Church-Rosser Theorem for a Rewriting System on Categorical Combinators

Abstract This paper develops the Church-Rosser theorem for the rewriting system CCLβ on type-free categorial combinators introduced by Curien. The system CCLβ is not confluent. However we show that there are various sets D of categorical combinator terms such that each D satisfies the following two conditions: (1) D is closed under reduction by CCLβ; (2) CCLβ is confluent on D . Moreover we examine the relation among these sets.