Merge pull request #38 from AeneasVerif/son_fixes2

Simplify and add some lemmas

3 files changed, 14 insertions, 9 deletions

diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean
index f71f2de2..e90d1e0d 100644
--- a/backends/lean/Base/IList/IList.lean
+++ b/backends/lean/Base/IList/IList.lean
@@ -412,12 +412,11 @@ theorem index_itake_append_end [Inhabited α] (i j : Int) (l0 l1 : List α)
       simp_all
 
 @[simp]
-theorem index_ne
+theorem index_update_ne
   {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (j: ℤ) (x: α) :
-   0 ≤ i → i < l.len → 0 ≤ j → j < l.len → j ≠ i →
-    (l.update i x).index j = l.index j
+   j ≠ i → (l.update i x).index j = l.index j
   :=
-  λ _ _ _ _ _ => match l with
+  λ _ => match l with
   | [] => by simp at *
   | hd :: tl =>
     if h: i = 0 then
@@ -428,12 +427,11 @@ theorem index_ne
       by simp [*]
     else
       by
-        simp [*]
-        simp at *
-        apply index_ne <;> scalar_tac
+        simp_all
+        apply index_update_ne; scalar_tac
 
 @[simp]
-theorem index_eq
+theorem index_update_eq
   {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (x: α) :
    0 ≤ i → i < l.len →
     (l.update i x).index i = x
@@ -448,7 +446,7 @@ theorem index_eq
       by
         simp [*]
         simp at *
-        apply index_eq <;> scalar_tac
+        apply index_update_eq <;> scalar_tac
 
 theorem update_map_eq {α : Type u} {β : Type v} (ls : List α) (i : Int) (x : α) (f : α → β) :
   (ls.update i x).map f = (ls.map f).update i (f x) :=
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index cdd6d6f9..f74fecd4 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -427,6 +427,9 @@ def Scalar.cast {src_ty : ScalarTy} (tgt_ty : ScalarTy) (x : Scalar src_ty) : Re
 @[reducible] def U64   := Scalar .U64
 @[reducible] def U128  := Scalar .U128
 
+instance (ty : ScalarTy) : Inhabited (Scalar ty) := by
+  constructor; cases ty <;> apply (Scalar.ofInt 0)
+
 -- TODO: reducible?
 @[reducible] def core_isize_min : Isize := Scalar.ofInt Isize.min (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize))
 @[reducible] def core_isize_max : Isize := Scalar.ofInt Isize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize))
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
index e600a151..2c3fce91 100644
--- a/backends/lean/Base/Primitives/Vec.lean
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -37,6 +37,10 @@ example {a: Type u} (v : Vec a) : v.length ≤ Scalar.max ScalarTy.Usize := by
 
 def Vec.new (α : Type u): Vec α := ⟨ [], by apply Scalar.cMax_suffices .Usize; simp ⟩
 
+instance (α : Type u) : Inhabited (Vec α) := by
+  constructor
+  apply Vec.new
+
 -- TODO: very annoying that the α is an explicit parameter
 def Vec.len (α : Type u) (v : Vec α) : Usize :=
   Usize.ofIntCore v.val.len (by scalar_tac) (by scalar_tac)