Higher-Order Matching, Games and Automata

Higher-order matching is the problem given t = u where t, u are terms of simply typed λ-calculus and u is closed, is there a substitution θ such that tθ and u have the same normal form with respect to βη-equality: can t be pattern matched to u? This paper considers the question: can we characterize the set of all solution terms to a matching problem? We provide an automata-theoretic account that is relative to resource: given a matching problem and a finite set of variables and constants, the (possibly infinite) set of terms that are built from those components and that solve the problem is regular. The characterization uses standard bottom-up tree automata.

• Type: Conference
• Year: 2007
• Where: LICS
• Authors: Colin Stirling
• Keywords: Computer Science, LICS 2007, Matching Problem, Normal Form, Solution Terms