Reduction Relations

Grzegorz Bancerek

Institute of Mathematics, Polish Academy of Sciences

Summary.

The goal of the article is to start the formalization of Knuth-Bendix completion method (see [2], [10] or [1]; see also [11],[9]), i.e. to formalize the concept of the completion of a reduction relation. The completion of a reduction relation $R$ is a complete reduction relation equivalent to $R$ such that convertible elements have the same normal forms. The theory formalized in the article includes concepts and facts concerning normal forms, terminating reductions, Church-Rosser property, and equivalence of reduction relations.

MML Identifier: REWRITE1

Contents (PDF format)

1. Forgetting concatenation and reduction sequence
2. Reducibility, convertibility and normal forms
3. Terminating reductions
4. Church-Rosser property
5. Completion method

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