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| author | Ryan Lahfa | 2024-04-23 14:59:48 +0200 |
|---|---|---|
| committer | Ryan Lahfa | 2024-04-23 14:59:48 +0200 |
| commit | e49b92903cbd3dc7c981789cb4121dc89569bed3 (patch) | |
| tree | c44c327e9848ddc3d4991bb9f7de2847276d94a3 /backends | |
| parent | 00fb0b9dee66a5ba012170c3313454934c976d5e (diff) | |
feat(backends/lean): scalars form a linear order
More than c1c33de8, actually, scalars form a linear order with a
decidable ≤ operation which is induced by the integer (Z) model.
Signed-off-by: Ryan Lahfa <ryan.lahfa@inria.fr>
Diffstat (limited to '')
| -rw-r--r-- | backends/lean/Base/Primitives/Scalar.lean | 15 |
1 files changed, 15 insertions, 0 deletions
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean index be930754..014decb1 100644 --- a/backends/lean/Base/Primitives/Scalar.lean +++ b/backends/lean/Base/Primitives/Scalar.lean @@ -1404,6 +1404,21 @@ instance (ty: ScalarTy) : Preorder (Scalar ty) where trans (a: Int) ≤ (b: Int) ∧ ¬ (b: Int) ≤ (a: Int); exact lt_iff_le_not_le repeat rewrite [← Scalar.le_equiv]; rfl +instance (ty: ScalarTy) : PartialOrder (Scalar ty) where + le_antisymm := fun a b Hab Hba => Scalar.eq_imp _ _ ((@le_antisymm Int _ _ _ ((Scalar.le_equiv a b).1 Hab) ((Scalar.le_equiv b a).1 Hba))) + +instance ScalarDecidableLE (ty: ScalarTy) : DecidableRel (· ≤ · : Scalar ty -> Scalar ty -> Prop) := by + simp [instLEScalar] + -- Lift this to the decidability of the Int version. + infer_instance + +instance (ty: ScalarTy) : LinearOrder (Scalar ty) where + le_total := fun a b => by + rcases (Int.le_total a b) with H | H + left; exact (Scalar.le_equiv _ _).2 H + right; exact (Scalar.le_equiv _ _).2 H + decidableLE := ScalarDecidableLE ty + -- Leading zeros def core.num.Usize.leading_zeros (x : Usize) : U32 := sorry def core.num.U8.leading_zeros (x : U8) : U32 := sorry |