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TypeCompose

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Contents

1 Abstract

TypeCompose provides some classes & instances for forms of type composition. It also includes a very simple implementation of data-driven computation.

TypeCompose is used in Phooey, a functional GUI library.

2 Type composition

For now, see the Haddock docs and source code.

3 Data-driven computation

The representation of data-driven computations is quite simple and general. They have a news publisher (
news
) and a source of new values (
src
). Clients interested in the value subscribe to
news
and extract a new value from
src
when notified that the value may have changed. 
type DataDrivenG news src = Compose ((,) news) src
Thanks to properties of <div class="inline-code">
Compose
</div>, when
news
is a monoid and
src
is an applicative functor,
DataDriven news src
is an applicative functor also. The applicative property is very convenient for composition. To see how our simple definitions manage data-driven computations, expand the
Applicative
instances of
Compose
and
(,) a
: 
instance (Applicative src) => Applicative (DataDrivenG news src) where
  pure a = Comp (mempty, pure a)
  Comp (newsf,srcf) <*> Comp (newsx, srcx) =
    Comp (newsf `mappend` newsx) (getf <*> getx)
The idea here is that
mempty
is publisher that never has news to report, while
mappend
combines publishers into one that reports all the news of either. Thus
DataDrivenG
accumulates event sources as it composes, as well as delegating to whatever composition is done by
src
.

3.1 Specializing

Specializing, introduce types of "updaters" (actions), "sinks" (consumers) of values, and "news publishers" (somewhere to register updaters to be executed when events occur). 

type Updater src = src ()
type Sink src a  = a -> Updater src
type News src    = Sink src (Updater src)
And specialize
DataDriven
for news publishers: 
type DataDriven src = DataDrivenG (News src) src

For instance, the "Source" types used in Phooey are defined simply as 

type Source = DataDriven IO
Note that
News src
is a monoid when
src ()
is. In particular, given any applicative functor
f
, we can supply the following: 
-- Standard instance: Applicative functor applied to monoid
instance Monoid a => Monoid (f a) where { mempty = pure mempty; mappend = (*>) }
Note that
()
is a monoid. See an example in the <div class="inline-code">
Control.Instances
</div> module.
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