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UID:7234@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20181004T110000
DTEND;TZID=Europe/Paris:20181004T123000
DTSTAMP:20241120T203457Z
URL:https://www.i2m.univ-amu.fr/evenements/revisiting-call-by-value-bohm-t
 rees-in-light-of-their-taylor-expansion/
SUMMARY:Giulio Manzonetto (LIPN\, Université Paris 13): Revisiting Call-by
 -value Bohm trees in light of their Taylor expansion
DESCRIPTION:Giulio Manzonetto: The call-by-value lambda calculus can be end
 owed with permutation rules\, arising from linear logic proof-nets\, havin
 g the advantage of unblocking some redexes that otherwise get stuck during
  the reduction. We show that such an extension allows to define a satisfyi
 ng notion of Bohm(-like) tree and a theory of program approximation in the
  call-by-value setting. We prove that all lambda terms having the same Boh
 m tree are observationally equivalent\, and characterize those Bohm-like t
 rees arising as actual Bohm trees of lambda terms.\nWe also compare this a
 pproach with Ehrhard's theory of program approximation based on the Taylor
  expansion of lambda terms\, translating each lambda term into a possibly 
 infinite set of so-called resource terms. We provide sufficient and necess
 ary conditions for a set of resource terms in order to be the Taylor expan
 sion of a lambda term. Finally\, we show that the normal form of the Taylo
 r expansion of a lambda term can be computed by performing a normalized Ta
 ylor expansion of its Bohm tree. From this it follows that two lambda term
 s have the same Bohm tree if and only if the normal forms of their Taylor 
 expansions coincide.\nJoint work with Emma Kerinec and Michele Pagani.\n\n
 \n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Giulio_Manzonetto.jpg
CATEGORIES:Séminaire,Logique et Interactions
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