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A very standard infinite data structure is the stream which lazily determines its current and next values and even whether they exist or not! This data structure is useful for describing computations which are generated and consumed step-by-step and is a powerful basic tool for many lazy algorithms.
Included in this module are two submodules, Infinite and Finite. Infinite streams are streams which are guaranteed to always have a next value and Finite streams are streams which may terminate but are not obliged to.
Mathematically, Infinite streams are the greatest fixed point of the functor F X = A * X and Finite streams are the greatest fixed point of the functor F X = 1 + A * X.