Call - by - name , call - by - value , call - by - need , and the linear

Girard described two translations of intuitionistic logic into linear logic, one where A ! B maps to (!A) ? B, and another where it maps to !(A ? B). We detail the action of these translations on terms, and show that the rst corresponds to a call-by-name calculus, while the second corresponds to call-by-value. We further show that if the target of the translation is taken to be an aane calculus, where ! controls contraction but weakening is allowed everywhere, then the second translation corresponds to a call-by-need calculus, as recently deened by Ariola, Felleisen, Maraist, Odersky, and Wadler. Thus the diierent calling mechanisms can be explained in terms of logical translations, bringing them into the scope of the Curry-Howard isomorphism.