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We develop a correspondence between the theory of sequential algorithms andclassical reasoning, via Kreisel's no-counterexample interpretation. Ourframework views realizers of the no-counterexample interpretation as dynamicprocesses which interact with an oracle, and allows these processes to bemodelled at any given level of abstraction. We discuss general constructions onalgorithms which represent specific patterns which often appear in classicalreasoning, and in particular, we develop a computational interpretation of therule of dependent choice which is phrased purely on the level of algorithms,giving us a clearer insight into the computational meaning of proofs inclassical analysis.

Sequential algorithms and the computational content of classical proofs