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Evaluation is MSOL-compatible Salvati, Sylvain Walukiewicz, Igor Simply typed $lambda Y$-calculus; Monadic second order 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sylvain Salvati and Igor Walukiewicz 2013 Is Part Of LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2013.103 urn:nbn:de:0030-drops-43652 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.103 eng https://creativecommons.org/licenses/by/3.0/legalcode