2df35360ee
and new option `set_option allowUnsafeReductibility true` to override validation. --------- Co-authored-by: Mario Carneiro <di.gama@gmail.com>
48 lines
1.6 KiB
Text
48 lines
1.6 KiB
Text
class OpAssoc (op : α → α → α) : Prop where
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protected op_assoc (x y z) : op (op x y) z = op x (op y z)
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abbrev op_assoc (op : α → α → α) [self : OpAssoc op] := self.op_assoc
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structure SemigroupSig (α) where
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op : α → α → α
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structure SemiringSig (α) where
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add : α → α → α
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mul : α → α → α
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def SemiringSig.toAddSemigroupSig (s : SemiringSig α) : SemigroupSig α where
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op := s.add
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def SemiringSig.toMulSemigroupSig (s : SemiringSig α) : SemigroupSig α where
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op := s.mul
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unif_hint (s : SemiringSig α) (t : SemigroupSig α) where
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t =?= s.toAddSemigroupSig ⊢ t.op =?= s.add
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unif_hint (s : SemiringSig α) (t : SemigroupSig α) where
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t =?= s.toMulSemigroupSig ⊢ t.op =?= s.mul
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class Semigroup (s : SemigroupSig α) : Prop where
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protected op_assoc (x y z) : s.op (s.op x y) z = s.op x (s.op y z)
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instance Semirgoup.toOpAssoc (s : SemigroupSig α) [Semigroup s] : OpAssoc (no_index s.op) := ⟨Semigroup.op_assoc⟩
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class Semiring (s : SemiringSig α) : Prop where
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protected add_assoc (x y z) : s.add (s.add x y) z = s.add x (s.add y z)
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protected mul_assoc (x y z) : s.mul (s.mul x y) z = s.mul x (s.mul y z)
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instance Semiring.toAddSemigroup (s : SemiringSig α) [Semiring s] : Semigroup (no_index s.toAddSemigroupSig) where
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op_assoc := Semiring.add_assoc
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instance Semiring.toMulSemigroup (s : SemiringSig α) [Semiring s] : Semigroup (no_index s.toMulSemigroupSig) where
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op_assoc := Semiring.mul_assoc
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section Test
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variable (s : SemiringSig α) [Semiring s]
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local infix:70 " ⋆ " => s.mul
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example (w x y z : α) : (w ⋆ x) ⋆ (y ⋆ z) = w ⋆ ((x ⋆ y) ⋆ z) := by
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repeat rw [op_assoc (.⋆.)]
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end Test
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