Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts

We illustrate a methodology for formalizing and reasoning about Abadi and Cardelli’s object-based calculi, in (co)inductive type theory, such as the Calculus of (Co)Inductive Constructions, by taking advantage of natural deduction semantics and coinduction in combination with weak higher-order abstr...

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Bibliographic Details
Published in:Journal of automated reasoning Vol. 39; no. 1; pp. 1 - 47
Main Authors: Ciaffaglione, Alberto, Liquori, Luigi, Miculan, Marino
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.07.2007
Springer Verlag
Series:Journal of Automated Reasoning
Subjects:
Calculi
Computation and Language
Computer Science
Deduction
Logic in Computer Science
Programming Languages
Reasoning
Semantics
Syntax
Theory
Interactive Theorem Proving
Logical Foundations of Programming
Coinductive Type Theories
Functional and Imperative Object-calculi
JAR
Logical Frameworks
ISSN:0168-7433, 1573-0670
Online Access:Get full text
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Summary:We illustrate a methodology for formalizing and reasoning about Abadi and Cardelli’s object-based calculi, in (co)inductive type theory, such as the Calculus of (Co)Inductive Constructions, by taking advantage of natural deduction semantics and coinduction in combination with weak higher-order abstract syntax and the Theory of Contexts. Our methodology allows us to implement smoothly the calculi in the target metalanguage; moreover, it suggests novel presentations of the calculi themselves. In detail, we present a compact formalization of the syntax and semantics for the functional and the imperative variants of the ς-calculus. Our approach simplifies the proof of subject deduction theorems, which are proved formally in the proof assistant Coq with a relatively small overhead.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-006-9061-y