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Abstract: We introduce a new class of higher order rewriting systems, called Interaction Systems (IS's). IS's come from Lafont's (Intuitionistic) Interaction Nets [Lafont 1990] by dropping the linearity constraint. In particular, we borrow from Interaction Nets the syntactical bipartitions of operators into constructors and destructors and the principle of binary interaction. As a consequence, IS's are a subclass of Klop's Combinatory Reduction Systems [Klop 1980] where the Curry-Howard analogy... (Update)
Context of citations to this paper: More
...structures [62, 17] and the term generating power of context free jungle grammars [35] The area of graph reduction for the lambda calculus is related to term graph rewriting, but is beyond the scope of this survey. For information about this topic, we refer to [8, 5] and...
...in Ax(A0x) would become free. A rule like f(A) x(A) is also allowed, but an assignment 0 with z A0 is not. The recursor rule from [AsLa93] is written as (AzA) t(AzA) z)A. SzA ( z(A) z)A and zA SzA A VzVy(A A (y z)A z y) are rules corresponding to familiar...
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BibTeX entry: (Update)
A. Asperti and C. Laneve. Interaction Systems I: the theory of optimal reductions. Technical Report 1748, INRIA-Rocquencourt, September 1992. A revised version will appear on the journal Mathematical Structures in Computer Science. http://citeseer.ist.psu.edu/asperti94interaction.html More
@article{ asperti94interaction,
author = "Andrea Asperti and Cosimo Laneve",
title = "Interaction Systems I: The Theory of Optimal Reductions",
journal = "Mathematical Structures in Computer Science",
volume = "4",
number = "4",
pages = "457-504",
year = "1994",
url = "citeseer.ist.psu.edu/asperti94interaction.html" }
Citations (may not include all citations):268 Proofs and Types (context) - Girard, Taylor et al. - 1989 ACM
242 Linear Logic (context) - Girard - 1986
174 Combinatory Reduction System (context) - Klop - 1980
109 Interaction Nets (context) - Lafont - 1990 ACM DBLP
75 The geometry of optimal lambda reduction - Gonthier, Abadi et al.
70 An algorithm for optimal lambda calculus reductions (context) - Lamping - 1990
63 Optimal reductions in the lambda-calculus (context) - L'evy - 1980
42 Linear logic without boxes - Gonthier, Abadi et al. DBLP
41 Interaction Systems I: the theory of optimal reductions - Asperti, Laneve - 1992 DBLP
41 R'eductions correctes et optimales dans le lambda calcul (context) - L'evy - 1978
37 A general Church-Rosser theorem (context) - Aczel - 1978
22 a Logique Lin'eare appliqu'ee `a l"etude de divers processus.. (context) - Danos - 1990
20 Optimal Interpreters for lambda-calculus based functional la.. (context) - Kathail - 1990
13 Some results on the interpretation of -calculus in operator .. (context) - Malacaria, Regnier - 1991
11 Computations and Labels in the -calculus (context) - Asperti, Paths
9 Optimal Reductions in Interaction Systems (context) - Asperti, Laneve ACM DBLP
4 Optimality and Concurrency in Interaction Systems (context) - Laneve - 1993
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