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A HigherOrder Specification of the πCalculus
, 2000
"... We present a formalization of a typed picalculus in the Calculus of Inductive Constructions. We give the rules for typechecking and for evaluation and formalize a proof of type preservation in the Coq system. The encoding of the picalculus in Coq uses Coq fonctions to represent bindings of variab ..."
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We present a formalization of a typed picalculus in the Calculus of Inductive Constructions. We give the rules for typechecking and for evaluation and formalize a proof of type preservation in the Coq system. The encoding of the picalculus in Coq uses Coq fonctions to represent bindings of variables. This kind of encoding is called a higherorder specication. It provides a concise description of the calculus, leading to simple proofs. The specification we propose for the picalculus formalizes communication by means of function application.
A Formalization of a Concurrent Object Calculus Up to AlphaConversion
, 1999
"... We experiment a method for representing a concurrent object calculus in the Calculus of Inductive Constructions. Terms are first defined in de Bruijn style, then names are reintroduced in binders. The terms of the calculus are formalized in the mechanized logic by suitable subsets of the de Bruijn ..."
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We experiment a method for representing a concurrent object calculus in the Calculus of Inductive Constructions. Terms are first defined in de Bruijn style, then names are reintroduced in binders. The terms of the calculus are formalized in the mechanized logic by suitable subsets of the de Bruijn terms; namely those whose de Bruijn indices are relayed beyond the scene. The ffequivalence relation is the Leibnitz equality and the substitution functions can de defined as sets of partial rewriting rules on these terms. We prove induction schemes for both the terms and some properties of the calculus which internalize the renaming of bound variables . We show that, despite that the terms which formalize the calculus are not generated by a last fixed point relation, we can prove the desire inversion lemmas. We formalize the computational part of the semantic and a simple type system of the calculus. At least, we prove a subject reduction theorem and see that the specications and proofs have the nice feature of not mixing de Bruijn technical manipulations with real proofs.
Formalization of a Concurrent Object Calculus Up to AlphaConversion
, 1999
"... We present a formalization of a concurrent object calculus in the Calculus of Inductive Constructions. We use de Bruijn technique in an intermediate syntax, but de Bruijn indices do not appear in the final formalization of the terms of the calculus, which are still dened up to ffconversion. We deri ..."
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We present a formalization of a concurrent object calculus in the Calculus of Inductive Constructions. We use de Bruijn technique in an intermediate syntax, but de Bruijn indices do not appear in the final formalization of the terms of the calculus, which are still dened up to ffconversion. We derive substitution rewriting rules and an inductive principle on the subset of the terms which formalize the calculus. Once a certain amount of preliminary work has been done on the intermediate syntax this induction theorem makes possible natural proofs which do not deal with de Bruijn number.