Abstract
A λ-language over simple type structures is considered. The type γ=(0 → (0 → 0)) → (0 → 0) is called a binary tree type because of the isomorphism between binary trees and closed terms of this type. Therefore any closed term of type γ → (γ → ... → (γ →) ...) represents an n-ary tree function. The problem is to characterize tree operations represented by the closed terms of the examined type. It is proved that the set of λ definable tree operations is the minimal set containing constant functions, projections and closed under composition and the limited version of recursion. This result should be contrasted with the results of Schwichtenberg and Statman (cf. [Sch75], [Sta79]) which characterize the λ definable functions over the natural number type (0 → 0) → (0 → 0) by composition only, as well as with the result of Zaionc (cf [Zai87]) for word λ definable functions over type (0 → 0) → ((0 → 0) → (0 → 0)) which are also characterized by means of composition.
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© 1990 Springer-Verlag Berlin Heidelberg
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Zaionc, M. (1990). On the λ-definable tree operations. In: Bergman, C.H., Maddux, R.D., Pigozzi, D.L. (eds) Algebraic Logic and Universal Algebra in Computer Science. ALUACS 1988. Lecture Notes in Computer Science, vol 425. Springer, New York, NY. https://doi.org/10.1007/BFb0043090
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DOI: https://doi.org/10.1007/BFb0043090
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