Ross Paterson writes: > On Sat, Feb 18, 2006 at 12:26:36AM +0000, Ross Paterson wrote: > > Martin Sulzmann <[EMAIL PROTECTED]> writes: > > > Result2: > > > Assuming we can guarantee termination, then type inference > > > is complete if we can satisfy > > > - the Bound Variable Condition, > > > - the Weak Coverage Condition, > > > - the Consistency Condition, and > > > - and FDs are full. > > > Effectively, the above says that type inference is sound, > > > complete but semi-decidable. That is, we're complete > > > if each each inference goal terminates. > > > > I think that this is a little stronger than Theorem 2 from the paper, > > which assumes that the CHR derived from the instances is terminating. > > If termination is obtained via a depth limit (as in hugs -98 and ghc > > -fallow-undecidable-instances), it is conceivable that for a particular > > goal, one strategy might run into the limit and fail, while a different > > strategy might reach success in fewer steps. >
Yes, the above is stronger than Theorem 2. > Rereading, I see you mentioned dynamic termination checks, but not > depth limits. Can you say a bit more about termination? It seems to > be crucial for your proofs of confluence. > A depth limit is not enough. For confluence we need that *all* derivations for a particular goal terminate. Once we have confluence we get completeness of the inference checks. I think you're asking: If one derivation for a particular goal terminates will all other derivations for that goal terminate as well? (BTW, such a result can be proven for range restriction). It might hold (assuming the usual restrictions, instances terminate, weak coverage holds etc) by I'm not sure (means, I couldn't come up with a counter-example but a formal proof is still missing). Martin _______________________________________________ Haskell-prime mailing list Haskell-prime@haskell.org http://haskell.org/mailman/listinfo/haskell-prime
