Abstract
In Chapter 8, we studied the total type structure Ct based on the concept of ‘continuous functionals acting on continuous data’, and its substructure Cteff of ‘effective functionals on continuous data’. The purpose of the present chapter is to study a somewhat similar model based on the idea of ‘effective functionals on effective data’. This model was first defined in Kreisel [152] in the context of constructive interpretations of analysis. Further investigations, including equivalence proofs for various characterizations, were undertaken by Gandy [99], Troelstra [288], Hyland [120], Ershov [73, 74] and Bezem [35]. The model is generally known in the literature as HEO, the type structure of hereditarily effective operations.
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© 2015 Springer-Verlag Berlin Heidelberg
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Longley, J., Normann, D. (2015). The Hereditarily Effective Operations. In: Higher-Order Computability. Theory and Applications of Computability. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47992-6_9
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DOI: https://doi.org/10.1007/978-3-662-47992-6_9
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