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**1 - 3**of**3**### Efficient simulation of forward-branching systems with constructor systems

- Journal of Symbolic Computation
, 1989

"... Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. Thatte found a transformation that allows us to simulate any orthogonal system with a constructor system. Unfortunately, this transformation does not generally preserve strong sequentiality. On the othe ..."

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Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms. Thatte found a transformation that allows us to simulate any orthogonal system with a constructor system. Unfortunately, this transformation does not generally preserve strong sequentiality. On the other hand, the class of forward-branching systems contains the class of strongly sequential constructor systems. Moreover, it admits a reduction algorithm similar to the reduction algorithm of the strongly sequential constructor class, but less efficient on the entire class of forward-branching systems. In this article, we present a new transformation which transforms any forward-branching system into a strongly sequential constructor system. The size of the system increases only modestly over that of the original one in many practical situation. We give an algorithm for this transformation and we prove its correctness and completeness. The new system is then proved to be equivalent to the input system, with respect to the behavior and the semantics. We then give a new transformation algorithm which increases the size of the system only linearly.

### Abstract

"... Constructor Systems (CSs) are an important subclass of Term Rewriting Systems (TRSs) which can be used as an abstract model of some programming languages. While normalizing strategies are always desirable for achieving a good computational behavior of programs, when dealing with lazy languages infin ..."

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Constructor Systems (CSs) are an important subclass of Term Rewriting Systems (TRSs) which can be used as an abstract model of some programming languages. While normalizing strategies are always desirable for achieving a good computational behavior of programs, when dealing with lazy languages infinitary normalizing strategies should be considered instead since (finite approximations of) infinite data structures can be returned as the result of computations. We have shown that NV-sequential TRSs (hence strongly sequential TRSs, a subclass of them) provide an appropriate basis for the effective definition of normalizing and infinitary normalizing strategies. In this paper, we show that strongly sequential and NV-sequential CSs coincide. Since the implementation of NV-sequential TRSs has been underexplored in comparison to strongly sequential TRSs, this coincidence suggests that, in programming languages, it is a good option to implement NV-sequentiality as strong sequentiality.

### Strong and NV-sequentiality of constructor systems

, 2004

"... of Term Rewriting Systems (TRSs) which can be used as an abstract model of some programming languages. While normalizing strategies are always desirable for achieving a good computational behavior of programs, when dealing with lazy languages in nitary normalizing strategies should be considered in ..."

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of Term Rewriting Systems (TRSs) which can be used as an abstract model of some programming languages. While normalizing strategies are always desirable for achieving a good computational behavior of programs, when dealing with lazy languages in nitary normalizing strategies should be considered instead since ( nite approximations of) in nite data structures can be returned as the result of computations. We have shown that NV-sequential TRSs (hence strongly sequential TRSs, a subclass of them) provide an appropriate basis for the eective de nition of normalizing and in- nitary normalizing strategies. In this paper, we show that strongly sequential and NV-sequential CSs coincide. Since the implementation of NV-sequential TRSs has been underexplored in comparison to strongly sequential TRSs, this coincidence suggests that, in programming languages, it is a good option to implement NV-sequentiality as strong sequentiality.