[Alta-Logic] peripatetic seminar Friday, August 11, at 2pm

[Jonathan Gallagher]

Speaker: Jonathan Gallagher
Location: ICT 616 @ 2 pm on Friday, August 11
Title: Scott, Koymans, and Beyond
Abstract:
Dana Scott, in "Relating theories of the lambda calculus" sought
to show that the same techniques for modelling the simply
typed lambda calculus can be used to model the untyped
lambda calculus.  He essentially constructed an adjunction
between lambda theories T and cartesian closed categories X with
a chosen reflexive object U:
     CL(T) ---> (X,U)
     -----------------------
      T ---> Th(X,U)
with the property that
     Th(CL(T)) \simeq T
In other words, every lambda theory T has a model M, whose
theory is equivalent to T.  This is now called the Scott-Koymans
theorem.

In this talk, we will give a modern presentation of the classifying category
of a lambda theory, and the theory of a model, using Turing categories
with an extra property called canonical codes (or perhaps latently closed),
and use this to reconstruct the Scott-Koymans theorem.

Footnote: Koymans' contribution was to characterize the difference between
lambda-algebras and lambda-models.  One can make a subtle mistake about
substitutional properties when interpreting into points via a
pseudostructure
on X(1,U).  Koymans' contribution is vital, but we will steer around issues
with points.
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