While I agree with your general argument, I wonder if you realize
that functional dependencies have a strong, general, and elegant
mathematical foundation that long predates their use in Haskell?
If you want even a brief glimpse, there's s short article at
http://en.wikipedia.org/wiki/Functional_dependencies that might
give you some ideas. The mathematics of functional dependencies
plays an important role in the theory of relational databases.
I don't know what you consider as the mathematical foundations
for associated types, nor do I know why you consider that to be
either more general or more "mathematical" (whatever that means)
but I hope you'll enjoy the material on functional dependencies.
I admit I was being unfair on fundeps in calling them less
mathematical. Nonetheless, something about their addition to Haskell
grates on my mathematical sensitivities. They feel "bolted on" in a
way that associated types don't. Probably this is because of my own
bias which leads me to see Haskell as a subset of dependent type
theory, and ATs as some kind of sigma type (though I've never tried to
make this precise).
Barney.
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