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2004
Springer

Generalization Algorithms for Second-Order Terms

10 years 9 months ago
Generalization Algorithms for Second-Order Terms
In this paper, we study the generalization algorithms for second-order terms, which are treated as first-order terms with function variables, under an instantiation order denoted by . First, we extend the least generalization algorithm lg for a pair of first-order terms under , introduced by Plotkin and Reynolds, to the one for a pair of second-order terms. The extended algorithm lg, however, is insufficient to characterize the generalization for a pair of second-order terms, because it computes neither the least nor the minimal generalization under . Since the transformation rule for second-order matching algorithm consists of an imitation and a projection, in this paper, we introduce the imitation-free generalization algorithm ifg and the projection-free generalization algorithm pfg. Then, we show that ifg computes the minimal generalization under of any pair of second-order terms, whereas pfg computes the generalization equivalent to lg under . Nevertheless, neither lg, ifg nor pf...
Kouichi Hirata, Takeshi Ogawa, Masateru Harao
Added 02 Jul 2010
Updated 02 Jul 2010
Type Conference
Year 2004
Where ILP
Authors Kouichi Hirata, Takeshi Ogawa, Masateru Harao
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