Editing GADTs for dummies (section)

== Type functions ==

A <hask>data</hask> declaration is a way to declare both type constructor and data
constructors. For example,

<haskell>
data Either a b = Left a | Right b
</haskell>

declares type constructor <hask>Either</hask> and two data constructors <hask>Left</hask>
and <hask>Right</hask>. Ordinary Haskell functions work with data constructors:

<haskell>
isLeft :: Either a b -> Bool
isLeft (Left _) = True
isLeft (Right _) = False
</haskell>

but there is also an analogous way to work with type constructors!

<haskell>
type X a = Either a a
</haskell>

declares a TYPE FUNCTION named <hask>X</hask>. Its parameter <hask>a</hask> must be some type
and it returns some type as its result. We can't use <hask>X</hask> on data values,
but we can use it on type values. Type constructors declared with
<hask>data</hask> statements and type functions declared with <hask>type</hask> statements
can be used together to build arbitrarily complex types. In such
"computations" type constructors serves as basic "values" and type
functions as a way to process them.

Indeed, type functions in Haskell are very limited compared to
ordinary functions - they don't support pattern matching,
nor multiple statements, nor recursion.