Toward a geometric view on computations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports Year : 2005

Toward a geometric view on computations


We interpret Intersection Types as the closed sets of some Zariski topology on pure lambda-terms. In this view, the parallel or operator introduced by Boudol is the multiplication for an underlying ring structure. We propose a new calculus which extends pure $\lambda$-calculus along the same lines as relative numbers $Z$ extend natural numbers , the ring operations expressing computation rules on terms. Thus, types are interpreted as the zeros sets for some notion of polynomial ideals (algebraic sets). Terms properties (strong normalisation, confluence, full abstraction) are investigated. Among similarities with Algebraic Geometry, we suggest that terms of interest, such as normalising terms or convergent programs are rare; divergence is a generic property for programs.


Other [cs.OH]
Fichier principal
Vignette du fichier
RR-5492.pdf (286.88 Ko) Télécharger le fichier

Dates and versions

inria-00070515 , version 1 (19-05-2006)


  • HAL Id : inria-00070515 , version 1


Philippe Audebaud. Toward a geometric view on computations. RR-5492, INRIA. 2005, pp.16. ⟨inria-00070515⟩
83 View
58 Download


Gmail Facebook Twitter LinkedIn More