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Hereditarily sequential functionals

  • Hanno Nickau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 813)

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.

Keywords

Partial Function Finite Type Sequential Algorithm High Type Sequential Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Hanno Nickau
    • 1
  1. 1.Theoretische Informatik, FB 6Universität-GH-SiegenSiegenGermany

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