TY - GEN
T1 - Arrows are strong monads
AU - Asada, Kazuyuki
PY - 2010
Y1 - 2010
N2 - Hughes' arrows were shown, by Jacobs et al., to be roughly monads in the bicategory Prof of profunctors (distributors, modules). However in their work as well as others', the categorical nature of the first operator was not pursued and its formulation remained rather ad hoc. In this paper, we identify first with strength for a monad, therefore: arrows are strong monads in Prof. Strong monads have been widely used in the semantics of functional programming after Moggi's seminal work, therefore our observation establishes categorical canonicity of the notion of arrow.
AB - Hughes' arrows were shown, by Jacobs et al., to be roughly monads in the bicategory Prof of profunctors (distributors, modules). However in their work as well as others', the categorical nature of the first operator was not pursued and its formulation remained rather ad hoc. In this paper, we identify first with strength for a monad, therefore: arrows are strong monads in Prof. Strong monads have been widely used in the semantics of functional programming after Moggi's seminal work, therefore our observation establishes categorical canonicity of the notion of arrow.
KW - arrow
KW - computational effect
KW - freyd category
KW - profunctor
KW - strong monad
UR - http://www.scopus.com/inward/record.url?scp=78249232945&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78249232945&partnerID=8YFLogxK
U2 - 10.1145/1863597.1863607
DO - 10.1145/1863597.1863607
M3 - Conference contribution
AN - SCOPUS:78249232945
SN - 9781450302555
T3 - Proceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP
SP - 33
EP - 41
BT - MSFP'10 - Proceedings of the 2010 ACM SIGPLAN Workshop on Mathematically Structured Functional Programming, Co-located with ICFP'10
T2 - 3rd Workshop on Mathematically Structured Functional Programming, MSFP 2010
Y2 - 25 September 2010 through 25 September 2010
ER -