Re: [stack] Motivations to embrace decidable type systems

On Apr 4, 2009, at 9:01 PM, hallucious wrote:

> One motivation for this work was to broaden the range of functions  
> which can be investigated by looking at their type, which can be  
> useful to see their effect.

You may want to look at Djinn if you haven't already:
http://lambda-the-ultimate.org/node/1178

> Another was to allow the programmer to provide additional  
> constraints. I also hoped that the type would form a basis for  
> proving properties of any function, using denotation provided by the  
> programmer.

In my opinion, it would be more useful to add types dependent on  
values rather than (or in addition to) higher rank polymorphism and  
subtyping if your goal to allow programmers to prove things. There  
are, as you probably know, a large number of languages that already  
take this approach (Agda, Coq, Epigram, Dependent ML, ATS, etc).

> I do not expect that there is any automated (unguided) procedure to  
> check, for instance, whether two type formulas are equivalent in  
> this system. (Is this what decidable type inference means?)

In practice, I believe undecidable just means "not guaranteed to  
terminate". For example, type inference is undecidable in a language  
like Agda because certain programs will cause the type checking stage  
to never finish.

- John