Opening Keynote: There and Back Again
Mathematicians usually teach abstract algebra from groups and build up from there. Having inverses allows them to prove many non-trivial results. Functional programmers more often descend to working with monoids, or even semigroups. They give up the power of inverses to gain many more examples. You don’t often hear about the shadowy realm between. Perfect inverses don’t always exist, nor do we want them to. Going on a journey and returning rarely leaves the protagonist unchanged. If it does, this is usually taken as a poor example of the author’s craft. We’ll explore the middle-ground of regular and inverse semigroups, inverse monoids, even inverse categories. In this space where inverses may not invert, we’ll develop examples and counter-examples. We’ll gain some insight into spoken Australian English along the way. Join us.