问题描述
我发现逻辑和编程之间存在同构,称为,那么类别理论是否有这样的等价性,这有助于理解Functors或Monads之类的东西?
是的!它被称为 - 它将类别对象映射到类型和态射到术语。因此,键入的lambda(没有名称的函数)或甚至函数可以表示为, Unite类型成为,类型集合(或更复杂的结构)是,并且应用+咖啡因。
I found that there is an isomorphism between logic and programming, called Curry-Howard correspondence, so is there any such equivalence for Category theory, which helps to understand things like Functors or Monads?
Yes! It's called Curry–Howard–Lambek - it maps Category objects to types and morphisms to terms. So, typed lambda (function without name) or even function may be represented as cartesian-closed category, where Unite-type becomes a terminal object, set of types (or more complex structure) is product, and apply+currying is exponential.
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