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Strong normalisation in the $$\pi$$-calculus. (English) Zbl 1101.68705
Summary: We introduce a typed $$\pi$$-calculus where strong normalisation is ensured by typability. Strong normalisation is a useful property in many computational contexts, including distributed systems. In spite of its simplicity, our type discipline captures a wide class of converging name-passing interactive behaviour. The proof of strong normalisability combines methods from typed $$\lambda$$-calculi and linear logic with process-theoretic reasoning. It is adaptable to systems involving state, non-determinism, polymorphism, control and other extensions. Strong normalisation is shown to have significant consequences, including finite axiomatisation of weak bisimilarity, a fully abstract embedding of the simply typed $$\lambda$$-calculus with products and sums and basic liveness in interaction. Strong normalisability has been extensively studied as a fundamental property in functional calculi, term rewriting and logical systems. This work is one of the first steps to extend theories and proof methods for strong normalisability to the context of name-passing processes.

##### MSC:
 68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
##### Software:
Automath; PIPER; PLAN
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