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A Context-Free Grammar Representation for Normal Inhabitants of Types in TAλ

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Book cover Progress in Artificial Intelligence (EPIA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2258))

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Abstract

In [10] it was shown that it is possible to describe the set of normal inhabitants of a given type τ, in the standard simple type system, using an infinitary extension of the concept of context-free grammar, which allows for an infinite number of non-terminal symbols as well as production rules. The set of normal inhabitants of τ corresponds then to the set of terms generated by this, possibly infinitary, grammar plus all terms obtained from those by η-reduction. In this paper we show that the set of normal inhabitants of a type τ can in fact be described using a standard (finite) context-free grammar, and more interestingly that normal inhabitants of types with the same structure are described by identical context-free grammars, up to renaming of symbols.

i.e. M is an inhabitant of τ

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References

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Author information

Authors and Affiliations

  1. DCC-FC & LIACC, Universidade do Porto, R. do Campo Alegre, 823, 4150-180, Porto, Portugal

    Sabine Broda & Luís Damas

Authors
  1. Sabine Broda
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  2. Luís Damas
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Editors and Affiliations

  1. Faculty of Economics LIACC, Laboratório de Inteligência Artificial e Ciência de Computadores, University of Porto, Rua do Campo Alegre, 823, 4150-180, Porto, Portugal

    Pavel Brazdil  & Alípio Jorge  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Broda, S., Damas, L. (2001). A Context-Free Grammar Representation for Normal Inhabitants of Types in TAλ. In: Brazdil, P., Jorge, A. (eds) Progress in Artificial Intelligence. EPIA 2001. Lecture Notes in Computer Science(), vol 2258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45329-6_32

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  • DOI: https://doi.org/10.1007/3-540-45329-6_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43030-8

  • Online ISBN: 978-3-540-45329-1

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