Results 1 
3 of
3
Orderincompleteness and finite lambda models, extended abstract, in: LICS ’96
 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Society
, 1996
"... Many familiar models of the typefree 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 ofβ orβηconversion, the partial order is ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
Many familiar models of the typefree 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 ofβ orβηconversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the typefree lambda calculus cannot be nontrivially partially ordered. Our second result is a syntactical characterization, in terms of socalled generalized Mal’cev operators, of those lambda theories which cannot be induced by any nontrivially partially ordered model. We also consider a notion of finite models for the typefree lambda calculus. We introduce partial syntactical lambda models, which are derived from Plotkin’s syntactical models of reduction, and we investigate how these models can be used as practical tools for giving finitary proofs of term inequalities. We give a 3element model as an example. 1
Functionality, polymorphism, and concurrency: a mathematical investigation of programming paradigms
, 1997
"... ..."