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Imperative Object-Based Calculi in Co-inductive Type Theories

Alberto Ciaffaglione 1, 2 Luigi Liquori 2, 3 Marino Miculan 1
2 MIRHO - Objects, types and prototypes : semantics and validation
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7503
Abstract : We discuss the formalization of Abadi and Cardelli's impς, a para-digmatic object-based calculus with types and side effects, in Co-Inductive Type Theories, such as the Calculus of (Co)Inductive Constructions (CC (Co)Ind). Instead of representing directly the original system "as it is" , we reformulate its syntax and semantics bearing in mind the proof-theoretical features provided by the target metalanguage. On one hand, this methodology allows for a smoother implementation and treatment of the calculus in the metalanguage. On the other, it is possible to see the calculus from a new perspective, thus having the occasion to suggest original and cleaner presentations. We give hence a new presentation of impς, exploiting natural deduction semantics, (weak) higher-order abstract syntax, and, for a significant fragment of the calculus, coinductive typing systems. This presentation is easier to use and implement than the original one, and the proofs of key metaproperties, e.g. subject reduction, are much simpler. Although all proof developments have been carried out in the Coq system, the solutions we have devised in the encoding of and metareasoning on impς can be applied to other imperative calculi and proof environments with similar features.
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Alberto Ciaffaglione, Luigi Liquori, Marino Miculan. Imperative Object-Based Calculi in Co-inductive Type Theories. Logic for Programming, Artificial Intelligence, and Reasoning, 10th International Conference, LPAR 2003, Almaty, Kazakhstan, September 22-26, 2003. Proceedings, Sep 2003, Almaty, Kazakhstan. pp.59-77, ⟨10.1007/978-3-540-39813-4_4⟩. ⟨hal-01149867⟩

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