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UID:8470@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230622T110000
DTEND;TZID=Europe/Paris:20230622T123000
DTSTAMP:20241124T135425Z
URL:https://www.i2m.univ-amu.fr/evenements/strategies-as-resource-terms-an
 d-their-categorical-semantics/
SUMMARY: (...): Strategies as Resource Terms\, and their Categorical Semant
 ics
DESCRIPTION:: As shown by Tsukada and Ong\, normal (extensional) simply-typ
 ed resource terms correspond to playsin Hyland-Ong games\, quotiented by M
 elliès’ homotopy equivalence. Though inspiring\, their proofis indirect
 \, relying on the injectivity of the relational model w.r.t. both sides of
  the correspondence —in particular\, the dynamics of the resource calcul
 us is taken into account only via the compatibilityof the relational model
  with the composition of normal terms defined by normalization.\n\nWe revi
 sit and extend these results. Our first contribution is to restatethe corr
 espondence by considering causal structures we call augmentations\, which 
 are canonicalrepresentatives of Hyland-Ong plays up to homotopy. This allo
 ws us to give a direct and explicitaccount of the connection with normal r
 esource terms. As a second contribution\, we extend thisaccount to the red
 uction of resource terms: building on a notion of strategies as weighted s
 ums ofaugmentations\, we provide a denotational model of the resource calc
 ulus\, invariant under reduction.A key step — and our third contribution
  — is a categorical model we call a resource category\, whichis to the r
 esource calculus what differential categories are to the differential λ-c
 alculus.
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire2 (RdC)\, 163 Avenue de
  Luminy\, 13009 Marseille\, France\, 
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 U\, Salle Séminaire2 (RdC):geo:0,0
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