This note reexamines Spector’s remarkable computational interpretation of full classical analysis. Spector’s interpretation makes use of a rather abstruse recursion schema, so-called bar recursion, used to interpret the double negation shift DNS. In this note bar recursion is presented as a generalisation of a simpler primitive recursive functional needed for the interpretation of a finite (int...

During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with some form of bar recursion, which realizes the negative translation of either countable or countable dependent choice. In this work we present the many varia...

This paper presents an approach to the problem of introducing non-primitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially non-terminating. Once we have proved termination, the original specification can be derived easily. A collection of algorithms are presented whi...

Current business trends, policy markets, production requirements, etc., have created the need for integrating pre-existing Multi Agent Systems (MAS). In the agent-specialized literature, we have found very little work about agent architectures and methodologies that allow us to carry out recursive and dynamic analysis, design, and implementation of MASs. Several difficult challenges for automat...

Presented at a meeting of the British Mathematics Colloquium; received by the editors February 10,1988. 1980 Mathematics Subject Class~fication (1985 Revision). Primary 05A99; Secondary 15A03.