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تسجيل مستخدم جديدModels and theories of lambda calculus
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Giulio Manzonetto
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In this paper we briefly summarize the contents of Manzonettos 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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This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda calculus, the
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first time admit an adequacy theorem relating the operational and denotational views. This resolves the main issue left open in (Bacci et al. 2018).
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