The Lambda Calculus and Adjoint Functors

  • Saunders Mac Lane
Part of the Synthese Library book series (SYLI, volume 305)

Abstract

The well known lambda calculus was first formulated by Alonzo Church (1932). It was originally intended as a new foundation of mathematics; but soon the remarkable connection between lambda definability and recursive functions was developed. Only much later was the connection with rewrite systems noted, while the remarkable influence of the calculus in computer languages was also noted later. This note is to point out that the Galois connections and this lambda calculus are perhaps the first appearances of an explicit pair of adjoint functors. These functors in general were not found until the work of Daniel Kan in 1958.1

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References

  1. Church, A. 1936 Mathematical logic, Department of Mathematics, Princeton University, mimeographed notes (113 pages); reviewed in The Journal of Symbolic Logic, vol. 2, p. 39.Google Scholar
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Copyright information

© Springer Science+Business Media Dordrecht 2001

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  • Saunders Mac Lane

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