On the productivity of recursive list definitions

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Abstract
Several related notions of the productivity are presented for functional languages with lazy evaluation. The notion of productivity captures the idea of computability, of progress of infinite-list programs. If an infinite-list program is productive , then every element of the list can be computed in finite “time.” These notions are used to study recursive list definitions, that is, lists defined by l where l = fl . Sufficient conditions are given in terms of the function f that either guarantee the productivity of the list or its unproductivity. Furthermore, a calculus is developed that can be used in verifying that lists defined by l where l = f I are productive. The power and the usefulness of our theory are demonstrated by several nontrivial examples. Several observations are given in conclusion.

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