Gudmund S. Frandsen and Carl Sturtivant. What is an ecient implementation of the -calculus? 1991 ACM Conference on Functional Programming and Computer Architecture (J. Hughes, ed.), LNCS 523, pp. 289-312.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... pE = O(n) On the other hand, E normalizes to K 3 (n) and an ordinary step can at most square the length of a term, hence n 2 (b E ) K 3 (n) from which we derive b E = K 1 (n) hence b E = K (p E ) 2 The corollary answers a question raised by Frandsen and Sturtivant in [FS91], who exhibited a set of terms where b 5p, and conjectured that a set of terms existed where b = 3 p ) In [LM96] a set of terms was constructed where b = 1 2 p ) We remark also that the Main Theorem gives bounds on the complexity of cut elimination in multiplicativeexponential linear ....

Gudmund S. Frandsen and Carl Sturtivant. What is an ecient implementation of the -calculus? 1991 ACM Conference on Functional Programming and Computer Architecture (J. Hughes, ed.), LNCS 523, pp. 289-312.

....2 n . The reduction of 2 0 2 2 to K 2 2 (1) thus requires K 2 (1) ordinary fi steps, but only c2 2 parallel fi steps for some small constant c; as a function of , certainly K 2 (1) Omega Gamma K (c2 2 ) The corollary answers a question raised by Frandsen and Sturtivant in [FS91], who exhibited a set of terms where b 5p, and conjectured that a set of terms existed where b = Omega Gamma1 p ) In [LM96] a set of terms was constructed where b = Omega Gamma1 2 p ) The Main Theorem also gives bounds on the complexity of cut elimination in ....

Gudmund S. Frandsen and Carl Sturtivant. What is an efficient implementation of the -calculus? 1991 ACM Conference on Functional Programming and Computer Architecture (J. Hughes, ed.), LNCS 523, pp. 289--312.

....the number of ordinary fi steps taken, and pE the number of parallel fi steps taken in a reduction to normal form. Then there exists an infinite set of terms E where b E = Omega Gamma K (p E ) for any fixed integer 0. The corollary answers a question raised by Frandsen and Sturtivant in [FS91], who exhibited a set of terms where b 5p, and conjectured that a set of terms existed where b = Omega Gamma3 p ) In [LM96] a set of terms was constructed where b = Omega Gamma1 2 p ) We remark also that the Main Theorem gives bounds on the complexity of cut elimination in ....

Gudmund S. Frandsen and Carl Sturtivant. What is an efficient implementation of the -calculus? 1991 ACM Conference on Functional Programming and Computer Architecture (J. Hughes, ed.), LNCS 523, pp. 289--312.

....obscured the complexity analysis of reduction. In particular, in what sense is the graph technology algorithmically efficient A recent paper by Frandsen and Sturtivant proposed the cost of a reduction to be the number of parallel fi reduction steps, plus the lengths of the initial and final terms [FS91]. Unfortunately, graph reduction may require interaction of sharing nodes that grows exponentially in the number of parallel fi steps, a result derived independently by Asperti [Asp96] and in a simplified way by the authors [LM96] As a consequence, initial and final terms can be short, parallel ....

Gudmund S. Frandsen and Carl Sturtivant. What is an efficient implementation of the -calculus? 1991 ACM Conference on Functional Programming and Computer Architecture (J. Hughes, ed.), LNCS 523, pp. 289--312.

....maintenance of deBruijn indices for intermediate terms. We give another lower bound showing that sharing graphs can do Omega Gammao n ) work (via fan interactions) on graphs that have no fi redexes. Finally, we criticize a proposed cost model for calculus given by Frandsen and Sturtivant [FS91], showing by example that the model does not take account of the size of intermediate forms. Our example is a term requiring Theta(2 n ) steps while having proposed cost Theta(n) We propose some cost models that both reflect this parameter, and simultaneously reconcile key concepts from ....

.... efficient are optimal evaluators do they simulate machine models well What are the relevant cost models More generally, can we speak of the complexity of a functional program in a machine independent way These kinds of questions were asked in a provocative paper by Frandsen and Sturtivant [FS91], who proposed various implementation independent cost models for the calculus, and showed that several well known implementation techniques (Turner combinators [Tur79] Hughes supercombinators [Hug82] are too inefficient to satisfy these cost models. They leave as an open question whether ....

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Gudmund S. Frandsen and Carl Sturtivant. What is an efficient implementation of the -calculus? 1991 ACM Conference on Functional Programming and Computer Architecture (J. Hughes, ed.), pp. 289--312.

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