Lecture Notes in Computer Science Volume 431, 1990, pp 206-220
Date: 01 Jun 2005

ML typability is dexptime-complete

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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 \((2^{n^{O(1)} } )\) . 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 acyclic semi-unification. We prove that ML typability and acyclic semi-unification are log-space equivalent problems. We believe this result is of independent interest.

(Extended Summary)
This work is partly supported by NSF grant CCR-8901647 and by a grant of the Polish Ministry of National Education, No. RP.I.09