Evaluation is MSOL-compatible

Authors Sylvain Salvati, Igor Walukiewicz

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Sylvain Salvati
Igor Walukiewicz

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Sylvain Salvati and Igor Walukiewicz. Evaluation is MSOL-compatible. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 103-114, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


We consider simply-typed lambda calculus with fixpoint operators. Evaluation of a term gives as a result the Böhm tree of the term. We show that evaluation is compatible with monadic second-order logic (MSOL). This means that for a fixed finite vocabulary of terms, the MSOL properties of Böhm trees of terms are effectively MSOL properties of terms themselves. Theorems of this kind have been known for some graph operations: unfolding, and Muchnik iteration. Similarly to those results, our main theorem has diverse applications. It can be used to show decidability results, to construct classes of graphs with decidable MSOL theory, or to obtain MSOL formulas expressing behavioral properties of terms. Another application is decidability of a control-flow synthesis problem.
  • Simply typed $lambda Y$-calculus; Monadic second order


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