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

  • Authors:
  • Alberto Ciaffaglione;Luigi Liquori;Marino Miculan

  • Affiliations:
  • Dipartimento di Matematica e Informatica, Università di Udine, Udine, Italy 206-33100;INRIA, Sophia Antipolis, France;Dipartimento di Matematica e Informatica, Università di Udine, Udine, Italy 206-33100

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2007

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Abstract

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 驴-calculus. Our approach simplifies the proof of subject deduction theorems, which are proved formally in the proof assistant Coq with a relatively small overhead.