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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of automated reasoning Jg. 39; H. 1; S. 1 - 47
Hauptverfasser: Ciaffaglione, Alberto, Liquori, Luigi, Miculan, Marino
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Nature B.V 01.07.2007
Springer Verlag
Schriftenreihe:Journal of Automated Reasoning
Schlagworte:
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-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-006-9061-y