Efficient algorithms for isomorphisms of simple types

Abstract

The first order isomorphism problem is to decide whether two nonrecursive 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 2 is the input size. This result improves upon the space bounds of the best previous algorithm. We also describe an time algorithm for the linear isomorphism problem, which does not include the distributive axiom, whereby improving upon the time of the best previous algorithm for this problem.