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SUMMARY:Fibrational Parametricity - Neil Ghani\, University of Strathclyde
DTSTART:20131025T150000Z
DTEND:20131025T160000Z
UID:TALK46200@talks.cam.ac.uk
CONTACT:Jonathan Hayman
DESCRIPTION:Category theory offers a simple and unifying understanding of 
 many of the foundations of modern functional programming. It is well known
 \, for example\, that data types can be understood via initial algebras\, 
 effects can be understood via monads\, and dependent types can be understo
 od via fibrations. However\, one area in which category theory has thus fa
 r been less successful is in providing an elegant and prescriptive underst
 anding of parametricity. Theories such as dinaturality and strong dinatura
 lity have been proposed but they are\, unfortunately\, insufficient to ful
 ly capture all key aspects of parametricity. \n\nI will do my best to rect
 ify this situation by offering an alternative categorical perspective on p
 arametricity. This alternative perspective is based on fibrations. Specifi
 cally\, I'll show that the fibrational perspective i) sheds new light on t
 he conceptual essence of parametricity\; iI) provides simple and natural f
 ormulations of the key constructions of parametricity\; and iii) is robust
  enough not only to cover known models of parametricity\, but to suggest n
 ew ones as well.\n
LOCATION:Room FW26\, Computer Laboratory\, William Gates Building
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