Abstract

We introduce the lambda-coiteration schema for a distributive law lambda of a functor T over a functor F. Under certain conditions it can be shown to uniquely characterise functions into the carrier of a final F-coalgebra, generalising the basic coiteration schema as given by finality. The duals of primitive recursion and course-of-value iteration, which are known extensions of coiteration, arise as instances of our framework. One can furthermore obtain schemata justifying recursive specifications that involve operators such as addition of power series, regular operators on languages, or parallel and sequential composition of processes. Next...

Citations

2971	Communication and Concurrency - Milner - 1989
279	Universal coalgebra: a theory of systems - Rutten - 2000
214	A Tutorial on (Co)Algebras and (Co)Induction - Jacobs, Rutten - 1997
169	Bisimulation Can’t Be Traced - Bloom, Istrael, et al. - 1995
156	N.: A Final Coalgebra Theorem - Aczel, Mendler - 1989
122	G.: Towards a mathematical operational semantics - Turi, Plotkin - 1997
92	Introduction to Process Algebra - Fokkink - 2000
88	Process Algebra, volume 18 of Cambridge Tracts - Baeten, Weijland - 1990
64	On the bisimulation proof method - Sangiorgi - 1998
51	Automata and Coinduction (An Exercise in Coalgebra - Rutten - 1998
42	Behavioural Differential Equations: a Coinductive Calculus - Rutten - 2003
22	Distributivity for Endofunctors, Pointed and Co-pointed Endofunctors, Monads and Comonads - Lenisa, Power, et al. - 2000
20	On the Productivity of Recursive List Definitions - Sijtsma - 1989
11	From set-theoretic coinduction to coalgebraic coinduction: some results, some problems - Lenisa - 1999
5	Distributivity for a monad and a comonad - Power, Watanabe - 1999
4	A coalgebraic view of in trees and iteration - Aczel, Adamek, et al. - 2001
3	Behavioural dierential equations: a coinductive calculus of streams, automata, and power series - Rutten - 2000
3	Functional pearl: Power series, power serious - McIlroy - 1999
2	Hamming's exercise in SASL. Personal Note EWD792, see http://www.cs.utexas.edu/users/EWD - Dijkstra - 1981
1	On the Productivity of Recursive List De - Sijtsma - 1989