Modified bar recursion

Authors:
Ulrich Berger;Paulo Oliva
Affiliations:
Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP, United Kingdom;Department of Computer Science, Queen Mary, University of London, Mile End Road, London E3 1NS, United Kingdom
Venue:
Mathematical Structures in Computer Science
Year:
2006

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Abstract

This paper studies modified bar recursion, a higher type recursion scheme, which has been used in Berardi et al. (1998) and Berger and Oliva (2005) for a realisability interpretation of classical analysis. A complete clarification of its relation to Spector's and Kohlenbach's bar recursion, the fan functional, Gandy's functional $\Gamma$ and Kleene's notion of S1–S9 computability is given.