Confluence of Untyped Lambda Calculus via Simple Types

  • Authors:

  • Silvia Ghilezan;Viktor Kuncak

  • Affiliations:

  • -;-

  • Venue:
  • ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
  • Year:
  • 2001

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Abstract

We present a new proof of confluence of the untyped lambda calculus by reducing the confluence of 脽-reduction in the untyped lambda calculus to the confluence of 脽-reduction in the simply typed lambda calculus. This is achieved by embedding typed lambda terms into simply typed lambda terms. Using this embedding, an auxiliary reduction, and 脽-reduction on simply typed lambda terms we define a new reduction on all lambda terms. The transitive closure of the reduction defined is 脽-reduction on all lambda terms. This embedding allows us to use the confluence of 脽-reduction on simply typed lambda terms and thus prove the confluence of the reduction defined. As a consequence we obtain the confluence of 脽-reduction in the untyped lambda calculus.