Unsolvable terms in typed lambda calculus with fix-point operators: Extended abstract

  • Irina Bercovici
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 193)


We consider the finitely typed lambda calculus with "fixed-point" combinators Yσ of each type (σ→σ)→σ satisfying the equation Y=λf:σ→σ.f(Yf). (1) This formal system models computations with recursively defined equations. The decision problem for equality of terms of this calculus is open. We present a procedure for deciding when a λ-Y-term is "unsolvable"; this implies decidability of equations between λ-Y-terms and λ-terms without Y's. We also give tight characterizations of unsolvable terms under certain syntactic constraints.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Bar]
    Barendregt, H. The lambda calculus, its syntax and semantics, North-Holland (1981).Google Scholar
  2. [Cou]
    Courcelle, B. Fundamental properties of infinite trees, TCS, 25 (1983), 95–169.Google Scholar
  3. [P]
    Plotkin, G. A note on functions definable in simple typed lambda calculus, unpublished manuscript, Jan. 1983.Google Scholar
  4. [Sta]
    Statman, R. The typed lambda calculus is not elementary recursive, TCS, 9 (1979), 73–81.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Irina Bercovici
    • 1
  1. 1.MIT Laboratory for Computer Science and CCS Dept.University of MichiganUSA

Personalised recommendations