Let's see how things unfold.: reconciling the infinite with the intensional (extended abstract)

Coinductive types model infinite structures unfolded on demand, like politicians' excuses: for each attack, there is a defence but no likelihood of resolution. Representing such evolving processes coinductively is often more attractive than representing them as functions from a set of permitted observations, such as projections or finite approximants, as it can be tricky to ensure that observations are meaningful and consistent. As programmers and reasoners, we need coinductive definitions in our toolbox, equipped with appropriate computational and logical machinery.