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Hereditarily sequential functionals

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Logical Foundations of Computer Science (LFCS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 813))

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Abstract

In order to define models of simply typed functional programming languages being closer to the operational semantics of these languages, the notions of sequentiality, stability and seriality were introduced. These works originated from the definability problem for PCF, posed in [Sco72], and the full abstraction problem for PCF, raised in [Plo77].

The presented computation model, forming the class of hereditarily sequential functionals, is based on a game in which each play describes the interaction between a functional and its arguments during a computation. This approach is influenced by the work of Kleene [Kle78], Gandy [Gan67], Kahn and Plotkin [KP78], Berry and Curien [BC82, Cur86, Cur92], and Cartwright and Felleisen [CF92].

We characterize the computable elements in this model in two different ways: (a) by recursiveness requirements for the game, and (b) as definability with the schemata (S1)-(S8), (S11), which is related to definability in PCF. It turns out that both definitions give the same class of computable functionals. So a robust notion of (sequential) computability on higher types is presented.

This research was supported in part by ESPRIT BRA 3230 and BRA 7232

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Authors and Affiliations

  1. Theoretische Informatik, FB 6, Universität-GH-Siegen, D-57068, Siegen, Germany

    Hanno Nickau

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  1. Hanno Nickau
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Anil Nerode Yu. V. Matiyasevich

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© 1994 Springer-Verlag Berlin Heidelberg

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Nickau, H. (1994). Hereditarily sequential functionals. In: Nerode, A., Matiyasevich, Y.V. (eds) Logical Foundations of Computer Science. LFCS 1994. Lecture Notes in Computer Science, vol 813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58140-5_25

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  • DOI: https://doi.org/10.1007/3-540-58140-5_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58140-6

  • Online ISBN: 978-3-540-48442-4

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