pointless-fun-1.1.0: Some common point-free combinators.

Data.Function.Pointless

Description

Pointless fun :)

Synopsis

• (\$::) :: (a -> b) -> ((a -> b) -> c -> d) -> c -> d
• (~>) :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d
• (!~>) :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d
• (.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> d
• (.^) :: (a -> c -> d) -> (b -> c) -> a -> b -> d
• (.!) :: (b -> c) -> (a -> b) -> a -> c

Multicomposition

Based on http://matt.immute.net/content/pointless-fun. These combinators allow you to easily modify the types of a many-argument function with syntax that looks like giving type signatures. For example,

``` foo    :: A -> B -> C

albert :: A -> X
beth   :: B -> Y
carol  :: C -> Z

bar :: X -> Y -> Z
bar = foo \$:: albert ~> beth ~> carol
```

(\$::) :: (a -> b) -> ((a -> b) -> c -> d) -> c -> dSource

Lift a function for multicomposition. This is like the `::` of a type signature.

(~>) :: (a -> b) -> (c -> d) -> (b -> c) -> a -> dSource

Multicompose a function on the appropriate argument. This is like the `->` arrows in a type signature.

(!~>) :: (a -> b) -> (c -> d) -> (b -> c) -> a -> dSource

Multicompose a function on the appropriate argument, calling the left function eagerly. That is, the resulting function will be strict in `a` if the left argument is strict in `a` (assuming the final function of the multicomposition, the one applied to the return value, is also strict).

Composition for arity 2

(.:) :: (c -> d) -> (a -> b -> c) -> a -> b -> dSource

Binary composition: pass two args to the right argument before composing.

``` (f .: g) x y = f (g x y)
```

or,

``` f .: g = curry (f . uncurry g)
```

This is the same as the common idiom `(f .) . g` but more easily extended to multiple uses, due to the fixity declaration.

(.^) :: (a -> c -> d) -> (b -> c) -> a -> b -> dSource

Secondary composition: compose the right argument on the second arg of the left argument.

``` (f .^ g) x y = f x (g y)
```

Strict composition

(.!) :: (b -> c) -> (a -> b) -> a -> cSource

Function composition which calls the right-hand function eagerly; i.e., making the left-hand function strict in its first argument.

``` (f .! g) x = f \$! g x
```

This defines the composition for the sub-category of strict Haskell functions. If the `Functor` class were parameterized by the domain and codomain categories (e.g., a regular `Functor f` would be `CFunctor (->) (->) f` instead) then this would allow us to define functors `CFunctor (->) (!->) f` where `fmap f . fmap g = fmap (f .! g)`.