the MPTC Dilemma (please solve)

[Martin Sulzmann]

Ross Paterson writes:
 > On Sat, Feb 18, 2006 at 12:26:36AM +0000, Ross Paterson wrote:
 > > Martin Sulzmann <sulzmann at comp.nus.edu.sg> 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