ten

A mirrored typeclass hierarchy of Functor etc. for (k -> Type) -> Type.

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Overview

This gives equivalents of Functor, Applicative, Foldable, Traversable, and Representable for types whose parameter is a "wrapper" type constructor rather than just a concrete type.

The naming convention Functor10 comes from the fact that it's a functor from the category of objects with one type parameter to the category of objects with zero type parameters. See hakaru for precedent for this naming convention. From there, since everyone will end up pronouncing it "functor-ten", we pick "ten" as the package name and module namespace.

The two categories involved are:

The source category Hask{k}, denoting the category whose objects are Haskell type constructors of kind k -> Type, and whose morphisms m ~> n are quantified functions forall a. m a -> n a. Objects in this category are commonly Functors, although they don't have to be; examples include Identity, Const String, and Maybe. Morphisms in this category are parametric functions, such as maybeToList :: Maybe ~> [] or Const . length :: [] ~> Const Int. Note this is actually a collection of related categories: Type -> Type is a different category from Nat -> Type; for convenience we often hand-wave this fact away and say "the" category. Since these categories' defining characteristic is that their objects have one type parameter, we abbreviate it to "1".

The target category Hask, the normal category of Haskell types and functions. By the same convention as the last paragraph, we abbreviate this category to "0".

Then, functors from Hask{k} to Hask are functors from "1" to "0", and thus we call them Functor10. One common kind of functor between these two categories is "higher-kinded-data" records like data Thing f = Thing (f Int) (f Bool). This kind of usage is the main focus of the library, and has the most fully-formed functionality. Other things exist, too, which might have different instances of f in each value, or even existentially-quantified instances of f. These are available in varying states of completeness.