Algorithms for Extended Alpha-Equivalence and Complexity

Authors Manfred Schmidt-Schauß, Conrad Rau, David Sabel

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Manfred Schmidt-Schauß
Conrad Rau
David Sabel

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Manfred Schmidt-Schauß, Conrad Rau, and David Sabel. Algorithms for Extended Alpha-Equivalence and Complexity. In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 255-270, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


Equality of expressions in lambda-calculi, higher-order programming languages, higher-order programming calculi and process calculi is defined as alpha-equivalence. Permutability of bindings in let-constructs and structural congruence axioms extend alpha-equivalence. We analyse these extended alpha-equivalences and show that there are calculi with polynomial time algorithms, that a multiple-binding "let" may make alpha-equivalence as hard as finding graph-isomorphisms, and that the replication operator in the pi-calculus may lead to an EXPSPACE-hard alpha-equivalence problem.
  • alpha-equivalence
  • higher-order calculi
  • deduction
  • pi-calculus


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