Separating weakening and contraction in a linear lambda calculus

We present a separated-linear lambda calculus based on a refinement of linear logic which allows separate control of weakening and contraction. The calculus satisfies subject reduction and confluence, has a straightforward notion of standard evaluation, and inherits previous results on the relationship of Girard\u27s two translations from minimal intuitionistic logic to linear logic with call-by-name and call-by-value. We construct a hybrid translation from Girard\u27s two which is sound and complete for mapping types, reduction sequences and standard evaluation sequences from call-by-need into separated-linear lambda, a more satisfying treatment of call-by-need than in previous work, which now allows a contrasting of all three reduction strategies in the manner (for example) that the CPS transla- tions allow for call-by-name and call-by-value

Separating Weakening and Contraction in a Linear Lambda Calculus (Unabridged)

. We present a separated-linear lambda calculus based on a refinement of linear logic which allows separate control of weakening and contraction. The calculus satisfies subject reduction and confluence, 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 hybrid translation from Girard's two which is sound and complete for mapping types, reduction sequences and standard evaluation sequences from call-by-need into separated-linear , a more satisfying treatment of call-by-need than in previous work, which now allows a contrasting of all three reduction strategies in the manner (for example) that the CPS translations allow for callby -name and call-by-value. O ne fundamental application of the continuationpassing transformations is to explain the different parameter-passing mechanisms of call-by-name and call..