Abstract
Higher-order abstract syntax is a natural way to formalize programming languages with binders, like the π-calculus, because α-conversion, instantiations and capture avoidance are delegated to the meta-level of the provers, making tedious substitutions superfluous. However, such formalizations usually lack structural induction, which makes syntax-analysis impossible. Moreover, when applied in logical frameworks with object-logics, like Isabelle/HOL or standard extensions of Coq, exotic terms can be defined, for which important syntactic properties become invalid.
The paper presents a formalization of the π-calculus in Isabelle/HOL, using well-formedness predicates which both eliminate exotic terms and yield structural induction. These induction-principles are then used to derive the Theory of Contexts fully within the mechanization.
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Röckl, C., Hirschkoff, D., Berghofer, S. (2001). Higher-Order Abstract Syntax with Induction in Isabelle/HOL: Formalizing the π-Calculus and Mechanizing the Theory of Contexts. In: Honsell, F., Miculan, M. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2001. Lecture Notes in Computer Science, vol 2030. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45315-6_24
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