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In this paper we define an extension ofF≤ [CUG92] to which we add functions that dispatch on different terms according to the type they receive as argument. In other words, we enrich the explicit parametric polymorphism ofF≤ by an explicit \"ad hoc\" polymorphism (according the classification of [Str67]). We prove that the calculus we obtain, calledF≤&, enjoys the properties of Church-Rosser and Subject Reduction and that its proof system is coherent. We also define a significant subcalculus for which the subtyping is decidable. This extension has not only a logical interest but it is strongly motivated by the foundation of a broadly used programming style: object-oriented programming. The connections betweenF≤& and object-oriented languages are widely stressed, and the modelling byF≤& of some features of the object-oriented style is described, continuing the work of [CGL96].

Integration of parametric and “ad hoc” second order polymorphism in a calculus with subtyping