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TypeCompose

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Contents

1 Abstract

Warning: The Haddock docs are out of date. I'm trying to get a working haddock 2.0 running (on my windows machine).

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.

Please leave comments at the Talk page.

2 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
    .

3 Other features

3.1 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.

3.2 Pair- & function-like types

The
Data.Pair
and
Data.Lambda
patterns emerged while working on DeepArrow and Eros.
Data.Pair
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.

3.3 References

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

3.4 Titling

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

3.5 Partial values

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

3.6 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.