By Giuseppe Castagna (auth.)
by Luea Cardelli Ever for the reason that Strachey's paintings within the 1960's, polymorphism has been categorized into the parametric and overloading kinds. Parametric polymorphism has been the topic of in depth learn for over 20 years. Overloading, however, has frequently been thought of too advert hoc to deserve a lot cognizance although it has been, in a few shape, an factor of just about each programming lan guage (much extra so than parametric polymorphism). With the creation of object-oriented languages, and particularly with multiple-dispatch object-oriented languages, overloading has turn into much less of a programming comfort and extra of a basic characteristic short of right clarification. This ebook presents a compelling framework for the examine of run-time over loading and of its interactions with subtyping and with parametric polymorphism. The e-book additionally describes functions to object-oriented programming. This new framework is stimulated by way of the particularly contemporary unfold of programming languages which are completely in accordance with run-time overloading; this truth most likely explains why this topic used to be no longer investigated prior. as soon as thoroughly understood, overloading finds itself suitable additionally to the examine of older and extra traditional (single dispatch) object-oriented languages, clarifying soft problems with covariance and contravariance of approach kinds, and of run-time variety research. within the ultimate chapters, a synthesis is made among parametric and overloading polymorphism.
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Extra info for Object-Oriented Programming A Unified Foundation
We denote a recursive type by I-'t. T, where t is a type variable and I-' is a binder that bounds the occurrences of tin T. (int x t). T To define the subtyping relation we have to introduce the definition of type constraint environment. In this context, a type constraint environment is a set of subtyping constraints of the form (s ~ t), where sand t are type variables, and is used to record the subtyping relation on the (type) variables of recursion. T To subtype two recursive types we subtype their bodies under the hypothesis that the respective variables of recursion are in subtyping relation.
Thus, we sought an alternative model. &-calculus [CGL95]. But upon closer examination of the mechanisms present in our model, we realized that, instead of describing an alternative model to the record-based one, we had modeled a different programming style that corresponded to the one based on generic functions. It is an interesting fact that starting from a purely theoretical demarche we arrived at a programming model that already existed. Moreover, the results of this demarche apply well beyond the particular programming.
This independence holds for the term M above since both the terms generated by the two reductions further reduce to x; thus whichever reduction we 2 Strictly speaking axioms should be topped by an horizontal bar to indicate that they are deduction rules with an empty set of premises, but we will always omit the bar in this case. 2. Simply-typed A -calculus 15 decide to calculate yields the same result, x. 7 (Confluence) For every MEA" if M 1>* N\ and M 1>* N2 then there exists N3 E At such that N\ I> * N3 and N2 I> * N3.
Object-Oriented Programming A Unified Foundation by Giuseppe Castagna (auth.)