Call - by - need splits the mode !

We present a separated-linear lambda calculus based on a reenement of linear logic which allows separate control of weakening and contraction. The calculus satisses subject reduction and connuence, has a straightforward notion of standard evaluation, and inherits previous results on the relationship of Girard's two translations from minimal intuitionistic logic to linear logic with call-by-name and call-by-value. We construct a new translation, a hybrid of Girard's two, which is sound and complete for mapping types, reduction sequences and standard evaluation sequences from call-by-need into separated-linear. This treatment of call-by-need is more satisfying than in previous work, allowing a contrasting of all three reduction strategies in the manner that (for example) the CPS translations allow for call-by-name and call-by-value.