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SUMMARY:Mathematical Structures for Data Types with Restricted Parameteric
 ity - Dominic Orchard (University of Cambridge)
DTSTART:20120608T141500Z
DTEND:20120608T151500Z
UID:TALK38205@talks.cam.ac.uk
CONTACT:Dominic Orchard
DESCRIPTION:(aka. Fixing the maths for real-world data types)\n\nFunctiona
 l programming continues to adopt concepts from category theory to provide 
 abstraction mechanisms for structuring programs. For example\, many parame
 trically polymorphic data types are instances of functors and monads. Othe
 r parametric data types have their polymorphism restricted for implementat
 ion efficiency e.g. unboxed arrays require primitive element types Int\, F
 loat\, etc. Traditionally\, mathematical abstractions in Haskell are endof
 unctor-based\, however such data types do not fit this model. This paper i
 nstead interprets restricted polymorphism as subcategory specification. No
 tions of functors\, monads and comonads are redefined over (full and non-f
 ull ) subcategories\, providing non-endofunctors (with distinct source and
  target categories)\, relative monads and relative comonads. These structu
 res not only provide a more accurate model of restricted polymorphism but 
 can also be defined within Haskell itself using GHC’s new constraint kin
 ds extension. \n\nThis is a practice talk for TFP'12. Joint work with Alan
  Mycroft.
LOCATION:SS03\, Computer Laboratory
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