TIL, #Haskell classes are _collection of_ types. They themselves are not types. It's a bit different from OO world, where classes _are_ types.
In that sense, Functor is a collection of classes, it allows me to map from type `a` to type `b` in a particular class. 🤔
#TypeClasses
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Seeing classes as a subset of types (equivalently, a constraint on what types are allowed) is great!
I think looking at Functor as a collection of classes is wrong, though. Instead, it's a collection of (or constraint on) type *constructors*.
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> classes as a subset of types
Yeah, that's another way to look at it, and really good one. Thanks Chris!
> Functor is a collection of classes
Well, if a class (* -> *) is collection of types, then Functor ((* -> *) -> *) feels more like collection of classes.
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(* -> *) isn't a class, though. That's a type constructor (or a type family, etc.). If you want to think of a type class as mapping a type to something, then it maps types to *values*. This is something you can't really express in Haskell directly.
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I see.. I mix up `class` and `data` construct of Haskell, I guess. Can you point to thing in which I can express it (Idris 🤔) or related material?
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Great question! Idris lets types depend on values, but values that depend on types are just plain polymorphism, and actually many languages do that!
To define an arbitrary map from types to values is "ad hoc polymorphism". Haskell can actually do that... using type classes.
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Oh yes, that's polymorphism. I can't help but wonder whether we have a concept of first-class polymorphism? Hmm.. I think, almost all the languages have special construct for polymorphism, e.g. Haskell's `class`.. Would it be beneficial to have them as first-class entity? 🤔
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You can see Haskell's TypeApplications language extension as a step in this direction. But type parameters are only sometimes treated as parameters, and other times are inferred, and it gets messy.
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Yeah I prefer how in languages like Agda you can see which one parameters are inferred with the brace syntax.