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Finitary matching problems are those that have finitely many solutions. Pattern calculi generalize the lambda-calculus, replacing the abstraction over variables by an abstraction over terms that are called patterns. Consequently, reduction requires solving a pattern matching problem. The framework described in this paper considers the case when such problems are finitary. It is parametrized by the solving function, which is responsible for computing solutions to the matching problems. A concrete instance of the function gives a concrete version of the pattern calculus. We impose conditions on the solving function, obtaining a generic confluence proof for a class of pattern calculi with finitary matching. Instances of the solving function are presented.

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This special issue collects selected articles from the Third International Workshop on Linearity (LINEARITY 2014), which was held in Vienna, on July 13th, 2014. The workshop was a one-day satellite event of FLoC 2014, the sixth Federated Logic Conference, which was held as part of the 2014 Vienna Summer of Logic. Copyright © Cambridge University Press 2016

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