## A Complete Proof System for Nested Term Graphs (1995)

Venue: | In Proc. HOA '95 |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Blom95acomplete,

author = {Stefan Blom},

title = {A Complete Proof System for Nested Term Graphs},

booktitle = {In Proc. HOA '95},

year = {1995},

pages = {74--89}

}

### OpenURL

### Abstract

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

### Citations

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The Lambda Calculus: Its Syntax and Semantics
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- 1984
(Show Context)
Citation Context ...at the source level, after parsing, in the intermediate program representation and during program execution. However, traditional computational models such as term rewriting systems [8] and -calculus =-=[3]-=- do not allow to reason about them directly. A natural way to capture sharing and cycles is to rewrite graphs instead of terms. Since the graphs considered here have locally the same structure as term... |

578 | Term Rewriting Systems
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Citation Context ... fact, they occur at the source level, after parsing, in the intermediate program representation and during program execution. However, traditional computational models such as term rewriting systems =-=[8]-=- and -calculus [3] do not allow to reason about them directly. A natural way to capture sharing and cycles is to rewrite graphs instead of terms. Since the graphs considered here have locally the same... |

561 |
The implementation of functional programming languages
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Citation Context ...milar characterization for Nested Term Graphs. The semantics of tree unwinding is presented via bisimulations. 1 Introduction Sharing and cycles are essential features in a program development system =-=[10]-=-. In fact, they occur at the source level, after parsing, in the intermediate program representation and during program execution. However, traditional computational models such as term rewriting syst... |

128 |
A complete inference system for a class of regular behaviours
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Citation Context ...1], where complete refers to the semantics of -terms obtained by infinite tree unwinding, or what is equivalent, to bisimilarity. This proof system is very reminiscent of the complete proof system in =-=[9]-=- for recursive expressions in the area of communicating processes. In the present paper we generalize -terms to our nested term graphs (NTG's) and also construct a complete proof system for these NTG'... |

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- 1995
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Citation Context ... term graphs as is nowadays common practice [11]. A term graph can be represented as sets of nodes and edges [4, 12, 5], as terms with loop-back operators [7, 13, 6] or as sets of recursive equations =-=[1]-=-. In this paper we will follow the latter approach. Actually we will consider not only 'flat' systems of recursion equations, but also allow nesting of the recursion construct in the same way as it wa... |

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Citation Context ...he same structure as terms, we will call them term graphs as is nowadays common practice [11]. A term graph can be represented as sets of nodes and edges [4, 12, 5], as terms with loop-back operators =-=[7, 13, 6]-=- or as sets of recursive equations [1]. In this paper we will follow the latter approach. Actually we will consider not only 'flat' systems of recursion equations, but also allow nesting of the recurs... |

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Citation Context ...paper we will follow the latter approach. Actually we will consider not only 'flat' systems of recursion equations, but also allow nesting of the recursion construct in the same way as it was done in =-=[2]-=- for the -calculus. This is inspired by the simple and elegant -calculus in which many recursive behaviors can be expressed. Clearly the -calculus can also be viewed as a simple form of a calculus for... |

20 |
Term graph reduction
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Citation Context ...ince the graphs considered here have locally the same structure as terms, we will call them term graphs as is nowadays common practice [11]. A term graph can be represented as sets of nodes and edges =-=[4, 12, 5]-=-, as terms with loop-back operators [7, 13, 6] or as sets of recursive equations [1]. In this paper we will follow the latter approach. Actually we will consider not only 'flat' systems of recursion e... |

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- 1994
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Citation Context ...he same structure as terms, we will call them term graphs as is nowadays common practice [11]. A term graph can be represented as sets of nodes and edges [4, 12, 5], as terms with loop-back operators =-=[7, 13, 6]-=- or as sets of recursive equations [1]. In this paper we will follow the latter approach. Actually we will consider not only 'flat' systems of recursion equations, but also allow nesting of the recurs... |

6 |
Types and Computations in Lambda Calculi and Graph Rewrite Systems
- Barendsen
- 1995
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Citation Context ...ince the graphs considered here have locally the same structure as terms, we will call them term graphs as is nowadays common practice [11]. A term graph can be represented as sets of nodes and edges =-=[4, 12, 5]-=-, as terms with loop-back operators [7, 13, 6] or as sets of recursive equations [1]. In this paper we will follow the latter approach. Actually we will consider not only 'flat' systems of recursion e... |

4 |
Graph Rewriting and Functional Languages
- Smetsers
- 1993
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Citation Context ...ince the graphs considered here have locally the same structure as terms, we will call them term graphs as is nowadays common practice [11]. A term graph can be represented as sets of nodes and edges =-=[4, 12, 5]-=-, as terms with loop-back operators [7, 13, 6] or as sets of recursive equations [1]. In this paper we will follow the latter approach. Actually we will consider not only 'flat' systems of recursion e... |