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Call-by-Value Separability and Computability

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Theoretical Computer Science (ICTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2202))

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Abstract

The aim of this paper is to study the notion of separability in the call-by-value setting.

Separability is the key notion used in the Böhm Theorem, proving that syntactically different βη-normal forms are separable in the classical λ-calculus endowed with β-reduction, i.e. in the call-by-name setting.

In the case of call-by-value λ-calculus endowed with β v-reduction and η v-reduction (see Plotkin [7]), it turns out that two syntactically different βη v-normal forms are separable too, while the notion of β v-normal form and βη v-normal form is semantically meaningful.

An explicit representation of Kleene’s recursive functions is presented. The separability result guarantees that the representation makes sense in every consistent theory of call-by-value, i.e. theories in which not all terms are equals.

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References

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© 2001 Springer-Verlag Berlin Heidelberg

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Paolini, L. (2001). Call-by-Value Separability and Computability. In: Theoretical Computer Science. ICTCS 2001. Lecture Notes in Computer Science, vol 2202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45446-2_5

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  • DOI: https://doi.org/10.1007/3-540-45446-2_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42672-1

  • Online ISBN: 978-3-540-45446-5

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