Formal Aspects of Computing

, Volume 8, Issue 3, pp 247–293 | Cite as

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

Article
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Abstract

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].

Keywords

Type theory Typed foundation of object-oriented programming Second order λ-calculus Bounded polymorphism 
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Copyright information

© BCS 1996

Authors and Affiliations

  1. 1.Laboratoire d'Informatique de l'École Normale SupérieureC.N.R.S.ParisFrance

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