diff options
Diffstat (limited to 'backends/lean/Base/Primitives')
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 226 |
1 files changed, 198 insertions, 28 deletions
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index 9e65d3c0..ec9665a5 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -533,6 +533,36 @@ 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} @@ -582,6 +612,36 @@ 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) @@ -628,6 +688,36 @@ 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} @@ -681,6 +771,48 @@ 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} @@ -734,6 +866,41 @@ 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 @@ -751,33 +918,34 @@ def U128.ofIntCore := @Scalar.ofIntCore .U128 -- ofInt -- TODO: typeclass? -def Isize.ofInt := @Scalar.ofInt .Isize -def I8.ofInt := @Scalar.ofInt .I8 -def I16.ofInt := @Scalar.ofInt .I16 -def I32.ofInt := @Scalar.ofInt .I32 -def I64.ofInt := @Scalar.ofInt .I64 -def I128.ofInt := @Scalar.ofInt .I128 -def Usize.ofInt := @Scalar.ofInt .Usize -def U8.ofInt := @Scalar.ofInt .U8 -def U16.ofInt := @Scalar.ofInt .U16 -def U32.ofInt := @Scalar.ofInt .U32 -def U64.ofInt := @Scalar.ofInt .U64 -def U128.ofInt := @Scalar.ofInt .U128 - -postfix:74 "%isize" => Isize.ofInt -postfix:74 "%i8" => I8.ofInt -postfix:74 "%i16" => I16.ofInt -postfix:74 "%i32" => I32.ofInt -postfix:74 "%i64" => I64.ofInt -postfix:74 "%i128" => I128.ofInt -postfix:74 "%usize" => Usize.ofInt -postfix:74 "%u8" => U8.ofInt -postfix:74 "%u16" => U16.ofInt -postfix:74 "%u32" => U32.ofInt -postfix:74 "%u64" => U64.ofInt -postfix:74 "%u128" => U128.ofInt - -example : Result U32 := 1%u32 + 2%u32 +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 + +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 : 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 @@ -819,7 +987,6 @@ example : Result U32 := 1%u32 + 2%u32 @[simp] theorem U128.ofInt_val_eq (h : Scalar.min ScalarTy.U128 ≤ x ∧ x ≤ Scalar.max ScalarTy.U128) : (U128.ofInt x h).val = x := by apply Scalar.ofInt_val_eq h - -- Comparisons instance {ty} : LT (Scalar ty) where lt a b := LT.lt a.val b.val @@ -847,6 +1014,9 @@ instance (ty : ScalarTy) : DecidableEq (Scalar ty) := instance (ty : ScalarTy) : CoeOut (Scalar ty) Int where coe := λ v => v.val +@[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 + -- -- We now define a type class that subsumes the various machine integer types, so -- -- as to write a concise definition for scalar_cast, rather than exhaustively -- -- enumerating all of the possible pairs. We remark that Rust has sane semantics |