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authorSon HO2024-04-23 16:49:31 +0200
committerGitHub2024-04-23 16:49:31 +0200
commit1be37966ceea2510b911b119a96246b4657a62fd (patch)
tree85ed42e1be3a26741c26843ea06ada806170663a /backends
parentf3007820a21d11721507f5054b30bf5ae99a7b95 (diff)
parente49b92903cbd3dc7c981789cb4121dc89569bed3 (diff)
Merge pull request #156 from RaitoBezarius/orders
feat(backends/lean): scalars form a linear order
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