By Davide Sangiorgi, Jan Rutten
Coinduction is a technique for specifying and reasoning approximately limitless info forms and automata with countless behaviour. in recent times, it has come to play an ever extra vital position within the idea of computing. it's studied in lots of disciplines, together with procedure idea and concurrency, modal common sense and automata conception. in general, coinductive proofs reveal the equivalence of 2 gadgets by way of developing an appropriate bisimulation relation among them. This choice of surveys is aimed toward either researchers and Master's scholars in desktop technology and arithmetic and bargains with numerous facets of bisimulation and coinduction, with an emphasis on method conception. Seven chapters disguise the subsequent themes: historical past, algebra and coalgebra, algorithmics, common sense, higher-order languages, improvements of the bisimulation evidence procedure, and chances. routines also are integrated to assist the reader grasp new material.
Contents: 1. Origins of bisimulation and coinduction (Davide Sangiorgi) — 2. An advent to (co)algebra and (co)induction (Bart Jacobs and Jan Rutten) — three. The algorithmics of bisimilarity (Luca Aceto, Anna Ingolfsdottir and Jiří Srba) — four. Bisimulation and common sense (Colin Stirling) — five. Howe’s technique for higher-order languages (Andrew Pitts) — 6. improvements of the bisimulation evidence technique (Damien Pous and Davide Sangiorgi) — 7. Probabilistic bisimulation (Prakash Panangaden)
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Additional info for Advanced Topics in Bisimulation and Coinduction
Also, the fixed-point properties of the Y combinator of the λ-calculus had been known for a long time (used for instance by Curry, Feys, Landin, and Strachey), but the precise mathematical meaning of Y as fixed point remains unclear until Scott works out his theory of reflexive domains, at the end of 1969 [Sco69b, Sco69a]; see [Par70]. (Another relevant paper is [Sco69c], in which fixed points appear but which precedes the discovery of reflexive domains. We may also recall James H. ) During the 1970s, further fixed-point techniques and rules are put forward.
IEEE, 1977. Final version in Computing, 21(4):273– 294, 1979. Based on Clarke’s PhD thesis, Completeness and Incompleteness Theorems for Hoare-like Axiom Systems, Cornell University, 1976. V. Devid´e. On monotonous mappings of complete lattices. Fundamenta Mathematicae, LIII:147–154, 1963. P. de Roever. On backtracking and greatest fixpoints. In Arto Salomaa and Magnus Steinby, editors, Fourth Colloquium on Automata, Languages and Programming (ICALP), volume 52 of Lecture Notes in Computer Science, pages 412–429.
Greatest fixed points, and related coinductive techniques, begin to appear as well in the 1970s. It is hard to tell what is the first appearance. One reason for this is that the rules for greatest fixed points are not surprising, being the dual of rules for least fixed points that had already been studied. I would think however that the first to make explicit and non-trivial use of greatest fixed points is David Park, who, throughout the 1970s, works intensively on fairness issues for programs that may contain constructs for parallelism and that may not terminate.