A model for behavioural properties of higher-order programs

Sylvain Salvati (1, 2) , Igor Walukiewicz (2)

1 PoSET - Models for a Structured Programming of Space and Time
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We consider simply typed lambda-calculus with fixpoints as a non-interpreted functional programming language: the result of the execution of a program is its normal form that can be seen as a potentially infinite tree of calls to built-in operations. Properties of such trees are properties of executions of programs and monadic second-order logic (MSOL) is well suited to express them. For a given MSOL property we show how to construct a finitary model recognizing it. In other words, the value of a lambda-term in the model determines if the tree that is the result of the execution of the term satisfies the property. The finiteness of the construction has as consequences many known results about the verification of higher-order programs in this framework.

Domaines: Informatique [cs]; Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]; Performance et fiabilité [cs.PF]

Sylvain Salvati, Igor Walukiewicz. A model for behavioural properties of higher-order programs. 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, Sep 2015, Berlin, Germany. ⟨10.4230/LIPIcs.CSL.2015.229⟩. ⟨hal-01145494⟩