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SUMMARY:No-Go Theorems for Distributive Laws - Maaike Zwart (University of
  Oxford)
DTSTART:20181023T131500Z
DTEND:20181023T141500Z
UID:TALK112525@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:Beck’s distributive laws provide sufficient conditions under
  which two monads can be composed\, and monads arising from distributive l
 aws have many desirable theoretical properties. Unfortunately\, finding an
 d verifying distributive laws\, or establishing if one even exists\, can b
 e extremely difficult and error-prone.\n\nIn this talk I will describe two
  general-purpose techniques for showing when there can be no distributive 
 law between two monads. The first widely generalizes ideas from a countere
 xample attributed to Plotkin\, yielding general-purpose theorems that reco
 ver the known situations in which no distributive law can exist. The secon
 d approach is entirely novel\, encompassing practical situations beyond th
 e generalisation of Plotkin's argument\, including a negative answer to th
 e open question of whether the list monad distributes over itself. As an i
 llustration of our no-go theorems\, I will give an overview of the (im)pos
 sibility of distributive laws between members of an extension of the Boom 
 hierarchy\; a hierarchy of datatypes well-known to functional programmers.
 \n\nThe work I present is done in collaboration with Dan Marsden. To estab
 lish our theorems\, we used an algebraic perspective on monads\, exploitin
 g a syntactic characterization of distributive laws. This approach is key 
 to generalizing beyond what has been achieved by direct calculations in pr
 evious work. 
LOCATION:MR4\, Centre for Mathematical Sciences
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