The Minimal Graph Model of Lambda Calculus

Antonio Bucciarelli (1) , Antonino Salibra (2)

1 PPS - Preuves, Programmes et Systèmes
2 Dipartimento di Informatica

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 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 in which the equations satisfied are exactly those satisfied in any graph model.

Domaines: Logique en informatique [cs.LO]

Antonio Bucciarelli, Antonino Salibra. The Minimal Graph Model of Lambda Calculus. Mathematical Foundations of Computer Science, 2003, Bratislava, Slovakia. pp.300-307. ⟨hal-00149557⟩