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Equational term graph rewriting
 Fundamenta Informaticae
, 1996
"... and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of ..."
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Cited by 79 (7 self)
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and their applications. SMC is sponsored by the Netherlands Organization for Scientific Research (NWO). CWI is a member of
Lambda Calculus with Explicit Recursion
 Information and Computation
, 1996
"... This paper is concerned with the study of calculus with explicit recursion, namely of cyclic graphs. The starting point is to treat a graph as a system of recursion equations involving terms, and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible fo ..."
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Cited by 43 (5 self)
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This paper is concerned with the study of calculus with explicit recursion, namely of cyclic graphs. The starting point is to treat a graph as a system of recursion equations involving terms, and to manipulate such systems in an unrestricted manner, using equational logic, just as is possible for firstorder term rewriting. Surprisingly, now the confluence property breaks down in an essential way. Confluence can be restored by introducing a restraining mechanism on the `substitution' operation. This leads to a family of graph calculi, which can be seen as an extension of the family of oecalculi (calculi with explicit substitution). While the oecalculi treat the letconstruct as a firstclass citizen, our calculi support the letrec, a feature that is essential to reason about time and space behavior of functional languages and also about compilation and optimizations of programs. CR Subject Classification (1991): D.1.1, D.3.1, F.1.1, F.4.1, F.4.2 Keywords & Phrases: lambda cal...
Relating Graph and Term Rewriting via Böhm Models
 in Engineering, Communication and Computing 7
, 1993
"... . Dealing properly with sharing is important for expressing some of the common compiler optimizations, such as common subexpressions elimination, lifting of free expressions and removal of invariants from a loop, as sourcetosource transformations. Graph rewriting is a suitable vehicle to accommoda ..."
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Cited by 8 (4 self)
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. Dealing properly with sharing is important for expressing some of the common compiler optimizations, such as common subexpressions elimination, lifting of free expressions and removal of invariants from a loop, as sourcetosource transformations. Graph rewriting is a suitable vehicle to accommodate these concerns. In [4] we have presented a term model for graph rewriting systems (GRSs) without interfering rules, and shown the partial correctness of the aforementioned optimizations. In this paper we define a different model for GRSs, which allows us to prove total correctness of those optimizations. Differently from [4] we will discard sharing from our observations and introduce more restrictions on the rules. We will introduce the notion of Bohm tree for GRSs, and show that in a system without interfering and nonleft linear rules (orthogonal GRSs), Bohm tree equivalence defines a congruence. Total correctness then follows in a straightforward way from showing that if a program M co...
A Complete Proof System for Nested Term Graphs
 In Proc. HOA '95
, 1995
"... Nested Term Graphs are syntactic representations of cyclic term graphs. Via a simple translation they contain terms as a subset. There exists a characterization of the terms that unwind to the same tree, presented as a complete proof system. This paper gives a similar characterization for Nested T ..."
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Cited by 2 (0 self)
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Nested Term Graphs are syntactic representations of cyclic term graphs. Via a simple translation they contain terms as a subset. There exists a characterization of the terms that unwind to the same tree, presented as a complete proof system. This paper gives a similar characterization for Nested Term Graphs. The semantics of tree unwinding is presented via bisimulations. 1