Abstract
A specification is a mathematical description of the intent we want a program to behave, while an algorithm is a formal description of a program that satisfies the specification. When we want to write an algorithm by defining data domains and functions over these domains, it is common to use recursion equations for function definitions. However, recursion equations lack imaginability such as existential quantifiers in predicate calculus. In this paper we show how executable algorithms are derived from specifications written in ordinary set-theoretic formulas, and illustrate it by deriving several kinds of sorting algorithms as well as a graph algorithm.
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