A Semantics for a Stratified λ&-Early: A Calculus with Overloading and Early Binding (1993)
BibTeX
@MISC{Castagna93asemantics,
author = {Giuseppe Castagna and Giorgio Ghelli and Giuseppe Longo},
title = {A Semantics for a Stratified λ&-Early: A Calculus with Overloading and Early Binding},
year = {1993}
}
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Abstract
The role of λ-calculus as core functional language is due to its nature as "pure" theory of functions. In the present approach we use the functional expressiveness of typed λ-calculus and extend it with our understanding of some relevant features of a broadly used programming style: Object-Oriented Programming (OOP). The core notion we focus on, yields a form of "dependency on input types" (or "on the types of the inputs") and formalizes "overloading" as implicitly used in OOP. The basis of this work has been laid in [CGL92], where the main syntactic properties of this extension have been shown. In this paper, we investigate an elementary approach to its mathematical meaning. The approach is elementary, as we tried to follow the most immediate semantic intuition which underlies our system; yet it gives a rigorous mathematical model. Indeed, our semantics provides an understanding of a slightly modified version of the normalizing system in [CGL92]: we had, so far, to restrict our att...
