From fc0b39c4fe48fdbab06d5fd32e0a2b7dcae674e6 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Thu, 4 Apr 2024 15:29:11 +0200
Subject: Fix the coerce notation for scalars and update some lemmas

---
 backends/lean/Base/Primitives/Scalar.lean | 19 +++++++++++++++----
 1 file changed, 15 insertions(+), 4 deletions(-)

(limited to 'backends/lean')

diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index 3d90f1a5..7668bc59 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -265,6 +265,14 @@ theorem Scalar.cMax_suffices ty (h : x ≤ Scalar.cMax ty) : x ≤ Scalar.max ty
   have := Scalar.cMax_bound ty
   linarith
 
+/-- The scalar type.
+
+    We could use a subtype, but it using a custom structure type allows us
+    to have more control over the coercions and the simplifications (we tried
+    using a subtype and it caused issues especially as we had to make the Scalar
+    type non-reducible, so that we could have more control, but leading to
+    some natural equalities not being obvious to the simplifier anymore).
+ -/
 structure Scalar (ty : ScalarTy) where
   val : Int
   hmin : Scalar.min ty ≤ val
@@ -274,6 +282,9 @@ deriving Repr
 instance (ty : ScalarTy) : CoeOut (Scalar ty) Int where
   coe := λ v => v.val
 
+/- Activate the ↑ notation -/
+attribute [coe] Scalar.val
+
 theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
   Scalar.cMin ty ≤ x ∧ x ≤ Scalar.cMax ty ->
   Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty
@@ -1119,19 +1130,19 @@ theorem Scalar.eq_equiv {ty : ScalarTy} (x y : Scalar ty) :
 
 -- This is sometimes useful when rewriting the goal with the local assumptions
 @[simp] theorem Scalar.eq_imp {ty : ScalarTy} (x y : Scalar ty) :
-  x = y → (↑x : Int) = ↑y := (eq_equiv x y).mp
+  (↑x : Int) = ↑y → x = y := (eq_equiv x y).mpr
 
 theorem Scalar.lt_equiv {ty : ScalarTy} (x y : Scalar ty) :
   x < y ↔ (↑x : Int) < ↑y := by simp [LT.lt]
 
 @[simp] theorem Scalar.lt_imp {ty : ScalarTy} (x y : Scalar ty) :
-  x < y → (↑x : Int) < ↑y := (lt_equiv x y).mp
+  (↑x : Int) < (↑y) → x < y := (lt_equiv x y).mpr
 
 theorem Scalar.le_equiv {ty : ScalarTy} (x y : Scalar ty) :
   x ≤ y ↔ (↑x : Int) ≤ ↑y := by simp [LE.le]
 
 @[simp] theorem Scalar.le_imp {ty : ScalarTy} (x y : Scalar ty) :
-  x ≤ y → (↑x : Int) ≤ ↑y := (le_equiv x y).mp
+  (↑x : Int) ≤ ↑y → x ≤ y := (le_equiv x y).mpr
 
 instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
 instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
@@ -1152,6 +1163,6 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
     | isFalse h => isFalse (Scalar.ne_of_val_ne h)
 
 @[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
+  simp [eq_equiv]
 
 end Primitives
-- 
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