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

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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 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.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze, 206-33100, Udine, Italy

    Alberto Ciaffaglione & Marino Miculan

  2. INRIA, Sophia Antipolis, France

    Luigi Liquori

Authors
  1. Alberto Ciaffaglione
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  2. Luigi Liquori
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  3. Marino Miculan
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Correspondence to Marino Miculan.

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Supported by UE project IST-CA-510996 Types and French grant CNRS ACI Modulogic.

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Ciaffaglione, A., Liquori, L. & Miculan, M. Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts. J Autom Reasoning 39, 1–47 (2007). https://doi.org/10.1007/s10817-006-9061-y

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