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Math & Stats Seminar (@CAT)

Universal updates for symmetric lenses presented by:

Bob Rosebrugh (Mount Allison)

Time

Location

Chase Building, Math & Stats, Colloquium Room, Dalhousie University

Additional Information

 

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)