We introduce a new kind of tree automaton, a dependency tree automaton, that is suitable for deciding properties of classes of terms with binding. Two kinds of such automaton are defined, nondeterministic and alternating. We show that the nondeterministic automata have a decidable nonemptiness problem and leave as an open question whether this is true for the alternating version. The families of trees that both kinds recognise are closed under intersection and union. To illustrate the utility of the automata, we apply them to terms of simply typed lambda calculus and provide an automata-theoretic characterisation of solutions to the higher-order matching problem.


Tree automata binding terms typed lambda calculus 


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Colin Stirling
    • 1
  1. 1.School of Informatics Informatics ForumUniversity of EdinburghUK

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