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Infinite normal forms for the λ-calculus

  • Reiji Nakajima
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 37)

Abstract

The notion of C-function is introduced to λ-calculus with η-convertibility as a generalization of normal forms. C is a function from the λ-expressions, Λ, onto a partially ordered set, ℂfin. The D-value of X ε Λ is characterized by C(X) ε ℂfin. Extending the syntactical structure of ℂfin into ℂinf, we generalize Λ to Λ, the infinite λ-expressions. The lattice topology of Λ and Λ induced by D is equivalent to the lattice topology of ℂinf Since ℂinf is deduced from Λ independent of D, ℂinf can be said to give a natural lattice structure of Λ.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Reiji Nakajima
    • 1
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeley

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