diff options
Diffstat (limited to 'backends/lean/Base/Primitives/Scalar.lean')
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 144 |
1 files changed, 71 insertions, 73 deletions
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index 3d90f1a5..c298ba92 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -339,7 +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.ofIntCore x (Scalar.check_bounds_prop h) + ok (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) @@ -573,7 +573,7 @@ instance {ty} : HAnd (Scalar ty) (Scalar ty) (Scalar ty) where theorem Scalar.add_spec {ty} {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x + y.val) (hmax : ↑x + ↑y ≤ Scalar.max ty) : - (∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y) := by + (∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y) := by -- Applying the unfoldings only on the left conv => congr; ext; lhs; unfold HAdd.hAdd instHAddScalarResult; simp [add, tryMk] split @@ -582,7 +582,7 @@ theorem Scalar.add_spec {ty} {x y : Scalar ty} theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} (hmax : ↑x + ↑y ≤ Scalar.max ty) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by have hmin : Scalar.min ty ≤ ↑x + ↑y := by have hx := x.hmin have hy := y.hmin @@ -591,57 +591,57 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} /- Fine-grained theorems -/ @[pspec] theorem Usize.add_spec {x y : Usize} (hmax : ↑x + ↑y ≤ Usize.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U8.add_spec {x y : U8} (hmax : ↑x + ↑y ≤ U8.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U16.add_spec {x y : U16} (hmax : ↑x + ↑y ≤ U16.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U32.add_spec {x y : U32} (hmax : ↑x + ↑y ≤ U32.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U64.add_spec {x y : U64} (hmax : ↑x + ↑y ≤ U64.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem U128.add_spec {x y : U128} (hmax : ↑x + ↑y ≤ U128.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := by + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := by apply Scalar.add_unsigned_spec <;> simp [ScalarTy.isSigned, Scalar.max, *] @[pspec] theorem Isize.add_spec {x y : Isize} (hmin : Isize.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ Isize.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I8.add_spec {x y : I8} (hmin : I8.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I8.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I16.add_spec {x y : I16} (hmin : I16.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I16.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I32.add_spec {x y : I32} (hmin : I32.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I32.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I64.add_spec {x y : I64} (hmin : I64.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I64.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax @[pspec] theorem I128.add_spec {x y : I128} (hmin : I128.min ≤ ↑x + ↑y) (hmax : ↑x + ↑y ≤ I128.max) : - ∃ z, x + y = ret z ∧ (↑z : Int) = ↑x + ↑y := + ∃ z, x + y = ok z ∧ (↑z : Int) = ↑x + ↑y := Scalar.add_spec hmin hmax -- Generic theorem - shouldn't be used much @@ -649,7 +649,7 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} theorem Scalar.sub_spec {ty} {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ Scalar.max ty) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by conv => congr; ext; lhs; simp [HSub.hSub, sub, tryMk, Sub.sub] split . simp [pure] @@ -658,7 +658,7 @@ theorem Scalar.sub_spec {ty} {x y : Scalar ty} theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned) {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by have : ↑x - ↑y ≤ Scalar.max ty := by have hx := x.hmin have hxm := x.hmax @@ -669,64 +669,64 @@ theorem Scalar.sub_unsigned_spec {ty : ScalarTy} (s : ¬ ty.isSigned) /- Fine-grained theorems -/ @[pspec] theorem Usize.sub_spec {x y : Usize} (hmin : Usize.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U8.sub_spec {x y : U8} (hmin : U8.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U16.sub_spec {x y : U16} (hmin : U16.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U32.sub_spec {x y : U32} (hmin : U32.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U64.sub_spec {x y : U64} (hmin : U64.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem U128.sub_spec {x y : U128} (hmin : U128.min ≤ ↑x - ↑y) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := by + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := by apply Scalar.sub_unsigned_spec <;> simp_all [Scalar.min, ScalarTy.isSigned] @[pspec] theorem Isize.sub_spec {x y : Isize} (hmin : Isize.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ Isize.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I8.sub_spec {x y : I8} (hmin : I8.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I8.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I16.sub_spec {x y : I16} (hmin : I16.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I16.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I32.sub_spec {x y : I32} (hmin : I32.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I32.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I64.sub_spec {x y : I64} (hmin : I64.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I64.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax @[pspec] theorem I128.sub_spec {x y : I128} (hmin : I128.min ≤ ↑x - ↑y) (hmax : ↑x - ↑y ≤ I128.max) : - ∃ z, x - y = ret z ∧ (↑z : Int) = ↑x - ↑y := + ∃ z, x - y = ok z ∧ (↑z : Int) = ↑x - ↑y := Scalar.sub_spec hmin hmax -- Generic theorem - shouldn't be used much theorem Scalar.mul_spec {ty} {x y : Scalar ty} (hmin : Scalar.min ty ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ Scalar.max ty) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by conv => congr; ext; lhs; simp [HMul.hMul] simp [mul, tryMk] split @@ -736,7 +736,7 @@ theorem Scalar.mul_spec {ty} {x y : Scalar ty} theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} (hmax : ↑x * ↑y ≤ Scalar.max ty) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by have : Scalar.min ty ≤ ↑x * ↑y := by have hx := x.hmin have hy := y.hmin @@ -745,57 +745,57 @@ theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} /- Fine-grained theorems -/ @[pspec] theorem Usize.mul_spec {x y : Usize} (hmax : ↑x * ↑y ≤ Usize.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U8.mul_spec {x y : U8} (hmax : ↑x * ↑y ≤ U8.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U16.mul_spec {x y : U16} (hmax : ↑x * ↑y ≤ U16.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U32.mul_spec {x y : U32} (hmax : ↑x * ↑y ≤ U32.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U64.mul_spec {x y : U64} (hmax : ↑x * ↑y ≤ U64.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem U128.mul_spec {x y : U128} (hmax : ↑x * ↑y ≤ U128.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := by + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := by apply Scalar.mul_unsigned_spec <;> simp_all [Scalar.max, ScalarTy.isSigned] @[pspec] theorem Isize.mul_spec {x y : Isize} (hmin : Isize.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ Isize.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I8.mul_spec {x y : I8} (hmin : I8.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I8.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I16.mul_spec {x y : I16} (hmin : I16.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I16.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I32.mul_spec {x y : I32} (hmin : I32.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I32.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I64.mul_spec {x y : I64} (hmin : I64.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I64.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax @[pspec] theorem I128.mul_spec {x y : I128} (hmin : I128.min ≤ ↑x * ↑y) (hmax : ↑x * ↑y ≤ I128.max) : - ∃ z, x * y = ret z ∧ (↑z : Int) = ↑x * ↑y := + ∃ z, x * y = ok z ∧ (↑z : Int) = ↑x * ↑y := Scalar.mul_spec hmin hmax -- Generic theorem - shouldn't be used much @@ -804,15 +804,14 @@ theorem Scalar.div_spec {ty} {x y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) (hmin : Scalar.min ty ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ Scalar.max ty) : - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := by simp [HDiv.hDiv, div, Div.div] simp [tryMk, *] - simp [pure] rfl theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by have h : Scalar.min ty = 0 := by cases ty <;> simp [ScalarTy.isSigned, min] at * have hx := x.hmin have hy := y.hmin @@ -828,69 +827,69 @@ theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S /- Fine-grained theorems -/ @[pspec] theorem Usize.div_spec (x : Usize) {y : Usize} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U8.div_spec (x : U8) {y : U8} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U16.div_spec (x : U16) {y : U16} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U32.div_spec (x : U32) {y : U32} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U64.div_spec (x : U64) {y : U64} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U128.div_spec (x : U128) {y : U128} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x / y = ret z ∧ (↑z : Int) = ↑x / ↑y := by + ∃ z, x / y = ok z ∧ (↑z : Int) = ↑x / ↑y := by apply Scalar.div_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem Isize.div_spec (x : Isize) {y : Isize} (hnz : ↑y ≠ (0 : Int)) (hmin : Isize.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ Isize.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I8.div_spec (x : I8) {y : I8} (hnz : ↑y ≠ (0 : Int)) (hmin : I8.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I8.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I16.div_spec (x : I16) {y : I16} (hnz : ↑y ≠ (0 : Int)) (hmin : I16.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I16.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I32.div_spec (x : I32) {y : I32} (hnz : ↑y ≠ (0 : Int)) (hmin : I32.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I32.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I64.div_spec (x : I64) {y : I64} (hnz : ↑y ≠ (0 : Int)) (hmin : I64.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I64.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax @[pspec] theorem I128.div_spec (x : I128) {y : I128} (hnz : ↑y ≠ (0 : Int)) (hmin : I128.min ≤ scalar_div ↑x ↑y) (hmax : scalar_div ↑x ↑y ≤ I128.max): - ∃ z, x / y = ret z ∧ (↑z : Int) = scalar_div ↑x ↑y := + ∃ z, x / y = ok z ∧ (↑z : Int) = scalar_div ↑x ↑y := Scalar.div_spec hnz hmin hmax -- Generic theorem - shouldn't be used much @@ -899,15 +898,14 @@ theorem Scalar.rem_spec {ty} {x y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) (hmin : Scalar.min ty ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ Scalar.max ty) : - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := by simp [HMod.hMod, rem] simp [tryMk, *] - simp [pure] rfl theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : Scalar ty} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by have h : Scalar.min ty = 0 := by cases ty <;> simp [ScalarTy.isSigned, min] at * have hx := x.hmin have hy := y.hmin @@ -923,62 +921,62 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S simp [*] @[pspec] theorem Usize.rem_spec (x : Usize) {y : Usize} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U8.rem_spec (x : U8) {y : U8} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U16.rem_spec (x : U16) {y : U16} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U32.rem_spec (x : U32) {y : U32} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U64.rem_spec (x : U64) {y : U64} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem U128.rem_spec (x : U128) {y : U128} (hnz : ↑y ≠ (0 : Int)) : - ∃ z, x % y = ret z ∧ (↑z : Int) = ↑x % ↑y := by + ∃ z, x % y = ok z ∧ (↑z : Int) = ↑x % ↑y := by apply Scalar.rem_unsigned_spec <;> simp [ScalarTy.isSigned, *] @[pspec] theorem I8.rem_spec (x : I8) {y : I8} (hnz : ↑y ≠ (0 : Int)) (hmin : I8.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I8.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I16.rem_spec (x : I16) {y : I16} (hnz : ↑y ≠ (0 : Int)) (hmin : I16.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I16.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I32.rem_spec (x : I32) {y : I32} (hnz : ↑y ≠ (0 : Int)) (hmin : I32.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I32.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I64.rem_spec (x : I64) {y : I64} (hnz : ↑y ≠ (0 : Int)) (hmin : I64.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I64.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax @[pspec] theorem I128.rem_spec (x : I128) {y : I128} (hnz : ↑y ≠ (0 : Int)) (hmin : I128.min ≤ scalar_rem ↑x ↑y) (hmax : scalar_rem ↑x ↑y ≤ I128.max): - ∃ z, x % y = ret z ∧ (↑z : Int) = scalar_rem ↑x ↑y := + ∃ z, x % y = ok z ∧ (↑z : Int) = scalar_rem ↑x ↑y := Scalar.rem_spec hnz hmin hmax -- ofIntCore @@ -1152,6 +1150,6 @@ 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 |