Dijkstra, E. W. On the productivity of recursive definitions. Personal note EWD 749, University of Texas at Austin, 1980.

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Proving the Correctness of Reactive Systems Using Sized Types - Hughes, Pareto, Sabry (1996)   (62 citations)  (Correct)

....n s) s of type St St A more interesting program is: letrec ones = Mk 1 ones in ones which computes an infinite stream of 1 s. In other words, for any natural number i, a request for the first i elements of the stream is guaranteed to be processed in finite time: the program is productive [5, 17]. A slight modification of the program to: letrec ones = Mk 1 (tail ones ) in ones is not productive; it cannot compute the first i elements of the stream for any i 1. To understand the problem, assume that after unfolding the recursion i times, we obtain a stream s with i 1 elements. The ....

Dijkstra, E. W. On the productivity of recursive definitions. Personal note EWD 749, University of Texas at Austin, 1980.

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