Adjunctions for exceptions

Jean-Guillaume Dumas (1) , Dominique Duval (1) , Laurent Fousse (1) , Jean-Claude Reynaud (2)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 RC - Reynaud Consulting

An algebraic method is used to study the semantics of exceptions in computer languages. The exceptions form a computational effect, in the sense that there is an apparent mismatch between the syntax of exceptions and their intended semantics. We solve this apparent contradiction by efining a logic for exceptions with a proof system which is close to their syntax and where their intended semantics can be seen as a model. This requires a robust framework for logics and their morphisms, which is provided by categorical tools relying on adjunctions, fractions and limit sketches.

Mots clés: Morphisms of logics; Computational effects; Semantics of exceptions; Adjunction; Categorical fractions; Limit sketches; Diagrammatic logics; Decorated proof system

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]

Jean-Guillaume Dumas, Dominique Duval, Laurent Fousse, Jean-Claude Reynaud. Adjunctions for exceptions. [Research Report] LJK. 2012. ⟨hal-00714710v2⟩