calculus was for a long time considered as a computational artefact. But Church already felt the interest of the calculus, in its explicitely typed variant, from a logical point of view. This was later more deeply investigated by mathematicians, among them Curry, and then Howard (and many others, of course)… But wait, <em>Curry</em> … <em>Howard</em> … that sounds familiar. What we will investigate now is a deep connection between calculating using the lambda-calculus, as we did in the previous sectio