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UID:4840@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230629T103000
DTEND;TZID=Europe/Paris:20230629T111500
DTSTAMP:20260107T155822Z
URL:https://www.i2m.univ-amu.fr/evenements/strategies-as-resource-terms-an
 d-their-categorical-semantics-2/
SUMMARY:Lison Blondeau-Patissier (I2M & LIS): Strategies as Resource Terms\
 , and their Categorical Semantics
DESCRIPTION:Lison Blondeau-Patissier: As shown by Tsukada and Ong\, normal 
 (extensional) simply-typed resource terms correspond to playsin Hyland-Ong
  games\, quotiented by Melliès’ homotopy equivalence. Though inspiring\
 , their proofis indirect\, relying on the injectivity of the relational mo
 del w.r.t. both sides of the correspondence —in particular\, the dynamic
 s of the resource calculus is taken into account only via the compatibilit
 yof the relational model with the composition of normal terms defined by n
 ormalization.\n\nWe revisit and extend these results. Our first contributi
 on is to restatethe correspondence by considering causal structures we cal
 l augmentations\, which are canonicalrepresentatives of Hyland-Ong plays u
 p to homotopy. This allows us to give a direct and explicitaccount of the 
 connection with normal resource terms. As a second contribution\, we exten
 d thisaccount to the reduction of resource terms: building on a notion of 
 strategies as weighted sums ofaugmentations\, we provide a denotational mo
 del of the resource calculus\, invariant under reduction.A key step — an
 d our third contribution — is a categorical model we call a resource cat
 egory\, whichis to the resource calculus what differential categories are 
 to the differential λ-calculus.
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire2 (RdC)\, 163 Avenue de
  Luminy\, 13009 Marseille\, France\, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, 1300
 9 Marseille\, France\, ;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - Ancienne B
 U\, Salle Séminaire2 (RdC):geo:0,0
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