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arXiv · 0904.4756

Models and theories of lambda calculus

Giulio Manzonetto
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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).

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Giulio Manzonetto. 2009-04-30. Models and theories of lambda calculus. https://arxiv.org/abs/0904.4756

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