%0 Conference Proceedings
%T Product Rules and Distributive Laws
%+ University of Warsaw (UW)
%A Winter, Joost
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 13th International Workshop on Coalgebraic Methods in Computer Science (CMCS)
%C Eindhoven, Netherlands
%Y Ichiro Hasuo
%3 Coalgebraic Methods in Computer Science
%V LNCS-9608
%P 114-135
%8 2016-04-02
%D 2016
%R 10.1007/978-3-319-40370-0_8
%Z Computer Science [cs]Conference papers
%X We give a categorical perspective on various product rules, including Brzozowski’s product rule $(st)_a = s_a t + o(s) t_a$ and the familiar rule of calculus $(st)_a = s_a t + s t_a$ It is already known that these product rules can be represented using distributive laws, e.g. via a suitable quotient of a GSOS law. In this paper, we cast these product rules into a general setting where we have two monads <i>S</i> and<i>T</i>, a (possibly copointed) behavioural functor <i>F</i>, a distributive law of <i>T</i> over <i>S</i>, a distributive law of <i>S</i> over<i> F</i>, and a suitably defined distributive law $TF \Rightarrow FST$ We introduce a coherence axiom giving a sufficient and necessary condition for such triples of distributive laws to yield a new distributive law of the composite monad <i>ST</i> over <i>F</i>, allowing us to determinize <i>FST</i>-coalgebras into lifted <i>F</i> coalgebras via a two step process whenever this axiom holds.
%G English
%Z TC 1
%Z WG 1.3
%2 https://inria.hal.science/hal-01446036/document
%2 https://inria.hal.science/hal-01446036/file/418352_1_En_8_Chapter.pdf
%L hal-01446036
%U https://inria.hal.science/hal-01446036
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC1
%~ IFIP-LNCS-9608
%~ IFIP-WG1-3
%~ IFIP-CMCS