English

Models and theories of lambda calculus

Logic in Computer Science 2009-05-01 v1

Abstract

In this paper we briefly summarize the contents of Manzonetto's PhD thesis which concerns denotational semantics and equational/order theories of the pure untyped lambda-calculus. The main research achievements include: (i) a general construction of lambda-models from reflexive objects in (possibly non-well-pointed) categories; (ii) a Stone-style representation theorem for combinatory algebras; (iii) a proof that no effective lambda-model can have lambda-beta or lambda-beta-eta as its equational theory (this can be seen as a partial answer to an open problem introduced by Honsell-Ronchi Della Rocca in 1984).

Keywords

Cite

@article{arxiv.0904.4756,
  title  = {Models and theories of lambda calculus},
  author = {Giulio Manzonetto},
  journal= {arXiv preprint arXiv:0904.4756},
  year   = {2009}
}
R2 v1 2026-06-21T12:56:44.442Z