[Haskell-cafe] Abstraction in data types

[Stephen Tetley]

On 18 March 2010 05:48, Brandon S. Allbery KF8NH <allbery at ece.cmu.edu> wrote:

> They can be mixed only with significant effort.  And you can't really
> prevent it once your users know the magic of existential quantification;
> *but* those lists won't typecheck when passed to your routines expecting a
> Polygon, because you will be expecting a (Point a => Polygon [a]) but they
> will be passing a (Polygon [forall a. Point a => a]) or something similar.


If you can live without constructors, an ADT view is another possibility...

Jeremy Gibbons gives a clear explanation of using an ADT to implement
complex numbers with polar and cartesian representations. Both
representations share the same type, so can be stored together in
lists - figuratively speaking the the existential type has been moved
"further down" inside the type.

See section 2:
http://www.comlab.ox.ac.uk/jeremy.gibbons/publications/adt.pdf

Best wishes

Stephen