[Alta-Logic] peripatetic seminar tomorrow

[Jonathan]

Where: ICT 616

When: 10:01 am

Who: Jonathan Gallagher

What:  Title: Linear Turing Categories

Why: Abstract:

We revisit Abramsky et al's Linear Combinatory Algebras.   The models of
linear combinatory algebras they describe arise from combinatory systems in
a symmetric monoidal category with a weak comonad (weak in the sense that
counit and comultiplication are pointwise natural), that lifts via
standardization, to a normal combinatory algebra.  This allowed a bridge
from a "geometry of interaction situation" to a combinatory algebra, as
geometry of interaction situations naturally give rise to such combinatory
systems.

We will revisit and simplify the notion of linear combinatory algebra to
sort out some of the finer points of the structural story behind linear
combinatory algebras.  We will do so by dropping the comonad altogether and
focusing on just the "linear" maps.   We will introduce the notion of a
linear Turing category, which generalizes the Abramsky et al's class of
examples, and show that there is a nice correspondence between linear Turing
categories and our simplified linear combinatory algebras.

 

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