  We show that the principal types of the closed terms of the affine fragment
of $\lambda$-calculus, with respect to a simple type discipline, are
structurally isomorphic to their interpretations, as partial involutions, in a
natural Geometry of Interaction model \`a la Abramsky. This permits to explain
in elementary terms the somewhat awkward notion of linear application arising
in Geometry of Interaction, simply as the resolution between principal types
using an alternate unification algorithm. As a consequence, we provide an
answer, for the purely affine fragment, to the open problem raised by Abramsky
of characterising those partial involutions which are denotations of
combinatory terms.
