78 lines
2.2 KiB
Text
78 lines
2.2 KiB
Text
class One (α : Type u) where
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one : α
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instance One.toOfNat1 {α} [One α] : OfNat α (nat_lit 1) where
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ofNat := ‹One α›.1
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class MulOneClass (M : Type u) extends One M, Mul M
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class FunLike (F : Sort _) (α : outParam (Sort _)) (β : outParam <| α → Sort _) where
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coe : F → ∀ a : α, β a
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instance (priority := 100) [FunLike F α β] : CoeFun F fun _ => ∀ a : α, β a where coe := FunLike.coe
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section One
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variable [One M] [One N]
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structure OneHom (M : Type _) (N : Type _) [One M] [One N] where
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toFun : M → N
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map_one' : toFun 1 = 1
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class OneHomClass (F : Type _) (M N : outParam (Type _)) [One M] [One N]
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extends FunLike F M fun _ => N where
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map_one : ∀ f : F, f 1 = 1
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@[simp]
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theorem map_one [OneHomClass F M N] (f : F) : f 1 = 1 :=
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OneHomClass.map_one f
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end One
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section Mul
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variable [Mul M] [Mul N]
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structure MulHom (M : Type _) (N : Type _) [Mul M] [Mul N] where
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toFun : M → N
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map_mul' : ∀ x y, toFun (x * y) = toFun x * toFun y
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infixr:25 " →ₙ* " => MulHom
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class MulHomClass (F : Type _) (M N : outParam (Type _)) [Mul M] [Mul N]
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extends FunLike F M fun _ => N where
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map_mul : ∀ (f : F) (x y : M), f (x * y) = f x * f y
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@[simp]
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theorem map_mul [MulHomClass F M N] (f : F) (x y : M) : f (x * y) = f x * f y :=
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MulHomClass.map_mul f x y
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end Mul
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section mul_one
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variable [MulOneClass M] [MulOneClass N]
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structure MonoidHom (M : Type _) (N : Type _) [MulOneClass M] [MulOneClass N] extends
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OneHom M N, M →ₙ* N
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infixr:25 " →* " => MonoidHom
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class MonoidHomClass (F : Type _) (M N : outParam (Type _)) [MulOneClass M] [MulOneClass N] extends MulHomClass F M N, OneHomClass F M N
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instance (F : Type _) (M N : outParam (Type _)) [MulOneClass M] [MulOneClass N] [MonoidHomClass F M N] : CoeTC F (M →* N) :=
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⟨fun f => {
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toFun := f,
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map_one' := map_one f,
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map_mul' := map_mul f
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}⟩
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-- Now we reverse the order of the parents in the extends clause:
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class MonoidHomClass' (F : Type _) (M N : outParam (Type _)) [MulOneClass M] [MulOneClass N] extends OneHomClass F M N, MulHomClass F M N
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instance [MonoidHomClass' F M N] : CoeTC F (M →* N) :=
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⟨fun f => {
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toFun := f,
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map_one' := map_one f,
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map_mul' := map_mul f
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}⟩
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