Merge branch 'son/update-lean' into has-int-pred

1 files changed, 40 insertions, 114 deletions

diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index 8fb067e1..9f809ead 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -1,6 +1,5 @@
 import Lean
 import Lean.Meta.Tactic.Simp
-import Mathlib.Tactic.Linarith
 import Base.Primitives.Base
 import Base.Primitives.Core
 import Base.Diverge.Base
@@ -9,6 +8,9 @@ import Base.Arith.Int
 
 namespace Primitives
 
+-- Deactivate the warnings which appear when we use `#assert`
+set_option linter.hashCommand false
+
 ----------------------
 -- MACHINE INTEGERS --
 ----------------------
@@ -279,11 +281,11 @@ theorem Scalar.cMax_bound ty : Scalar.cMax ty ≤ Scalar.max ty := by
 
 theorem Scalar.cMin_suffices ty (h : Scalar.cMin ty ≤ x) : Scalar.min ty ≤ x := by
   have := Scalar.cMin_bound ty
-  linarith
+  omega
 
 theorem Scalar.cMax_suffices ty (h : x ≤ Scalar.cMax ty) : x ≤ Scalar.max ty := by
   have := Scalar.cMax_bound ty
-  linarith
+  omega
 
 /-- The scalar type.
 
@@ -310,40 +312,15 @@ theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
   Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty
   :=
   λ h => by
-  apply And.intro <;> have hmin := Scalar.cMin_bound ty <;> have hmax := Scalar.cMax_bound ty <;> linarith
+  apply And.intro <;> have hmin := Scalar.cMin_bound ty <;> have hmax := Scalar.cMax_bound ty <;> omega
 
-/- [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)
+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)
+@[reducible] def Scalar.ofInt {ty : ScalarTy} (x : Int)
+  (hInBounds : Scalar.cMin ty ≤ x ∧ x ≤ Scalar.cMax ty := by decide) : Scalar ty :=
+  Scalar.ofIntCore x (Scalar.bound_suffices ty x hInBounds)
 
 @[simp] abbrev Scalar.in_bounds (ty : ScalarTy) (x : Int) : Prop :=
   Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty
@@ -351,10 +328,17 @@ instance [Decide (Scalar.cMin ty ≤ v ∧ v ≤ Scalar.cMax ty)] : InBounds ty
 @[simp] abbrev Scalar.check_bounds (ty : ScalarTy) (x : Int) : Bool :=
   (Scalar.cMin ty ≤ x || Scalar.min ty ≤ x) ∧ (x ≤ Scalar.cMax ty || x ≤ Scalar.max ty)
 
+/- Discussion:
+   This coercion can be slightly annoying at times, because if we write
+   something like `u = 3` (where `u` is, for instance, as `U32`), then instead of
+   coercing `u` to `Int`, Lean will lift `3` to `U32`).
+   For now we deactivate it.
+
 -- TODO(raitobezarius): the inbounds constraint is a bit ugly as we can pretty trivially
 -- discharge the lhs on ≥ 0.
 instance {ty: ScalarTy} [InBounds ty (Int.ofNat n)]: OfNat (Scalar ty) (n: â„•) where
   ofNat := Scalar.ofInt n
+-/
 
 theorem Scalar.check_bounds_imp_in_bounds {ty : ScalarTy} {x : Int}
   (h: Scalar.check_bounds ty x) :
@@ -363,7 +347,7 @@ theorem Scalar.check_bounds_imp_in_bounds {ty : ScalarTy} {x : Int}
   have ⟨ hmin, hmax ⟩ := h
   have hbmin := Scalar.cMin_bound ty
   have hbmax := Scalar.cMax_bound ty
-  cases hmin <;> cases hmax <;> apply And.intro <;> linarith
+  cases hmin <;> cases hmax <;> apply And.intro <;> omega
 
 theorem Scalar.check_bounds_eq_in_bounds (ty : ScalarTy) (x : Int) :
   Scalar.check_bounds ty x ↔ Scalar.in_bounds ty x := by
@@ -405,9 +389,8 @@ theorem Scalar.tryMk_eq (ty : ScalarTy) (x : Int) :
   simp [tryMk, ofOption, tryMkOpt]
   split_ifs <;> simp
 
-instance (ty: ScalarTy) : InBounds ty 0 where
-  hInBounds := by
-    induction ty <;> simp [Scalar.cMax, Scalar.cMin, Scalar.max, Scalar.min] <;> decide
+@[simp] theorem zero_in_cbounds {ty : ScalarTy} : Scalar.cMin ty ≤ 0 ∧ 0 ≤ Scalar.cMax ty := by
+  cases ty <;> simp [Scalar.cMax, Scalar.cMin, Scalar.max, Scalar.min] <;> decide
 
 def Scalar.neg {ty : ScalarTy} (x : Scalar ty) : Result (Scalar ty) := Scalar.tryMk ty (- x.val)
 
@@ -749,7 +732,6 @@ theorem Scalar.add_spec {ty} {x y : Scalar ty}
   (∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y) := by
   have h := @add_equiv ty x y
   split at h <;> simp_all
-  apply h
 
 theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
   (hmax : ↑x + ↑y ≤ Scalar.max ty) :
@@ -757,7 +739,7 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty}
   have hmin : Scalar.min ty ≤ ↑x + ↑y := by
     have hx := x.hmin
     have hy := y.hmin
-    cases ty <;> simp [min, ScalarTy.isSigned] at * <;> linarith
+    cases ty <;> simp [min, ScalarTy.isSigned] at * <;> omega
   apply add_spec <;> assumption
 
 /- Fine-grained theorems -/
@@ -844,7 +826,6 @@ theorem Scalar.sub_spec {ty} {x y : Scalar ty}
   ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by
   have h := @sub_equiv ty x y
   split at h <;> simp_all
-  apply h
 
 theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned)
   {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x - ↑y) :
@@ -853,7 +834,7 @@ theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned)
     have hx := x.hmin
     have hxm := x.hmax
     have hy := y.hmin
-    cases ty <;> simp [min, max, ScalarTy.isSigned] at * <;> linarith
+    cases ty <;> simp [min, max, ScalarTy.isSigned] at * <;> omega
   intros
   apply sub_spec <;> assumption
 
@@ -1049,11 +1030,11 @@ theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S
   have hx := x.hmin
   have hy := y.hmin
   simp [h] at hx hy
-  have hmin : 0 ≤ ↑x / ↑y := Int.ediv_nonneg hx hy
+  have hmin : 0 ≤ x.val / y.val := Int.ediv_nonneg hx hy
   have hmax : ↑x / ↑y ≤ Scalar.max ty := by
     have := Int.ediv_le_self ↑y hx
     have := x.hmax
-    linarith
+    omega
   have hs := @div_spec ty x y hnz
   simp [*] at hs
   apply hs
@@ -1170,7 +1151,7 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S
     have h : (0 : Int) < y := by int_tac
     have h := Int.emod_lt_of_pos ↑x h
     have := y.hmax
-    linarith
+    omega
   have hs := @rem_spec ty x y hnz
   simp [*] at hs
   simp [*]
@@ -1261,73 +1242,18 @@ def U128.ofIntCore  := @Scalar.ofIntCore .U128
 
 --  ofInt
 -- TODO: typeclass?
-@[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
-postfix:max "#i16"   => I16.ofInt
-postfix:max "#i32"   => I32.ofInt
-postfix:max "#i64"   => I64.ofInt
-postfix:max "#i128"  => I128.ofInt
-postfix:max "#usize" => Usize.ofInt
-postfix:max "#u8"    => U8.ofInt
-postfix:max "#u16"   => U16.ofInt
-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
+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
 
 -- TODO: factor those lemmas out
 @[simp] theorem Scalar.ofInt_val_eq {ty} (h : Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty) : (Scalar.ofIntCore x h).val = x := by
@@ -1457,18 +1383,18 @@ theorem coe_max {ty: ScalarTy} (a b: Scalar ty): ↑(Max.max a b) = (Max.max (â†
 -- Max theory
 -- TODO: do the min theory later on.
 
-theorem Scalar.zero_le_unsigned {ty} (s: ¬ ty.isSigned) (x: Scalar ty): Scalar.ofInt 0 ≤ x := by
+theorem Scalar.zero_le_unsigned {ty} (s: ¬ ty.isSigned) (x: Scalar ty): Scalar.ofInt 0 (by simp) ≤ x := by
   apply (Scalar.le_equiv _ _).2
   convert x.hmin
   cases ty <;> simp [ScalarTy.isSigned] at s <;> simp [Scalar.min]
 
 @[simp]
 theorem Scalar.max_unsigned_left_zero_eq {ty} [s: Fact (¬ ty.isSigned)] (x: Scalar ty):
-  Max.max (Scalar.ofInt 0) x = x := max_eq_right (Scalar.zero_le_unsigned s.out x)
+  Max.max (Scalar.ofInt 0 (by simp)) x = x := max_eq_right (Scalar.zero_le_unsigned s.out x)
 
 @[simp]
 theorem Scalar.max_unsigned_right_zero_eq {ty} [s: Fact (¬ ty.isSigned)] (x: Scalar ty):
-  Max.max x (Scalar.ofInt 0) = x := max_eq_left (Scalar.zero_le_unsigned s.out x)
+  Max.max x (Scalar.ofInt 0 (by simp)) = x := max_eq_left (Scalar.zero_le_unsigned s.out x)
 
 -- Leading zeros
 def core.num.Usize.leading_zeros (x : Usize) : U32 := sorry