%u32 0%usize
+.
+
+(** [arrays::sum2]: loop 0:
+    Source: 'src/arrays.rs', lines 252:0-261:1 *)
+Fixpoint sum2_loop
+  (n : nat) (s : slice u32) (s2 : slice u32) (sum1 : u32) (i : usize) :
+  result u32
+  :=
+  match n with
+  | O => Fail_ OutOfFuel
+  | S n1 =>
+    let i1 := slice_len u32 s in
+    if i s< i1
+    then (
+      i2 <- slice_index_usize u32 s i;
+      i3 <- slice_index_usize u32 s2 i;
+      i4 <- u32_add i2 i3;
+      sum3 <- u32_add sum1 i4;
+      i5 <- usize_add i 1%usize;
+      sum2_loop n1 s s2 sum3 i5)
+    else Return sum1
+  end
+.
+
+(** [arrays::sum2]:
+    Source: 'src/arrays.rs', lines 252:0-252:41 *)
+Definition sum2 (n : nat) (s : slice u32) (s2 : slice u32) : result u32 :=
+  let i := slice_len u32 s in
+  let i1 := slice_len u32 s2 in
+  if negb (i s= i1) then Fail_ Failure else sum2_loop n s s2 0%u32 0%usize
+.
+
+(** [arrays::f0]:
+    Source: 'src/arrays.rs', lines 263:0-263:11 *)
+Definition f0 : result unit :=
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  let (s, to_slice_mut_back) := p in
+  p1 <- slice_index_mut_usize u32 s 0%usize;
+  let (_, index_mut_back) := p1 in
+  s1 <- index_mut_back 1%u32;
+  _ <- to_slice_mut_back s1;
+  Return tt
+.
+
+(** [arrays::f1]:
+    Source: 'src/arrays.rs', lines 268:0-268:11 *)
+Definition f1 : result unit :=
+  p <-
+    array_index_mut_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize;
+  let (_, index_mut_back) := p in
+  _ <- index_mut_back 1%u32;
+  Return tt
+.
+
+(** [arrays::f2]:
+    Source: 'src/arrays.rs', lines 273:0-273:17 *)
+Definition f2 (i : u32) : result unit :=
+  Return tt.
+
+(** [arrays::f4]:
+    Source: 'src/arrays.rs', lines 282:0-282:54 *)
+Definition f4
+  (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
+  core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
+    (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
+    {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
+.
+
+(** [arrays::f3]:
+    Source: 'src/arrays.rs', lines 275:0-275:18 *)
+Definition f3 (n : nat) : result u32 :=
+  i <-
+    array_index_usize u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize;
+  _ <- f2 i;
+  let b := array_repeat u32 32%usize 0%u32 in
+  s <- array_to_slice u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  s1 <- f4 b 16%usize 18%usize;
+  sum2 n s s1
+.
+
+(** [arrays::SZ]
+    Source: 'src/arrays.rs', lines 286:0-286:19 *)
+Definition sz_body : result usize := Return 32%usize.
+Definition sz_c : usize := sz_body%global.
+
+(** [arrays::f5]:
+    Source: 'src/arrays.rs', lines 289:0-289:31 *)
+Definition f5 (x : array u32 32%usize) : result u32 :=
+  array_index_usize u32 32%usize x 0%usize
+.
+
+(** [arrays::ite]:
+    Source: 'src/arrays.rs', lines 294:0-294:12 *)
+Definition ite : result unit :=
+  p <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s, to_slice_mut_back) := p in
+  p1 <- index_mut_slice_u32_0 s;
+  let (_, s1) := p1 in
+  p2 <- array_to_slice_mut u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  let (s2, to_slice_mut_back1) := p2 in
+  p3 <- index_mut_slice_u32_0 s2;
+  let (_, s3) := p3 in
+  _ <- to_slice_mut_back1 s3;
+  _ <- to_slice_mut_back s1;
+  Return tt
+.
+
+End Arrays.
diff --git a/tests/coq/arrays/Makefile b/tests/coq/arrays/Makefile
new file mode 100644
index 00000000..1a5aee4a
--- /dev/null
+++ b/tests/coq/arrays/Makefile
@@ -0,0 +1,23 @@
+# This file was automatically generated - modify ../Makefile.template instead
+# Makefile originally taken from coq-club
+
+%: Makefile.coq phony
+	+make -f Makefile.coq $@
+
+all: Makefile.coq
+	+make -f Makefile.coq all
+
+clean: Makefile.coq
+	+make -f Makefile.coq clean
+	rm -f Makefile.coq
+
+Makefile.coq: _CoqProject Makefile
+	coq_makefile -f _CoqProject | sed 's/$$(COQCHK) $$(COQCHKFLAGS) $$(COQLIBS)/$$(COQCHK) $$(COQCHKFLAGS) $$(subst -Q,-R,$$(COQLIBS))/' > Makefile.coq
+
+_CoqProject: ;
+
+Makefile: ;
+
+phony: ;
+
+.PHONY: all clean phony
diff --git a/tests/coq/arrays/Primitives.v b/tests/coq/arrays/Primitives.v
new file mode 100644
index 00000000..990e27e4
--- /dev/null
+++ b/tests/coq/arrays/Primitives.v
@@ -0,0 +1,899 @@
+Require Import Lia.
+Require Coq.Strings.Ascii.
+Require Coq.Strings.String.
+Require Import Coq.Program.Equality.
+Require Import Coq.ZArith.ZArith.
+Require Import Coq.ZArith.Znat.
+Require Import List.
+Import ListNotations.
+
+Module Primitives.
+
+  (* TODO: use more *)
+Declare Scope Primitives_scope.
+
+(*** Result *)
+
+Inductive error :=
+  | Failure
+  | OutOfFuel.
+
+Inductive result A :=
+  | Return : A -> result A
+  | Fail_ : error -> result A.
+
+Arguments Return {_} a.
+Arguments Fail_ {_}.
+
+Definition bind {A B} (m: result A) (f: A -> result B) : result B :=
+  match m with
+  | Fail_ e => Fail_ e
+  | Return x => f x
+  end.
+
+Definition return_ {A: Type} (x: A) : result A := Return x.
+Definition fail_ {A: Type} (e: error) : result A := Fail_ e.
+
+Notation "x <- c1 ; c2" := (bind c1 (fun x => c2))
+  (at level 61, c1 at next level, right associativity).
+
+(** Monadic assert *)
+Definition massert (b: bool) : result unit :=
+  if b then Return tt else Fail_ Failure.
+
+(** Normalize and unwrap a successful result (used for globals) *)
+Definition eval_result_refl {A} {x} (a: result A) (p: a = Return x) : A :=
+  match a as r return (r = Return x -> A) with
+  | Return a' => fun _  => a'
+  | Fail_ e   => fun p' =>
+      False_rect _ (eq_ind (Fail_ e)
+          (fun e : result A =>
+          match e with
+          | Return _ => False
+          | Fail_ e => True
+          end)
+        I (Return x) p')
+  end p.
+
+Notation "x %global" := (eval_result_refl x eq_refl) (at level 40).
+Notation "x %return" := (eval_result_refl x eq_refl) (at level 40).
+
+(* Sanity check *)
+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 core_mem_replace (a : Type) (x : a) (y : a) : a * a := (x, x) .
+
+Record mut_raw_ptr (T : Type) := { mut_raw_ptr_v : T }.
+Record const_raw_ptr (T : Type) := { const_raw_ptr_v : T }.
+
+(*** Scalars *)
+
+Definition i8_min   : Z := -128%Z.
+Definition i8_max   : Z := 127%Z.
+Definition i16_min  : Z := -32768%Z.
+Definition i16_max  : Z := 32767%Z.
+Definition i32_min  : Z := -2147483648%Z.
+Definition i32_max  : Z := 2147483647%Z.
+Definition i64_min  : Z := -9223372036854775808%Z.
+Definition i64_max  : Z := 9223372036854775807%Z.
+Definition i128_min : Z := -170141183460469231731687303715884105728%Z.
+Definition i128_max : Z := 170141183460469231731687303715884105727%Z.
+Definition u8_min   : Z := 0%Z.
+Definition u8_max   : Z := 255%Z.
+Definition u16_min  : Z := 0%Z.
+Definition u16_max  : Z := 65535%Z.
+Definition u32_min  : Z := 0%Z.
+Definition u32_max  : Z := 4294967295%Z.
+Definition u64_min  : Z := 0%Z.
+Definition u64_max  : Z := 18446744073709551615%Z.
+Definition u128_min : Z := 0%Z.
+Definition u128_max : Z := 340282366920938463463374607431768211455%Z.
+
+(** The bounds of [isize] and [usize] vary with the architecture. *)
+Axiom isize_min : Z.
+Axiom isize_max : Z.
+Definition usize_min : Z := 0%Z.
+Axiom usize_max : Z.
+
+Open Scope Z_scope.
+
+(** We provide those lemmas to reason about the bounds of [isize] and [usize] *)
+Axiom isize_min_bound : isize_min <= i32_min.
+Axiom isize_max_bound : i32_max <= isize_max.
+Axiom usize_max_bound : u32_max <= usize_max.
+
+Inductive scalar_ty :=
+  | Isize
+  | I8
+  | I16
+  | I32
+  | I64
+  | I128
+  | Usize
+  | U8
+  | U16
+  | U32
+  | U64
+  | U128
+.
+
+Definition scalar_min (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => isize_min
+  | I8 => i8_min
+  | I16 => i16_min
+  | I32 => i32_min
+  | I64 => i64_min
+  | I128 => i128_min
+  | Usize => usize_min
+  | U8 => u8_min
+  | U16 => u16_min
+  | U32 => u32_min
+  | U64 => u64_min
+  | U128 => u128_min
+end.
+
+Definition scalar_max (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => isize_max
+  | I8 => i8_max
+  | I16 => i16_max
+  | I32 => i32_max
+  | I64 => i64_max
+  | I128 => i128_max
+  | Usize => usize_max
+  | U8 => u8_max
+  | U16 => u16_max
+  | U32 => u32_max
+  | U64 => u64_max
+  | U128 => u128_max
+end.
+
+(** We use the following conservative bounds to make sure we can compute bound
+    checks in most situations *)
+Definition scalar_min_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_min
+  | Usize => u32_min
+  | _ => scalar_min ty
+end.
+
+Definition scalar_max_cons (ty: scalar_ty) : Z :=
+  match ty with
+  | Isize => i32_max
+  | Usize => u32_max
+  | _ => scalar_max ty
+end.
+
+Lemma scalar_min_cons_valid : forall ty, scalar_min ty <= scalar_min_cons ty .
+Proof.
+  destruct ty; unfold scalar_min_cons, scalar_min; try lia.
+  - pose isize_min_bound; lia.
+  - apply Z.le_refl.
+Qed.
+
+Lemma scalar_max_cons_valid : forall ty, scalar_max ty >= scalar_max_cons ty .
+Proof.
+  destruct ty; unfold scalar_max_cons, scalar_max; try lia.
+  - pose isize_max_bound; lia.
+  - pose usize_max_bound. lia.
+Qed.
+
+Definition scalar (ty: scalar_ty) : Type :=
+ { x: Z | scalar_min ty <= x <= scalar_max ty }.
+
+Definition to_Z {ty} (x: scalar ty) : Z := proj1_sig x.
+
+(** Bounds checks: we start by using the conservative bounds, to make sure we
+    can compute in most situations, then we use the real bounds (for [isize]
+    and [usize]). *)
+Definition scalar_ge_min (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb (scalar_min_cons ty) x || Z.leb (scalar_min ty) x.
+
+Definition scalar_le_max (ty: scalar_ty) (x: Z) : bool :=
+  Z.leb x (scalar_max_cons ty) || Z.leb x (scalar_max ty).
+
+Lemma scalar_ge_min_valid (ty: scalar_ty) (x: Z) :
+  scalar_ge_min ty x = true -> scalar_min ty <= x .
+Proof.
+  unfold scalar_ge_min.
+  pose (scalar_min_cons_valid ty).
+  lia.
+Qed.
+
+Lemma scalar_le_max_valid (ty: scalar_ty) (x: Z) :
+  scalar_le_max ty x = true -> x <= scalar_max ty .
+Proof.
+  unfold scalar_le_max.
+  pose (scalar_max_cons_valid ty).
+  lia.
+Qed.
+
+Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool :=
+  scalar_ge_min ty x && scalar_le_max ty x .
+
+Lemma scalar_in_bounds_valid (ty: scalar_ty) (x: Z) :
+  scalar_in_bounds ty x = true -> scalar_min ty <= x <= scalar_max ty .
+Proof.
+  unfold scalar_in_bounds.
+  intros H.
+  destruct (scalar_ge_min ty x) eqn:Hmin.
+  - destruct (scalar_le_max ty x) eqn:Hmax.
+    + pose (scalar_ge_min_valid ty x Hmin).
+      pose (scalar_le_max_valid ty x Hmax).
+      lia.
+    + inversion H.
+  - inversion H.
+Qed.
+
+Import Sumbool.
+
+Definition mk_scalar (ty: scalar_ty) (x: Z) : result (scalar ty) :=
+  match sumbool_of_bool (scalar_in_bounds ty x) with
+  | left H => Return (exist _ x (scalar_in_bounds_valid _ _ H))
+  | right _ => Fail_ Failure
+  end.
+
+Definition scalar_add {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x + to_Z y).
+
+Definition scalar_sub {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x - to_Z y).
+
+Definition scalar_mul {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (to_Z x * to_Z y).
+
+Definition scalar_div {ty} (x y: scalar ty) : result (scalar ty) :=
+  if to_Z y =? 0 then Fail_ Failure else
+  mk_scalar ty (to_Z x / to_Z y).
+
+Definition scalar_rem {ty} (x y: scalar ty) : result (scalar ty) := mk_scalar ty (Z.rem (to_Z x) (to_Z y)).
+  
+Definition scalar_neg {ty} (x: scalar ty) : result (scalar ty) := mk_scalar ty (-(to_Z x)).
+
+Axiom scalar_xor : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_or : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_and : forall ty, scalar ty -> scalar ty -> scalar ty. (* TODO *)
+Axiom scalar_shl : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+Axiom scalar_shr : forall ty0 ty1, scalar ty0 -> scalar ty1 -> result (scalar ty0). (* TODO *)
+
+(** Cast an integer from a [src_ty] to a [tgt_ty] *)
+(* TODO: check the semantics of casts in Rust *)
+Definition scalar_cast (src_ty tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) :=
+  mk_scalar tgt_ty (to_Z x).
+
+(* This can't fail, but for now we make all casts faillible (easier for the translation) *)
+Definition scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) :=
+  mk_scalar tgt_ty (if x then 1 else 0).
+
+(** Comparisons *)
+Definition scalar_leb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.leb (to_Z x) (to_Z y) .
+
+Definition scalar_ltb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.ltb (to_Z x) (to_Z y) .
+
+Definition scalar_geb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.geb (to_Z x) (to_Z y) .
+
+Definition scalar_gtb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.gtb (to_Z x) (to_Z y) .
+
+Definition scalar_eqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  Z.eqb (to_Z x) (to_Z y) .
+
+Definition scalar_neqb {ty : scalar_ty} (x : scalar ty) (y : scalar ty) : bool :=
+  negb (Z.eqb (to_Z x) (to_Z y)) .
+
+
+(** The scalar types *)
+Definition isize := scalar Isize.
+Definition i8    := scalar I8.
+Definition i16   := scalar I16.
+Definition i32   := scalar I32.
+Definition i64   := scalar I64.
+Definition i128  := scalar I128.
+Definition usize := scalar Usize.
+Definition u8    := scalar U8.
+Definition u16   := scalar U16.
+Definition u32   := scalar U32.
+Definition u64   := scalar U64.
+Definition u128  := scalar U128.
+
+(** Negaion *)
+Definition isize_neg := @scalar_neg Isize.
+Definition i8_neg    := @scalar_neg I8.
+Definition i16_neg   := @scalar_neg I16.
+Definition i32_neg   := @scalar_neg I32.
+Definition i64_neg   := @scalar_neg I64.
+Definition i128_neg  := @scalar_neg I128.
+
+(** Division *)
+Definition isize_div := @scalar_div Isize.
+Definition i8_div    := @scalar_div I8.
+Definition i16_div   := @scalar_div I16.
+Definition i32_div   := @scalar_div I32.
+Definition i64_div   := @scalar_div I64.
+Definition i128_div  := @scalar_div I128.
+Definition usize_div := @scalar_div Usize.
+Definition u8_div    := @scalar_div U8.
+Definition u16_div   := @scalar_div U16.
+Definition u32_div   := @scalar_div U32.
+Definition u64_div   := @scalar_div U64.
+Definition u128_div  := @scalar_div U128.
+
+(** Remainder *)
+Definition isize_rem := @scalar_rem Isize.
+Definition i8_rem    := @scalar_rem I8.
+Definition i16_rem   := @scalar_rem I16.
+Definition i32_rem   := @scalar_rem I32.
+Definition i64_rem   := @scalar_rem I64.
+Definition i128_rem  := @scalar_rem I128.
+Definition usize_rem := @scalar_rem Usize.
+Definition u8_rem    := @scalar_rem U8.
+Definition u16_rem   := @scalar_rem U16.
+Definition u32_rem   := @scalar_rem U32.
+Definition u64_rem   := @scalar_rem U64.
+Definition u128_rem  := @scalar_rem U128.
+
+(** Addition *)
+Definition isize_add := @scalar_add Isize.
+Definition i8_add    := @scalar_add I8.
+Definition i16_add   := @scalar_add I16.
+Definition i32_add   := @scalar_add I32.
+Definition i64_add   := @scalar_add I64.
+Definition i128_add  := @scalar_add I128.
+Definition usize_add := @scalar_add Usize.
+Definition u8_add    := @scalar_add U8.
+Definition u16_add   := @scalar_add U16.
+Definition u32_add   := @scalar_add U32.
+Definition u64_add   := @scalar_add U64.
+Definition u128_add  := @scalar_add U128.
+
+(** Substraction *)
+Definition isize_sub := @scalar_sub Isize.
+Definition i8_sub    := @scalar_sub I8.
+Definition i16_sub   := @scalar_sub I16.
+Definition i32_sub   := @scalar_sub I32.
+Definition i64_sub   := @scalar_sub I64.
+Definition i128_sub  := @scalar_sub I128.
+Definition usize_sub := @scalar_sub Usize.
+Definition u8_sub    := @scalar_sub U8.
+Definition u16_sub   := @scalar_sub U16.
+Definition u32_sub   := @scalar_sub U32.
+Definition u64_sub   := @scalar_sub U64.
+Definition u128_sub  := @scalar_sub U128.
+
+(** Multiplication *)
+Definition isize_mul := @scalar_mul Isize.
+Definition i8_mul    := @scalar_mul I8.
+Definition i16_mul   := @scalar_mul I16.
+Definition i32_mul   := @scalar_mul I32.
+Definition i64_mul   := @scalar_mul I64.
+Definition i128_mul  := @scalar_mul I128.
+Definition usize_mul := @scalar_mul Usize.
+Definition u8_mul    := @scalar_mul U8.
+Definition u16_mul   := @scalar_mul U16.
+Definition u32_mul   := @scalar_mul U32.
+Definition u64_mul   := @scalar_mul U64.
+Definition u128_mul  := @scalar_mul U128.
+
+(** Xor *)
+Definition u8_xor := @scalar_xor U8.
+Definition u16_xor := @scalar_xor U16.
+Definition u32_xor := @scalar_xor U32.
+Definition u64_xor := @scalar_xor U64.
+Definition u128_xor := @scalar_xor U128.
+Definition usize_xor := @scalar_xor Usize.
+Definition i8_xor := @scalar_xor I8.
+Definition i16_xor := @scalar_xor I16.
+Definition i32_xor := @scalar_xor I32.
+Definition i64_xor := @scalar_xor I64.
+Definition i128_xor := @scalar_xor I128.
+Definition isize_xor := @scalar_xor Isize.
+
+(** Or *)
+Definition u8_or := @scalar_or U8.
+Definition u16_or := @scalar_or U16.
+Definition u32_or := @scalar_or U32.
+Definition u64_or := @scalar_or U64.
+Definition u128_or := @scalar_or U128.
+Definition usize_or := @scalar_or Usize.
+Definition i8_or := @scalar_or I8.
+Definition i16_or := @scalar_or I16.
+Definition i32_or := @scalar_or I32.
+Definition i64_or := @scalar_or I64.
+Definition i128_or := @scalar_or I128.
+Definition isize_or := @scalar_or Isize.
+
+(** And *)
+Definition u8_and := @scalar_and U8.
+Definition u16_and := @scalar_and U16.
+Definition u32_and := @scalar_and U32.
+Definition u64_and := @scalar_and U64.
+Definition u128_and := @scalar_and U128.
+Definition usize_and := @scalar_and Usize.
+Definition i8_and := @scalar_and I8.
+Definition i16_and := @scalar_and I16.
+Definition i32_and := @scalar_and I32.
+Definition i64_and := @scalar_and I64.
+Definition i128_and := @scalar_and I128.
+Definition isize_and := @scalar_and Isize.
+
+(** Shift left *)
+Definition u8_shl {ty} := @scalar_shl U8 ty.
+Definition u16_shl {ty} := @scalar_shl U16 ty.
+Definition u32_shl {ty} := @scalar_shl U32 ty.
+Definition u64_shl {ty} := @scalar_shl U64 ty.
+Definition u128_shl {ty} := @scalar_shl U128 ty.
+Definition usize_shl {ty} := @scalar_shl Usize ty.
+Definition i8_shl {ty} := @scalar_shl I8 ty.
+Definition i16_shl {ty} := @scalar_shl I16 ty.
+Definition i32_shl {ty} := @scalar_shl I32 ty.
+Definition i64_shl {ty} := @scalar_shl I64 ty.
+Definition i128_shl {ty} := @scalar_shl I128 ty.
+Definition isize_shl {ty} := @scalar_shl Isize ty.
+
+(** Shift right *)
+Definition u8_shr {ty} := @scalar_shr U8 ty.
+Definition u16_shr {ty} := @scalar_shr U16 ty.
+Definition u32_shr {ty} := @scalar_shr U32 ty.
+Definition u64_shr {ty} := @scalar_shr U64 ty.
+Definition u128_shr {ty} := @scalar_shr U128 ty.
+Definition usize_shr {ty} := @scalar_shr Usize ty.
+Definition i8_shr {ty} := @scalar_shr I8 ty.
+Definition i16_shr {ty} := @scalar_shr I16 ty.
+Definition i32_shr {ty} := @scalar_shr I32 ty.
+Definition i64_shr {ty} := @scalar_shr I64 ty.
+Definition i128_shr {ty} := @scalar_shr I128 ty.
+Definition isize_shr {ty} := @scalar_shr Isize ty.
+
+(** Small utility *)
+Definition usize_to_nat (x: usize) : nat := Z.to_nat (to_Z x).
+
+(** Notations *)
+Notation "x %isize" := ((mk_scalar Isize x)%return) (at level 9).
+Notation "x %i8"    := ((mk_scalar I8    x)%return) (at level 9).
+Notation "x %i16"   := ((mk_scalar I16   x)%return) (at level 9).
+Notation "x %i32"   := ((mk_scalar I32   x)%return) (at level 9).
+Notation "x %i64"   := ((mk_scalar I64   x)%return) (at level 9).
+Notation "x %i128"  := ((mk_scalar I128  x)%return) (at level 9).
+Notation "x %usize" := ((mk_scalar Usize x)%return) (at level 9).
+Notation "x %u8"    := ((mk_scalar U8    x)%return) (at level 9).
+Notation "x %u16"   := ((mk_scalar U16   x)%return) (at level 9).
+Notation "x %u32"   := ((mk_scalar U32   x)%return) (at level 9).
+Notation "x %u64"   := ((mk_scalar U64   x)%return) (at level 9).
+Notation "x %u128"  := ((mk_scalar U128  x)%return) (at level 9).
+
+Notation "x s= y" := (scalar_eqb x y)  (at level 80) : Primitives_scope.
+Notation "x s<> y" := (scalar_neqb x y) (at level 80) : Primitives_scope.
+Notation "x s<= y" := (scalar_leb x y)  (at level 80) : Primitives_scope.
+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.
+
+(** 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_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 {_ _}.
+
+(* 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_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 {_}.
+
+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 * (T -> result T)) :=
+  Return (x, fun x => 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;
+|}.
+
+
+(*** Arrays *)
+Definition array T (n : usize) := { l: list T | Z.of_nat (length l) = to_Z n}.
+
+Lemma le_0_usize_max : 0 <= usize_max.
+Proof.
+  pose (H := usize_max_bound).
+  unfold u32_max in H.
+  lia.
+Qed.
+
+Lemma eqb_imp_eq (x y : Z) : Z.eqb x y = true -> x = y.
+Proof.
+  lia.
+Qed.
+
+(* TODO: finish the definitions *)
+Axiom mk_array : forall (T : Type) (n : usize) (l : list T), 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).
+
+Definition array_index_mut_usize (T : Type) (n : usize) (a : array T n) (i : usize) :
+  result (T * (T -> result (array T n))) :=
+  match array_index_usize T n a i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_update_usize T n a i)
+  end.
+
+(*** 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_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).
+
+Definition slice_index_mut_usize (T : Type) (s : slice T) (i : usize) :
+  result (T * (T -> result (slice T))) :=
+  match slice_index_usize T s i with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, slice_update_usize T s i)
+  end.
+
+(*** Subslices *)
+
+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).
+
+Definition array_to_slice_mut (T : Type) (n : usize) (a : array T n) :
+  result (slice T * (slice T -> result (array T n))) :=
+  match array_to_slice T n a with
+  | Fail_ e => Fail_ e
+  | Return x => Return (x, array_from_slice T n a)
+  end.
+
+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 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 alloc_vec_Vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+
+Definition alloc_vec_Vec_to_list {T: Type} (v: alloc_vec_Vec T) : list T := proj1_sig 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 alloc_vec_Vec_new (T: Type) : alloc_vec_Vec T := (exist _ [] le_0_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 alloc_vec_Vec_length, usize_min.
+  split.
+  - lia.
+  - apply (proj2_sig v).
+Qed.
+
+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 :=
+  match l with
+  | []     => []
+  | x :: t => match n with
+    | 0%nat => a :: t
+    | S m => x :: (list_update t m a)
+end end.
+
+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.
+
+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])).
+
+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).
+
+(* Helper *)
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), 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).
+
+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.
+
+(* 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 * (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_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_unchecked {_ _}.
+Arguments core_slice_index_SliceIndex_get_unchecked_mut {_ _}.
+Arguments core_slice_index_SliceIndex_index {_ _}.
+Arguments core_slice_index_SliceIndex_index_mut {_ _}.
+
+(* [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.
+
+(* [core::slice::index::Range:::get]: forward function *)
+Axiom core_slice_index_RangeUsize_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_RangeUsize_get_mut :
+  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
+  (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_RangeUsize_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_RangeUsize_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_RangeUsize_index_mut :
+  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) *
+          (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) *
+          (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
+  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
+
+(* Trait implementation: [core::slice::index::Range] *)
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
+  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_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;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (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::[T]] *)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  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;
+|}.
+
+(* Trait implementation: [core::array::[T; N]] *)
+Definition core_ops_index_IndexArrayInst (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_ops_index_IndexMutArrayInst (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_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::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 * (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 * (T -> result (slice T))).
+
+(* Trait implementation: [core::slice::index::private_slice_index::usize] *)
+Definition core_slice_index_private_slice_index_SealedUsizeInst
+  : core_slice_index_private_slice_index_Sealed usize := tt.
+
+(* Trait implementation: [core::slice::index::usize] *)
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
+  core_slice_index_SliceIndex usize (slice T) := {|
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
+  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_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;
+|}.
+
+(* [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) *
+          (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;
+|}.
+
+(*** Theorems *)
+
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+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_mut_usize v i.
+
+End Primitives.
diff --git a/tests/coq/arrays/_CoqProject b/tests/coq/arrays/_CoqProject
new file mode 100644
index 00000000..a4e82408
--- /dev/null
+++ b/tests/coq/arrays/_CoqProject
@@ -0,0 +1,7 @@
+# This file was automatically generated - see ../Makefile
+-R . Lib
+-arg -w
+-arg all
+
+Arrays.v
+Primitives.v