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authorRyan Lahfa2024-04-23 14:59:48 +0200
committerRyan Lahfa2024-04-23 14:59:48 +0200
commite49b92903cbd3dc7c981789cb4121dc89569bed3 (patch)
treec44c327e9848ddc3d4991bb9f7de2847276d94a3 /backends
parent00fb0b9dee66a5ba012170c3313454934c976d5e (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.lean15
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