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CATEGORIES:Category Theory Seminar
SUMMARY:No-Go Theorems for Distributive Laws - Maaike Zwar
t (University of Oxford)
DTSTART;TZID=Europe/London:20181023T141500
DTEND;TZID=Europe/London:20181023T151500
UID:TALK112525AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/112525
DESCRIPTION:Beck’s distributive laws provide sufficient condit
ions under which two monads can be composed\, and
monads arising from distributive laws have many de
sirable theoretical properties. Unfortunately\, fi
nding and verifying distributive laws\, or establi
shing if one even exists\, can be extremely diffic
ult and error-prone.\n\nIn this talk I will descri
be two general-purpose techniques for showing when
there can be no distributive law between two mona
ds. The first widely generalizes ideas from a coun
terexample attributed to Plotkin\, yielding genera
l-purpose theorems that recover the known situatio
ns in which no distributive law can exist. The sec
ond approach is entirely novel\, encompassing prac
tical situations beyond the generalisation of Plot
kin's argument\, including a negative answer to th
e open question of whether the list monad distribu
tes over itself. As an illustration of our no-go t
heorems\, I will give an overview of the (im)possi
bility of distributive laws between members of an
extension of the Boom hierarchy\; a hierarchy of d
atatypes well-known to functional programmers.\n\n
The work I present is done in collaboration with D
an Marsden. To establish our theorems\, we used an
algebraic perspective on monads\, exploiting a sy
ntactic characterization of distributive laws. Thi
s approach is key to generalizing beyond what has
been achieved by direct calculations in previous w
ork.
LOCATION:MR4\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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