Advertisement

Higher-Order and Symbolic Computation

, Volume 20, Issue 3, pp 199–207 | Cite as

A call-by-name lambda-calculus machine

  • Jean-Louis Krivine
Article

Abstract

We present a particularly simple lazy lambda-calculus machine, which was introduced twenty-five years ago. It has been, since, used and implemented by several authors, but remained unpublished. We also build an extension, with a control instruction and continuations. This machine was conceived in order to execute programs obtained from mathematical proofs, by means of the Curry-Howard (also known as “proof-program”) correspondence. The control instruction corresponds to the axiom of excluded middle.

Keywords

Lambda-calculus machine Control instruction Curry-Howard correspondence 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Biernacka, M., Danvy, O.: A syntactic correspondence between context-sensitive calculi and abstract machines. Theor. Comput. Sci. 375(1–3), 76–108 (2007). Extended version available as the research report BRICS RS-06-18 zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Danos, V., Krivine, J.-L.: Disjunctive tautologies and synchronisation schemes. In: Computer Science Logic’00. Lecture Notes in Computer Science, vol. 1862, pp. 292–301 (2000) Google Scholar
  3. 3.
    de Bruijn, N.G.: Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indag. Math. 34, 381–392 (1972) Google Scholar
  4. 4.
    Griffin, T.: A formulæ-as-type notion of control. In: Conference Record of the 17th A.C.M. Symposium on Principles of Programming Languages (1990) Google Scholar
  5. 5.
    Krivine, J.-L.: Lambda-Calculus, Types and Models. Ellis Horwood, Chichester (1993) zbMATHGoogle Scholar
  6. 6.
    Krivine, J.-L.: Typed λ-calculus in classical Zermelo-Frænkel set theory. Arch. Math. Log. 40(3), 189–205 (2001) zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Krivine, J.-L.: Dependent choice, ‘quote’ and the clock. Theor. Comput. Sci. 308, 259–276 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Landin, P.J.: The mechanical evaluation of expressions. Comput. J. 6, 308–320 (1964) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.C.N.R.S.University Paris VIIParis cedex 05France

Personalised recommendations