[Alta-Logic] two mini-talks on Monday 1pm

[Jonathan Gallagher]

There will be two mini talks given:

Location: ICT 616
Time: Monday, December 18, in ICT 616, at 1pm.

Speaker: Jonathan Gallagher

Mini-title: Infinitely short paths
Abstract:
Let X be a space, that is, a type in homotopy type theory.
Obtain two points in X that are infinitesimally close.  We
ask the following question: given a fixed point A, is the set
of infinitesimally close points to A a reasonable notion of
tangent space?  This talk is based on conversations with
Felix Wellen.

Mini-title: Productive expansion reduction in the differential lambda
calculus
Abstract:
Consider computing the derivative (f(x))'.  One may use the chain rule to
change this to f(x)'*x'; x' is of course 1, so f(x)' = f(x)'. In rewriting
theory,
we can consider the chain rule as a kind of expansion rule, and expansions
like the above are not productive in the sense that they do not contribute
towards a normal form.  In this talk, we will introduce productive expansion
reduction systems, and show how differentiation gives rise to a system
where only 'good' expansions are performed.

The notion of expansion reduction was used by Blute, Cockett, Seely, and
Trimble
in exploring circuits for linearly distributive categories.  We had to tweak
their definition slightly to get it to work for differentiation, but the
idea
is theirs.
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