Abstract

This paper makes several contributions towards a clarified view of schema-based program development. First, we propose that schemata can be understood, formalized, and used in a simple way: program development schemata are derived rules. We mean this in the standard sense of a derived rule of inference in logic. A schema like Figure i can be formulated as a rule stating that the conclusion follows from the premises defining F, G, and the applicability conditions. By deriving the rule in an axiomatic theory, we validate a semantic statement about it: the conclusion of the rule holds in every model where both the axioms of the theory and the premises of the rule are true. Hence, by selecting a language to work in we control which development schemata are formalizable, and by selecting a theory we determine which schemata are derivable

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