Abstract
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.KeywordsGraph ModelEquational TheoryApply LogicCongruence RelationLambda CalculusThese 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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