[Haskell-cafe] question about type lambda and decidability of typechecking

Robert Dockins robdockins at fastmail.fm
Fri Feb 10 18:19:27 EST 2006

For the record, a little more digging turned up this


which answers most of my questions.

On Feb 10, 2006, at 2:02 PM, Robert Dockins wrote:

> OK.  I've been doing a little thinking about type lambda in Haskell.
> Now, I understand the prevailing wisdom is that adding type lambda  
> and/or partially applied type synonyms to the haskell type system  
> would make type checking/inference undecidable.  The reason given  
> is that higher-order unification is undecidable.
> I have to admit that I don't fully understand this reason.  Setting  
> aside typeclasses for now, it seems to me that type expressions  
> together with the kind system are just the simply-typed lambda  
> calculus with unit, which is well known to be strong normalizing.   
> So any type with kind * has a normal form with (by definition) no  
> internal redexes.  I think this is sufficient to guarantee that all  
> type lambdas are removed.  Now you can proceed using first-order  
> unification, which is decidable.  Of course, all valid expressions  
> have kind * (ignoring unboxing and other trickiness for now).
> So where have I gone wrong?  Do typeclasses complicate the matter?   
> Or have I missed something more basic?
> Thanks,
> Rob Dockins
> Speak softly and drive a Sherman tank.
> Laugh hard; it's a long way to the bank.
>           -- TMBG
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Speak softly and drive a Sherman tank.
Laugh hard; it's a long way to the bank.
           -- TMBG

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