diff options
Diffstat (limited to 'backends/lean/Base/Primitives/Scalar.lean')
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 123 |
1 files changed, 21 insertions, 102 deletions
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index 157ade2c..f4264b9b 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -312,38 +312,13 @@ 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 -/- [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 @@ -412,9 +387,8 @@ 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) @@ -1268,73 +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 @@ -1464,18 +1383,18 @@ theorem coe_max {ty: ScalarTy} (a b: Scalar ty): ↑(Max.max a b) = (Max.max (↠-- 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 |