The lambda calculus is algebraic

PETER SELINGER
2002 Journal of functional programming  
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 ξ-rule, which
more » ... that equations should be preserved under binders, and which fails to be sound for the usual interpretation.
doi:10.1017/s0956796801004294 fatcat:n34nmya5tfbbjddyepeomcwgjq