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Evaluation is MSOL compatible

Abstract : 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 properties of terms. Another application is decidability of a control-flow synthesis problem.
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https://hal.inria.fr/hal-00773126
Contributor : Sylvain Salvati Connect in order to contact the contributor
Submitted on : Friday, January 11, 2013 - 4:22:46 PM
Last modification on : Monday, December 20, 2021 - 4:50:11 PM
Long-term archiving on: : Saturday, April 1, 2017 - 4:11:19 AM

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  • HAL Id : hal-00773126, version 1

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Sylvain Salvati, Igor Walukiewicz. Evaluation is MSOL compatible. [Research Report] 2013, pp.42. ⟨hal-00773126v1⟩

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