Paper: Extending the lambda calculus with surjective pairing is conservative (at LICS 1989)

Authors: Roel C. de Vrijer

Abstract

Consideration is given to the equational theory λπ of lambda calculus extended with constants π, π₀, π₁ and axioms for subjective pairing: π₀(πXY)=X, π₁(πXY)=Y, π(π₀X )(π₁X)=X. The reduction system that one obtains by reading the equations are reductions (from left to right) is not Church-Rosser. Despite this failure, the author obtains a syntactic consistency proof of λπ and shows that it is a conservative extension of the pure λ calculus

BibTeX

  @InProceedings{deVrijer-Extendingthelambdac,
    author = 	 {Roel C. de Vrijer},
    title = 	 {Extending the lambda calculus with surjective pairing is conservative },
    booktitle =  {Proceedings of the Fourth Annual IEEE Symposium on Logic in Computer Science (LICS 1989)},
    year =	 {1989},
    month =	 {June}, 
    pages =      {204--215},
    location =   {Pacific Grove, CA, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }