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The Evaluation Strategy for Head Normal Form With and Without onDemand Flags
, 2001
"... We propose two conditions of the Estrategy with and without ondemand flags on which an evaluated term is always in head normal form. In rewriting with the Estrategy without (or with) ondemand flags, terms are evaluated according to a list of natural numbers (or integers) given to each function s ..."
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Cited by 17 (2 self)
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We propose two conditions of the Estrategy with and without ondemand flags on which an evaluated term is always in head normal form. In rewriting with the Estrategy without (or with) ondemand flags, terms are evaluated according to a list of natural numbers (or integers) given to each function symbol. The first (or second) condition is that if there exists a rule such that a function symbol f occurs in its lefthand side and its ith argument is not a variable, a list of f must contain i (or i), and if f is also a defined one, a list of f must contain 0 at the end. While there is no restriction w.r.t. the first condition, the second one can only be applied to leftlinear constructor TRSs. But, There are cases in which rewriting with the Estrategy with ondemand flags terminates properly while that with the Estrategy without ondemand flags does not. We also propose a method of obtaining normal forms if a way to get head normal forms is given.
Completeness and Strictness Analysis for the Evaluation Strategy
 RIEC, Tohoku University
, 2001
"... We propose two analyses of the evaluation strategy (the Estrategy). Firstly, we analyze a completeness of the Estrategy. For a complete Estrategy each evaluated term is guaranteed to be a normal form. In this paper we define the notion of the completeness for the contextsensitive rewriting, c ..."
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Cited by 3 (1 self)
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We propose two analyses of the evaluation strategy (the Estrategy). Firstly, we analyze a completeness of the Estrategy. For a complete Estrategy each evaluated term is guaranteed to be a normal form. In this paper we define the notion of the completeness for the contextsensitive rewriting, called completeness, and show a condition of the Estrategy to satisfy the completeness. Secondarily, we give a strictness analysis for the Estrategy. A function is called strict in a certain argument if the evaluation of that argument does not change the termination behaviour. From the analyses, we can define a method to get a more effective default strategy for the Estrategy.
Evaluation Strategies for Term Rewriting Systems
, 2002
"... Term rewriting systems are widely used in computer science as a model of computation to relate syntax and semantics. In order to implement term rewriting system we need to use a strategy since there are many reduction sequences from a term in general. A strategy chooses one from such sequences. It i ..."
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Cited by 2 (0 self)
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Term rewriting systems are widely used in computer science as a model of computation to relate syntax and semantics. In order to implement term rewriting system we need to use a strategy since there are many reduction sequences from a term in general. A strategy chooses one from such sequences. It is a function that takes a term to be rewritten and returns a term obtained by rewriting from the input term. There are two wellknown strategies: innermost strategies (or eager evaluation) and outermost strategies (or lazy evaluation). Innermost strategies can be implemented much more efficiently than outermost ones, while outermost strategies often have a better termination behavior than innermost ones. The evaluation strategy (the Estrategy), which is adopted by the family of OBJ algebraic specification languages, is one of the compromises between them. The Estrategy is more flexible than other fixed order of evaluation because each function symbol can have its own local strategy...