Higher-Order Equational Pattern Anti-Unification

Authors David M. Cerna, Temur Kutsia

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David M. Cerna
  • Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria
Temur Kutsia
  • Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria

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David M. Cerna and Temur Kutsia. Higher-Order Equational Pattern Anti-Unification. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of generalizations contains finitely many elements. We define the notion of optimal solution and investigate special fragments of the problem for which the optimal solution can be computed in linear or polynomial time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
  • Theory of computation → Higher order logic
  • Simply typed lambda calculus
  • anti-unification
  • equational theories


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