LAMBDA-REPRESENTABLE FUNCTIONS OVER TERM ALGEBRAS

Abstract

In this paper, we study λ→-representability of functions over (open or closed) term algebras. First, by extending the standard notion of λ→-representation of closed (or variable-free) terms to open terms and extending the notion of λ→-representable functions accordingly, we give a recursion-theoretic characterization of the class of λ→-representable functions over open term algebras. Then, based on this result, we obtain two characterizations of the class of λ→-representable functions over closed term algebras (i.e., free structures). As a related topic, in the Appendix we give a simple formulation of the recursive word functions, and study their properties in relation to recursive functions on natural numbers and type-free pure λ-calculus.