We present a formalization of a typed pi-calculus in the Calculus of Inductive Constructions. We give the rules for type-checking and for evaluation and formalize a proof of type preservation in the Coq system. The encoding of the pi-calculus in Coq uses Coq fonctions to represent bindings of variables. This kind of encoding is called a higher-order specication. It provides a concise description of the calculus, leading to simple proofs. The specification we propose for the pi-calculus formalizes communication by means of function application.

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 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.