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A callbyneed lambdacalculus with locally bottomavoiding choice: Context lemma and correctness of transformations
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2008
"... We present a higherorder callbyneed lambda calculus enriched with constructors, caseexpressions, recursive letrecexpressions, a seqoperator for sequential evaluation and a nondeterministic operator amb that is locally bottomavoiding. We use a smallstep operational semantics in form of a sin ..."
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Cited by 18 (11 self)
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We present a higherorder callbyneed lambda calculus enriched with constructors, caseexpressions, recursive letrecexpressions, a seqoperator for sequential evaluation and a nondeterministic operator amb that is locally bottomavoiding. We use a smallstep operational semantics in form of a singlestep rewriting system that defines a (nondeterministic) normal order reduction. This strategy can be made fair by adding resources for bookkeeping. As equational theory we use contextual equivalence, i.e. terms are equal if plugged into any program context their termination behaviour is the same, where we use a combination of may as well as mustconvergence, which is appropriate for nondeterministic computations. We show that we can drop the fairness condition for equational reasoning, since the valid equations w.r.t. normal order reduction are the same as for fair normal order reduction. We evolve different proof tools for proving correctness of program transformations, in particular, a context lemma for may as well as mustconvergence is proved, which restricts the number of contexts that need to be examined for proving contextual equivalence. In combination with socalled complete sets of commuting and forking diagrams we show that
all the deterministic reduction rules and also some additional transformations preserve contextual equivalence.We also prove a standardisation theorem for fair normal order reduction. The structure of the ordering <= c is also analysed: Ω is not a least element, and <=c already implies contextual equivalence w.r.t. mayconvergence.
7th International Workshop on Computing with Terms and Graphs
, 2013
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Interaction Nets vs. the ρcalculus: Introducing Bigraphical Nets
"... The ρcalculus generalises both term rewriting and the λcalculus in a uniform framework. Interaction nets are a form of graph rewriting which proved most successful in understanding the dynamics of the λcalculus, the prime example being the implementation of optimal βreduction. It is thus natural ..."
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The ρcalculus generalises both term rewriting and the λcalculus in a uniform framework. Interaction nets are a form of graph rewriting which proved most successful in understanding the dynamics of the λcalculus, the prime example being the implementation of optimal βreduction. It is thus natural to study interaction net encodings of the ρcalculus as a first step towards the definition of efficient reduction strategies. We give two interaction net encodings which bring a new understanding to the operational semantics of the ρcalculus; however, these encodings have some drawbacks and to overcome them we introduce bigraphical nets—a new paradigm of computation inspired by Lafont’s interactions nets and Milner’s bigraphs.
This work is licensed under the Creative Commons Attribution License. PORGY: StrategyDriven Interactive Transformation of Graphs∗
"... This paper investigates the use of graph rewriting systems as a modelling tool, and advocates the embedding of such systems in an interactive environment. One important application domain is the modelling of biochemical systems, where states are represented by port graphs and the dynamics is driven ..."
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This paper investigates the use of graph rewriting systems as a modelling tool, and advocates the embedding of such systems in an interactive environment. One important application domain is the modelling of biochemical systems, where states are represented by port graphs and the dynamics is driven by rules and strategies. A graph rewriting tool’s capability to interactively explore the features of the rewriting system provides useful insights into possible behaviours of the model and its properties. We describe PORGY, a visual and interactive tool we have developed to model complex systems using port graphs and port graph rewrite rules guided by strategies, and to navigate in the derivation history. We demonstrate via examples some functionalities provided by PORGY. 1