Fusion laws permit to eliminate various of the intermediate data structures that are created in function compositions. The fusion laws associated with the traditional recursive operators on datatypes cannot, in genera...
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Fusion laws permit to eliminate various of the intermediate data structures that are created in function compositions. The fusion laws associated with the traditional recursive operators on datatypes cannot, in general, be used to transform recursive programs with effects. Motivated by this fact, this paper addresses the definition of two recursive operators on datatypes that capture functional programs with effects. Effects are assumed to be modeled by monads. The main goal is thus the derivation of fusion laws for the new operators. One of the new operators is called monadic unfold. It captures programs (with effects) that generate a data structure in a standard way. The other operator is called monadic hylomorphism, and corresponds to programs formed by the composition of a monadic unfold followed by a function defined by structural induction on the data structure that the monadic unfold generates. (C) 2001 Published by Elsevier Science B.V.
The interest is in characterizing insightfully the power of program self-reference in effective programming systems (epses), the computability-theoretic analogs of programming languages (for the partial computable fun...
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The interest is in characterizing insightfully the power of program self-reference in effective programming systems (epses), the computability-theoretic analogs of programming languages (for the partial computable functions). In an eps in which the constructive form of Kleene's Recursion Theorem (KRT) holds, it is possible to construct, algorithmically, from an arbitrary algorithmic task, a self-referential program that, in a sense, creates a self-copy and then performs that task on the self-copy. In an eps in which the not-necessarily-constructive form of Kleene's Recursion Theorem (krt) holds, such self-referential programs exist, but cannot, in general, be found algorithmically. In an earlier effort, Royer proved that there is no collection of recursive denotational control structures whose implementability characterizes the epses in which KRT holds. One main result herein, proven by a finite injury priority argument, is that the epses in which krt holds are, similarly, not characterized by the implementability of some collection of recursive denotational control structures. On the positive side, however, a characterization of such epses of a rather different sort is shown herein. Though, perhaps not the insightful characterization sought after, this surprising result reveals that a hidden and inherent constructivity is always present in krt.
The computational complexity properties of a hierarchy of classes of subrecursive schemata are investigated. The schemata are derived from the multiple recursive operators of Peter. Concrete complexity measures based ...
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The computational complexity properties of a hierarchy of classes of subrecursive schemata are investigated. The schemata are derived from the multiple recursive operators of Peter. Concrete complexity measures based on specific computation rules and an underlying random-access stored-program machine (RASP) model are defined and the complexity properties induced by certain structural features are studied.
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