We show that the principal types of the closed terms of the affine fragment of λ-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry of Interaction model à 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 characterizing those partial involutions which are denotations of combinatory terms.
Principal types as partial involutions
Honsell F.
;Lenisa M.;Scagnetto I.
2025-01-01
Abstract
We show that the principal types of the closed terms of the affine fragment of λ-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry of Interaction model à 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 characterizing those partial involutions which are denotations of combinatory terms.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
