Abstract

Peter Selinger Department of Mathematics University of Pennsylvania 209 S. 33rd Street Philadelphia, PA 19104-6395 selinger@math.upenn.edu Abstract Many familiar models of the type-free lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory of fi- or fij-conversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the type-free lambda calculus cannot be non-trivially partially ordered. Our second result is a syntactical characterization, in terms of so-called generalized Mal'cev operators, of those lambda theories which cannot be induced by any non-trivially partially ordered model. We also consider a notion of finite models for the type-free lambda calculus. We introduce partial syntactical lambda models, which are derived from Plotkin's syntactical models of redu...

Citations

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