Generalised coinduction

Final coalgebras of a functor F are suited for an abstract description of infinite datatypes and dynamical systems. Functions into such a domain are specified by coinductive definitions. The format these specifications take when their justification is directly based on finality is called the coiteration schema here. In applications it often turns out to be too rigid to allow for a convenient description of the functions under consideration. Thus, generalisations or variations are desired. We introduce a generic ?-coiteration schema that can be instantiated by a distributive law ? of some functor T over F and show that - under mild assumptions on the underlying category - one obtains principles which uniquely characterise arrows into the carrier of a final F-coalgebra as well. Certain instances of ?-coiteration can be shown to specify arrows that fail to be coiterative. Examples are the duals of primitive recursion and course-of-value iteration, which are known extensions of coiteration. One can furthermore obtain schemata justifying recursive specifications that involve operators such as arithmetic operations on power series, regular operators for languages, or parallel and sequential composition of processes. Next, the same type of distributive law ? is used to generalise coinductive proof techniques. To this end, we introduce the notion of a ?-bisimulation relation, many instances of which are weaker than the conventional definition of a bisimulation. It specialises e.g. to what could be called bisimulation up-to-equality or bisimulation up-to-context for contexts built from operators of the type mentioned above. We give a proof showing that every ?-bisimulation only contains pairs of bisimilar states. This principle leads to simpler proofs through the use of less complex relations

ABSTRACT GSOS for Probabilistic Transition Systems

CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms

Why Do the Rich Oppose Redistribution? An Experiment with America’s Top 5%

Wealthy individuals have a disproportionate influence on politics and firms. We study attitudes toward redistribution of a large sample of the top 5% in the U.S. in terms of income and financial assets, and find that they prefer less redistribution than a representative sample of the bottom 95%. The differences in tax attitudes and political views can be largely attributed to differences in distributional preferences, which we measured in an experiment where choices affected the pay of pairs of workers in a real-effort task. Wealthy Americans redistribute less to the low-income worker, thus accepting more inequality than the rest of the population. The gap in distributional preferences is primarily driven by individuals who acquired wealth over their lifetime rather than those who were born into wealth. Our findings raise the possibility that wealthy individuals contribute to the persistent income inequality in the U.S