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Abstract: In this paper, we develop new variations of methods from operational semantics, and show how to apply these to a linear type theory which has a lazy operational semantics. In particular, we consider how one can establish contextual equivalences in a linear theory with function types and tensor types by instead establishing bisimulations. Thus bisimilarity is sound for contextual equivalence. Further, we show that bisimilarity is complete for contextual equivalence. (Update)
Active bibliography (related documents): More All
2.3: Completeness of Bisimilarity for Contextual Equivalence in Linear.. - Crole (2001) (Correct)
0.5: Mechanized Operational Semantics via (Co)Induction - Simon J. Ambler, Roy L. Crole (1999) (Correct)
0.3: An Operational Semantics for I/O in a Lazy Functional Language - Gordon (1993) (Correct)
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BibTeX entry: (Update)
@misc{ crole-completeness,
author = "Roy L. Crole",
title = "Completeness of Bisimilarity for Contextual Equivalence in Linear Theories",
url = "citeseer.ist.psu.edu/648173.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1986
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447 Prentice-Hall International (context) - Milner, Concurrency - 1989
233 Computational interpretations of linear logic - Abramsky - 1993
233 Natural semantics (context) - Kahn - 1988
179 The lazy lambda calculus - Abramsky - 1990
133 Cambridge Tracts in Theoretical Computer Science (context) - Girard, Types - 1989
112 Bisimilarity as a theory of functional programming (context) - Gordon - 1995
109 Programming in Martin-Lof 's Type Theory (context) - Nordstrom, Petersson et al. - 1990
94 Equality in lazy computation systems - Howe - 1989
60 A Term Calculus for Intuitionistic Linear Logic - Benton, Bierman et al. - 1993
48 Operationally Based Theories of Program Equivalence - Pitts - 1997
46 On Intuitionistic Linear Logic (context) - Bierman - 1993
42 volume 752 of Lecture Notes In Mathematics (context) - Barr, Categories - 1979
30 Distinguished dissertations in Computer Science (context) - Gordon, Input et al. - 1994
17 Some notes on inductive and coinductive techniques in the se.. (context) - Pitts - 1994
13 Operational theories of improvement in functional languages - Sands - 1991
13 Research Institute for Mathematical Sciences (context) - Hashimoto, Ohori et al. - 1996
7 Proving congruence of simulation orderings in functional lan.. (context) - Howe - 1993
6 The Girard Translation Extended with Recursion (context) - Brauner - 1995
6 Relating Operational and Denotational Semantics for Input /O.. - Crole, Gordon - 1996
6 Observations on a Linear PCF - Bierman - 1997
5 How Linear is Howe (context) - Crole - 1996
4 Mechanised Operational Semantics via (context) - Ambler, Crole - 1999
4 Department of Mathematics and Computer Science Lecture Notes (context) - Crole, Theory - 1995
3 Available as Technical Report (context) - Gordon, Input et al. - 1993
2 Electronic Notes in Theoretical Computer Science (context) - Pitts, Operational - 1998
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