Coinduction Resources

Here are some materials I've found useful in trying to understand coinduction and related notions. Most of them involve some pretty heavy mathematics, but their introductions usually provide an overview and some examples that will help you develop your intuitions even if the math is over your head.

Some major figures, all of whom have made many publications available on their homepages:

• Jan Rutten
• Bart Jacobs
• Peter Wegner
• Dina Goldin
• Davide Sangiorgi
• Robin Milner

A good place to start is An introduction to (co)algebra and (co)induction (PDF) by Rutten and Jacobs. (in Advanced Topics in Bisimulation and Coinduction).  The first part gives several concrete examples that will help you understand coinduction.

Coinductive Models of Finite Computing Agents by Wegner and Goldin.  Free version available on their homepages.

Communicating and Mobile Systems: the Pi Calculus, Milner.  Not easy to read, but well worth the effort.

An interesting paper showing how the concepts of bisimulation and bisimilarity emerged independently in computer science, philosophical logic, and set theory:  On the Origins of Bisimulation and Coinduction, Sangiorgi.  Free version available on author's homepage.

Universal coalgebra: a theory of systems, Rutten.  A landmark paper, I gather.  You can find a free version on Rutten's homepage.

Coalgebraically Thinking, David Corfield (blog post, n-Category Cafe, 2008)

This seems to be a growth industry; a number of introductory texts have been published in the past few years:

• Interactive Computation: The New Paradigm, Goldin, Smolka, Wegner, Eds. 2006
• Introduction to Bisimulation and Coinduction,  Sangiorgi, 2012
• Introduction to Coalgebra.  Towards Mathematics of States and Observations, Jacobs 2012 (PDF)
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