In a previous paper we have established the theory of transfinite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of infinitary rewriting, the Böhm model of the lambda calculus can be seen as an infinitary term model. In contrast to term rewriting, there are several different possible notions of infinite term, which give rise to different Böhm-like models, which embody different notions of lazy or eager computation.

Combinatory logic and lambda-calculus (msc 03B40)
Department of Computer Science [CS]
Specification and Analysis of Embedded Systems

Kennaway, J.R, Klop, J.W, Sleep, M.R, & de Vries, F.-J. (1995). Infinitary lambda calculus. Department of Computer Science [CS]. CWI.