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Abstract: Girard described two translations of intuitionistic logic into linear logic, one where A ! B maps to (!A) \Gammaffi B, and another where it maps to !(A \Gammaffi B). We detail the action of these translations on terms, and show that the first 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 affine calculus, where ! controls contraction but weakening is allowed everywhere, then the... (Update)
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...by computation. Wadler and colleagues show that this kind of term system has connections with functional programming [160, 278, 279, 281, 280, 282, 283]. 2.11 Structurally Free Logic A very recent innovation in the proof theory of substructural logics is the advent of...
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2: Entailment: the Logic of Relevance and Necessity (context) - Anderson, Belnap - 1975
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BibTeX entry: (Update)
JOHN MARAIST, MARTIN ODERSKY, DAVID N. TURNER, AND PHILIP WADLER. "Call-by-name, call-by-value, call-by-need, and the linear lambda calculus". In 11th International Conference on the Mathematical Foundations of Programming Semantics, New Orleans, Lousiana, March--April 1995. http://citeseer.ist.psu.edu/article/maraist94callbyname.html More
@misc{ maraist95callbyname,
author = "J. MARAIST and M. ODERSKY and D. TURNER and P. WADLER",
title = "Call-by-name, call-by-value, call-by-need, and the linear lambda calculus",
text = "JOHN MARAIST, MARTIN ODERSKY, DAVID N. TURNER, AND PHILIP WADLER. Call-by-name,
call-by-value, call-by-need, and the linear lambda calculus. In 11th International
Conference on the Mathematical Foundations of Programming Semantics, New
Orleans, Lousiana, March--April 1995.",
year = "1995",
url = "citeseer.ist.psu.edu/article/maraist94callbyname.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard, logic - 1987
729 The Lambda Calculus: Its Syntax and Semantics (context) - Barendregt - 1981
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283 Theoretical Computer Science (context) - Plotkin, call-by-value et al. - 1975
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169 The call-by-need lambda calculus - Ariola, Felleisen - 1994
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48 Laboratory for the Foundations of Computer Science (context) - Moggi, lambda-calculus et al. - 1988
47 Lilac: a functional programming language based on linear log.. (context) - Mackie - 1991
33 The noble art of linear decorating (context) - Schellinx - 1994
29 A syntax for linear logic - Wadler - 1993
24 The call-by-need lambda calculus - Maraist, Odersky et al. - 1994
24 Lisp and Symbolic Computation (context) - Reynolds, of - 1993
21 A linear functional language (context) - Holmstrom - 1988
14 Lambda calculus and intuitionistic linear logic (context) - Rocca, Roversi - 1994
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4 Types in Lambda Calculus and Programming Languages (context) - Barendregt, Hemerik - 1990
4 private communication (context) - Plotkin - 1993
3 Symposium on Principles of Programming Languages (context) - Launchbury, semantics et al. - 1993
1 linear' electronic mailing list (context) - Girard, to - 1992
1 Available from bjacobs@cwi (context) - Jacobs, weakening et al. - 1992
Documents on the same site (http://www.cis.unisa.edu.au/~cisjpm/Papers/all.html): More
The Call-by-Need Lambda Calculus (Unabridged) - Maraist, Odersky, Wadler (1994) (Correct)
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Separating Weakening and Contraction in a Linear Lambda Calculus - Maraist (1996) (Correct)
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