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

Alberto Ciaffaglione (1) , Luigi Liquori (2) , Marino Miculan (1)

1 DIMI - Dipartimento di Matematica e Informatica - Universita Udine
2 MASCOTTE - Algorithms, simulation, combinatorics and optimization for telecommunications

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 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 Reduction theorems, which are proved formally in the proof assistant Coq with a relatively small overhead.

Mots clés: Functional and Imperative Object-calculi; Logical Foundations of Programming; Coinductive Type Theories; Logical Frameworks; Interactive Theorem Proving; JAR

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]; Informatique et langage [cs.CL]

Alberto Ciaffaglione, Luigi Liquori, Marino Miculan. Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts. Journal of Automated Reasoning, 2007, Journal of Automated Reasoning, 39 (1), pp.1-47. ⟨10.1007/s10817-006-9061-y⟩. ⟨hal-01148347⟩