[L7] ================================================ AMAST Links 02 02 Two papers by Danos and Regnier These papers are available on the WWW at URL: http://boole.logique.jussieu.fr/www.danos/experience.html and _also_ at URL: ftp://lmd.univ-mrs.fr/pub/regnier/Papers.html or by _anonymous ftp_ from the directory at URL: ftp://lmd.univ-mrs.fr/pub/regnier/ The file revirrev.[dvi, ps].[Z, gz] is the paper Reversible and Irreversible Computations (GOI & Environment Machines) We present a sequential _reversible_ computation scheme for lambda-calculus coming from the _geometry of interaction_. The computation consists in pushing a token (finite list of symbols) along the term (adequately represented as a net), each traversal of a node acting reversibly (i.e., one-one'ly) on that token. Then we define an optimization of that scheme taking advantage of its ``call/return'' symmetry that was recently discovered (see the _legality_ condition of Asperti and Laneve). Moves in this case are no longer reversible and correspond exactly to the transitions of a simple environment machine. This result provides a clearcut correspondence between reversible and irreversible means of computation (and it is fun also to know that GOI gives a simpler account of computations than environment machines). The file pnh.[dvi, ps].[Z, gz] is the paper Proof-nets and the Hilbert space to appear in Proceedings of the Linear Logic Workshop, Cornell, 1993. Girard's execution formula is a decomposition of usual beta-reduction (or cut-elimination) in reversible, local and asynchronous elementary moves. It can easily be presented, when applied to a lambda-term or a net, as the sum of maximal paths on the lambda-term/net that are not cancelled by the algebra LS (as was done in Danos' and Regnier's theses). It is then natural to ask for a characterization of those paths, that would be only of geometric nature. We prove here that they are exactly those paths that have residuals in any reduct of the lambda-term/net. Remarkably, the proof puts to use for the first time the interpretation of lambda-terms/nets as operators on the Hilbert space.