Efficient algorithms for isomorphisms of simple types

Authors:
Yoav Zibin;Joseph (Yossi) Gil;Jeffrey Considine
Affiliations:
Technion---Israel Institute of Technology;Technion---Israel Institute of Technology;Boston University
Venue:
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Year:
2003

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Abstract

The first order isomorphism problem is to decide whether two non-recursive types using product- and function-type constructors, are isomorphic under the axioms of commutative and associative products, and currying and distributivity of functions over products. We show that this problem can be solved in O(n log2 n) time and O(n) space, where is n the input size. This result improves upon the O(n log2 n) time and O(n2) space bounds of the best previous algorithm. We also describe an O(n) time algorithm for the linear isomorphism problem, which does not include the distributive axiom, whereby improving upon the O(n log n) time of the best previous algorithm for this problem.