On Delphi Lemmas and other Memoing Techniques for Deterministic Logic Programs

Three orthogonal memoing techniques for deterministic logic programs are introduced and evaluated on the basis of their empirical performance. They share the same basic idea: eecient memoing is achieved by losing information gracefully, i.e., memoing beneets from a form of abstraction. Abstract answers are most general computed answers of deterministic logic programs obtained through repeated applications of a simple clause composition operator. After describing a meta-interpreter returning abstract answers we derive a class of program transformations that compute abstract answers more eeciently: they are ideal lemmas due to their goal independent nature. For this reason their`hit rate' is usually higher than in the case of conventional memoing. Indexing by structural properties of terms is an eeective way to speed up retrieval of lemmas especially in the case of simple programs using linear recursion. Delphi Lemmas add a self-adjusting control mechanism on the amount of memoing. Answers are memoized only by acquiescence of an oracle. We Revised version of the paper Memoing with Abstract Answers and Delphi Lemmas presented at the LOPSTR'93 Workshop 26]. 2 show that random oracles perform surprisingly well as Delphi lemmas tend naturally to cover thèhot spots' of the program. A subset of our memoing techniques has been incorporated in BinProlog 5.00 with a declaration based preprocessor.