We consider łY-calculus as a non-interpreted functional programming language: the result of the execution of a program is its normal form that can be seen as the tree of calls to built-in operations. Weak monadic second-order logic (wMSO) is well suited to express properties of such trees. We give a type system for ensuring that the result of the execution of a λY-program satisfies a given wMSO property. In order to prove soundness and completeness of the system we construct a denotational semantics of λY-calculus that is capable of computing properties expressed in wMSO.


Model Check Type System Complete Lattice Functional Program Tree Automaton 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Sylvain Salvati
    • 1
  • Igor Walukiewicz
    • 1
  1. 1.CNRS, Université de Bordeaux, INRIAPessacFrance

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