Sequential products in effect categories

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

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

A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks (Monads, Arrows, Freyd categories), we distinguish two kinds of functions. In addition, we also distinguish two kinds of equations. Then, we are able to define a kind of product, that generalizes the usual categorical product. This yields a powerful tool for deriving many results about languages with effects.

Mots clés: imperative languages; computational effects; monads; Arrows; Freyd categories; cartesian categories; cartesian effect categories; products; sequential products; decorated categories.; decorated categories

Domaines: Catégories et ensembles [math.CT]; Langage de programmation [cs.PL]

Jean-Guillaume Dumas, Dominique Duval, Jean-Claude Reynaud. Sequential products in effect categories. [Research Report] Université Grenoble Alpes (UGA). 2007. ⟨hal-00161303⟩