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Efficient algorithms for isomorphisms of simple types

  • JOSEPH (YOSSI) GIL (a1) and YOAV ZIBIN (a1)

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 $O(n \log^2 n)$ time and $O(n)$ space, where $n$ is the input size. This result improves upon the $O(n^2 \log n)$ time and $O(n^2)$ 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, thereby improving upon the $O(n \log n)$ time of the best previous algorithm for this problem.

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A preliminary version of this paper was published in the proceedings of POPL'03 (Zibin et al. 2003).
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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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