On Wed, Sep 29, 2010 at 11:15 PM, DavidA
Ryan Ingram
writes: Haskell doesn't have true type functions; what you are really saying is
instance Monad (\v -> Vect k (Monomial v))
Yes, that is exactly what I am trying to say. And since I'm not allowed to say it like that, I was trying to say it using a type synonym parameterised over v instead. It appears that GHC won't let you use partially applied type synonyms as type constructors for instance declarations. Is this simply because the GHC developers didn't think anyone would want to, or is there some theoretical reason why it's hard, or a bad idea?
The version of the lambda calculus (System Fc) GHC uses for its internal representation doesn't support lambdas at the type level. I've bumped up against this limitation myself, and don't know of any way to 'cheat' it (which makes sense, given that it's so fundamental). You can use newtypes, and recursive definitions (sometimes with overlap and/or fundeps) work for some cases, though they can get quite nasty in the harder ones. I have to assume upgrading the type system to support this would highly nontrivial, though I don't know exactly how high, nor what drawbacks there might be.
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