Bindings Mobility of Bindings and the Quantifier An Abstract 1st Edition by Dale Miller ISBN 9783540301240

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ISBN 13: 9783540301240
Author: Dale Miller

We 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.

Bindings Mobility of Bindings and the Quantifier An Abstract 1st Table of contents:

1. Abstract syntax for binders
2. Generic judgments and the ∇-quantification
3. Inference rules for non-logical constants and equality
4. Example: π-calculus

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