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

Robert Dockins robdockins at fastmail.fm
Fri Feb 10 14:02:35 EST 2006

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?

Rob Dockins

Speak softly and drive a Sherman tank.
Laugh hard; it's a long way to the bank.
           -- TMBG

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