The Minimal Graph Model of Lambda Calculus

  • Antonio Bucciarelli
  • Antonino Salibra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


A longstanding open problem in lambda-calculus, raised by G.Plotkin, is whether there exists a continuous model of the untyped lambda-calculus whose theory is exactly the beta-theory or the beta-eta-theory. A related question, raised recently by C.Berline, is whether, given a class of lambda-models, there is a minimal equational theory represented by it.

In this paper, we give a positive answer to this latter question for the class of graph models à la Plotkin-Scott-Engeler. In particular, we build a graph model the equational theory of which is exactly the set of equations satisfied in any graph model.


Graph Model Equational Theory Apply Logic Congruence Relation Lambda Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Antonio Bucciarelli
    • 1
  • Antonino Salibra
    • 2
  1. 1.Université Paris 7ParisFrance
  2. 2.Dipartimento di InformaticaUniversità Ca’Foscari di VeneziaVeneziaItalia

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