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TypeCompose provides some classes & instances for forms of type composition, as well as some modules that haven't found another home.

Besides this wiki page, here are more ways to find out about TypeCompose:

  • Visit the Hackage page for library documentation and to download & install.
  • Or install with cabal install TypeCompose.
  • Get the code repository: git clone git@github.com:conal/TypeCompose.git.

Type composition

The Control.Compose module includes

  • Various type compositions (unary/unary, binary/unary, etc). Most are from Applicative Programming with Effects. In particular, g `O` f composes functors in to functors and applicative functors (AFs) into AFs. (In contrast, monads do not in general compose.) Composition makes AF-based programming simple and elegant, partly because we don't need an AF counterpart to monad transformers.
  • Cofunctors (contravariant functors). Great for "consumer" types, just as functors suit "producer" (container) types. There are several composition options.
  • Type argument flip. Handy for cofunctors: use Flip (->) o, for (-> o).
  • Constructor in pairs: (f a, g a).
  • Constructor in arrows/functions: f a ~> g a.

Other features

Composable bijections

Given all the type constructors and compositions of them, I found myself writing some pretty awkward code to wrap & unwrap through multiple layers. Composable bijections help a lot.

The Data.Bijection module is inspired by There and Back Again: Arrows for Invertible Programming, though done here in a less general setting.

Pair- & function-like types

The Data.Zip and Data.Lambda patterns emerged while working on DeepArrow and Eros. Data.Zip generalizes zip and unzip from [] to other functors. It also provides variants of type f a -> f (a,b) and f a -> f (a,b). Data.Lambda is similar with classes for lambda-like constructions.

For example uses of Pair and Lambda, see TV and Eros.


Monads with references. Direct rip-off from Global Variables in Haskell.


For giving titles to things. I know it sounds kind of random. More useful than I first thought. Used in Phooey, TV, and Eros.

Partial values

A monoid of partial values. See the teaser and solution blog posts.

Context-dependent monoids

Bit of an oddball also. Data.CxMonoid defines a sort of meta-monoid, that can be supplied dynamically with choices of mempty and mappend. Used in Phooey (starting with version 1.3) so that layout could be a monoid but still vary in style.