Coherence and Transitivity of Subtyping as Entailment (1996)
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@MISC{Longo96coherenceand,
author = {Giuseppe Longo and Uperieure S Ormale and Sergei SOLOVIEV and N Ecole and Of Subtyping As Entailment and Of Subtyping As Entailment and Kathleen MILSTED and Kathleen Milsted},
title = {Coherence and Transitivity of Subtyping as Entailment},
year = {1996}
}
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Abstract
The relation of inclusion between types has been suggested by the practice of programming as it enriches the polymorphism of functional languages. We propose a simple (and linear) sequent calculus for subtyping as logical entailment. This allows us to derive a complete and coherent approach to subtyping from a few, logically meaningful sequents. In particular, transitivity and anti-symmetry will be derived from elementary logical principles. 1 Introduction 1.1 Motivations, theories and models In recent years, several extensions of core functional languages have been proposed to deal with the notion of subtyping; see, for example, [CW85, Mit88, BL90, BCGS91, CMMS91, CG92, PS94, Tiu96, TU96]. These extensions were suggested by the practice of programming in computer science. In particular, they were inspired by the notion of inheritance as used in object-oriented programming languages, or by other concrete implementations of the following form of polymorphism: data living in a type oe, ...
