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UID:5324@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20241010T110000
DTEND;TZID=Europe/Paris:20241010T123000
DTSTAMP:20240920T113607Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-154/
SUMMARY:Paolo Pistone (LIP\, ÉNS Lyon): Tropical Mathematics and The Lambd
 a Calculus
DESCRIPTION:Paolo Pistone: We explore the interpretation of the lambda-calc
 ulus in a framework\nbased on tropical mathematics\, and we show that it p
 rovides a unifying\nframework for two well-developed quantitative approach
 es to program semantics:\non the one hand program metrics\, based on the a
 nalysis of program sensitivity\nvia Lipschitz conditions\, on the other ha
 nd resource analysis\, based on linear\nlogic and higher-order program dif
 ferentiation. To do that\, we focus on the\nsemantics arising from the rel
 ational model weighted over the tropical\nsemiring\, and we discuss its ap
 plication to the study of “best case” program\nbehavior for languages 
 with probabilistic and non-deterministic effects.\nFinally\, we show that 
 a general foundation for this approach is provided by an\nabstract corresp
 ondence between tropical algebra and Lawvere’s theory of\ngeneralized me
 tric spaces.
CATEGORIES:Séminaire,Logique et Interactions
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