Logic program schema

A similar study is made by [O Keefe 90], who uses algebraic specifications. The predicates of such specifications can be directly plugged into given logic program schemas. Several schemas may be applicable according to the properties (associativity, commutativity, existence of left identities, and so on) of the identified predicates. 

Hermann, M. (1992), On the relation between primitive recursion, schema-tization, and divergence, in H. Kirchner k G. Levi, eds, Proceedings 3rd Conference on Algebraic and Logic Programming, Volterra (Italy) , Vol. 632 of Lecture Notes in Computer Science, Springer-Verlag, pp. 115-127. 

We thus quickly enumerate here a few approaches to using schemas for assisting the manual construction of logic programs. 

In defense of our hardwiring the divide-and-conquer schema, we should however make the following two remarks. First, the hardwired sequence of predicate-variable instantiations is justifiable by our arguing (see Section 11.3 and Section 12.3.2) that this sequence is probably the only one in the context of logic programming. Second, the hardwired mapping between the predicate-variables and the methods of the toolbox is justifiable by pure common sense. 

A few researchers have tackled this lack of discipline in the synthesis of recursive logic programs from examples for instance, [Tinkham 90] and [Sterling and Kirschenbaum 93] investigate the use of schemas to guide synthesis. Curiously, the now virtually defunct research on trace-based synthesis of functional programs from examples [Summers 77] [Biermann 78] did not suffer from such a marked lack of discipline , even though this research preceded ILP research. 

P. Flener and Y. Deville. Towards stepwise, schema-guided synthesis of logic programs. In [Clement and Lau 92], pp. 46-64. 

In this chapter, we develop the Proofs-as-Programs Method, which adds atoms to a logic algorithm so that some correctness criteria wrt a set of properties become satisfied. This method is part of our tool-box of methods for instantiating the predicate-variables of a schema. First, in Section 9.1, we state the problem. Then, in Section 9.2, we explain a method to solve this problem, and discuss its correctness in Section 9.3. In Section 9.4, we illustrate this method on a few sample problems. Future work and related work are discussed in Section 9.5 and Section 9.6, respectively, before drawing some conclusions in Section 9.7. 

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