Extending Homeomorphic Embedding in the Context of Logic Programming

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 deened suuers from several inadequacies which make it less suitable in a logic programming context. We present several increasingly reened ways to remedy this problem by providing more sophisticated treatments of variables and present a new, extended homeomorphic embedding relation. 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 deened suuers from several inadequacies which make it less suitable in a logic programming context. We present several increasingly reened ways to remedy this problem by providing more sophisticated treatments of variables and present a new, extended homeomorphic embedding relation.