Math & Stats Seminar (@CAT)
Universal updates for symmetric lenses presented by:
Bob Rosebrugh (Mount Allison)
Chase Building, Math & Stats, Colloquium Room, Dalhousie University
Abstract: "Asymmetric" lenses provide a strategy to lift updates in a model
domain along a morphism of model domains. A "symmetric" lens between two
model domains has state synchronization data and resynchronization operations.
When the model domains are categories we speak of delta-lenses (or d-lenses).
In previous work we showed that (certain equivalence classes of) spans of
asymmetric d-lenses represent symmetric d-lenses. Asymmetric c-lenses are a
special case of asymmetric d-lenses whose updates satisfy a universal property
which can be construed as "least-change''. So it was natural to hope that symmetric
c-lenses characterize the symmetric d-lenses which satisfy a natural universal property.
Instead, we'll explain why we do not expect all symmetric c-lenses (viewed as
equivalence classes of spans of c-lenses) to be central to developing universal
properties for symmetric d-lenses. We consider instead cospans of c-lenses and
show that they generate symmetric c-lenses with a universal property. That property
is further analyzed towards obtaining universal, least-change, properties for symmetric
d-lenses. We also explore how to characterize those symmetric d-lenses that arise from
cospans of c-lenses.
(Joint work with Michael Johnson)Math & Stats Seminar (@CAT)