Re: [Haskell-cafe] Infinite types should be optionally allowed

I'm pretty sure that the problem is decidable, at least with haskell 98 types (other type extensions may complicate things a bit). It ends up being a graph unification algorithm. I've tried some simple algorithms and they seem to work. What do you mean by "the inference engine is only half of the story"?

From what I understand, the inference engine infers types via unification, if the types unify, then the unified types are the inferred types, if the types don't unify, then type check fails. Am I missing/misunderstanding something?

I almost think that the problem might be solvable by just generating the appropriate newtype whenever an infinite type shows up, and doing the wrapping/unwrapping behind the scenes. This would be a hacked up way to do it, but I think it would work. On Fri, Feb 13, 2009 at 6:09 PM, Luke Palmer wrote:

On Fri, Feb 13, 2009 at 4:04 PM, Luke Palmer wrote:

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On Fri, Feb 13, 2009 at 3:13 PM, Job Vranish wrote:

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There are good reasons against allowing infinite types by default (mostly, that a lot of things type check that are normally not what we want). An old haskell cafe conversation on the topic is here:

http://www.nabble.com/There%27s-nothing-wrong-with-infinite-types!-td7713737...

However, I think infinite types should be allowed, but only with an explicit type signature. In other words, don't allow infinite types to be inferred, but if they are specified, let them pass. I think it would be very hard to shoot yourself in the foot this way.

Oops! I'm sorry, I completely misread the proposal. Or read it correctly, saw an undecidability hiding in there, and got carried away.

What you are proposing is called equi-recursive types, in contrast to the more popular iso-recursive types (which Haskell uses). There are plentiful undecidable problems with equi-recursive types, but there are ways to pull it off. The question is whether these ways play nicely with Haskell's type system.

But because of the fundamental computational problems associated, there needs to be a great deal of certainty that this is even possible before considering its language design implications.

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That inference engine seems to be a pretty little proof-of-concept, doesn't it? But it is sweeping some very important stuff under the carpet.

The proposal is to infer the type of a term, then check it against an annotation. Thus every program is well-typed, but it's the compiler's job to check that it has the type the user intended. I like the idea.

But the inference engine is only half of the story. It does no type checking. Although checking is often viewed as the easier of the two problems, in this case it is not. A term has no normal form if and only if its type is equal to (forall a. a). You can see the problem here.

Luke

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Newtype is the standard solution to situations where you really need an infinite type, but in some cases this can be a big annoyance. Using newtype sacrifices data type abstraction and very useful type classes like Functor. You can use multiparameter type classes and functional dependencies to recover some of the lost abstraction, but then type checking becomes harder to reason about and the code gets way more ugly (If you doubt, let me know, I have some examples). Allowing infinite types would fix this.

I'm imagining a syntax something like this: someFunctionThatCreatesInfiniteType :: a -> b | b = [(a, b)]

Thoughts? Opinions? Am I missing anything obvious?

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