Constrained partial deduction and the preservation of characteristic trees

Abstract

Partial deduction strategies for logic programs often use an abstraction operator to guarantee the finiteness of the set of goals for which partial deductions are produced. Finding an abstraction operator which guarantees finiteness and does not lose relevant information is a difficult problem. In earlier work Gallagher and Bruynooghe proposed to base the abstraction operator oncharacteristic paths andtrees, which capture the structure of the generated incomplete SLDNF-tree for a given goal. In this paper we exhibit the advantages of characteristic trees over purely syntactical measures: if characteristic trees can be preserved upon generalisation, then we obtain an almost perfect abstraction operator, providing just enough polyvariance to avoid any loss of local specialisation. Unfortunately, the abstraction operators proposed in earlier work do not always preserve the characteristic trees upon generalisation. We show that this can lead to important specialisation losses as well as to non-termination of the partial deduction algorithm. Furthermore, this problem cannot be adequately solved in the ordinary partial deduction setting. We therefore extend the expressivity and precision of the Lloyd and Shepherdson partial deduction framework by integrating constraints. We provide formal correctness results for the so obtained generic framework ofconstrained partial deduction. Within this new framework we are, among others, able to overcome the above mentioned problems by introducing an alternative abstraction operator, based on so calledpruning constraints. We thus present a terminating partial deduction strategy which, for purely determinate unfolding rules, induces no loss of local specialisation due to the abstraction while ensuring correctness of the specialised programs.