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57 lines
1.1 KiB
Markdown
57 lines
1.1 KiB
Markdown
# alstruct
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代数的構造を表すトレイトや、それにかかるパッチを提供するモジュール。
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* member
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## BinOp
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```erg
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BinOp Op: Kind 2 = Subsume Op(Self, Self.ReturnTypeOf Op), Additional: {
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.ReturnTypeof = TraitType -> Type
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}
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Nat <: BinOp Add
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assert Nat.ReturnTypeof(Add) == Nat
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assert Nat.ReturnTypeof(Sub) == Int
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assert Nat.ReturnTypeof(Mul) == Nat
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assert Nat.ReturnTypeof(Div) == Positive Ratio
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```
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## SemiGroup
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```erg
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SemiGroup Op: Kind 2 = Op(Self, Self)
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IntIsSemiGroupAdd = Patch Int, Impl=SemiGroup Add
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Int <: SemiGroup Add
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```
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## Functor
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```erg
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## * Identity law: x.map(id) == x
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## * Composition law: x.map(f).map(g) == x.map(f.then g)
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Functor = Trait {
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.map|T, U: Type| = (Self(T), T -> U) -> Self U
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}
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```
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## Applicative
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```erg
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## * Identity law: x.app(X.pure(id)) == x
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Applicative = Subsume Functor, Additional: {
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.pure|T: Type| = T -> Self T
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.app|T, U: Type| = (Self(T), Self(T -> U)) -> Self U
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}
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```
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## Monad
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```erg
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Monad = Subsume Applicative, Additional: {
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.bind|T, U: Type| = (Self(T), T -> Self U) -> Self U
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}
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```
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