The Minimal Graph Model of Lambda Calculus [chapter]

Antonio Bucciarelli, Antonino Salibra
2003 Lecture Notes in Computer Science  
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 modelsà la Plotkin-Scott-Engeler. In particular, we
more » ... ld a graph model the equational theory of which is exactly the set of equations satisfied in any graph model. ¾ ¼ models in each of them inducing pairwise distinct lambda theories [14] [15].
doi:10.1007/978-3-540-45138-9_24 fatcat:dpc7xdg6qze7fj3ewmpinj5sky