erg/doc/zh_TW/API/modules/external/alstruct.md
2022-10-15 16:18:18 +08:00

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# 結構
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模塊為它們提供代表代數結構和補丁的Trait
* 成員
## BinOp(二進制運算)
```python
BinOp Op: Kind 2 = Subsume Op(Self, Self.ReturnTypeOf Op), Additional: {
.ReturnTypeof = TraitType -> Type
}
Nat <: BinOp Add
assert Nat. ReturnTypeof(Add) == Nat
assert Nat. ReturnTypeof(Sub) == Int
assert Nat. ReturnTypeof(Mul) == Nat
assert Nat.ReturnTypeof(Div) == Positive Ratio
```
## SemiGroup(半群)
```python
SemiGroup Op: Kind 2 = Op(Self, Self)
IntIsSemiGroupAdd = Patch Int, Impl=SemiGroupAdd
Int <: SemiGroup Add
```
## Functor(函子)
```python
# * Identity law: x.map(id) == x
# * Composition law: x.map(f).map(g) == x.map(f.then g)
Functor = Trait {
.map|T, U: Type| = (Self(T), T -> U) -> Self U
}
```
## Applicative(應用)
```python
# * Identity law: x.app(X.pure(id)) == x
Applicative = Subsume Functor, Additional: {
.pure|T: Type| = T -> Self T
.app|T, U: Type| = (Self(T), Self(T -> U)) -> Self U
}
```
## Monad(單子)
```python
Monad = Subsume Applicative, Additional: {
.bind|T, U: Type| = (Self(T), T -> Self U) -> Self U
}
```