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A syntax for linear logic
 Presented at Conference on Mathematical Foundations of Programming Language Semantics
, 1993
"... Abstract. This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types’. The presentation of linear logic is simplified by basing it on the Logic of Unity. An app ..."
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Cited by 71 (5 self)
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Abstract. This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as Types’. The presentation of linear logic is simplified by basing it on the Logic of Unity. An application to the array update problem is briefly discussed. 1
CallbyName, CallbyValue, CallbyNeed, and the Linear Lambda Calculus
, 1994
"... Girard described two translations of intuitionistic logic into linear logic, one where A > B maps to (!A) o B, and another where it maps to !(A o B). We detail the action of these translations on terms, and show that the first corresponds to a callbyname calculus, while the second correspond ..."
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Cited by 29 (5 self)
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Girard described two translations of intuitionistic logic into linear logic, one where A > B maps to (!A) o B, and another where it maps to !(A o B). We detail the action of these translations on terms, and show that the first corresponds to a callbyname calculus, while the second corresponds to callbyvalue. We further show that if the target of the translation is taken to be an affine calculus, where ! controls contraction but weakening is allowed everywhere, then the second translation corresponds to a callbyneed calculus, as recently defined by Ariola, Felleisen, Maraist, Odersky, and Wadler. Thus the different calling mechanisms can be explained in terms of logical translations, bringing them into the scope of the CurryHoward isomorphism.
Discontinuity and the Lambek Calculus
, 1994
"... This paper is concerned with the treatment of discontinuous constituency within Categorial Grammar ..."
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Cited by 13 (2 self)
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This paper is concerned with the treatment of discontinuous constituency within Categorial Grammar
Separating Weakening and Contraction in a Linear Lambda Calculus
 in: Proc. CATS'98, Computing: the Fourth Australian Theory Symposium (Perth
, 1996
"... . We present a separatedlinear lambda calculus of resource consumption based on a refinement of linear logic which allows separate control of weakening and contraction. The calculus satisfies subject reduction and confluence, and inherits previous results on the relationship of Girard's two tr ..."
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Cited by 2 (1 self)
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. We present a separatedlinear lambda calculus of resource consumption based on a refinement of linear logic which allows separate control of weakening and contraction. The calculus satisfies subject reduction and confluence, and inherits previous results on the relationship of Girard's two translations from minimal intuitionistic logic to linear logic with callbyname and callbyvalue. We construct a hybrid translation from Girard's two which is sound and complete for mapping types and reduction sequences from callbyneed into separatedlinear . This treatment of callbyneed is more satisfying than in previous work, allowing a contrasting of all three reduction strategies in the manner (for example) that the CPS translations allow for callbyname and callbyvalue. H OW can we explain the differences between parameterpassing styles? With the continuationpassing style (CPS) transforms [24, 25], one makes the flow of control explicit. Each parameterpassing style is associated ...
CallbyNeed Splits the Mode!
, 1993
"... We present a separatedlinear 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 relations ..."
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We present a separatedlinear 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 callbyname and callbyvalue. 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 callbyneed into separatedlinear . This treatment of callbyneed 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 callbyname and callbyvalue. Introduction One fundamental application of the continuationpassing transformations is to explain the different parameterpassing mechanisms of callby...