Typed operational semantics for higher-order subtyping

Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce F ω ⩽ , a variant of F <: ω with this feature and with Cardelli and Wegner’s kernel Fun rule for quantifiers. We define a...

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Bibliographic Details
Published in:Information and computation Vol. 184; no. 2; pp. 242 - 297
Main Authors: Compagnoni, Adriana, Goguen, Healfdene
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 01.08.2003
Elsevier
Subjects:
Applied sciences
Computer science; control theory; systems
Dependent kinds
Exact sciences and technology
General logic
Lambda calculus
Logic and foundations
Mathematical logic, foundations, set theory
Mathematical programming
Mathematics
Operational research and scientific management
Operational research. Management science
Programming languages
Sciences and techniques of general use
Software
Subtyping
Type theory
Typed-operational semantics
Type theory
Typed-operational semantics
Subtyping
Dependent kinds
Lambda calculus
Admissibility
Decidability
Computer theory
Programming language
Operational semantics
Dependent kind
Object oriented programming
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary:Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce F ω ⩽ , a variant of F <: ω with this feature and with Cardelli and Wegner’s kernel Fun rule for quantifiers. We define a typed-operational semantics with subtyping and prove that it is equivalent with F ω ⩽ , using logical relations to prove soundness. The typed-operational semantics provides a powerful and uniform technique to study metatheoretic properties of F ω ⩽ , such as Church–Rosser, subject reduction, the admissibility of structural rules, and the equivalence with the algorithmic presentation of the system that performs weak-head reductions. Furthermore, we can show decidability of subtyping using the typed-operational semantics and its equivalence with the usual presentation. Hence, this paper demonstrates for the first time that logical relations can be used to show decidability of subtyping.
ISSN:0890-5401
1090-2651
DOI:10.1016/S0890-5401(03)00062-2