Numbering matters: first-order canonical forms for second-order recursive types

Authors:
Nadji Gauthier;François Pottier
Affiliations:
INRIA;INRIA
Venue:
Proceedings of the ninth ACM SIGPLAN international conference on Functional programming
Year:
2004

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Abstract

We study a type system equipped with universal types and equire-cursive types, which we refer to as F͘. We show that type equality may be decided in time O(nlog n), an improvement over the previous known bound of O(n2 ). In fact, we show that two more general problems, namely entailment of type equations and type unification, may be decided in time O(nlog n), a new result. To achieve this bound, we associate, with every F͘ type, a first-order canonical form, which may be computed in time O(nlogn). By exploiting this notion, we reduce all three problems to equality and unification of first-order recursive terms, for which efficient algorithms are known.