Ensuring termination by typability

A term terminates if all its reduction sequences are of finite length. We show four type systems that ensure termination of well-typed π-calculus processes. The systems are obtained by successive refinements of the types of the simply typed π-calculus. For all (but one of) the type systems we also present upper bounds to the number of steps well-typed processes take to terminate. The termination proofs use techniques from term rewriting systems. We show the usefulness of the type systems on some non-trivial examples: the encodings of primitive recursive functions, the protocol for encoding separate choice in terms of parallel composition, a symbol table implemented as a dynamic chain of cells.

Authors

• Yuxin Deng
• Davide Sangiorgi

Keywords

• The π-calculus
• Types
• Termination
• Term rewriting techniques