Subtyping can have a simple semantics

doi:10.1016/S0304-3975(06)80005-8

Theoretical Computer Science

Volume 87, Issue 1, 16 September 1991, Pages 81-96

https://doi.org/10.1016/S0304-3975(06)80005-8 Get rights and content

Under an Elsevier user license

open archive

Abstract

Consider a first order typed language, with semantics 〚〛 for expressions and types. Adding subtyping means that a partial order ⩽ on types is defined and that the typing rules are extended to the effect that expression e has type τ whenever e has type σ and σ ⩽ τ. We show how to adapt the semantics 〚〛 in a simple set theoretic way, obtaining a semantics

that satisfies, in addition to some obvious requirements, also the property

, whenever, σ ⩽ τ.

Cited by (0)

: This work was partly conducted within the PRISMA project, a joint effort with Philips Research Eindhoven, partially supported by the Dutch “Stimulerings Projectteam Informaticaonderzoek Nederland (SPIN)”.

^**: Currently at Centre for Mathematics and Computer Science, Amsterdam.