On Wed, Nov 25, 2020 at 07:56:49PM +0000, Barak A. Pearlmutter wrote:
True. And their use in Arrow is a great example of pairs that do *not* work well as instances of Foldable as currently defined. Arrow is using pairs as abstract Cartesian products, and the natural isomorphism A×B≅B×A is used implicitly all the time. The Foldable definition for pairs breaks that symmetry inappropriately.
The "symmetry breaking" is not a result of the perhaps regrettable Foldable instance, rather it is a basic consequence of the fact that given: data Foo a b = Foo a b we immediately get a Functor "Foo a :: * -> *" for each a, of which "(,) a" is but one example. I find nothing objectionable in the Functor instance "(,) a" or the Bifunctor instance "(,)". It is only the Traversable and Foldable instances of "(,) a" that have the noted unexpected behaviour. -- Viktor.