LambdaY-Calculus With Priorities

Igor Walukiewicz (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The lambdaY-calculus with priorities is a variant of the simply-typed lambda calculus designed for higher-order model-checking. The higher-order model-checking problem asks if a given parity tree automaton accepts the Böhm tree of a given term of the simply-typed lambda calculus with recursion. We show that this problem can be reduced to the same question but for terms of lambdaY-calculus with priorities and visibly parity automata; a subclass of parity automata. The latter question can be answered by evaluating terms in a simple powerset model with least and greatest fixpoints. We prove that the recognizing power of powerset models and visibly parity automata are the same. So, up to conversion to the lambdaY-calculus with priorities, powerset models with least and greatest fixpoints are indeed the right semantic framework for the model-checking problem. The reduction to lambdaY-calculus with priorities is also efficient algorithmically: it gives an algorithm of the same complexity as direct approaches to the higher-order model-checking problem. This indicates that the task of calculating the value of a term in a powerset model is a central algo-rithmic problem for higher-order model-checking.

Domaines: Logique en informatique [cs.LO]

Igor Walukiewicz. LambdaY-Calculus With Priorities. LICS, 2019, Vancouver, Canada. pp.1-13. ⟨hal-02100196⟩