# TypeCompose

## Abstract

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

- Read the Haddock docs (with source code, additional examples, and Comment/Talk links).
- Get the code repository:
, or`darcs get http://darcs.haskell.org/packages/TypeCompose` - Grab a distribution tarball.
- See the version changes.

TypeCompose is used in Phooey, a functional GUI library.

## Type composition

For now, see the Haddock docs and source code.

## 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 = (,) news `O` src
```

Thanks to properties of type composition (`O`

), 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) (srcf <*> srcx)
```

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`

.

### 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 `Control.Instances`

module.