From 1fc263ec0f527698b2f4d734d9757c9f723d0bee Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Mon, 18 Sep 2023 12:25:40 +0200
Subject: Improve scalar_tac

---
 backends/lean/Base/Arith/Int.lean         |  8 ++--
 backends/lean/Base/Arith/Scalar.lean      | 17 +++++++-
 backends/lean/Base/Primitives/Scalar.lean | 67 ++++++++-----------------------
 3 files changed, 36 insertions(+), 56 deletions(-)

(limited to 'backends/lean')

diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
index eb6701c2..3359ecdb 100644
--- a/backends/lean/Base/Arith/Int.lean
+++ b/backends/lean/Base/Arith/Int.lean
@@ -211,9 +211,11 @@ def intTacPreprocess (extraPreprocess :  Tactic.TacticM Unit) : Tactic.TacticM U
   let _ ← introHasIntPropInstances
   -- Extra preprocessing, before we split on the disjunctions
   extraPreprocess
-  -- Split
-  let asms ← introInstances ``PropHasImp.concl lookupPropHasImp
-  splitOnAsms asms.toList
+  -- Split - note that the extra-preprocessing step might actually have
+  -- proven the goal (by doing simplifications for instance)
+  Tactic.allGoals do
+    let asms ← introInstances ``PropHasImp.concl lookupPropHasImp
+    splitOnAsms asms.toList
 
 elab "int_tac_preprocess" : tactic =>
   intTacPreprocess (do pure ())
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
index db672489..47751c8a 100644
--- a/backends/lean/Base/Arith/Scalar.lean
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -16,14 +16,15 @@ def scalarTacExtraPreprocess : Tactic.TacticM Unit := do
    add (← mkAppM ``Scalar.cMin_bound #[.const ``ScalarTy.Isize []])
    add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Usize []])
    add (← mkAppM ``Scalar.cMax_bound #[.const ``ScalarTy.Isize []])
-   -- Reveal the concrete bounds
+   -- Reveal the concrete bounds, simplify calls to [ofInt]
    Utils.simpAt [``Scalar.min, ``Scalar.max, ``Scalar.cMin, ``Scalar.cMax,
                  ``I8.min, ``I16.min, ``I32.min, ``I64.min, ``I128.min,
                  ``I8.max, ``I16.max, ``I32.max, ``I64.max, ``I128.max,
                  ``U8.min, ``U16.min, ``U32.min, ``U64.min, ``U128.min,
                  ``U8.max, ``U16.max, ``U32.max, ``U64.max, ``U128.max,
                  ``Usize.min
-                 ] [] [] .wildcard
+                 ] [``Scalar.ofInt_val_eq, ``Scalar.neq_to_neq_val] [] .wildcard
+   
 
 elab "scalar_tac_preprocess" : tactic =>
   intTacPreprocess scalarTacExtraPreprocess
@@ -50,4 +51,16 @@ example (x y : U32) : x.val ≤ Scalar.max ScalarTy.U32 := by
 example (x : U32 × U32) : 0 ≤ x.fst.val := by
   scalar_tac
 
+-- Checking that we properly handle [ofInt]
+example : U32.ofInt 1 ≤ U32.max := by
+  scalar_tac
+
+example (x : Int) (h0 : 0 ≤ x) (h1 : x ≤ U32.max) :
+  U32.ofInt x (by constructor <;> scalar_tac) ≤ U32.max := by
+  scalar_tac
+
+-- Not equal
+example (x : U32) (h0 : ¬ x = U32.ofInt 0) : 0 < x.val := by
+  scalar_tac
+
 end Arith
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index ffc969f3..aa1d452d 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -709,60 +709,22 @@ def U128.ofIntCore  := @Scalar.ofIntCore .U128
 
 --  ofInt
 -- TODO: typeclass?
-def Isize.ofInt := @Scalar.ofInt .Isize
-def I8.ofInt    := @Scalar.ofInt .I8
-def I16.ofInt   := @Scalar.ofInt .I16
-def I32.ofInt   := @Scalar.ofInt .I32
-def I64.ofInt   := @Scalar.ofInt .I64
-def I128.ofInt  := @Scalar.ofInt .I128
-def Usize.ofInt := @Scalar.ofInt .Usize
-def U8.ofInt    := @Scalar.ofInt .U8
-def U16.ofInt   := @Scalar.ofInt .U16
-def U32.ofInt   := @Scalar.ofInt .U32
-def U64.ofInt   := @Scalar.ofInt .U64
-def U128.ofInt  := @Scalar.ofInt .U128
-
--- TODO: factor those lemmas out
+@[reducible] def Isize.ofInt := @Scalar.ofInt .Isize
+@[reducible] def I8.ofInt    := @Scalar.ofInt .I8
+@[reducible] def I16.ofInt   := @Scalar.ofInt .I16
+@[reducible] def I32.ofInt   := @Scalar.ofInt .I32
+@[reducible] def I64.ofInt   := @Scalar.ofInt .I64
+@[reducible] def I128.ofInt  := @Scalar.ofInt .I128
+@[reducible] def Usize.ofInt := @Scalar.ofInt .Usize
+@[reducible] def U8.ofInt    := @Scalar.ofInt .U8
+@[reducible] def U16.ofInt   := @Scalar.ofInt .U16
+@[reducible] def U32.ofInt   := @Scalar.ofInt .U32
+@[reducible] def U64.ofInt   := @Scalar.ofInt .U64
+@[reducible] def U128.ofInt  := @Scalar.ofInt .U128
+
 @[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofInt x h).val = x := by
   simp [Scalar.ofInt, Scalar.ofIntCore]
 
-@[simp] theorem Isize.ofInt_val_eq (h : Scalar.min ScalarTy.Isize ≤ x ∧ x ≤ Scalar.max ScalarTy.Isize) : (Isize.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem I8.ofInt_val_eq (h : Scalar.min ScalarTy.I8 ≤ x ∧ x ≤ Scalar.max ScalarTy.I8) : (I8.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem I16.ofInt_val_eq (h : Scalar.min ScalarTy.I16 ≤ x ∧ x ≤ Scalar.max ScalarTy.I16) : (I16.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem I32.ofInt_val_eq (h : Scalar.min ScalarTy.I32 ≤ x ∧ x ≤ Scalar.max ScalarTy.I32) : (I32.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem I64.ofInt_val_eq (h : Scalar.min ScalarTy.I64 ≤ x ∧ x ≤ Scalar.max ScalarTy.I64) : (I64.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem I128.ofInt_val_eq (h : Scalar.min ScalarTy.I128 ≤ x ∧ x ≤ Scalar.max ScalarTy.I128) : (I128.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem Usize.ofInt_val_eq (h : Scalar.min ScalarTy.Usize ≤ x ∧ x ≤ Scalar.max ScalarTy.Usize) : (Usize.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem U8.ofInt_val_eq (h : Scalar.min ScalarTy.U8 ≤ x ∧ x ≤ Scalar.max ScalarTy.U8) : (U8.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem U16.ofInt_val_eq (h : Scalar.min ScalarTy.U16 ≤ x ∧ x ≤ Scalar.max ScalarTy.U16) : (U16.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem U32.ofInt_val_eq (h : Scalar.min ScalarTy.U32 ≤ x ∧ x ≤ Scalar.max ScalarTy.U32) : (U32.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem U64.ofInt_val_eq (h : Scalar.min ScalarTy.U64 ≤ x ∧ x ≤ Scalar.max ScalarTy.U64) : (U64.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-@[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofInt x h).val = x := by
-  apply Scalar.ofInt_val_eq h
-
-
 -- Comparisons
 instance {ty} : LT (Scalar ty) where
   lt a b := LT.lt a.val b.val
@@ -790,6 +752,9 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
 instance (ty : ScalarTy) : CoeOut (Scalar ty) Int where
   coe := λ v => v.val
 
+@[simp] theorem Scalar.neq_to_neq_val {ty} : ∀ {i j : Scalar ty}, (¬ i = j) ↔ ¬ i.val = j.val := by
+  intro i j; cases i; cases j; simp
+
 -- -- We now define a type class that subsumes the various machine integer types, so
 -- -- as to write a concise definition for scalar_cast, rather than exhaustively
 -- -- enumerating all of the possible pairs. We remark that Rust has sane semantics
-- 
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