Data Combinator Generator
Generate a special combinator from any data type.
Description
This library provides a function to generate a special combinator from any data type (GADTs are not currently supported).
This was inspired by the recursionschemes library where they have a function to automagically generate a base functor. Although, this new base functor data type has custom constructors and to define the *morphism algebras turns into boring pattern matching.
So, this library provides a function called makeCombinator
that produces a
nice combinator to deal with data types as they were defined in terms of Pairs
((,)
) and Sums (Either
). With this nice combinator we are able to view a
data type as its equivalent categorical isomorphism and manipulate it with an
interface similar as the either
function provided from base
.
Example
To create this special combinator you just need to call makeCombinator ''<data type name
as in the example below:
 List type
data List a = Nil  List a (List a)
makeCombinator ''List
This example will generate the following code:
makeCombinator ''ListF
======>
listf f_acw7 f_acw8 Nil = f_acw7 ()
listf f_acw7 f_acw8 (Cons a_acw9 a_acwa) = f_acw8 (a_acw9, a_acwa)
As you can see it's pretty close as to have the type defined as the set of
sums and pairs data List a = Either () (a, List a)
, which we could then use
either
function as well as other convinent (,)
combinators.
An important note is that the generated function has always the same name as the data type but in low characters and the order of the functions to be applied to the type constructors it's the same order which they were declared.
A simple example on how we can beneficiate from using this special combinator when defining catamorphisms using recursionschemes:

Without the combinator:
length :: [a] > Int length = cata gene where gene Nil = 0 gene (Cons a x) = x + 1

With the combinator:
makeCombinator'' ListF length :: [a] > Int length = cata (listf (const 0) (succ . snd))
I recognize that for such a simple data type and catamorphism it's hard to see any gain in readability/implementation. But with this special combinator it's a lot easier to go from paper to code as it's almost a direct translation.
There's a fully working example in the examples
folder that uses the
recursionschemes library as well as a nice small program calculus (AoP
inspired) combinators library to show how simple and straightforward it is to
use it with this new combinator.