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A recursive second order initial algebra specification of primitive recursion

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Abstract

Theoretical results on the scope and limits of first order algebraic specifications can be used to show that certain natural algebras have no recursively enumerable equational specification under first order initial algebra semantics. A well known example is the algebraPℛ of primitive recursive functions over the natural numbers. In this paper we show thatPℛ has a recursive equational specification under second order initial algebra semantics. It follows that higher order initial algebra specifications are strictly more powerful than first order initial algebra specifications.

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  1. Department of Computer Science, University College of Swansea, Singleton Park, SA2 8PP, Swansea, UK

    Karl Meinke

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  1. Karl Meinke
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Meinke, K. A recursive second order initial algebra specification of primitive recursion. Acta Informatica 31, 329–340 (1994). https://doi.org/10.1007/BF01178510

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