diff options
Diffstat (limited to '')
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 191 |
1 files changed, 179 insertions, 12 deletions
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index aa1d452d..1d31b04a 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -491,6 +491,36 @@ theorem Scalar.add_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} ∃ z, x + y = ret z ∧ z.val = x.val + y.val := by apply Scalar.add_unsigned_spec <;> simp only [Scalar.max, *] +@[cepspec] theorem Isize.add_spec {x y : Isize} + (hmin : Isize.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ Isize.max) : + ∃ z, x + y = ret z ∧ z.val = x.val + y.val := + Scalar.add_spec hmin hmax + +@[cepspec] theorem I8.add_spec {x y : I8} + (hmin : I8.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I8.max) : + ∃ z, x + y = ret z ∧ z.val = x.val + y.val := + Scalar.add_spec hmin hmax + +@[cepspec] theorem I16.add_spec {x y : I16} + (hmin : I16.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I16.max) : + ∃ z, x + y = ret z ∧ z.val = x.val + y.val := + Scalar.add_spec hmin hmax + +@[cepspec] theorem I32.add_spec {x y : I32} + (hmin : I32.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I32.max) : + ∃ z, x + y = ret z ∧ z.val = x.val + y.val := + Scalar.add_spec hmin hmax + +@[cepspec] theorem I64.add_spec {x y : I64} + (hmin : I64.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I64.max) : + ∃ z, x + y = ret z ∧ z.val = x.val + y.val := + Scalar.add_spec hmin hmax + +@[cepspec] theorem I128.add_spec {x y : I128} + (hmin : I128.min ≤ x.val + y.val) (hmax : x.val + y.val ≤ I128.max) : + ∃ z, x + y = ret z ∧ z.val = x.val + y.val := + Scalar.add_spec hmin hmax + -- Generic theorem - shouldn't be used much @[cpspec] theorem Scalar.sub_spec {ty} {x y : Scalar ty} @@ -540,6 +570,36 @@ theorem Scalar.sub_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} ∃ z, x - y = ret z ∧ z.val = x.val - y.val := by apply Scalar.sub_unsigned_spec <;> simp only [Scalar.min, *] +@[cepspec] theorem Isize.sub_spec {x y : Isize} (hmin : Isize.min ≤ x.val - y.val) + (hmax : x.val - y.val ≤ Isize.max) : + ∃ z, x - y = ret z ∧ z.val = x.val - y.val := + Scalar.sub_spec hmin hmax + +@[cepspec] theorem I8.sub_spec {x y : I8} (hmin : I8.min ≤ x.val - y.val) + (hmax : x.val - y.val ≤ I8.max) : + ∃ z, x - y = ret z ∧ z.val = x.val - y.val := + Scalar.sub_spec hmin hmax + +@[cepspec] theorem I16.sub_spec {x y : I16} (hmin : I16.min ≤ x.val - y.val) + (hmax : x.val - y.val ≤ I16.max) : + ∃ z, x - y = ret z ∧ z.val = x.val - y.val := + Scalar.sub_spec hmin hmax + +@[cepspec] theorem I32.sub_spec {x y : I32} (hmin : I32.min ≤ x.val - y.val) + (hmax : x.val - y.val ≤ I32.max) : + ∃ z, x - y = ret z ∧ z.val = x.val - y.val := + Scalar.sub_spec hmin hmax + +@[cepspec] theorem I64.sub_spec {x y : I64} (hmin : I64.min ≤ x.val - y.val) + (hmax : x.val - y.val ≤ I64.max) : + ∃ z, x - y = ret z ∧ z.val = x.val - y.val := + Scalar.sub_spec hmin hmax + +@[cepspec] theorem I128.sub_spec {x y : I128} (hmin : I128.min ≤ x.val - y.val) + (hmax : x.val - y.val ≤ I128.max) : + ∃ z, x - y = ret z ∧ z.val = x.val - y.val := + 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.val * y.val) @@ -586,6 +646,36 @@ theorem Scalar.mul_unsigned_spec {ty} (s: ¬ ty.isSigned) {x y : Scalar ty} ∃ z, x * y = ret z ∧ z.val = x.val * y.val := by apply Scalar.mul_unsigned_spec <;> simp only [Scalar.max, *] +@[cepspec] theorem Isize.mul_spec {x y : Isize} (hmin : Isize.min ≤ x.val * y.val) + (hmax : x.val * y.val ≤ Isize.max) : + ∃ z, x * y = ret z ∧ z.val = x.val * y.val := + Scalar.mul_spec hmin hmax + +@[cepspec] theorem I8.mul_spec {x y : I8} (hmin : I8.min ≤ x.val * y.val) + (hmax : x.val * y.val ≤ I8.max) : + ∃ z, x * y = ret z ∧ z.val = x.val * y.val := + Scalar.mul_spec hmin hmax + +@[cepspec] theorem I16.mul_spec {x y : I16} (hmin : I16.min ≤ x.val * y.val) + (hmax : x.val * y.val ≤ I16.max) : + ∃ z, x * y = ret z ∧ z.val = x.val * y.val := + Scalar.mul_spec hmin hmax + +@[cepspec] theorem I32.mul_spec {x y : I32} (hmin : I32.min ≤ x.val * y.val) + (hmax : x.val * y.val ≤ I32.max) : + ∃ z, x * y = ret z ∧ z.val = x.val * y.val := + Scalar.mul_spec hmin hmax + +@[cepspec] theorem I64.mul_spec {x y : I64} (hmin : I64.min ≤ x.val * y.val) + (hmax : x.val * y.val ≤ I64.max) : + ∃ z, x * y = ret z ∧ z.val = x.val * y.val := + Scalar.mul_spec hmin hmax + +@[cepspec] theorem I128.mul_spec {x y : I128} (hmin : I128.min ≤ x.val * y.val) + (hmax : x.val * y.val ≤ I128.max) : + ∃ z, x * y = ret z ∧ z.val = x.val * y.val := + Scalar.mul_spec hmin hmax + -- Generic theorem - shouldn't be used much @[cpspec] theorem Scalar.div_spec {ty} {x y : Scalar ty} @@ -639,6 +729,48 @@ theorem Scalar.div_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S ∃ z, x / y = ret z ∧ z.val = x.val / y.val := by apply Scalar.div_unsigned_spec <;> simp [Scalar.max, *] +@[cepspec] theorem Isize.div_spec (x : Isize) {y : Isize} + (hnz : y.val ≠ 0) + (hmin : Isize.min ≤ scalar_div x.val y.val) + (hmax : scalar_div x.val y.val ≤ Isize.max): + ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := + Scalar.div_spec hnz hmin hmax + +@[cepspec] theorem I8.div_spec (x : I8) {y : I8} + (hnz : y.val ≠ 0) + (hmin : I8.min ≤ scalar_div x.val y.val) + (hmax : scalar_div x.val y.val ≤ I8.max): + ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := + Scalar.div_spec hnz hmin hmax + +@[cepspec] theorem I16.div_spec (x : I16) {y : I16} + (hnz : y.val ≠ 0) + (hmin : I16.min ≤ scalar_div x.val y.val) + (hmax : scalar_div x.val y.val ≤ I16.max): + ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := + Scalar.div_spec hnz hmin hmax + +@[cepspec] theorem I32.div_spec (x : I32) {y : I32} + (hnz : y.val ≠ 0) + (hmin : I32.min ≤ scalar_div x.val y.val) + (hmax : scalar_div x.val y.val ≤ I32.max): + ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := + Scalar.div_spec hnz hmin hmax + +@[cepspec] theorem I64.div_spec (x : I64) {y : I64} + (hnz : y.val ≠ 0) + (hmin : I64.min ≤ scalar_div x.val y.val) + (hmax : scalar_div x.val y.val ≤ I64.max): + ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := + Scalar.div_spec hnz hmin hmax + +@[cepspec] theorem I128.div_spec (x : I128) {y : I128} + (hnz : y.val ≠ 0) + (hmin : I128.min ≤ scalar_div x.val y.val) + (hmax : scalar_div x.val y.val ≤ I128.max): + ∃ z, x / y = ret z ∧ z.val = scalar_div x.val y.val := + Scalar.div_spec hnz hmin hmax + -- Generic theorem - shouldn't be used much @[cpspec] theorem Scalar.rem_spec {ty} {x y : Scalar ty} @@ -692,20 +824,55 @@ theorem Scalar.rem_unsigned_spec {ty} (s: ¬ ty.isSigned) (x : Scalar ty) {y : S ∃ z, x % y = ret z ∧ z.val = x.val % y.val := by apply Scalar.rem_unsigned_spec <;> simp [Scalar.max, *] +@[cepspec] theorem I8.rem_spec (x : I8) {y : I8} + (hnz : y.val ≠ 0) + (hmin : I8.min ≤ scalar_rem x.val y.val) + (hmax : scalar_rem x.val y.val ≤ I8.max): + ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val := + Scalar.rem_spec hnz hmin hmax + +@[cepspec] theorem I16.rem_spec (x : I16) {y : I16} + (hnz : y.val ≠ 0) + (hmin : I16.min ≤ scalar_rem x.val y.val) + (hmax : scalar_rem x.val y.val ≤ I16.max): + ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val := + Scalar.rem_spec hnz hmin hmax + +@[cepspec] theorem I32.rem_spec (x : I32) {y : I32} + (hnz : y.val ≠ 0) + (hmin : I32.min ≤ scalar_rem x.val y.val) + (hmax : scalar_rem x.val y.val ≤ I32.max): + ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val := + Scalar.rem_spec hnz hmin hmax + +@[cepspec] theorem I64.rem_spec (x : I64) {y : I64} + (hnz : y.val ≠ 0) + (hmin : I64.min ≤ scalar_rem x.val y.val) + (hmax : scalar_rem x.val y.val ≤ I64.max): + ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val := + Scalar.rem_spec hnz hmin hmax + +@[cepspec] theorem I128.rem_spec (x : I128) {y : I128} + (hnz : y.val ≠ 0) + (hmin : I128.min ≤ scalar_rem x.val y.val) + (hmax : scalar_rem x.val y.val ≤ I128.max): + ∃ z, x % y = ret z ∧ z.val = scalar_rem x.val y.val := + Scalar.rem_spec hnz hmin hmax + -- ofIntCore -- TODO: typeclass? -def Isize.ofIntCore := @Scalar.ofIntCore .Isize -def I8.ofIntCore := @Scalar.ofIntCore .I8 -def I16.ofIntCore := @Scalar.ofIntCore .I16 -def I32.ofIntCore := @Scalar.ofIntCore .I32 -def I64.ofIntCore := @Scalar.ofIntCore .I64 -def I128.ofIntCore := @Scalar.ofIntCore .I128 -def Usize.ofIntCore := @Scalar.ofIntCore .Usize -def U8.ofIntCore := @Scalar.ofIntCore .U8 -def U16.ofIntCore := @Scalar.ofIntCore .U16 -def U32.ofIntCore := @Scalar.ofIntCore .U32 -def U64.ofIntCore := @Scalar.ofIntCore .U64 -def U128.ofIntCore := @Scalar.ofIntCore .U128 +@[reducible] def Isize.ofIntCore := @Scalar.ofIntCore .Isize +@[reducible] def I8.ofIntCore := @Scalar.ofIntCore .I8 +@[reducible] def I16.ofIntCore := @Scalar.ofIntCore .I16 +@[reducible] def I32.ofIntCore := @Scalar.ofIntCore .I32 +@[reducible] def I64.ofIntCore := @Scalar.ofIntCore .I64 +@[reducible] def I128.ofIntCore := @Scalar.ofIntCore .I128 +@[reducible] def Usize.ofIntCore := @Scalar.ofIntCore .Usize +@[reducible] def U8.ofIntCore := @Scalar.ofIntCore .U8 +@[reducible] def U16.ofIntCore := @Scalar.ofIntCore .U16 +@[reducible] def U32.ofIntCore := @Scalar.ofIntCore .U32 +@[reducible] def U64.ofIntCore := @Scalar.ofIntCore .U64 +@[reducible] def U128.ofIntCore := @Scalar.ofIntCore .U128 -- ofInt -- TODO: typeclass? |