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Recursion schemes and generalized interpretations

Extended abstract
  • Jean H. Gallier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)

Abstract

This paper investigates some of the underlying axioms allowing the fixpoint-semantics approach to hold for tree-like recursion schemes. The notions of scheme and interpretation are generalized. The axioms satisfied by "algebraic theories" are shown to be adequate for the definition of the notion of an interpretation. It is also shown that in order to provide the semantics of arbitrary finite recursion schemes, rational algebraic theories are insufficient and it is necessary to introduce a new class of "recursion-closed" algebraic theories. Finally, free recursion-closed algebraic theories are shown to exist.

Keywords

Algebraic Theory Main Procedure Recursion Scheme Unique Homomorphism Composition Operation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Jean H. Gallier
    • 1
  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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