Keynote by Dr. Emily Riehl C◦mp◦se :: Conference http://www.composeconference.org/ May 18, 2017 Slides: http://www.math.jhu.edu/~eriehl/compose.pdf Monads have famously been used to model computational effects, although, curiously, the computer science literature presents them in a form that is scarcely recognizable to a category theorist — I’d say instead that a monad is just a monoid in the category of endofunctors, what’s the problem? ;) To a categorical eye, computational effects are modeled using the Kleisli category of a monad, a perspective which suggests another categorical tool that might be used to reason about computation. The Kleisli category is closely related to another device for categorical universal algebra called a Lawvere theory, which may be a more natural framework to model computation (an idea suggested by Gibbons, Hinze, Hyland, Plotkin, Power and certainly others). This talk will survey monads, Lawvere theories, and the relationships between them and illustrate the advantages and disadvantages of each framework through a variety of examples: lists, exceptions, side effects, input-output, probabilistic non-determinism, and continuations.

reasoning about the system should be done recursively on its structure. ​ good software design is ultimately an art. ​ another example of reasoning via an interface. ​ I suspect that interfaces are in fact synonymous with compositionality. That is, compositionality is not just the ability to compose objects, but the ability to work with an object after intentionally forgetting how it was built. ​ can interact in complex ways that block understanding ​ More generally, I claim that the opposite of compositionality is emergent effects. The common definition of emergence is a system being ‘more than the sum of its parts’, and so it is easy to see that such a system cannot be understood only in terms of its parts, i.e. it is not compositional. Moreover I claim that non-compositionality is a barrier to scientific understanding, because it breaks the reductionist methodology of always dividing a system into smaller components and translating explanations into lower levels.