From 46b126f4e0e86f14475bc310e150948434726dc7 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Fri, 8 Mar 2024 08:50:50 +0100
Subject: Update the handling of notations like #u32 or #isize

---
 backends/lean/Base/Primitives/Scalar.lean | 168 ++++++++++++++++++------------
 1 file changed, 101 insertions(+), 67 deletions(-)

(limited to 'backends/lean/Base/Primitives/Scalar.lean')

diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index 3afd13d2..bf6b01a6 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -281,25 +281,38 @@ theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
   λ h => by
   apply And.intro <;> have hmin := Scalar.cMin_bound ty <;> have hmax := Scalar.cMax_bound ty <;> linarith
 
-def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
-  (hmin : Scalar.min ty ≤ x) (hmax : x ≤ Scalar.max ty) : Scalar ty :=
-  { val := x, hmin := hmin, hmax := hmax }
-
--- Tactic to prove that integers are in bounds
--- TODO: use this: https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/instance.20with.20tactic.20autoparam
-syntax "intlit" : tactic
-macro_rules
-  | `(tactic| intlit) => `(tactic| apply Scalar.bound_suffices; decide)
-
-def Scalar.ofInt {ty : ScalarTy} (x : Int)
-  (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty := by intlit) : Scalar ty :=
-  -- Remark: we initially wrote:
-  --  let ⟨ hmin, hmax ⟩ := h
-  --  Scalar.ofIntCore x hmin hmax
-  -- We updated to the line below because a similar pattern in `Scalar.tryMk`
-  -- made reduction block. Both versions seem to work for `Scalar.ofInt`, though.
-  -- TODO: investigate
-  Scalar.ofIntCore x h.left h.right
+/- [match_pattern] attribute: allows to us `Scalar.ofIntCore` inside of patterns.
+   This is particularly useful once we introduce notations like `#u32` (which
+   desugards to `Scalar.ofIntCore`) as it allows to write expressions like this:
+   Example:
+   ```
+   match x with
+   | 0#u32 => ...
+   | 1#u32 => ...
+   | ...
+   ```
+ -/
+@[match_pattern] def Scalar.ofIntCore {ty : ScalarTy} (x : Int)
+  (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : Scalar ty :=
+  { val := x, hmin := h.left, hmax := h.right }
+
+-- The definitions below are used later to introduce nice syntax for constants,
+-- like `1#u32`. We are reusing the technique described here: https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Different.20elaboration.20inside.2Foutside.20of.20match.20patterns/near/425455284
+
+class InBounds (ty : ScalarTy) (x : Int) :=
+  hInBounds : Scalar.cMin ty ≤ x ∧ x ≤ Scalar.cMax ty
+
+-- This trick to trigger reduction for decidable propositions comes from
+-- here: https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/instance.20with.20tactic.20autoparam/near/343495807
+class Decide (p : Prop) [Decidable p] : Prop where
+  isTrue : p
+instance : @Decide p (.isTrue h) := @Decide.mk p (_) h
+
+instance [Decide (Scalar.cMin ty ≤ v ∧ v ≤ Scalar.cMax ty)] : InBounds ty v where
+  hInBounds := Decide.isTrue
+
+@[reducible, match_pattern] def Scalar.ofInt {ty : ScalarTy} (x : Int) [InBounds ty x] : Scalar ty :=
+  Scalar.ofIntCore x (Scalar.bound_suffices ty x InBounds.hInBounds)
 
 @[simp] def Scalar.check_bounds (ty : ScalarTy) (x : Int) : Bool :=
   (Scalar.cMin ty ≤ x || Scalar.min ty ≤ x) ∧ (x ≤ Scalar.cMax ty || x ≤ Scalar.max ty)
@@ -326,7 +339,7 @@ def Scalar.tryMk (ty : ScalarTy) (x : Int) : Result (Scalar ty) :=
     -- ```
     -- then normalization blocks (for instance, some proofs which use reflexivity fail).
     -- However, the version below doesn't block reduction (TODO: investigate):
-    return Scalar.ofInt x (Scalar.check_bounds_prop h)
+    return Scalar.ofIntCore x (Scalar.check_bounds_prop h)
   else fail integerOverflow
 
 def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
@@ -439,8 +452,8 @@ 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))
+@[reducible] def core_isize_min : Isize := Scalar.ofIntCore Isize.min (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize))
+@[reducible] def core_isize_max : Isize := Scalar.ofIntCore Isize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Isize))
 @[reducible] def core_i8_min : I8 := Scalar.ofInt I8.min
 @[reducible] def core_i8_max : I8 := Scalar.ofInt I8.max
 @[reducible] def core_i16_min : I16 := Scalar.ofInt I16.min
@@ -453,8 +466,8 @@ instance (ty : ScalarTy) : Inhabited (Scalar ty) := by
 @[reducible] def core_i128_max : I128 := Scalar.ofInt I128.max
 
 -- TODO: reducible?
-@[reducible] def core_usize_min : Usize := Scalar.ofInt Usize.min
-@[reducible] def core_usize_max : Usize := Scalar.ofInt Usize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Usize))
+@[reducible] def core_usize_min : Usize := Scalar.ofIntCore Usize.min (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Usize))
+@[reducible] def core_usize_max : Usize := Scalar.ofIntCore Usize.max (by simp [Scalar.min, Scalar.max]; apply (Scalar.min_le_max .Usize))
 @[reducible] def core_u8_min : U8 := Scalar.ofInt U8.min
 @[reducible] def core_u8_max : U8 := Scalar.ofInt U8.max
 @[reducible] def core_u16_min : U16 := Scalar.ofInt U16.min
@@ -985,18 +998,18 @@ def U128.ofIntCore  := @Scalar.ofIntCore .U128
 
 --  ofInt
 -- TODO: typeclass?
-abbrev Isize.ofInt := @Scalar.ofInt .Isize
-abbrev I8.ofInt    := @Scalar.ofInt .I8
-abbrev I16.ofInt   := @Scalar.ofInt .I16
-abbrev I32.ofInt   := @Scalar.ofInt .I32
-abbrev I64.ofInt   := @Scalar.ofInt .I64
-abbrev I128.ofInt  := @Scalar.ofInt .I128
-abbrev Usize.ofInt := @Scalar.ofInt .Usize
-abbrev U8.ofInt    := @Scalar.ofInt .U8
-abbrev U16.ofInt   := @Scalar.ofInt .U16
-abbrev U32.ofInt   := @Scalar.ofInt .U32
-abbrev U64.ofInt   := @Scalar.ofInt .U64
-abbrev U128.ofInt  := @Scalar.ofInt .U128
+@[match_pattern] abbrev Isize.ofInt := @Scalar.ofInt .Isize
+@[match_pattern] abbrev I8.ofInt    := @Scalar.ofInt .I8
+@[match_pattern] abbrev I16.ofInt   := @Scalar.ofInt .I16
+@[match_pattern] abbrev I32.ofInt   := @Scalar.ofInt .I32
+@[match_pattern] abbrev I64.ofInt   := @Scalar.ofInt .I64
+@[match_pattern] abbrev I128.ofInt  := @Scalar.ofInt .I128
+@[match_pattern] abbrev Usize.ofInt := @Scalar.ofInt .Usize
+@[match_pattern] abbrev U8.ofInt    := @Scalar.ofInt .U8
+@[match_pattern] abbrev U16.ofInt   := @Scalar.ofInt .U16
+@[match_pattern] abbrev U32.ofInt   := @Scalar.ofInt .U32
+@[match_pattern] abbrev U64.ofInt   := @Scalar.ofInt .U64
+@[match_pattern] abbrev U128.ofInt  := @Scalar.ofInt .U128
 
 postfix:max "#isize" => Isize.ofInt
 postfix:max "#i8"    => I8.ofInt
@@ -1011,47 +1024,86 @@ postfix:max "#u32"   => U32.ofInt
 postfix:max "#u64"   => U64.ofInt
 postfix:max "#u128"  => U128.ofInt
 
+/- Testing the notations -/
+example := 0#u32
+example := 1#u32
+example := 1#i32
+example := 0#isize
+example := (-1)#isize
+example (x : U32) : Bool :=
+  match x with
+  | 0#u32 => true
+  | _ => false
+
+example (x : U32) : Bool :=
+  match x with
+  | 1#u32 => true
+  | _ => false
+
+example (x : I32) : Bool :=
+  match x with
+  | (-1)#i32 => true
+  | _ => false
+
+-- Notation for pattern matching
+-- We make the precedence looser than the negation.
+notation:70 a:70 "#scalar" => Scalar.mk (a) _ _
+
+example {ty} (x : Scalar ty) : ℤ :=
+  match x with
+  | v#scalar => v
+
+example {ty} (x : Scalar ty) : Bool :=
+  match x with
+  | 1#scalar => true
+  | _ => false
+
+example {ty} (x : Scalar ty) : Bool :=
+  match x with
+  | -(1 : Int)#scalar => true
+  | _ => false
+
 -- Testing the notations
 example : Result Usize := 0#usize + 1#usize
 
 -- TODO: factor those lemmas out
-@[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofInt x h).val = x := by
+@[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofIntCore 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
+@[simp] theorem Isize.ofInt_val_eq (h : Scalar.min ScalarTy.Isize ≤ x ∧ x ≤ Scalar.max ScalarTy.Isize) : (Isize.ofIntCore 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
+@[simp] theorem I8.ofInt_val_eq (h : Scalar.min ScalarTy.I8 ≤ x ∧ x ≤ Scalar.max ScalarTy.I8) : (I8.ofIntCore 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
+@[simp] theorem I16.ofInt_val_eq (h : Scalar.min ScalarTy.I16 ≤ x ∧ x ≤ Scalar.max ScalarTy.I16) : (I16.ofIntCore 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
+@[simp] theorem I32.ofInt_val_eq (h : Scalar.min ScalarTy.I32 ≤ x ∧ x ≤ Scalar.max ScalarTy.I32) : (I32.ofIntCore 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
+@[simp] theorem I64.ofInt_val_eq (h : Scalar.min ScalarTy.I64 ≤ x ∧ x ≤ Scalar.max ScalarTy.I64) : (I64.ofIntCore 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
+@[simp] theorem I128.ofInt_val_eq (h : Scalar.min ScalarTy.I128 ≤ x ∧ x ≤ Scalar.max ScalarTy.I128) : (I128.ofIntCore 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
+@[simp] theorem Usize.ofInt_val_eq (h : Scalar.min ScalarTy.Usize ≤ x ∧ x ≤ Scalar.max ScalarTy.Usize) : (Usize.ofIntCore 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
+@[simp] theorem U8.ofInt_val_eq (h : Scalar.min ScalarTy.U8 ≤ x ∧ x ≤ Scalar.max ScalarTy.U8) : (U8.ofIntCore 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
+@[simp] theorem U16.ofInt_val_eq (h : Scalar.min ScalarTy.U16 ≤ x ∧ x ≤ Scalar.max ScalarTy.U16) : (U16.ofIntCore 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
+@[simp] theorem U32.ofInt_val_eq (h : Scalar.min ScalarTy.U32 ≤ x ∧ x ≤ Scalar.max ScalarTy.U32) : (U32.ofIntCore 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
+@[simp] theorem U64.ofInt_val_eq (h : Scalar.min ScalarTy.U64 ≤ x ∧ x ≤ Scalar.max ScalarTy.U64) : (U64.ofIntCore 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
+@[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofIntCore x h).val = x := by
   apply Scalar.ofInt_val_eq h
 
 -- Comparisons
@@ -1133,22 +1185,4 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) :=
 --   else
 --     .fail integerOverflow
 
--- Notation for pattern matching
--- We make the precedence looser than the negation.
-notation:70 a:70 "#scalar" => Scalar.mk (a) _ _
-
-example {ty} (x : Scalar ty) : ℤ :=
-  match x with
-  | v#scalar => v
-
-example {ty} (x : Scalar ty) : Bool :=
-  match x with
-  | 1#scalar => true
-  | _ => false
-
-example {ty} (x : Scalar ty) : Bool :=
-  match x with
-  | -(1 : Int)#scalar => true
-  | _ => false
-
 end Primitives
-- 
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