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HigherOrder Dynamic Pattern Unification for Dependent Types and Records

Summary: Higher­Order Dynamic Pattern Unification for
Dependent Types and Records
Andreas Abel 1 and Brigitte Pientka 2
1 Institut f˜ur Informatik, Ludwig­Maximilians­Universit˜at, M˜unchen, Deutschland
2 School of Computer Science, McGill University, Montreal, Canada
Abstract. While higher­order pattern unification for # # ­calculus is de­
cidable and unique unifiers exists, we face several challenges in practice:
1) the pattern fragment itself is too restrictive for many applications; this
is typically addressed by solving sub­problems which satisfy the pattern
restriction eagerly but delay solving sub­problems which are non­patterns
until we have accumulated more information. This leads to a dynamic
pattern unification. 2) Many systems implement # ## calculus and hence
the known pattern unification algorithms for # # are too restrictive.
In this paper, we present a constraint­based unification algorithm for
# ## ­calculus which solves a richer class of patterns than currently pos­
sible; in particular it takes into account type isomorphisms to translate
unification problems containing #­types into problems only involving #­
types. We prove correctness of our algorithm and discuss its application.


Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München


Collections: Computer Technologies and Information Sciences