编程中类别的类比是什么？ [英] What is the analog of Category in programming

问题描述

我发现逻辑和编程之间存在同构，称为咖喱霍华德对应关系，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？

解决方案

是的！它被称为咖喱霍华德兰贝克 - 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笛卡尔封闭类别， Unite类型成为终端对象，类型集合（或更复杂的结构）是产品，并且应用+咖啡因 exponential 。

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?

解决方案

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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