Bindings, Mobility of Bindings, and the ∇-Quantifier: An Abstract

Abstract

AbstractWe present a meta-logic that contains a new quantifier ∇ (for encoding “generic judgments”) and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite π-calculus within this meta-logic. Since we restrict to the finite case, the ability of the meta-logic to reason within fixed points becomes a powerful and complete tool since simple proof search can compute the unique fixed point. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within π-calculus expressions and their executions (proofs). We shall illustrate several merits of the logical specifications we write: they are natural and declarative; they contain no-side conditions concerning names of bindings while maintaining a completely formal treatment of such bindings; differences between late and open bisimulation relations are easy to see declaratively; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for both one-step transitions and for bisimulation. This work is joint with Alwen Tiu and is described in more detail in the following papers.