From c6f0a8c8bfe04e83de4692a389daf8cde47b74d5 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Thu, 3 Aug 2023 00:24:02 +0200
Subject: Fix issues

---
 tests/lean/lakefile.lean | 1 +
 1 file changed, 1 insertion(+)

(limited to 'tests/lean')

diff --git a/tests/lean/lakefile.lean b/tests/lean/lakefile.lean
index ae63b129..cc63c48f 100644
--- a/tests/lean/lakefile.lean
+++ b/tests/lean/lakefile.lean
@@ -17,3 +17,4 @@ package «tests» {}
 @[default_target] lean_lib noNestedBorrows
 @[default_target] lean_lib paper
 @[default_target] lean_lib poloniusList
+@[default_target] lean_lib array
-- 
cgit v1.3.1


From fa682c18c8ffc5fa7224d9e9d0e0dd94250ada57 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Thu, 3 Aug 2023 00:28:10 +0200
Subject: Make a minor formatting modification for Lean

---
 compiler/Translate.ml             | 2 +-
 tests/lean/BetreeMain/Funs.lean   | 1 +
 tests/lean/BetreeMain/Types.lean  | 1 +
 tests/lean/Constants.lean         | 1 +
 tests/lean/External/Funs.lean     | 1 +
 tests/lean/External/Types.lean    | 1 +
 tests/lean/Hashmap/Funs.lean      | 1 +
 tests/lean/Hashmap/Types.lean     | 1 +
 tests/lean/HashmapMain/Funs.lean  | 1 +
 tests/lean/HashmapMain/Types.lean | 1 +
 tests/lean/Loops/Funs.lean        | 1 +
 tests/lean/Loops/Types.lean       | 1 +
 tests/lean/NoNestedBorrows.lean   | 1 +
 tests/lean/Paper.lean             | 1 +
 tests/lean/PoloniusList.lean      | 1 +
 15 files changed, 15 insertions(+), 1 deletion(-)

(limited to 'tests/lean')

diff --git a/compiler/Translate.ml b/compiler/Translate.ml
index c5f7df92..17355dfd 100644
--- a/compiler/Translate.ml
+++ b/compiler/Translate.ml
@@ -855,7 +855,7 @@ let extract_file (config : gen_config) (ctx : gen_ctx) (fi : extract_file_info)
       (* Always open the Primitives namespace *)
       Printf.fprintf out "open Primitives\n";
       (* If we are inside the namespace: declare it, otherwise: open it *)
-      if fi.in_namespace then Printf.fprintf out "namespace %s\n" fi.namespace
+      if fi.in_namespace then Printf.fprintf out "\nnamespace %s\n" fi.namespace
       else Printf.fprintf out "open %s\n" fi.namespace
   | HOL4 ->
       Printf.fprintf out "open primitivesLib divDefLib\n";
diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
index 142adf08..a6c6f496 100644
--- a/tests/lean/BetreeMain/Funs.lean
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -4,6 +4,7 @@ import Base
 import BetreeMain.Types
 import BetreeMain.FunsExternal
 open Primitives
+
 namespace betree_main
 
 /- [betree_main::betree::load_internal_node]: forward function -/
diff --git a/tests/lean/BetreeMain/Types.lean b/tests/lean/BetreeMain/Types.lean
index 783ade64..c02c148a 100644
--- a/tests/lean/BetreeMain/Types.lean
+++ b/tests/lean/BetreeMain/Types.lean
@@ -2,6 +2,7 @@
 -- [betree_main]: type definitions
 import Base
 open Primitives
+
 namespace betree_main
 
 /- [betree_main::betree::List] -/
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
index 4a5a7b8f..ec07d0fe 100644
--- a/tests/lean/Constants.lean
+++ b/tests/lean/Constants.lean
@@ -2,6 +2,7 @@
 -- [constants]
 import Base
 open Primitives
+
 namespace constants
 
 /- [constants::X0] -/
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
index 674aaebd..055d7860 100644
--- a/tests/lean/External/Funs.lean
+++ b/tests/lean/External/Funs.lean
@@ -4,6 +4,7 @@ import Base
 import External.Types
 import External.FunsExternal
 open Primitives
+
 namespace external
 
 /- [external::swap]: forward function -/
diff --git a/tests/lean/External/Types.lean b/tests/lean/External/Types.lean
index ba984e2a..71d70eed 100644
--- a/tests/lean/External/Types.lean
+++ b/tests/lean/External/Types.lean
@@ -2,6 +2,7 @@
 -- [external]: type definitions
 import Base
 open Primitives
+
 namespace external
 
 /- [core::num::nonzero::NonZeroU32] -/
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
index 870693b5..2fa981ce 100644
--- a/tests/lean/Hashmap/Funs.lean
+++ b/tests/lean/Hashmap/Funs.lean
@@ -3,6 +3,7 @@
 import Base
 import Hashmap.Types
 open Primitives
+
 namespace hashmap
 
 /- [hashmap::hash_key]: forward function -/
diff --git a/tests/lean/Hashmap/Types.lean b/tests/lean/Hashmap/Types.lean
index 6606cf9e..6455798d 100644
--- a/tests/lean/Hashmap/Types.lean
+++ b/tests/lean/Hashmap/Types.lean
@@ -2,6 +2,7 @@
 -- [hashmap]: type definitions
 import Base
 open Primitives
+
 namespace hashmap
 
 /- [hashmap::List] -/
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
index 610bae46..ea28b03f 100644
--- a/tests/lean/HashmapMain/Funs.lean
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -4,6 +4,7 @@ import Base
 import HashmapMain.Types
 import HashmapMain.FunsExternal
 open Primitives
+
 namespace hashmap_main
 
 /- [hashmap_main::hashmap::hash_key]: forward function -/
diff --git a/tests/lean/HashmapMain/Types.lean b/tests/lean/HashmapMain/Types.lean
index 3b3d0d7c..2b5cbd6c 100644
--- a/tests/lean/HashmapMain/Types.lean
+++ b/tests/lean/HashmapMain/Types.lean
@@ -2,6 +2,7 @@
 -- [hashmap_main]: type definitions
 import Base
 open Primitives
+
 namespace hashmap_main
 
 /- [hashmap_main::hashmap::List] -/
diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
index f7e6603d..fac0c5a9 100644
--- a/tests/lean/Loops/Funs.lean
+++ b/tests/lean/Loops/Funs.lean
@@ -3,6 +3,7 @@
 import Base
 import Loops.Types
 open Primitives
+
 namespace loops
 
 /- [loops::sum]: loop 0: forward function -/
diff --git a/tests/lean/Loops/Types.lean b/tests/lean/Loops/Types.lean
index f8bc193b..018af901 100644
--- a/tests/lean/Loops/Types.lean
+++ b/tests/lean/Loops/Types.lean
@@ -2,6 +2,7 @@
 -- [loops]: type definitions
 import Base
 open Primitives
+
 namespace loops
 
 /- [loops::List] -/
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
index bc707fd9..1a180c60 100644
--- a/tests/lean/NoNestedBorrows.lean
+++ b/tests/lean/NoNestedBorrows.lean
@@ -2,6 +2,7 @@
 -- [no_nested_borrows]
 import Base
 open Primitives
+
 namespace no_nested_borrows
 
 /- [no_nested_borrows::Pair] -/
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
index cee7128a..c15c5e4b 100644
--- a/tests/lean/Paper.lean
+++ b/tests/lean/Paper.lean
@@ -2,6 +2,7 @@
 -- [paper]
 import Base
 open Primitives
+
 namespace paper
 
 /- [paper::ref_incr]: merged forward/backward function
diff --git a/tests/lean/PoloniusList.lean b/tests/lean/PoloniusList.lean
index 1453c275..07f206a8 100644
--- a/tests/lean/PoloniusList.lean
+++ b/tests/lean/PoloniusList.lean
@@ -2,6 +2,7 @@
 -- [polonius_list]
 import Base
 open Primitives
+
 namespace polonius_list
 
 /- [polonius_list::List] -/
-- 
cgit v1.3.1


From c656688ff4895904b4bb5e2f89037f1e75c9fa00 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Fri, 4 Aug 2023 20:02:37 +0200
Subject: Make minor modifications

---
 backends/lean/Base/Primitives/Vec.lean | 8 ++++----
 tests/lean/Hashmap/Funs.lean           | 4 ++--
 tests/lean/HashmapMain/Funs.lean       | 4 ++--
 tests/lean/Loops/Funs.lean             | 2 +-
 4 files changed, 9 insertions(+), 9 deletions(-)

(limited to 'tests/lean')

diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
index d37fb5fd..c4c4d9f2 100644
--- a/backends/lean/Base/Primitives/Vec.lean
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -79,7 +79,7 @@ theorem Vec.insert_spec {α : Type u} (v: Vec α) (i: Usize) (x: α)
   ∃ nv, v.insert α i x = ret nv ∧ nv.val = v.val.update i.val x := by
   simp [insert, *]
 
-def Vec.index (α : Type u) (v: Vec α) (i: Usize) : Result α :=
+def Vec.index_shared (α : Type u) (v: Vec α) (i: Usize) : Result α :=
   match v.val.indexOpt i.val with
   | none => fail .arrayOutOfBounds
   | some x => ret x
@@ -90,10 +90,10 @@ def Vec.index (α : Type u) (v: Vec α) (i: Usize) : Result α :=
  -/
 
 @[pspec]
-theorem Vec.index_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
+theorem Vec.index_shared_spec {α : Type u} [Inhabited α] (v: Vec α) (i: Usize)
   (hbound : i.val < v.length) :
-  ∃ x, v.index α i = ret x ∧ x = v.val.index i.val := by
-  simp only [index]
+  ∃ x, v.index_shared α i = ret x ∧ x = v.val.index i.val := by
+  simp only [index_shared]
   -- TODO: dependent rewrite
   have h := List.indexOpt_eq_index v.val i.val (by scalar_tac) (by simp [*])
   simp [*]
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
index 2fa981ce..d6796932 100644
--- a/tests/lean/Hashmap/Funs.lean
+++ b/tests/lean/Hashmap/Funs.lean
@@ -239,7 +239,7 @@ def HashMap.contains_key
     let hash ← hash_key key
     let i := Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index (List T) self.slots hash_mod
+    let l ← Vec.index_shared (List T) self.slots hash_mod
     HashMap.contains_key_in_list T key l
 
 /- [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
@@ -262,7 +262,7 @@ def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T :=
     let hash ← hash_key key
     let i := Vec.len (List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index (List T) self.slots hash_mod
+    let l ← Vec.index_shared (List T) self.slots hash_mod
     HashMap.get_in_list T key l
 
 /- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
index ea28b03f..74fe8a54 100644
--- a/tests/lean/HashmapMain/Funs.lean
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -261,7 +261,7 @@ def hashmap.HashMap.contains_key
     let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index (hashmap.List T) self.slots hash_mod
+    let l ← Vec.index_shared (hashmap.List T) self.slots hash_mod
     hashmap.HashMap.contains_key_in_list T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
@@ -286,7 +286,7 @@ def hashmap.HashMap.get
     let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.slots
     let hash_mod ← hash % i
-    let l ← Vec.index (hashmap.List T) self.slots hash_mod
+    let l ← Vec.index_shared (hashmap.List T) self.slots hash_mod
     hashmap.HashMap.get_in_list T key l
 
 /- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
index fac0c5a9..5fbe200f 100644
--- a/tests/lean/Loops/Funs.lean
+++ b/tests/lean/Loops/Funs.lean
@@ -178,7 +178,7 @@ divergent def get_elem_shared_loop
 /- [loops::get_elem_shared]: forward function -/
 def get_elem_shared (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
   do
-    let l ← Vec.index (List Usize) slots (Usize.ofInt 0)
+    let l ← Vec.index_shared (List Usize) slots (Usize.ofInt 0)
     get_elem_shared_loop x l
 
 /- [loops::id_mut]: forward function -/
-- 
cgit v1.3.1


From d7b3155ad5583d5a92e85c69cc89a21a60e51df7 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Fri, 4 Aug 2023 20:03:42 +0200
Subject: Generate the Array example in Lean

---
 tests/lean/Array/Funs.lean  | 287 ++++++++++++++++++++++++++++++++++++++++++++
 tests/lean/Array/Types.lean |   8 ++
 2 files changed, 295 insertions(+)
 create mode 100644 tests/lean/Array/Funs.lean
 create mode 100644 tests/lean/Array/Types.lean

(limited to 'tests/lean')

diff --git a/tests/lean/Array/Funs.lean b/tests/lean/Array/Funs.lean
new file mode 100644
index 00000000..b1365143
--- /dev/null
+++ b/tests/lean/Array/Funs.lean
@@ -0,0 +1,287 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [array]: function definitions
+import Base
+import Array.Types
+open Primitives
+
+namespace array
+
+/- [array::array_to_shared_slice_]: forward function -/
+def array_to_shared_slice_
+  (T : Type) (s : Array T (Usize.ofInt 32)) : Result (Slice T) :=
+  Array.to_slice T (Usize.ofInt 32) s
+
+/- [array::array_to_mut_slice_]: forward function -/
+def array_to_mut_slice_
+  (T : Type) (s : Array T (Usize.ofInt 32)) : Result (Slice T) :=
+  Array.to_mut_slice T (Usize.ofInt 32) s
+
+/- [array::array_to_mut_slice_]: backward function 0 -/
+def array_to_mut_slice__back
+  (T : Type) (s : Array T (Usize.ofInt 32)) (ret0 : Slice T) :
+  Result (Array T (Usize.ofInt 32))
+  :=
+  Array.to_mut_slice_back T (Usize.ofInt 32) s ret0
+
+/- [array::array_len]: forward function -/
+def array_len (T : Type) (s : Array T (Usize.ofInt 32)) : Result Usize :=
+  do
+    let s0 ← Array.to_slice T (Usize.ofInt 32) s
+    let i := Slice.len T s0
+    Result.ret i
+
+/- [array::shared_array_len]: forward function -/
+def shared_array_len
+  (T : Type) (s : Array T (Usize.ofInt 32)) : Result Usize :=
+  do
+    let s0 ← Array.to_slice T (Usize.ofInt 32) s
+    let i := Slice.len T s0
+    Result.ret i
+
+/- [array::shared_slice_len]: forward function -/
+def shared_slice_len (T : Type) (s : Slice T) : Result Usize :=
+  let i := Slice.len T s
+  Result.ret i
+
+/- [array::index_array_shared]: forward function -/
+def index_array_shared
+  (T : Type) (s : Array T (Usize.ofInt 32)) (i : Usize) : Result T :=
+  Array.index_shared T (Usize.ofInt 32) s i
+
+/- [array::index_array_u32]: forward function -/
+def index_array_u32
+  (s : Array U32 (Usize.ofInt 32)) (i : Usize) : Result U32 :=
+  Array.index_shared U32 (Usize.ofInt 32) s i
+
+/- [array::index_array_generic]: forward function -/
+def index_array_generic
+  (N : Usize) (s : Array U32 N) (i : Usize) : Result U32 :=
+  Array.index_shared U32 N s i
+
+/- [array::index_array_generic_call]: forward function -/
+def index_array_generic_call
+  (N : Usize) (s : Array U32 N) (i : Usize) : Result U32 :=
+  index_array_generic N s i
+
+/- [array::index_array_copy]: forward function -/
+def index_array_copy (x : Array U32 (Usize.ofInt 32)) : Result U32 :=
+  Array.index_shared U32 (Usize.ofInt 32) x (Usize.ofInt 0)
+
+/- [array::index_mut_array]: forward function -/
+def index_mut_array
+  (T : Type) (s : Array T (Usize.ofInt 32)) (i : Usize) : Result T :=
+  Array.index_mut T (Usize.ofInt 32) s i
+
+/- [array::index_mut_array]: backward function 0 -/
+def index_mut_array_back
+  (T : Type) (s : Array T (Usize.ofInt 32)) (i : Usize) (ret0 : T) :
+  Result (Array T (Usize.ofInt 32))
+  :=
+  Array.index_mut_back T (Usize.ofInt 32) s i ret0
+
+/- [array::index_slice]: forward function -/
+def index_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
+  Slice.index_shared T s i
+
+/- [array::index_mut_slice]: forward function -/
+def index_mut_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
+  Slice.index_mut T s i
+
+/- [array::index_mut_slice]: backward function 0 -/
+def index_mut_slice_back
+  (T : Type) (s : Slice T) (i : Usize) (ret0 : T) : Result (Slice T) :=
+  Slice.index_mut_back T s i ret0
+
+/- [array::slice_subslice_shared_]: forward function -/
+def slice_subslice_shared_
+  (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  Slice.subslice_shared U32 x (Range.mk y z)
+
+/- [array::slice_subslice_mut_]: forward function -/
+def slice_subslice_mut_
+  (x : Slice U32) (y : Usize) (z : Usize) : Result (Slice U32) :=
+  Slice.subslice_mut U32 x (Range.mk y z)
+
+/- [array::slice_subslice_mut_]: backward function 0 -/
+def slice_subslice_mut__back
+  (x : Slice U32) (y : Usize) (z : Usize) (ret0 : Slice U32) :
+  Result (Slice U32)
+  :=
+  Slice.subslice_mut_back U32 x (Range.mk y z) ret0
+
+/- [array::array_to_slice_shared]: forward function -/
+def array_to_slice_shared
+  (x : Array U32 (Usize.ofInt 32)) : Result (Slice U32) :=
+  Array.to_slice U32 (Usize.ofInt 32) x
+
+/- [array::array_to_slice_mut]: forward function -/
+def array_to_slice_mut (x : Array U32 (Usize.ofInt 32)) : Result (Slice U32) :=
+  Array.to_mut_slice U32 (Usize.ofInt 32) x
+
+/- [array::array_to_slice_mut]: backward function 0 -/
+def array_to_slice_mut_back
+  (x : Array U32 (Usize.ofInt 32)) (ret0 : Slice U32) :
+  Result (Array U32 (Usize.ofInt 32))
+  :=
+  Array.to_mut_slice_back U32 (Usize.ofInt 32) x ret0
+
+/- [array::array_subslice_shared_]: forward function -/
+def array_subslice_shared_
+  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) :
+  Result (Slice U32)
+  :=
+  Array.subslice_shared U32 (Usize.ofInt 32) x (Range.mk y z)
+
+/- [array::array_subslice_mut_]: forward function -/
+def array_subslice_mut_
+  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) :
+  Result (Slice U32)
+  :=
+  Array.subslice_mut U32 (Usize.ofInt 32) x (Range.mk y z)
+
+/- [array::array_subslice_mut_]: backward function 0 -/
+def array_subslice_mut__back
+  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) (ret0 : Slice U32) :
+  Result (Array U32 (Usize.ofInt 32))
+  :=
+  Array.subslice_mut_back U32 (Usize.ofInt 32) x (Range.mk y z) ret0
+
+/- [array::index_slice_0]: forward function -/
+def index_slice_0 (T : Type) (s : Slice T) : Result T :=
+  Slice.index_shared T s (Usize.ofInt 0)
+
+/- [array::index_array_0]: forward function -/
+def index_array_0 (T : Type) (s : Array T (Usize.ofInt 32)) : Result T :=
+  Array.index_shared T (Usize.ofInt 32) s (Usize.ofInt 0)
+
+/- [array::index_index_array]: forward function -/
+def index_index_array
+  (s : Array (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32)) (i : Usize)
+  (j : Usize) :
+  Result U32
+  :=
+  do
+    let a ←
+      Array.index_shared (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32) s i
+    Array.index_shared U32 (Usize.ofInt 32) a j
+
+/- [array::update_update_array]: forward function -/
+def update_update_array
+  (s : Array (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32)) (i : Usize)
+  (j : Usize) :
+  Result Unit
+  :=
+  do
+    let a ← Array.index_mut (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32) s i
+    let a0 ← Array.index_mut_back U32 (Usize.ofInt 32) a j (U32.ofInt 0)
+    let _ ←
+      Array.index_mut_back (Array U32 (Usize.ofInt 32)) (Usize.ofInt 32) s i a0
+    Result.ret ()
+
+/- [array::array_local_deep_copy]: forward function -/
+def array_local_deep_copy (x : Array U32 (Usize.ofInt 32)) : Result Unit :=
+  Result.ret ()
+
+/- [array::f0]: forward function -/
+def f0 : Result Unit :=
+  do
+    let s ←
+      Array.to_mut_slice U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
+    let s0 ← Slice.index_mut_back U32 s (Usize.ofInt 0) (U32.ofInt 1)
+    let _ ←
+      Array.to_mut_slice_back U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ]) s0
+    Result.ret ()
+
+/- Unit test for [array::f0] -/
+#assert (f0 == .ret ())
+
+/- [array::f1]: forward function -/
+def f1 : Result Unit :=
+  do
+    let _ ←
+      Array.index_mut_back U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
+        (Usize.ofInt 0) (U32.ofInt 1)
+    Result.ret ()
+
+/- Unit test for [array::f1] -/
+#assert (f1 == .ret ())
+
+/- [array::sum]: loop 0: forward function -/
+divergent def sum_loop (s : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
+  let i0 := Slice.len U32 s
+  if i < i0
+  then
+    do
+      let i1 ← Slice.index_shared U32 s i
+      let sum1 ← sum0 + i1
+      let i2 ← i + (Usize.ofInt 1)
+      sum_loop s sum1 i2
+  else Result.ret sum0
+
+/- [array::sum]: forward function -/
+def sum (s : Slice U32) : Result U32 :=
+  sum_loop s (U32.ofInt 0) (Usize.ofInt 0)
+
+/- [array::sum2]: loop 0: forward function -/
+divergent def sum2_loop
+  (s : Slice U32) (s2 : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
+  let i0 := Slice.len U32 s
+  if i < i0
+  then
+    do
+      let i1 ← Slice.index_shared U32 s i
+      let i2 ← Slice.index_shared U32 s2 i
+      let i3 ← i1 + i2
+      let sum1 ← sum0 + i3
+      let i4 ← i + (Usize.ofInt 1)
+      sum2_loop s s2 sum1 i4
+  else Result.ret sum0
+
+/- [array::sum2]: forward function -/
+def sum2 (s : Slice U32) (s2 : Slice U32) : Result U32 :=
+  let i := Slice.len U32 s
+  let i0 := Slice.len U32 s2
+  if not (i = i0)
+  then Result.fail Error.panic
+  else sum2_loop s s2 (U32.ofInt 0) (Usize.ofInt 0)
+
+/- [array::f2]: forward function -/
+def f2 (i : U32) : Result Unit :=
+  Result.ret ()
+
+/- [array::f4]: forward function -/
+def f4
+  (x : Array U32 (Usize.ofInt 32)) (y : Usize) (z : Usize) :
+  Result (Slice U32)
+  :=
+  Array.subslice_shared U32 (Usize.ofInt 32) x (Range.mk y z)
+
+/- [array::f3]: forward function -/
+def f3 : Result U32 :=
+  do
+    let i ←
+      Array.index_shared U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
+        (Usize.ofInt 0)
+    let _ ← f2 i
+    let s ←
+      Array.to_slice U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
+    let s0 ←
+      f4
+        (Array.make U32 (Usize.ofInt 32) [
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0),
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0)
+          ]) (Usize.ofInt 16) (Usize.ofInt 18)
+    sum2 s s0
+
+end array
diff --git a/tests/lean/Array/Types.lean b/tests/lean/Array/Types.lean
new file mode 100644
index 00000000..407ce826
--- /dev/null
+++ b/tests/lean/Array/Types.lean
@@ -0,0 +1,8 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [array]: type definitions
+import Base
+open Primitives
+
+namespace array
+
+end array
-- 
cgit v1.3.1


From 74c2775c4484c70330bf97c8b11ac4b82bf21d36 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Fri, 4 Aug 2023 20:04:33 +0200
Subject: Add a forgotten file

---
 tests/lean/Array.lean | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 tests/lean/Array.lean

(limited to 'tests/lean')

diff --git a/tests/lean/Array.lean b/tests/lean/Array.lean
new file mode 100644
index 00000000..277b63d9
--- /dev/null
+++ b/tests/lean/Array.lean
@@ -0,0 +1 @@
+import Array.Funs
-- 
cgit v1.3.1


From 5e38184af1b99a307271f738329cd96cb364fc1d Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Fri, 4 Aug 2023 22:31:48 +0200
Subject: Update the Makefile and regenerate the test files

---
 Makefile                                        | 28 +++++----
 backends/coq/Primitives.v                       |  1 -
 tests/coq/betree/BetreeMain_Funs.v              |  5 ++
 tests/coq/betree/BetreeMain_Opaque.v            |  2 +
 tests/coq/betree/BetreeMain_Types.v             |  2 +
 tests/coq/betree/Primitives.v                   | 55 ++++++++++++++++--
 tests/coq/hashmap/Hashmap_Funs.v                |  2 +
 tests/coq/hashmap/Hashmap_Types.v               |  2 +
 tests/coq/hashmap/Primitives.v                  | 55 ++++++++++++++++--
 tests/coq/hashmap_on_disk/HashmapMain_Funs.v    |  2 +
 tests/coq/hashmap_on_disk/HashmapMain_Opaque.v  |  2 +
 tests/coq/hashmap_on_disk/HashmapMain_Types.v   |  2 +
 tests/coq/hashmap_on_disk/Primitives.v          | 55 ++++++++++++++++--
 tests/coq/misc/Constants.v                      |  2 +
 tests/coq/misc/External_Funs.v                  |  2 +
 tests/coq/misc/External_Opaque.v                |  2 +
 tests/coq/misc/External_Types.v                 |  2 +
 tests/coq/misc/Loops.v                          |  2 +
 tests/coq/misc/NoNestedBorrows.v                |  2 +
 tests/coq/misc/Paper.v                          |  2 +
 tests/coq/misc/PoloniusList.v                   |  2 +
 tests/coq/misc/Primitives.v                     | 55 ++++++++++++++++--
 tests/fstar/betree/Primitives.fst               | 75 +++++++++++++++++++++++++
 tests/fstar/betree_back_stateful/Primitives.fst | 75 +++++++++++++++++++++++++
 tests/fstar/hashmap/Primitives.fst              | 75 +++++++++++++++++++++++++
 tests/fstar/hashmap_on_disk/Primitives.fst      | 75 +++++++++++++++++++++++++
 tests/fstar/misc/Primitives.fst                 | 75 +++++++++++++++++++++++++
 tests/lean/Array/Funs.lean                      | 41 ++++++--------
 28 files changed, 637 insertions(+), 63 deletions(-)

(limited to 'tests/lean')

diff --git a/Makefile b/Makefile
index 8865746d..c94544be 100644
--- a/Makefile
+++ b/Makefile
@@ -125,15 +125,13 @@ thol4-paper: SUBDIR := misc-paper
 
 trans-array: OPTIONS += -no-state
 trans-array: SUBDIR := array
-tfstar-array: OPTIONS +=
-tcoq-array: OPTIONS +=
+tfstar-array: OPTIONS += -decreases-clauses -template-clauses
+tcoq-array: OPTIONS += -use-fuel
 tlean-array: SUBDIR :=
 tlean-array: OPTIONS +=
 thol4-array: OPTIONS +=
 
 # TODO: activate the arrays for all the backends
-tcoq-array:
-	echo "Ignoring the array test for Coq"
 thol4-array:
 	echo "Ignoring the array test for HOL4"
 
@@ -144,7 +142,7 @@ tcoq-loops: OPTIONS += -use-fuel -no-split-files
 tlean-loops: SUBDIR :=
 thol4-loops: SUBDIR := misc-loops
 
-trans-hashmap: OPTIONS += -no-state
+trans-hashmap: OPTIONS += -no-state -test-trans-units
 trans-hashmap: SUBDIR := hashmap
 tfstar-hashmap: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap: OPTIONS += -use-fuel
@@ -152,7 +150,7 @@ tlean-hashmap: SUBDIR :=
 tlean-hashmap: OPTIONS +=
 thol4-hashmap: OPTIONS +=
 
-trans-hashmap_main: OPTIONS +=
+trans-hashmap_main: OPTIONS += -test-trans-units
 trans-hashmap_main: SUBDIR := hashmap_on_disk
 tfstar-hashmap_main: OPTIONS += -decreases-clauses -template-clauses
 tcoq-hashmap_main: OPTIONS += -use-fuel
@@ -177,7 +175,7 @@ tlean-constants: OPTIONS +=
 thol4-constants: SUBDIR := misc-constants
 thol4-constants: OPTIONS +=
 
-trans-external: OPTIONS +=
+trans-external: OPTIONS += -test-trans-units
 trans-external: SUBDIR := misc
 tfstar-external: OPTIONS +=
 tcoq-external: OPTIONS +=
@@ -187,7 +185,7 @@ thol4-external: SUBDIR := misc-external
 thol4-external: OPTIONS +=
 
 BETREE_FSTAR_OPTIONS = -decreases-clauses -template-clauses
-transp-betree_main: OPTIONS += -backward-no-state-update
+transp-betree_main: OPTIONS += -backward-no-state-update -test-trans-units
 transp-betree_main: SUBDIR:=betree
 tfstarp-betree_main: OPTIONS += $(BETREE_FSTAR_OPTIONS)
 tcoqp-betree_main: OPTIONS += -use-fuel
@@ -239,20 +237,20 @@ transp-%: gen-llbcp-% tfstarp-% tcoqp-% tleanp-% thol4p-%
 	echo "# Test $* done"
 
 .PHONY: tfstar-%
-tfstar-%: OPTIONS += -backend fstar -test-trans-units
+tfstar-%: OPTIONS += -backend fstar
 tfstar-%: BACKEND_SUBDIR := fstar
 tfstar-%:
 	$(AENEAS_CMD)
 
 # "p" stands for "Polonius"
 .PHONY: tfstarp-%
-tfstarp-%: OPTIONS += -backend fstar -test-trans-units
+tfstarp-%: OPTIONS += -backend fstar
 tfstarp-%: BACKEND_SUBDIR := fstar
 tfstarp-%:
 	$(AENEAS_CMD)
 
 .PHONY: tcoq-%
-tcoq-%: OPTIONS += -backend coq -test-trans-units
+tcoq-%: OPTIONS += -backend coq
 tcoq-%: BACKEND_SUBDIR := coq
 tcoq-%:
 	$(AENEAS_CMD)
@@ -265,7 +263,7 @@ tcoqp-%:
 	$(AENEAS_CMD)
 
 .PHONY: tlean-%
-tlean-%: OPTIONS += -backend lean -test-trans-units
+tlean-%: OPTIONS += -backend lean
 tlean-%: BACKEND_SUBDIR := lean
 tlean-%:
 	$(AENEAS_CMD)
@@ -273,19 +271,19 @@ tlean-%:
 # "p" stands for "Polonius"
 .PHONY: tleanp-%
 
-tleanp-%: OPTIONS += -backend lean -test-trans-units
+tleanp-%: OPTIONS += -backend lean
 tleanp-%: BACKEND_SUBDIR := lean
 tleanp-%:
 	$(AENEAS_CMD)
 
 .PHONY: thol4-%
-thol4-%: OPTIONS += -backend hol4 -test-trans-units
+thol4-%: OPTIONS += -backend hol4
 thol4-%: BACKEND_SUBDIR := hol4
 thol4-%:
 	$(AENEAS_CMD)
 
 .PHONY: thol4p-%
-thol4p-%: OPTIONS += -backend hol4 -test-trans-units
+thol4p-%: OPTIONS += -backend hol4
 thol4p-%: BACKEND_SUBDIR := hol4
 thol4p-%:
 	$(AENEAS_CMD)
diff --git a/backends/coq/Primitives.v b/backends/coq/Primitives.v
index d462715f..71a2d9c3 100644
--- a/backends/coq/Primitives.v
+++ b/backends/coq/Primitives.v
@@ -213,7 +213,6 @@ Proof.
   pose (scalar_max_cons_valid ty).
   lia.
 Qed.
-Print scalar_le_max_valid.
 
 Definition scalar_in_bounds (ty: scalar_ty) (x: Z) : bool :=
   scalar_ge_min ty x && scalar_le_max ty x .
diff --git a/tests/coq/betree/BetreeMain_Funs.v b/tests/coq/betree/BetreeMain_Funs.v
index 86a9d5f2..85aecfc8 100644
--- a/tests/coq/betree/BetreeMain_Funs.v
+++ b/tests/coq/betree/BetreeMain_Funs.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Require Export BetreeMain_Types.
 Import BetreeMain_Types.
@@ -1190,4 +1192,7 @@ Definition betree_be_tree_lookup_back
 Definition main_fwd : result unit :=
   Return tt.
 
+(** Unit test for [betree_main::main] *)
+Check (main_fwd )%return.
+
 End BetreeMain_Funs .
diff --git a/tests/coq/betree/BetreeMain_Opaque.v b/tests/coq/betree/BetreeMain_Opaque.v
index bd49500b..ecd81b9d 100644
--- a/tests/coq/betree/BetreeMain_Opaque.v
+++ b/tests/coq/betree/BetreeMain_Opaque.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Require Export BetreeMain_Types.
 Import BetreeMain_Types.
diff --git a/tests/coq/betree/BetreeMain_Types.v b/tests/coq/betree/BetreeMain_Types.v
index 25f280dd..c8af54cd 100644
--- a/tests/coq/betree/BetreeMain_Types.v
+++ b/tests/coq/betree/BetreeMain_Types.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module BetreeMain_Types.
 
diff --git a/tests/coq/betree/Primitives.v b/tests/coq/betree/Primitives.v
index ae961ac2..71a2d9c3 100644
--- a/tests/coq/betree/Primitives.v
+++ b/tests/coq/betree/Primitives.v
@@ -394,13 +394,15 @@ 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.
 
-(*** Vectors *)
-
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+(*** Range *)
+Record range (T : Type) := mk_range {
+  start: T;
+  end_: T;
+}.
+Arguments mk_range {_}.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
-
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+(*** 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.
@@ -409,6 +411,47 @@ Proof.
   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.
+
+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).
+
+(*** 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).
+
+(*** 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_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).
+
+(*** Vectors *)
+
+Definition 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 vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+
 Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
 
 Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index c8630eb6..c412abcd 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Require Export Hashmap_Types.
 Import Hashmap_Types.
diff --git a/tests/coq/hashmap/Hashmap_Types.v b/tests/coq/hashmap/Hashmap_Types.v
index ce6e7dab..dbde6be9 100644
--- a/tests/coq/hashmap/Hashmap_Types.v
+++ b/tests/coq/hashmap/Hashmap_Types.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Hashmap_Types.
 
diff --git a/tests/coq/hashmap/Primitives.v b/tests/coq/hashmap/Primitives.v
index ae961ac2..71a2d9c3 100644
--- a/tests/coq/hashmap/Primitives.v
+++ b/tests/coq/hashmap/Primitives.v
@@ -394,13 +394,15 @@ 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.
 
-(*** Vectors *)
-
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+(*** Range *)
+Record range (T : Type) := mk_range {
+  start: T;
+  end_: T;
+}.
+Arguments mk_range {_}.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
-
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+(*** 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.
@@ -409,6 +411,47 @@ Proof.
   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.
+
+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).
+
+(*** 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).
+
+(*** 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_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).
+
+(*** Vectors *)
+
+Definition 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 vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+
 Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
 
 Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index 1b7304cc..e6095fe1 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Require Export HashmapMain_Types.
 Import HashmapMain_Types.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
index 1ad9c697..2d17cc29 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Opaque.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Require Export HashmapMain_Types.
 Import HashmapMain_Types.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Types.v b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
index b92cbf3a..36aaaf25 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Types.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Types.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module HashmapMain_Types.
 
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v
index ae961ac2..71a2d9c3 100644
--- a/tests/coq/hashmap_on_disk/Primitives.v
+++ b/tests/coq/hashmap_on_disk/Primitives.v
@@ -394,13 +394,15 @@ 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.
 
-(*** Vectors *)
-
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+(*** Range *)
+Record range (T : Type) := mk_range {
+  start: T;
+  end_: T;
+}.
+Arguments mk_range {_}.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
-
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+(*** 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.
@@ -409,6 +411,47 @@ Proof.
   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.
+
+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).
+
+(*** 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).
+
+(*** 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_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).
+
+(*** Vectors *)
+
+Definition 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 vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+
 Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
 
 Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index 14c05c61..710ae1d9 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Constants.
 
diff --git a/tests/coq/misc/External_Funs.v b/tests/coq/misc/External_Funs.v
index f18bbd1f..28370b2b 100644
--- a/tests/coq/misc/External_Funs.v
+++ b/tests/coq/misc/External_Funs.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Require Export External_Types.
 Import External_Types.
diff --git a/tests/coq/misc/External_Opaque.v b/tests/coq/misc/External_Opaque.v
index 1224f426..d2ee42d4 100644
--- a/tests/coq/misc/External_Opaque.v
+++ b/tests/coq/misc/External_Opaque.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Require Export External_Types.
 Import External_Types.
diff --git a/tests/coq/misc/External_Types.v b/tests/coq/misc/External_Types.v
index cec5b88e..1883fa6c 100644
--- a/tests/coq/misc/External_Types.v
+++ b/tests/coq/misc/External_Types.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module External_Types.
 
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index f17eb986..82e57576 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Loops.
 
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index 470a2cde..f93254e1 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module NoNestedBorrows.
 
diff --git a/tests/coq/misc/Paper.v b/tests/coq/misc/Paper.v
index 0f854f31..175a523d 100644
--- a/tests/coq/misc/Paper.v
+++ b/tests/coq/misc/Paper.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Paper.
 
diff --git a/tests/coq/misc/PoloniusList.v b/tests/coq/misc/PoloniusList.v
index e94b6dcb..54021bdf 100644
--- a/tests/coq/misc/PoloniusList.v
+++ b/tests/coq/misc/PoloniusList.v
@@ -3,6 +3,8 @@
 Require Import Primitives.
 Import Primitives.
 Require Import Coq.ZArith.ZArith.
+Require Import List.
+Import ListNotations.
 Local Open Scope Primitives_scope.
 Module PoloniusList.
 
diff --git a/tests/coq/misc/Primitives.v b/tests/coq/misc/Primitives.v
index ae961ac2..71a2d9c3 100644
--- a/tests/coq/misc/Primitives.v
+++ b/tests/coq/misc/Primitives.v
@@ -394,13 +394,15 @@ 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.
 
-(*** Vectors *)
-
-Definition vec T := { l: list T | Z.of_nat (length l) <= usize_max }.
+(*** Range *)
+Record range (T : Type) := mk_range {
+  start: T;
+  end_: T;
+}.
+Arguments mk_range {_}.
 
-Definition vec_to_list {T: Type} (v: vec T) : list T := proj1_sig v.
-
-Definition vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+(*** 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.
@@ -409,6 +411,47 @@ Proof.
   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.
+
+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).
+
+(*** 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).
+
+(*** 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_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).
+
+(*** Vectors *)
+
+Definition 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 vec_length {T: Type} (v: vec T) : Z := Z.of_nat (length (vec_to_list v)).
+
 Definition vec_new (T: Type) : vec T := (exist _ [] le_0_usize_max).
 
 Lemma vec_len_in_usize {T} (v: vec T) : usize_min <= vec_length v <= usize_max.
diff --git a/tests/fstar/betree/Primitives.fst b/tests/fstar/betree/Primitives.fst
index 98a696b6..9db82069 100644
--- a/tests/fstar/betree/Primitives.fst
+++ b/tests/fstar/betree/Primitives.fst
@@ -259,6 +259,81 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
+(*** Range *)
+type range (a : Type0) = {
+  start : a;
+  end_ : a;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+  (l : list a) :
+  Pure (array a n)
+  (requires (normalize_term(FStar.List.Tot.length l) = n))
+  (ensures (fun _ -> True)) =
+  normalize_term_spec (FStar.List.Tot.length l);
+  l
+
+let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+  if length s = n then Return s
+  else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+  admit()
+
+let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+  admit()
+
 (*** Vector *)
 type vec (a : Type0) = v:list a{length v <= usize_max}
 
diff --git a/tests/fstar/betree_back_stateful/Primitives.fst b/tests/fstar/betree_back_stateful/Primitives.fst
index 98a696b6..9db82069 100644
--- a/tests/fstar/betree_back_stateful/Primitives.fst
+++ b/tests/fstar/betree_back_stateful/Primitives.fst
@@ -259,6 +259,81 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
+(*** Range *)
+type range (a : Type0) = {
+  start : a;
+  end_ : a;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+  (l : list a) :
+  Pure (array a n)
+  (requires (normalize_term(FStar.List.Tot.length l) = n))
+  (ensures (fun _ -> True)) =
+  normalize_term_spec (FStar.List.Tot.length l);
+  l
+
+let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+  if length s = n then Return s
+  else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+  admit()
+
+let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+  admit()
+
 (*** Vector *)
 type vec (a : Type0) = v:list a{length v <= usize_max}
 
diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst
index 98a696b6..9db82069 100644
--- a/tests/fstar/hashmap/Primitives.fst
+++ b/tests/fstar/hashmap/Primitives.fst
@@ -259,6 +259,81 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
+(*** Range *)
+type range (a : Type0) = {
+  start : a;
+  end_ : a;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+  (l : list a) :
+  Pure (array a n)
+  (requires (normalize_term(FStar.List.Tot.length l) = n))
+  (ensures (fun _ -> True)) =
+  normalize_term_spec (FStar.List.Tot.length l);
+  l
+
+let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+  if length s = n then Return s
+  else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+  admit()
+
+let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+  admit()
+
 (*** Vector *)
 type vec (a : Type0) = v:list a{length v <= usize_max}
 
diff --git a/tests/fstar/hashmap_on_disk/Primitives.fst b/tests/fstar/hashmap_on_disk/Primitives.fst
index 98a696b6..9db82069 100644
--- a/tests/fstar/hashmap_on_disk/Primitives.fst
+++ b/tests/fstar/hashmap_on_disk/Primitives.fst
@@ -259,6 +259,81 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
+(*** Range *)
+type range (a : Type0) = {
+  start : a;
+  end_ : a;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+  (l : list a) :
+  Pure (array a n)
+  (requires (normalize_term(FStar.List.Tot.length l) = n))
+  (ensures (fun _ -> True)) =
+  normalize_term_spec (FStar.List.Tot.length l);
+  l
+
+let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+  if length s = n then Return s
+  else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+  admit()
+
+let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+  admit()
+
 (*** Vector *)
 type vec (a : Type0) = v:list a{length v <= usize_max}
 
diff --git a/tests/fstar/misc/Primitives.fst b/tests/fstar/misc/Primitives.fst
index 98a696b6..9db82069 100644
--- a/tests/fstar/misc/Primitives.fst
+++ b/tests/fstar/misc/Primitives.fst
@@ -259,6 +259,81 @@ let u32_mul = scalar_mul #U32
 let u64_mul = scalar_mul #U64
 let u128_mul = scalar_mul #U128
 
+(*** Range *)
+type range (a : Type0) = {
+  start : a;
+  end_ : a;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+  (l : list a) :
+  Pure (array a n)
+  (requires (normalize_term(FStar.List.Tot.length l) = n))
+  (ensures (fun _ -> True)) =
+  normalize_term_spec (FStar.List.Tot.length l);
+  l
+
+let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a =
+  if i < length x then Return (index x i)
+  else Fail Failure
+
+let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+  if i < length x then Return (list_update x i nx)
+  else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+  if length s = n then Return s
+  else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) =
+  admit()
+
+let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) =
+  admit()
+
+let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) =
+  admit()
+
+let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) =
+  admit()
+
 (*** Vector *)
 type vec (a : Type0) = v:list a{length v <= usize_max}
 
diff --git a/tests/lean/Array/Funs.lean b/tests/lean/Array/Funs.lean
index b1365143..8a2c1045 100644
--- a/tests/lean/Array/Funs.lean
+++ b/tests/lean/Array/Funs.lean
@@ -9,24 +9,24 @@ namespace array
 /- [array::array_to_shared_slice_]: forward function -/
 def array_to_shared_slice_
   (T : Type) (s : Array T (Usize.ofInt 32)) : Result (Slice T) :=
-  Array.to_slice T (Usize.ofInt 32) s
+  Array.to_slice_shared T (Usize.ofInt 32) s
 
 /- [array::array_to_mut_slice_]: forward function -/
 def array_to_mut_slice_
   (T : Type) (s : Array T (Usize.ofInt 32)) : Result (Slice T) :=
-  Array.to_mut_slice T (Usize.ofInt 32) s
+  Array.to_slice_mut T (Usize.ofInt 32) s
 
 /- [array::array_to_mut_slice_]: backward function 0 -/
 def array_to_mut_slice__back
   (T : Type) (s : Array T (Usize.ofInt 32)) (ret0 : Slice T) :
   Result (Array T (Usize.ofInt 32))
   :=
-  Array.to_mut_slice_back T (Usize.ofInt 32) s ret0
+  Array.to_slice_mut_back T (Usize.ofInt 32) s ret0
 
 /- [array::array_len]: forward function -/
 def array_len (T : Type) (s : Array T (Usize.ofInt 32)) : Result Usize :=
   do
-    let s0 ← Array.to_slice T (Usize.ofInt 32) s
+    let s0 ← Array.to_slice_shared T (Usize.ofInt 32) s
     let i := Slice.len T s0
     Result.ret i
 
@@ -34,7 +34,7 @@ def array_len (T : Type) (s : Array T (Usize.ofInt 32)) : Result Usize :=
 def shared_array_len
   (T : Type) (s : Array T (Usize.ofInt 32)) : Result Usize :=
   do
-    let s0 ← Array.to_slice T (Usize.ofInt 32) s
+    let s0 ← Array.to_slice_shared T (Usize.ofInt 32) s
     let i := Slice.len T s0
     Result.ret i
 
@@ -109,21 +109,22 @@ def slice_subslice_mut__back
   :=
   Slice.subslice_mut_back U32 x (Range.mk y z) ret0
 
-/- [array::array_to_slice_shared]: forward function -/
-def array_to_slice_shared
+/- [array::array_to_slice_shared_]: forward function -/
+def array_to_slice_shared_
   (x : Array U32 (Usize.ofInt 32)) : Result (Slice U32) :=
-  Array.to_slice U32 (Usize.ofInt 32) x
+  Array.to_slice_shared U32 (Usize.ofInt 32) x
 
-/- [array::array_to_slice_mut]: forward function -/
-def array_to_slice_mut (x : Array U32 (Usize.ofInt 32)) : Result (Slice U32) :=
-  Array.to_mut_slice U32 (Usize.ofInt 32) x
+/- [array::array_to_slice_mut_]: forward function -/
+def array_to_slice_mut_
+  (x : Array U32 (Usize.ofInt 32)) : Result (Slice U32) :=
+  Array.to_slice_mut U32 (Usize.ofInt 32) x
 
-/- [array::array_to_slice_mut]: backward function 0 -/
-def array_to_slice_mut_back
+/- [array::array_to_slice_mut_]: backward function 0 -/
+def array_to_slice_mut__back
   (x : Array U32 (Usize.ofInt 32)) (ret0 : Slice U32) :
   Result (Array U32 (Usize.ofInt 32))
   :=
-  Array.to_mut_slice_back U32 (Usize.ofInt 32) x ret0
+  Array.to_slice_mut_back U32 (Usize.ofInt 32) x ret0
 
 /- [array::array_subslice_shared_]: forward function -/
 def array_subslice_shared_
@@ -186,17 +187,14 @@ def array_local_deep_copy (x : Array U32 (Usize.ofInt 32)) : Result Unit :=
 def f0 : Result Unit :=
   do
     let s ←
-      Array.to_mut_slice U32 (Usize.ofInt 2)
+      Array.to_slice_mut U32 (Usize.ofInt 2)
         (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
     let s0 ← Slice.index_mut_back U32 s (Usize.ofInt 0) (U32.ofInt 1)
     let _ ←
-      Array.to_mut_slice_back U32 (Usize.ofInt 2)
+      Array.to_slice_mut_back U32 (Usize.ofInt 2)
         (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ]) s0
     Result.ret ()
 
-/- Unit test for [array::f0] -/
-#assert (f0 == .ret ())
-
 /- [array::f1]: forward function -/
 def f1 : Result Unit :=
   do
@@ -206,9 +204,6 @@ def f1 : Result Unit :=
         (Usize.ofInt 0) (U32.ofInt 1)
     Result.ret ()
 
-/- Unit test for [array::f1] -/
-#assert (f1 == .ret ())
-
 /- [array::sum]: loop 0: forward function -/
 divergent def sum_loop (s : Slice U32) (sum0 : U32) (i : Usize) : Result U32 :=
   let i0 := Slice.len U32 s
@@ -268,7 +263,7 @@ def f3 : Result U32 :=
         (Usize.ofInt 0)
     let _ ← f2 i
     let s ←
-      Array.to_slice U32 (Usize.ofInt 2)
+      Array.to_slice_shared U32 (Usize.ofInt 2)
         (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
     let s0 ←
       f4
-- 
cgit v1.3.1


From a106d3170eb784d23cd3614a21ef8f1bbb3be2f4 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Fri, 4 Aug 2023 22:59:21 +0200
Subject: Fix a heart beat issue in a Lean proof

---
 tests/lean/Hashmap/Properties.lean | 4 ++++
 1 file changed, 4 insertions(+)

(limited to 'tests/lean')

diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean
index 3652f608..ab95b854 100644
--- a/tests/lean/Hashmap/Properties.lean
+++ b/tests/lean/Hashmap/Properties.lean
@@ -284,6 +284,10 @@ def mk_opaque {α : Sort u} (x : α) : { y : α // y = x}  :=
 attribute [pp_dot] List.length -- use the dot notation when printing
 set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse)
 
+-- The proof below is a bit expensive, so we need to increase the maximum number
+-- of heart beats
+set_option maxHeartbeats 400000
+
 theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value : α)
   (hinv : hm.inv) (hnsat : hm.lookup key = none → hm.len_s < Usize.max) :
   ∃ nhm, hm.insert_no_resize α key value = ret nhm  ∧
-- 
cgit v1.3.1


From d25287dcc5435d3784de284dafe3746e13467f49 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Mon, 7 Aug 2023 08:59:59 +0200
Subject: Regenerate the test files

---
 tests/coq/array/Array_Funs.v      | 187 ++++++++++++++++++++++++--
 tests/coq/array/Array_Types.v     |   3 +
 tests/fstar/array/Array.Funs.fst  | 145 +++++++++++++++++++--
 tests/fstar/array/Array.Types.fst |   3 +
 tests/lean/Array/Funs.lean        | 267 ++++++++++++++++++++++++++++++++------
 tests/lean/Array/Types.lean       |   5 +
 6 files changed, 550 insertions(+), 60 deletions(-)

(limited to 'tests/lean')

diff --git a/tests/coq/array/Array_Funs.v b/tests/coq/array/Array_Funs.v
index 4a862d1b..6d791873 100644
--- a/tests/coq/array/Array_Funs.v
+++ b/tests/coq/array/Array_Funs.v
@@ -199,25 +199,156 @@ Definition array_local_deep_copy_fwd (x : array u32 32%usize) : result unit :=
   Return tt
 .
 
-(** [array::f0]: forward function *)
-Definition f0_fwd : result unit :=
+(** [array::take_array]: forward function *)
+Definition take_array_fwd (a : array u32 2%usize) : result unit :=
+  Return tt.
+
+(** [array::take_array_borrow]: forward function *)
+Definition take_array_borrow_fwd (a : array u32 2%usize) : result unit :=
+  Return tt
+.
+
+(** [array::take_slice]: forward function *)
+Definition take_slice_fwd (s : slice u32) : result unit :=
+  Return tt.
+
+(** [array::take_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition take_mut_slice_fwd_back (s : slice u32) : result (slice u32) :=
+  Return s
+.
+
+(** [array::take_all]: forward function *)
+Definition take_all_fwd : result unit :=
+  _ <- take_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_array_borrow_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
   s <-
-    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
-  s0 <- slice_index_mut_back u32 s 0%usize 1%u32;
+    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  _ <- take_slice_fwd s;
+  s0 <-
+    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s1 <- take_mut_slice_fwd_back s0;
   _ <-
-    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      s0;
+    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
+      s1;
   Return tt
 .
 
-(** [array::f1]: forward function *)
-Definition f1_fwd : result unit :=
+(** [array::index_array]: forward function *)
+Definition index_array_fwd (x : array u32 2%usize) : result u32 :=
+  array_index_shared u32 2%usize x 0%usize
+.
+
+(** [array::index_array_borrow]: forward function *)
+Definition index_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
+  array_index_shared u32 2%usize x 0%usize
+.
+
+(** [array::index_slice_u32_0]: forward function *)
+Definition index_slice_u32_0_fwd (x : slice u32) : result u32 :=
+  slice_index_shared u32 x 0%usize
+.
+
+(** [array::index_mut_slice_u32_0]: forward function *)
+Definition index_mut_slice_u32_0_fwd (x : slice u32) : result u32 :=
+  slice_index_shared u32 x 0%usize
+.
+
+(** [array::index_mut_slice_u32_0]: backward function 0 *)
+Definition index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) :=
+  _ <- slice_index_shared u32 x 0%usize; Return x
+.
+
+(** [array::index_all]: forward function *)
+Definition index_all_fwd : result u32 :=
+  i <- index_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i0 <- index_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i1 <- u32_add i i0;
+  i2 <- index_array_borrow_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i3 <- u32_add i1 i2;
+  s <-
+    array_to_slice_shared u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i4 <- index_slice_u32_0_fwd s;
+  i5 <- u32_add i3 i4;
+  s0 <-
+    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  i6 <- index_mut_slice_u32_0_fwd s0;
+  i7 <- u32_add i5 i6;
+  s1 <- index_mut_slice_u32_0_back s0;
   _ <-
-    array_index_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
-      0%usize 1%u32;
+    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
+      s1;
+  Return i7
+.
+
+(** [array::update_array]: forward function *)
+Definition update_array_fwd (x : array u32 2%usize) : result unit :=
+  _ <- array_index_mut_back u32 2%usize x 0%usize 1%u32; Return tt
+.
+
+(** [array::update_array_mut_borrow]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition update_array_mut_borrow_fwd_back
+  (x : array u32 2%usize) : result (array u32 2%usize) :=
+  array_index_mut_back u32 2%usize x 0%usize 1%u32
+.
+
+(** [array::update_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+Definition update_mut_slice_fwd_back (x : slice u32) : result (slice u32) :=
+  slice_index_mut_back u32 x 0%usize 1%u32
+.
+
+(** [array::update_all]: forward function *)
+Definition update_all_fwd : result unit :=
+  _ <- update_array_fwd (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  x <-
+    update_array_mut_borrow_fwd_back (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s <- array_to_slice_mut_fwd u32 2%usize x;
+  s0 <- update_mut_slice_fwd_back s;
+  _ <- array_to_slice_mut_back u32 2%usize x s0;
   Return tt
 .
 
+(** [array::range_all]: forward function *)
+Definition range_all_fwd : result unit :=
+  s <-
+    array_subslice_mut_fwd u32 4%usize
+      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ]) (mk_range 1%usize
+      3%usize);
+  s0 <- update_mut_slice_fwd_back s;
+  _ <-
+    array_subslice_mut_back u32 4%usize
+      (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ]) (mk_range 1%usize
+      3%usize) s0;
+  Return tt
+.
+
+(** [array::deref_array_borrow]: forward function *)
+Definition deref_array_borrow_fwd (x : array u32 2%usize) : result u32 :=
+  array_index_shared u32 2%usize x 0%usize
+.
+
+(** [array::deref_array_mut_borrow]: forward function *)
+Definition deref_array_mut_borrow_fwd (x : array u32 2%usize) : result u32 :=
+  array_index_shared u32 2%usize x 0%usize
+.
+
+(** [array::deref_array_mut_borrow]: backward function 0 *)
+Definition deref_array_mut_borrow_back
+  (x : array u32 2%usize) : result (array u32 2%usize) :=
+  _ <- array_index_shared u32 2%usize x 0%usize; Return x
+.
+
+(** [array::take_array_t]: forward function *)
+Definition take_array_t_fwd (a : array T_t 2%usize) : result unit :=
+  Return tt.
+
+(** [array::non_copyable_array]: forward function *)
+Definition non_copyable_array_fwd : result unit :=
+  _ <- take_array_t_fwd (mk_array T_t 2%usize [ TA; TB ]); Return tt
+.
+
 (** [array::sum]: loop 0: forward function *)
 Fixpoint sum_loop_fwd
   (n : nat) (s : slice u32) (sum : u32) (i : usize) : result u32 :=
@@ -268,6 +399,25 @@ Definition sum2_fwd (n : nat) (s : slice u32) (s2 : slice u32) : result u32 :=
   if negb (i s= i0) then Fail_ Failure else sum2_loop_fwd n s s2 0%u32 0%usize
 .
 
+(** [array::f0]: forward function *)
+Definition f0_fwd : result unit :=
+  s <-
+    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ]);
+  s0 <- slice_index_mut_back u32 s 0%usize 1%u32;
+  _ <-
+    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      s0;
+  Return tt
+.
+
+(** [array::f1]: forward function *)
+Definition f1_fwd : result unit :=
+  _ <-
+    array_index_mut_back u32 2%usize (mk_array u32 2%usize [ 1%u32; 2%u32 ])
+      0%usize 1%u32;
+  Return tt
+.
+
 (** [array::f2]: forward function *)
 Definition f2_fwd (i : u32) : result unit :=
   Return tt.
@@ -297,4 +447,21 @@ Definition f3_fwd (n : nat) : result u32 :=
   sum2_fwd n s s0
 .
 
+(** [array::ite]: forward function *)
+Definition ite_fwd : result unit :=
+  s <-
+    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s0 <-
+    array_to_slice_mut_fwd u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ]);
+  s1 <- index_mut_slice_u32_0_back s0;
+  _ <-
+    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
+      s1;
+  s2 <- index_mut_slice_u32_0_back s;
+  _ <-
+    array_to_slice_mut_back u32 2%usize (mk_array u32 2%usize [ 0%u32; 0%u32 ])
+      s2;
+  Return tt
+.
+
 End Array_Funs .
diff --git a/tests/coq/array/Array_Types.v b/tests/coq/array/Array_Types.v
index 7e1f2a07..7be6dc9b 100644
--- a/tests/coq/array/Array_Types.v
+++ b/tests/coq/array/Array_Types.v
@@ -8,4 +8,7 @@ Import ListNotations.
 Local Open Scope Primitives_scope.
 Module Array_Types.
 
+(** [array::T] *)
+Inductive T_t := | TA : T_t | TB : T_t.
+
 End Array_Types .
diff --git a/tests/fstar/array/Array.Funs.fst b/tests/fstar/array/Array.Funs.fst
index 985633bc..7c1d0b09 100644
--- a/tests/fstar/array/Array.Funs.fst
+++ b/tests/fstar/array/Array.Funs.fst
@@ -151,18 +151,125 @@ let update_update_array_fwd
 let array_local_deep_copy_fwd (x : array u32 32) : result unit =
   Return ()
 
-(** [array::f0]: forward function *)
-let f0_fwd : result unit =
-  let* s = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 1; 2 ]) in
-  let* s0 = slice_index_mut_back u32 s 0 1 in
-  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 1; 2 ]) s0 in
+(** [array::take_array]: forward function *)
+let take_array_fwd (a : array u32 2) : result unit =
   Return ()
 
-(** [array::f1]: forward function *)
-let f1_fwd : result unit =
-  let* _ = array_index_mut_back u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in
+(** [array::take_array_borrow]: forward function *)
+let take_array_borrow_fwd (a : array u32 2) : result unit =
+  Return ()
+
+(** [array::take_slice]: forward function *)
+let take_slice_fwd (s : slice u32) : result unit =
+  Return ()
+
+(** [array::take_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+let take_mut_slice_fwd_back (s : slice u32) : result (slice u32) =
+  Return s
+
+(** [array::take_all]: forward function *)
+let take_all_fwd : result unit =
+  let* _ = take_array_fwd (mk_array u32 2 [ 0; 0 ]) in
+  let* _ = take_array_borrow_fwd (mk_array u32 2 [ 0; 0 ]) in
+  let* s = array_to_slice_shared u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* _ = take_slice_fwd s in
+  let* s0 = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s1 = take_mut_slice_fwd_back s0 in
+  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
+  Return ()
+
+(** [array::index_array]: forward function *)
+let index_array_fwd (x : array u32 2) : result u32 =
+  array_index_shared u32 2 x 0
+
+(** [array::index_array_borrow]: forward function *)
+let index_array_borrow_fwd (x : array u32 2) : result u32 =
+  array_index_shared u32 2 x 0
+
+(** [array::index_slice_u32_0]: forward function *)
+let index_slice_u32_0_fwd (x : slice u32) : result u32 =
+  slice_index_shared u32 x 0
+
+(** [array::index_mut_slice_u32_0]: forward function *)
+let index_mut_slice_u32_0_fwd (x : slice u32) : result u32 =
+  slice_index_shared u32 x 0
+
+(** [array::index_mut_slice_u32_0]: backward function 0 *)
+let index_mut_slice_u32_0_back (x : slice u32) : result (slice u32) =
+  let* _ = slice_index_shared u32 x 0 in Return x
+
+(** [array::index_all]: forward function *)
+let index_all_fwd : result u32 =
+  let* i = index_array_fwd (mk_array u32 2 [ 0; 0 ]) in
+  let* i0 = index_array_fwd (mk_array u32 2 [ 0; 0 ]) in
+  let* i1 = u32_add i i0 in
+  let* i2 = index_array_borrow_fwd (mk_array u32 2 [ 0; 0 ]) in
+  let* i3 = u32_add i1 i2 in
+  let* s = array_to_slice_shared u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* i4 = index_slice_u32_0_fwd s in
+  let* i5 = u32_add i3 i4 in
+  let* s0 = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* i6 = index_mut_slice_u32_0_fwd s0 in
+  let* i7 = u32_add i5 i6 in
+  let* s1 = index_mut_slice_u32_0_back s0 in
+  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
+  Return i7
+
+(** [array::update_array]: forward function *)
+let update_array_fwd (x : array u32 2) : result unit =
+  let* _ = array_index_mut_back u32 2 x 0 1 in Return ()
+
+(** [array::update_array_mut_borrow]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+let update_array_mut_borrow_fwd_back (x : array u32 2) : result (array u32 2) =
+  array_index_mut_back u32 2 x 0 1
+
+(** [array::update_mut_slice]: merged forward/backward function
+    (there is a single backward function, and the forward function returns ()) *)
+let update_mut_slice_fwd_back (x : slice u32) : result (slice u32) =
+  slice_index_mut_back u32 x 0 1
+
+(** [array::update_all]: forward function *)
+let update_all_fwd : result unit =
+  let* _ = update_array_fwd (mk_array u32 2 [ 0; 0 ]) in
+  let* x = update_array_mut_borrow_fwd_back (mk_array u32 2 [ 0; 0 ]) in
+  let* s = array_to_slice_mut_fwd u32 2 x in
+  let* s0 = update_mut_slice_fwd_back s in
+  let* _ = array_to_slice_mut_back u32 2 x s0 in
+  Return ()
+
+(** [array::range_all]: forward function *)
+let range_all_fwd : result unit =
+  let* s =
+    array_subslice_mut_fwd u32 4 (mk_array u32 4 [ 0; 0; 0; 0 ]) (Mkrange 1 3)
+    in
+  let* s0 = update_mut_slice_fwd_back s in
+  let* _ =
+    array_subslice_mut_back u32 4 (mk_array u32 4 [ 0; 0; 0; 0 ]) (Mkrange 1 3)
+      s0 in
+  Return ()
+
+(** [array::deref_array_borrow]: forward function *)
+let deref_array_borrow_fwd (x : array u32 2) : result u32 =
+  array_index_shared u32 2 x 0
+
+(** [array::deref_array_mut_borrow]: forward function *)
+let deref_array_mut_borrow_fwd (x : array u32 2) : result u32 =
+  array_index_shared u32 2 x 0
+
+(** [array::deref_array_mut_borrow]: backward function 0 *)
+let deref_array_mut_borrow_back (x : array u32 2) : result (array u32 2) =
+  let* _ = array_index_shared u32 2 x 0 in Return x
+
+(** [array::take_array_t]: forward function *)
+let take_array_t_fwd (a : array t_t 2) : result unit =
   Return ()
 
+(** [array::non_copyable_array]: forward function *)
+let non_copyable_array_fwd : result unit =
+  let* _ = take_array_t_fwd (mk_array t_t 2 [ TA; TB ]) in Return ()
+
 (** [array::sum]: loop 0: forward function *)
 let rec sum_loop_fwd
   (s : slice u32) (sum : u32) (i : usize) :
@@ -203,6 +310,18 @@ let sum2_fwd (s : slice u32) (s2 : slice u32) : result u32 =
   let i0 = slice_len u32 s2 in
   if not (i = i0) then Fail Failure else sum2_loop_fwd s s2 0 0
 
+(** [array::f0]: forward function *)
+let f0_fwd : result unit =
+  let* s = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 1; 2 ]) in
+  let* s0 = slice_index_mut_back u32 s 0 1 in
+  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 1; 2 ]) s0 in
+  Return ()
+
+(** [array::f1]: forward function *)
+let f1_fwd : result unit =
+  let* _ = array_index_mut_back u32 2 (mk_array u32 2 [ 1; 2 ]) 0 1 in
+  Return ()
+
 (** [array::f2]: forward function *)
 let f2_fwd (i : u32) : result unit =
   Return ()
@@ -224,3 +343,13 @@ let f3_fwd : result u32 =
         ]) 16 18 in
   sum2_fwd s s0
 
+(** [array::ite]: forward function *)
+let ite_fwd : result unit =
+  let* s = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s0 = array_to_slice_mut_fwd u32 2 (mk_array u32 2 [ 0; 0 ]) in
+  let* s1 = index_mut_slice_u32_0_back s0 in
+  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s1 in
+  let* s2 = index_mut_slice_u32_0_back s in
+  let* _ = array_to_slice_mut_back u32 2 (mk_array u32 2 [ 0; 0 ]) s2 in
+  Return ()
+
diff --git a/tests/fstar/array/Array.Types.fst b/tests/fstar/array/Array.Types.fst
index d20f1718..5e8e81d8 100644
--- a/tests/fstar/array/Array.Types.fst
+++ b/tests/fstar/array/Array.Types.fst
@@ -5,3 +5,6 @@ open Primitives
 
 #set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
 
+(** [array::T] *)
+type t_t = | TA : t_t | TB : t_t
+
diff --git a/tests/lean/Array/Funs.lean b/tests/lean/Array/Funs.lean
index 8a2c1045..ad737dca 100644
--- a/tests/lean/Array/Funs.lean
+++ b/tests/lean/Array/Funs.lean
@@ -8,45 +8,45 @@ namespace array
 
 /- [array::array_to_shared_slice_]: forward function -/
 def array_to_shared_slice_
-  (T : Type) (s : Array T (Usize.ofInt 32)) : Result (Slice T) :=
-  Array.to_slice_shared T (Usize.ofInt 32) s
+  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result (Slice T0) :=
+  Array.to_slice_shared T0 (Usize.ofInt 32) s
 
 /- [array::array_to_mut_slice_]: forward function -/
 def array_to_mut_slice_
-  (T : Type) (s : Array T (Usize.ofInt 32)) : Result (Slice T) :=
-  Array.to_slice_mut T (Usize.ofInt 32) s
+  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result (Slice T0) :=
+  Array.to_slice_mut T0 (Usize.ofInt 32) s
 
 /- [array::array_to_mut_slice_]: backward function 0 -/
 def array_to_mut_slice__back
-  (T : Type) (s : Array T (Usize.ofInt 32)) (ret0 : Slice T) :
-  Result (Array T (Usize.ofInt 32))
+  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (ret0 : Slice T0) :
+  Result (Array T0 (Usize.ofInt 32))
   :=
-  Array.to_slice_mut_back T (Usize.ofInt 32) s ret0
+  Array.to_slice_mut_back T0 (Usize.ofInt 32) s ret0
 
 /- [array::array_len]: forward function -/
-def array_len (T : Type) (s : Array T (Usize.ofInt 32)) : Result Usize :=
+def array_len (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result Usize :=
   do
-    let s0 ← Array.to_slice_shared T (Usize.ofInt 32) s
-    let i := Slice.len T s0
+    let s0 ← Array.to_slice_shared T0 (Usize.ofInt 32) s
+    let i := Slice.len T0 s0
     Result.ret i
 
 /- [array::shared_array_len]: forward function -/
 def shared_array_len
-  (T : Type) (s : Array T (Usize.ofInt 32)) : Result Usize :=
+  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result Usize :=
   do
-    let s0 ← Array.to_slice_shared T (Usize.ofInt 32) s
-    let i := Slice.len T s0
+    let s0 ← Array.to_slice_shared T0 (Usize.ofInt 32) s
+    let i := Slice.len T0 s0
     Result.ret i
 
 /- [array::shared_slice_len]: forward function -/
-def shared_slice_len (T : Type) (s : Slice T) : Result Usize :=
-  let i := Slice.len T s
+def shared_slice_len (T0 : Type) (s : Slice T0) : Result Usize :=
+  let i := Slice.len T0 s
   Result.ret i
 
 /- [array::index_array_shared]: forward function -/
 def index_array_shared
-  (T : Type) (s : Array T (Usize.ofInt 32)) (i : Usize) : Result T :=
-  Array.index_shared T (Usize.ofInt 32) s i
+  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (i : Usize) : Result T0 :=
+  Array.index_shared T0 (Usize.ofInt 32) s i
 
 /- [array::index_array_u32]: forward function -/
 def index_array_u32
@@ -69,28 +69,28 @@ def index_array_copy (x : Array U32 (Usize.ofInt 32)) : Result U32 :=
 
 /- [array::index_mut_array]: forward function -/
 def index_mut_array
-  (T : Type) (s : Array T (Usize.ofInt 32)) (i : Usize) : Result T :=
-  Array.index_mut T (Usize.ofInt 32) s i
+  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (i : Usize) : Result T0 :=
+  Array.index_mut T0 (Usize.ofInt 32) s i
 
 /- [array::index_mut_array]: backward function 0 -/
 def index_mut_array_back
-  (T : Type) (s : Array T (Usize.ofInt 32)) (i : Usize) (ret0 : T) :
-  Result (Array T (Usize.ofInt 32))
+  (T0 : Type) (s : Array T0 (Usize.ofInt 32)) (i : Usize) (ret0 : T0) :
+  Result (Array T0 (Usize.ofInt 32))
   :=
-  Array.index_mut_back T (Usize.ofInt 32) s i ret0
+  Array.index_mut_back T0 (Usize.ofInt 32) s i ret0
 
 /- [array::index_slice]: forward function -/
-def index_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
-  Slice.index_shared T s i
+def index_slice (T0 : Type) (s : Slice T0) (i : Usize) : Result T0 :=
+  Slice.index_shared T0 s i
 
 /- [array::index_mut_slice]: forward function -/
-def index_mut_slice (T : Type) (s : Slice T) (i : Usize) : Result T :=
-  Slice.index_mut T s i
+def index_mut_slice (T0 : Type) (s : Slice T0) (i : Usize) : Result T0 :=
+  Slice.index_mut T0 s i
 
 /- [array::index_mut_slice]: backward function 0 -/
 def index_mut_slice_back
-  (T : Type) (s : Slice T) (i : Usize) (ret0 : T) : Result (Slice T) :=
-  Slice.index_mut_back T s i ret0
+  (T0 : Type) (s : Slice T0) (i : Usize) (ret0 : T0) : Result (Slice T0) :=
+  Slice.index_mut_back T0 s i ret0
 
 /- [array::slice_subslice_shared_]: forward function -/
 def slice_subslice_shared_
@@ -148,12 +148,12 @@ def array_subslice_mut__back
   Array.subslice_mut_back U32 (Usize.ofInt 32) x (Range.mk y z) ret0
 
 /- [array::index_slice_0]: forward function -/
-def index_slice_0 (T : Type) (s : Slice T) : Result T :=
-  Slice.index_shared T s (Usize.ofInt 0)
+def index_slice_0 (T0 : Type) (s : Slice T0) : Result T0 :=
+  Slice.index_shared T0 s (Usize.ofInt 0)
 
 /- [array::index_array_0]: forward function -/
-def index_array_0 (T : Type) (s : Array T (Usize.ofInt 32)) : Result T :=
-  Array.index_shared T (Usize.ofInt 32) s (Usize.ofInt 0)
+def index_array_0 (T0 : Type) (s : Array T0 (Usize.ofInt 32)) : Result T0 :=
+  Array.index_shared T0 (Usize.ofInt 32) s (Usize.ofInt 0)
 
 /- [array::index_index_array]: forward function -/
 def index_index_array
@@ -183,25 +183,168 @@ def update_update_array
 def array_local_deep_copy (x : Array U32 (Usize.ofInt 32)) : Result Unit :=
   Result.ret ()
 
-/- [array::f0]: forward function -/
-def f0 : Result Unit :=
+/- [array::take_array]: forward function -/
+def take_array (a : Array U32 (Usize.ofInt 2)) : Result Unit :=
+  Result.ret ()
+
+/- [array::take_array_borrow]: forward function -/
+def take_array_borrow (a : Array U32 (Usize.ofInt 2)) : Result Unit :=
+  Result.ret ()
+
+/- [array::take_slice]: forward function -/
+def take_slice (s : Slice U32) : Result Unit :=
+  Result.ret ()
+
+/- [array::take_mut_slice]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def take_mut_slice (s : Slice U32) : Result (Slice U32) :=
+  Result.ret s
+
+/- [array::take_all]: forward function -/
+def take_all : Result Unit :=
   do
+    let _ ←
+      take_array
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let _ ←
+      take_array_borrow
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
     let s ←
+      Array.to_slice_shared U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let _ ← take_slice s
+    let s0 ←
       Array.to_slice_mut U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
-    let s0 ← Slice.index_mut_back U32 s (Usize.ofInt 0) (U32.ofInt 1)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let s1 ← take_mut_slice s0
     let _ ←
       Array.to_slice_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ]) s0
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s1
     Result.ret ()
 
-/- [array::f1]: forward function -/
-def f1 : Result Unit :=
+/- [array::index_array]: forward function -/
+def index_array (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
+  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+
+/- [array::index_array_borrow]: forward function -/
+def index_array_borrow (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
+  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+
+/- [array::index_slice_u32_0]: forward function -/
+def index_slice_u32_0 (x : Slice U32) : Result U32 :=
+  Slice.index_shared U32 x (Usize.ofInt 0)
+
+/- [array::index_mut_slice_u32_0]: forward function -/
+def index_mut_slice_u32_0 (x : Slice U32) : Result U32 :=
+  Slice.index_shared U32 x (Usize.ofInt 0)
+
+/- [array::index_mut_slice_u32_0]: backward function 0 -/
+def index_mut_slice_u32_0_back (x : Slice U32) : Result (Slice U32) :=
   do
+    let _ ← Slice.index_shared U32 x (Usize.ofInt 0)
+    Result.ret x
+
+/- [array::index_all]: forward function -/
+def index_all : Result U32 :=
+  do
+    let i ←
+      index_array
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let i0 ←
+      index_array
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let i1 ← i + i0
+    let i2 ←
+      index_array_borrow
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let i3 ← i1 + i2
+    let s ←
+      Array.to_slice_shared U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let i4 ← index_slice_u32_0 s
+    let i5 ← i3 + i4
+    let s0 ←
+      Array.to_slice_mut U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let i6 ← index_mut_slice_u32_0 s0
+    let i7 ← i5 + i6
+    let s1 ← index_mut_slice_u32_0_back s0
     let _ ←
-      Array.index_mut_back U32 (Usize.ofInt 2)
-        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
-        (Usize.ofInt 0) (U32.ofInt 1)
+      Array.to_slice_mut_back U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s1
+    Result.ret i7
+
+/- [array::update_array]: forward function -/
+def update_array (x : Array U32 (Usize.ofInt 2)) : Result Unit :=
+  do
+    let _ ←
+      Array.index_mut_back U32 (Usize.ofInt 2) x (Usize.ofInt 0) (U32.ofInt 1)
+    Result.ret ()
+
+/- [array::update_array_mut_borrow]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def update_array_mut_borrow
+  (x : Array U32 (Usize.ofInt 2)) : Result (Array U32 (Usize.ofInt 2)) :=
+  Array.index_mut_back U32 (Usize.ofInt 2) x (Usize.ofInt 0) (U32.ofInt 1)
+
+/- [array::update_mut_slice]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def update_mut_slice (x : Slice U32) : Result (Slice U32) :=
+  Slice.index_mut_back U32 x (Usize.ofInt 0) (U32.ofInt 1)
+
+/- [array::update_all]: forward function -/
+def update_all : Result Unit :=
+  do
+    let _ ←
+      update_array
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let x ←
+      update_array_mut_borrow
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let s ← Array.to_slice_mut U32 (Usize.ofInt 2) x
+    let s0 ← update_mut_slice s
+    let _ ← Array.to_slice_mut_back U32 (Usize.ofInt 2) x s0
+    Result.ret ()
+
+/- [array::range_all]: forward function -/
+def range_all : Result Unit :=
+  do
+    let s ←
+      Array.subslice_mut U32 (Usize.ofInt 4)
+        (Array.make U32 (Usize.ofInt 4) [
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0)
+          ]) (Range.mk (Usize.ofInt 1) (Usize.ofInt 3))
+    let s0 ← update_mut_slice s
+    let _ ←
+      Array.subslice_mut_back U32 (Usize.ofInt 4)
+        (Array.make U32 (Usize.ofInt 4) [
+          (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0), (U32.ofInt 0)
+          ]) (Range.mk (Usize.ofInt 1) (Usize.ofInt 3)) s0
+    Result.ret ()
+
+/- [array::deref_array_borrow]: forward function -/
+def deref_array_borrow (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
+  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+
+/- [array::deref_array_mut_borrow]: forward function -/
+def deref_array_mut_borrow (x : Array U32 (Usize.ofInt 2)) : Result U32 :=
+  Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+
+/- [array::deref_array_mut_borrow]: backward function 0 -/
+def deref_array_mut_borrow_back
+  (x : Array U32 (Usize.ofInt 2)) : Result (Array U32 (Usize.ofInt 2)) :=
+  do
+    let _ ← Array.index_shared U32 (Usize.ofInt 2) x (Usize.ofInt 0)
+    Result.ret x
+
+/- [array::take_array_t]: forward function -/
+def take_array_t (a : Array T (Usize.ofInt 2)) : Result Unit :=
+  Result.ret ()
+
+/- [array::non_copyable_array]: forward function -/
+def non_copyable_array : Result Unit :=
+  do
+    let _ ← take_array_t (Array.make T (Usize.ofInt 2) [ T.A, T.B ])
     Result.ret ()
 
 /- [array::sum]: loop 0: forward function -/
@@ -243,6 +386,27 @@ def sum2 (s : Slice U32) (s2 : Slice U32) : Result U32 :=
   then Result.fail Error.panic
   else sum2_loop s s2 (U32.ofInt 0) (Usize.ofInt 0)
 
+/- [array::f0]: forward function -/
+def f0 : Result Unit :=
+  do
+    let s ←
+      Array.to_slice_mut U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
+    let s0 ← Slice.index_mut_back U32 s (Usize.ofInt 0) (U32.ofInt 1)
+    let _ ←
+      Array.to_slice_mut_back U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ]) s0
+    Result.ret ()
+
+/- [array::f1]: forward function -/
+def f1 : Result Unit :=
+  do
+    let _ ←
+      Array.index_mut_back U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 1), (U32.ofInt 2) ])
+        (Usize.ofInt 0) (U32.ofInt 1)
+    Result.ret ()
+
 /- [array::f2]: forward function -/
 def f2 (i : U32) : Result Unit :=
   Result.ret ()
@@ -279,4 +443,23 @@ def f3 : Result U32 :=
           ]) (Usize.ofInt 16) (Usize.ofInt 18)
     sum2 s s0
 
+/- [array::ite]: forward function -/
+def ite : Result Unit :=
+  do
+    let s ←
+      Array.to_slice_mut U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let s0 ←
+      Array.to_slice_mut U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ])
+    let s1 ← index_mut_slice_u32_0_back s0
+    let _ ←
+      Array.to_slice_mut_back U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s1
+    let s2 ← index_mut_slice_u32_0_back s
+    let _ ←
+      Array.to_slice_mut_back U32 (Usize.ofInt 2)
+        (Array.make U32 (Usize.ofInt 2) [ (U32.ofInt 0), (U32.ofInt 0) ]) s2
+    Result.ret ()
+
 end array
diff --git a/tests/lean/Array/Types.lean b/tests/lean/Array/Types.lean
index 407ce826..72241276 100644
--- a/tests/lean/Array/Types.lean
+++ b/tests/lean/Array/Types.lean
@@ -5,4 +5,9 @@ open Primitives
 
 namespace array
 
+/- [array::T] -/
+inductive T :=
+| A : T
+| B : T
+
 end array
-- 
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