## Extending Homeomorphic Embedding in the Context of Logic Programming (1997)

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### BibTeX

@TECHREPORT{Leuschel97extendinghomeomorphic,

author = {Michael Leuschel},

title = {Extending Homeomorphic Embedding in the Context of Logic Programming},

institution = {Departement Computerwetenschappen},

year = {1997}

}

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### Abstract

Recently well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. However, as we illustrate in the paper, the homeomorphic embedding relation as it is usually defined suffers from several inadequacies which make it less suitable in a logic programming context. We present several increasingly refined ways to remedy this problem by providing more sophisticated treatments of variables and present a new, extended homeomorphic embedding relation.

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Citation Context ...line setting, well-founded orders are sometimes too rigid or too complex. Recently, well-quasi orders have therefore gained popularity to ensure on-line termination of program manipulation techniques =-=[3, 41, 43, 26, 27, 13, 18, 1, 20, 46]-=-. Indeed, as we will see below, well-quasi orders are often much more flexible than well-founded orders in an on-line context. We start examining them in the next section. 2 Well-quasi orders and home... |

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Citation Context ...e functional programming, measures in addition to determinacy have to be adopted to ensure local termination. Luckily, more refined approaches to ensure termination of unfolding exist. The methods in =-=[4, 34, 33, 32]-=- are based on well-founded orders, inspired by their usefulness in the context of static termination analysis (see e.g. [8, 5]). These techniques ensure termination, while at the same time allowing un... |

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Citation Context ...n the context of term rewriting systems in [6, 7], and adapted for use in supercompilation ([45]) in [43]. Its usefulness as a stop criterion for partial evaluation is also discussed and advocated in =-=[31]-=-. Some complexity results can be found in [44] and [14] (also summarised in [31]). The following is the definition from [43], which adapts the pure homeomorphic embedding from [7] by adding a rudiment... |

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Citation Context ...er, the above definition is the one most often used in the context of termination. Both definitions are equivalent by Theorem 2.1 in [15]. A different (but equivalent) definition of a wqo is given in =-=[21, 47]: A quas-=-i-ordersV is a wqo iff for all quasi-orders �� V which containsV (i.e. v V v 0 ) v�� V v 0 ) the corresponding strict partial order OE V is a wfo. This insight can be used to dynamically const... |

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Citation Context ...not totally. A further step towards a solution is presented in [46]. In that light, it might be of interest to study whether the extensions of the homeomorphic embedding relation proposed in [39] and =-=[22]-=- (in the context of static termination analysis of term rewrite systems) can be useful in an on-line setting. We believe that \Theta can be of value in other contexts and for other languages (such as ... |

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