Introduction to higher order categorical logic
Introduction to higher order categorical logic
Lambda-calculus, types and models
Lambda-calculus, types and models
An initial algebra approach to term rewriting systems with variable binders
Higher-Order and Symbolic Computation
A Relational Model of a Parallel and Non-deterministic λ -Calculus
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
| Hi-index | 0.00 |
This paper serves as a self-contained, tutorial introduction to combinatory models of the untyped lambda calculus. We focus particularly on the interpretation of free variables. We argue that free variables should not be interpreted as elements in a model, as is usually done, but as indeterminates. We claim that the resulting interpretation is more natural and leads to a closer correspondence between models and theories. In particular, it solves the problem of the notorious ζ-rule, which asserts that equations should be preserved under binders, and which fails to be sound for the usual interpretation.