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[[Category:Applicative Functor]]
[[Category:Libraries]]
[[Category:Packages]]
[[Category:Type-level programming]]
== Abstract ==
== Abstract ==


'''TypeCompose''' provides some classes & instances for forms of type composition.  It also includes a very simple implementation of data-driven computation.
'''TypeCompose''' provides some classes & instances for forms of type composition, as well as some modules that haven't found another home.


* Read [http://darcs.haskell.org/packages/TypeCompose/doc/html the Haddock docs] (with source code, additional examples, and Comment/Talk links).
Besides this wiki page, here are more ways to find out about TypeCompose:
* Get the code repository: '''<tt>darcs get http://darcs.haskell.org/packages/TypeCompose</tt>''', or
* Visit the [http://hackage.haskell.org/cgi-bin/hackage-scripts/package/TypeCompose Hackage page] for library documentation and to download & install.
* Grab a [http://darcs.haskell.org/packages/TypeCompose/dist distribution tarball].
* Or install with <tt>cabal install TypeCompose</tt>.
* See the [http://darcs.haskell.org/packages/TypeCompose/CHANGES version changes].
* Get the code repository: <tt>git clone git@github.com:conal/TypeCompose.git</tt>.
<!--* See the [[TypeCompose/Versions| version history]].-->


TypeCompose is used in [[Phooey]], a functional GUI library.
== Type composition ==


== Type composition ==
The <hask>Control.Compose</hask> module includes
* Various type compositions (unary/unary, binary/unary, etc).  Most are from [http://www.soi.city.ac.uk/~ross/papers/Applicative.html Applicative Programming with Effects].  In particular, <hask>g `O` f</hask> 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 <hask>Flip (->) o</hask>, for <hask>(-> o)</hask>.
* Constructor in pairs: <hask>(f a, g a)</hask>.
* Constructor in arrows/functions: <hask>f a ~> g a</hask>.
 
== Other features ==
 
=== Composable bijections ===


For now, see the [http://darcs.haskell.org/packages/TypeCompose/doc/html/Control-Compose.html Haddock docs] and [http://darcs.haskell.org/packages/TypeCompose/doc/html/src.Control.Compose.hs.html source code].
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.


== Data-driven computation ==
The <hask>Data.Bijection</hask> module is inspired by [http://citeseer.ist.psu.edu/alimarine05there.html There and Back Again: Arrows for Invertible Programming], though done here in a less general setting.


The representation of data-driven computations is quite simple and general.  They have a ''news'' publisher (<hask>news</hask>) and a source of new values (<hask>src</hask>).  Clients interested in the value subscribe to <hask>news</hask> and extract a new value from <hask>src</hask> when notified that the value may have changed.
=== Pair- & function-like types ===


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


Thanks to properties of [http://darcs.haskell.org/packages/TypeCompose/doc/html/Control-Compose.html#t%3ACompose <hask>Compose</hask>], when <hask>news</hask> is a [http://www.haskell.org/ghc/docs/latest/html/libraries/base/Data-Monoid.html#t%3AMonoid monoid] and <hask>src</hask> is an [http://www.haskell.org/ghc/docs/latest/html/libraries/base/Control-Applicative.html#t%3AApplicative applicative functor], <hask>DataDriven news src</hask> is an applicative functor also.  The applicative property is very convenient for composition.
For example uses of <hask>Pair</hask> and <hask>Lambda</hask>, see [[TV]] and [[Eros]].


To see how our simple definitions manage data-driven computations, expand the <hask>Applicative</hask> instances of <hask>Compose</hask> and <hask>(,) a</hask>:
=== References ===
<haskell>
instance (Applicative src) => Applicative (DataDrivenG news src) where
  pure a = Comp (mempty, pure a)
  Comp (newsf,srcf) <*> Comp (newsx, srcx) =
    Comp (newsf `mappend` newsx) (srcf <*> srcx)
</haskell>


The idea here is that <hask>mempty</hask> is publisher that never has news to report, while <hask>mappend</hask> combines publishers into one that reports all the news of either. Thus <hask>DataDrivenG</hask> accumulates event sources as it composes, as well as delegating to whatever composition is done by <hask>src</hask>.
Monads with references.  Direct rip-off from [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.145 Global Variables in Haskell].


=== Specializing ===
=== Titling ===


Specializing, introduce types of "updaters" (actions), "sinks" (consumers) of values, and "news publishers" (somewhere to register updaters to be executed when events occur).
For giving titles to things.  I know it sounds kind of random.  More useful than I first thought.  Used in [[Phooey]], [[TV]], and [[Eros]].


<haskell>
=== Partial values ===
type Updater src = src ()
type Sink src a  = a -> Updater src
type News src    = Sink src (Updater src)
</haskell>


And specialize <hask>DataDriven</hask> for news publishers:
A monoid of partial values.  See the [http://conal.net/blog/posts/a-type-for-partial-values/ teaser] and [http://conal.net/blog/posts/implementing-a-type-for-partial-values/ solution] blog
<haskell>
posts.
type DataDriven src = DataDrivenG (News src) src
</haskell>


For instance, the "Source" types used in [[Phooey]] are defined simply as
=== Context-dependent monoids ===
<haskell>
type Source = DataDriven IO
</haskell>


Note that <hask>News src</hask> is a [http://www.haskell.org/ghc/docs/latest/html/libraries/base/Data-Monoid.html#t%3AMonoid monoid] when <hask>src ()</hask> is.  In particular, given any applicative functor <hask>f</hask>, we can supply the following:
Bit of an oddball also.  <hask>Data.CxMonoid</hask> defines a sort of meta-monoid, that can be supplied dynamically with choices of <hask>mempty</hask> and <hask>mappend</hask>.  Used in [[Phooey]] (starting with version 1.3) so that layout could be a monoid but still vary in style.
<haskell>
-- Standard instance: Applicative functor applied to monoid
instance Monoid a => Monoid (f a) where { mempty = pure mempty; mappend = (*>) }
</haskell>
Note that <hask>()</hask> is a monoid.  See an example in the [http://darcs.haskell.org/packages/TypeCompose/doc/html/src.Control.Instances.hs.html <hask>Control.Instances</hask> module].

Latest revision as of 22:44, 29 June 2021


Abstract

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.

References

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

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.

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.

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