An Analysis of ML Typability

Abstract

We carry out an analysis of typability of terms in ML. Our main result is that this problem is DEXPTIME-hard, where by DEXPTIME we mean DTIME(2<supscrpt>n</supscrpt><supscrpt>0(1)</supscrpt>). This, together with the known exponential-time algorithm that solves the problem, yields the DEXPTIME-completeness result. This settles an open problem of P. Kanellakis and J. C. Mitchell. Part of our analysis is an algebraic characterization of ML typability in terms of a restricted form of semi-unification, which we identify as <italic>acyclic semi-unification</italic>. We prove that ML typability and acyclic semi-unification can be reduced to each other in polynomial time. We believe this result is of independent interest.

DOI: 10.1145/174652.174659

Extracted Key Phrases

1 Figure or Table

Statistics

051015'95'98'01'04'07'10'13'16
Citations per Year

77 Citations

Semantic Scholar estimates that this publication has 77 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@article{Kfoury1994AnAO, title={An Analysis of ML Typability}, author={Assaf J. Kfoury and Jerzy Tiuryn and Pawel Urzyczyn}, journal={J. ACM}, year={1994}, volume={41}, pages={368-398} }