Hilbert-Post completeness for the state and the exception effects

Jean-Guillaume Dumas (1) , Dominique Duval (1) , Burak Ekici (1) , Jean-Claude Reynaud (2) , Damien Pous (3, 4)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 RC - Reynaud Consulting
3 LIP - Laboratoire de l'Informatique du Parallélisme
4 PLUME - Preuves et Langages

In this paper, we present a novel framework for studying the syntactic completeness of computational effects and we apply it to the exception effect. When applied to the states effect, our framework can be seen as a generalization of Pretnar's work on this subject. We first introduce a relative notion of Hilbert-Post completeness, well-suited to the composition of effects. Then we prove that the exception effect is relatively Hilbert-Post complete, as well as the " core " language which may be used for implementing it; these proofs have been formalized and checked with the proof assistant Coq.

Domaines: Logique en informatique [cs.LO]; Calcul formel [cs.SC]

Jean-Guillaume Dumas, Dominique Duval, Burak Ekici, Jean-Claude Reynaud, Damien Pous. Hilbert-Post completeness for the state and the exception effects. Sixth International Conference on Mathematical Aspects of Computer and Information Sciences, Nov 2015, Berlin, Germany. pp.596-610, ⟨10.1007/978-3-319-32859-1_51⟩. ⟨hal-01121924v3⟩