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SUMMARY:The Microcosm Principle and Coalgebraic Modeling of Component Calc
 uli - Ichiro Hasuo\, Kyoto
DTSTART:20091127T140000Z
DTEND:20091127T150000Z
UID:TALK21391@talks.cam.ac.uk
CONTACT:Sam Staton
DESCRIPTION:The microcosm principle is a terminology coined by Baez and Do
 lan to\ndescribe a phenomenon where a category C and its object X \\in C b
 oth\nhave the same algebraic structure\, i.e. an inner algebra X residing 
 in\nan outer algebra C.  A classic example is "a monoid object in a\nmonoi
 dal category."\n\nIn this talk I demonstrate another example--arising from
  process\ntheory--carried by "the final coalgebra in a category of coalgeb
 ras."\nHere the shared algebraic structure is that of some process\nalgebr
 a. This categorical view brings new insight to the study of\nsystems as co
 algebras which are composed to yield a larger system--via\na component cal
 culus. Our main result is a general compositionality\ntheorem: the behavio
 r of a composed system is determined by its\nconstituent systems (componen
 ts).\n\nI will also discuss the relationship to semantics of functional\np
 rogramming. A suitable axiomatization of Hughes' notion of arrow\nyields F
 reyd categories as models when it is interpreted in Sets\; we\npresent its
  model in CAT that uses coalgebras\, where the\naxiomatization plays a rol
 e of a component calculus. Again\ncompositionality is for free. I also wis
 h to mention recent work where\na GSOS specification is canonically turned
  into a component calculus\,\nfrom which we can derive parallel compositio
 n S||T of two LTSs\,\nreplication !S of an LTS S\, etc.\n\nThis talk is ba
 sed on joint work with Chris Heunen (Oxford)\, Bart\nJacobs (Nijmegen) and
  Ana Sokolova (Salzburg).\n\nhttp://www.kurims.kyoto-u.ac.jp/~ichiro/
LOCATION:Room FW11\, Computer Laboratory\, William Gates Building
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