Abstract
There is a standard syntax for Girard's linear logic, due to Abramsky, and a standard semantics, due to Seely. Alas, the former is incoherent with the latter: different derivations of the same syntax may be assigned different semantics. This paper reviews the standard syntax and semantics, and discusses the problem that arises and a standard approach to its solution. A new solution is proposed, based on ideas taken from Girard's Logic of Unity. The new syntax is based on pattern matching, allowing for concise expression of programs.
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S. Abramsky, Computational interpretations of linear logic. Presented at Workshop on Mathematical Foundations of Programming Language Semantics, 1990. To appear in Theoretical Computer Science.
S. Abramsky and R. Jagadeesan, New foundations for the geometry of interaction. In 7'th Symposium on Logic in Computer Science, IEEE Press, Santa Cruz, California, June 1992.
M. Barr, *-Autonomous Categories. Lecture Notes in Mathematics 752, Springer Verlag, 1979.
N. Benton, G. Bierman, V. de Paiva, and M. Hyland, Type assignment for intuitionistic linear logic. Draft paper, August 1992.
V. Breazu-Tannen, T. Coquand, C. A. Gunter, and A. Scedrov, Inheritance as explicit coercion. Information and Compututation, 93:172–221, 1991. (An earlier version appeared in Symposium on Logic in Computer Science, IEEE Press, Asilomar, California, June 1989.)
V. Breazu-Tannen, D. Kesner, L. Puel, A typed pattern calculus. In 8'th Symposium on Logic in Computer Science, Montreal, June 1993.
J. Chirimar, C. A. Gunter, and J. G. Riecke. Linear ML. In Symposium on Lisp and Functional Programming, ACM Press, San Francisco, June 1992.
A. Filinski, Linear continuations. In Symposium on Principles of Programming Languages, ACM Press, Albuquerque, New Mexico, January 1992.
J.-Y. Girard, Linear logic. Theoretical Computer Science, 50:1–102, 1987.
J.-Y. Girard, On the unity of logic. Manuscript, 1991.
S. Holmström, A linear functional language. Draft paper, Chalmers University of Technology, 1988.
Y. Lafont, The linear abstract machine. Theoretical Computer Science, 59:157–180, 1988.
P. Lincoln and J. Mitchell, Operational aspects of linear lambda calculus. In 7'th Symposium on Logic in Computer Science, IEEE Press, Santa Cruz, California, June 1992.
Y. Lafont and T. Streicher. Game semantics for linear logic. In 6'th Symposium on Logic in Computer Science, IEEE Press, Amsterdam, July 1991.
I. Mackie, Lilac: a functional programming language based on linear logic. Master's Thesis, Imperial College London, 1991.
E. Moggi, Computational lambda-calculus and monads. In 4'th Symposium on Logic in Computer Science, IEEE Press, Asilomar, California, June 1989.
P. W. O'Hearn, Linear logic and interference control. In Conference on Category Theory and Computer Science, Paris, September 1991. LNCS, Springer Verlag.
V. Pratt, Event spaces and their linear logic. In AMAST '91: Algebraic Methodology And Software Technology, Iowa City, Springer Verlag LNCS, 1992.
U. Reddy, Acceptors as Values. Manuscript, December 1991.
R. A. G. Seely, Linear logic, *-autonomous categories, and cofree coalgebras. In Categories in Computer Science and Logic, June 1989. AMS Contemporary Mathematics 92.
A. S. Troelstra, Lectures on Linear Logic. CSLI Lecture Notes, 1992.
P. Wadler, Linear types can change the world! In M. Broy and C. Jones, editors, Programming Concepts and Methods, Sea of Galilee, Israel, North Holland, April 1990.
P. Wadler, Is there a use for linear logic? In Conference on Partial Evaluation and Semantics-Based Program Manipulation (PEPM), New Haven, Connecticut, ACM Press, June 1991.
P. Wadler, There's no substitute for linear logic. Presented at Workshop on Mathematical Foundations of Programming Language Semantics, Oxford, April 1992.
P. Wadler, A taste of linear logic. In Mathematical Foundations of Computer Science, Gdansk, Poland, LNCS, Springer Verlag, August 1993.
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© 1994 Springer-Verlag Berlin Heidelberg
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Wadler, P. (1994). A syntax for linear logic. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_24
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DOI: https://doi.org/10.1007/3-540-58027-1_24
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