CODEWITHSUNDEEP
javascriptcategory-theoryfantasyland
Alper
Alper

Reputation: 3953

What does fantasy-land/id do?

fantasy-land/id :: Category c => () -> c a a

I don't really understand what this signature says? id is a method that takes zero parameters and returns something that is a Category and two other things.

Is that correct? What's the point of this?

Upvotes: 1

Views: 102

Answers (1)

Bartosz Milewski
Bartosz Milewski

Reputation: 11630

A category consists of objects and morphisms (arrows). If you want to define a category inside Haskell, you pretty much are stuck with objects as types. But for any two objects you may define a set of morphisms: the hom-set. Here, c is a type constructor that takes two objects (types), say a and b and produces a hom-set c a b. In the simplest example just replace c with (->). In this case c a b becomes a->b (using infix notation). By the same token c a a corresponds to a->a. One of these morphisms is designated as the identity morphism. The function () -> c a a picks that morphism. The complete definition must also include the composition operator (.) that takes two composable hom-sets and produces a third, and the laws. Unit and associativity laws are not expressible in Haskell, though.

Upvotes: 2

Related Questions