Pointless fun :)
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 :: X -> A beth :: Y -> B carol :: C -> Z bar :: X -> Y -> Z bar = foo $:: albert ~> beth ~> carol
Lift a function for multicomposition. This is like the
of a type signature.
Multicompose a function on the appropriate argument. This is
-> arrows in a type signature.
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
the final function of the multicomposition, the one applied to
the return value, is also strict).
Composition for arity 2
Binary composition: pass two args to the right argument before composing.
(f .: g) x y = f (g x y)
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.
Secondary composition: compose the right argument on the second arg of the left argument.
(f .^ g) x y = f x (g y)
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
CFunctor (->) (->) f instead) then this would allow
us to define functors
CFunctor (->) (!->) f where
fmap f . fmap g = fmap (f .! g).