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Thu Oct 27 10:05:16 EDT 2011

## Commuation

How to name this pattern?
What happens a lot to me when programming with type classes in Haskell
is that I run into commutation problems, meaning that I run into
operations like
a (b t) -> b (a t)
and their inverse that encode a morphism between the two types with
different nesting order, basically saying that a and b commute.
In general this doesn't hold: such functions usually do something
significant, and might overall not be invertible.
However in other cases the morphisms might be bidirectional and
somewhat trivial. Is there a way to represent such a morphism in an
abstract way? I.e. is there a way to automatically derive "trivial
morphisms" for cummutative type constructors?
Sorry, no example as this is just a vague hunch..

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