Taking Updates Seriously
Résumé
We show how “taking updates seriously” leads from state-based lenses
to update lenses and further; we witness a little hierarchy of types of
lens that arises in a systematic way. Lenses of each type are characterized
either as coalgebras of certain types of comonads or morphisms
between certain types of comonads. In each case, a lens is simulation
between two transition systems for suitable notions of transition system
and simulation.