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Dear Types, I am curious about the relative expressiveness of effects and coeffects. Has this been studied? The cleanest distinction I've seen is that effects capture the impact a program has on its environment, i.e. what it produces. Coeffects capture the requirements that a program puts on its environment: what it consumes. This is discussed, for example, in Gaboardi et al's ICFP 2016 paper, "Combining Effects and Coeffects via Grading" (and elsewhere). There is some useful intuition in this distinction, and it describes the different structure of checking rules in effect and coeffect systems. However, I don't find this distinction very helpful in thinking about expressiveness. It seems like many examples can be expressed in either an effect or a coeffect system. For example, an exception is a classic example of an effect (e.g. in the paper mentioned above, and many others). However, it seems to me that exceptions can also be modeled as coeffects: code that might throw an exception requires the caller to pass a handler for that exception to it--or perhaps an abstract "permission" to throw that exception. So in what sense are exceptions an effect, rather than a coeffect? Is this true of all the kinds of things that are typically expressed with effects and coeffects--that they could just as easily be expressed in the other style? If so, what are the benefits of one style vs. the other? Or are there examples that can only be expressed in one style--or for which expression in the other style is much more awkward? Perhaps these questions have been written about, but I haven't been able to find it. I would love to get some pointers. I am particularly interested in a practical explanation of the differences in expressiveness, or theoretical results that have a direct and explicit relationship to practice--with practical examples in either case. (co-)Monads and/or anything categorical are not a very helpful starting point for me, but effect systems and/or linear types are (I've done research on both). I am also more interested in the descriptive view of effects/coeffects (in the sense of Filinski, ICFP'11) than the prescriptive view. Thanks, Jonathan
