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A Generic Framework for Higher-Order Generalizations

Authors David M. Cerna, Temur Kutsia

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David M. Cerna
  • FMV and RISC, Johannes Kepler University Linz, Austria
Temur Kutsia
  • RISC, Johannes Kepler University Linz, Austria


We thank Tomer Libal for useful discussions on the early version of the paper.

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David M. Cerna and Temur Kutsia. A Generic Framework for Higher-Order Generalizations. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 10:1-10:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


We consider a generic framework for anti-unification of simply typed lambda terms. It helps to compute generalizations which contain maximally common top part of the input expressions, without nesting generalization variables. The rules of the corresponding anti-unification algorithm are formulated, and their soundness and termination are proved. The algorithm depends on a parameter which decides how to choose terms under generalization variables. Changing the particular values of the parameter, we obtained four new unitary variants of higher-order anti-unification and also showed how the already known pattern generalization fits into the schema.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
  • Theory of computation → Higher order logic
  • Theory of computation → Type theory
  • anti-unification
  • typed lambda calculus
  • least general generalization


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