On Correct Program Schemas

. We present our work on the representation and correctness of program schemas, in the context of logic program synthesis. Whereas most researchers represent schemas purely syntactically as higher-order expressions, we shall express a schema as an open first-order theory that axiomatises a problem domain, called a specification framework, containing an open program that represents the template of the schema. We will show that using our approach we can define a meaningful notion of correctness for schemas, viz. that correct program schemas can be expressed as parametric specification frameworks containing templates that are steadfast, i.e. programs that are always correct provided their open relations are computed correctly. 1 Introduction A program schema is an abstraction of a class of actual programs, in the sense that it represents their data-flow and control-flow, but does not contain (all) their actual computations or (all) their actual data structures. Program schemas have been ..