The system F of variable types, fifteen years later
Theoretical Computer Science
Filter models with polymorphic types
Theoretical Computer Science
Journal of Computer and System Sciences
A semantics for static type inference
Information and Computation - Special conference issue: international conference on theoretical aspects of computer software
Handbook of logic in computer science (vol. 3)
Information and Computation
Functionality, polymorphism, and concurrency: a mathematical investigation of programming paradigms
Functionality, polymorphism, and concurrency: a mathematical investigation of programming paradigms
Stable Models of Typed lambda-Calculi
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Countable Non-Determinism and Uncountable Limits
CONCUR '94 Proceedings of the Concurrency Theory
Graph models of $\lambda$-calculus at work, and variations
Mathematical Structures in Computer Science
Theoretical Computer Science - Algebraic methods in language processing
From λ-Calculus to Universal Algebra and Back
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On the completeness of order-theoretic models of the λ-calculus
Information and Computation
Effective λ-models versus recursively enumerable λ-theories
Mathematical Structures in Computer Science
A simple class of Kripke-style models in which logic and computation have equal standing
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Lambda theories of effective lambda models
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
| Hi-index | 5.23 |
Many familiar models of the untyped 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 β- or βη-conversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the untyped 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 untyped lambda calculus, or more precisely, finite models of reduction. We demonstrate how such models can be used as practical tools for giving finitary proofs of term inequalities.