John Maraist. Comparing Reduction Strategies in Resource-Conscious Lambda Calculi. Doctoral thesis, University of Karlsruhe, 1997. 16  Home/Search   Document Not in Database   Summary   Related Articles   Check

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John Maraist. Comparing Reduction Strategies in Resource-Conscious Lambda Calculi. Doctoral thesis, University of Karlsruhe, 1997. 16

....extensions of the translations to encompass term reduction became clear later. Both translations preserve typability of terms; the standard (respectively steadfast) translation is sound and complete (sound) for mapping general reduction sequences from call by name (call by value) Mackie, 1994; Maraist, 1997; Maraist et al. in press) both are sound and complete for mapping standard reduction sequences (Maraist, 1997) It is more difficult to apply these translations to the call by need calculus (Maraist et al. 1998) a more suitable basis for the analysis of lazy functional languages than ....

.... of terms; the standard (respectively steadfast) translation is sound and complete (sound) for mapping general reduction sequences from call by name (call by value) Mackie, 1994; Maraist, 1997; Maraist et al. in press) both are sound and complete for mapping standard reduction sequences (Maraist, 1997). It is more difficult to apply these translations to the call by need calculus (Maraist et al. 1998) a more suitable basis for the analysis of lazy functional languages than call by name. Although call by need uses a different notion of reduction than callby name, their observational ....

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J. Maraist, Comparing Reduction Strategies in Resource-Conscious Lambda Calculi (Doctoral thesis, University of Karlsruhe, 1997).

.... clear later: both translations preserve typability of terms; the standard (respectively steadfast) translation is sound and complete (sound) for mapping general reduction sequences from call by name (call by value) 17, 20] both are sound and complete for mapping standard reduction sequences [18]. The steadfast translation can also address call byneed. Call by need as we presented it with Ariola, Felleisen, Odersky and Wadler [2] is a more suitable basis for the analysis of lazy functional languages than call by name. Although call by need uses a different notion of reduction than ....

.... calculus have been presented, including (but not exhaustively) comments in Girard s original paper on linear logic [12] the work of Abramsky [1] Benton, Bierman, de Paiva and Hyland [6, 7, 8, 9] Plotkin and Barber [4] della Rocca and Roversi [23] and Wadler [24, 25] and our previous work [18, 20], which is the specific framework we extend here; all of these approaches have used a single mode for enabling both weakening and contraction. Jacobs [16] has addressed the issue of separate connectives for weakening and contraction, but for full linear logic and only in the model theory. To our ....

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J. Maraist, Comparing Reduction Strategies in ResourceConscious Lambda Calculi (Doctoral thesis, University of Karlsruhe, to appear Winter 1996/7).

....for our translation is an affine calculus, in which contraction is controlled by the connective but weakening is allowed everywhere. The use of distinct prefixes to control contraction and weakening separately has been studied first by Jacobs [18] for the full logic, and later by Maraist [24,25] for a lambda calculus. We derive the call by need calculus from the call by value calculus in two steps. The first step adds let terms, which enforce sharing, to the call by value calculus. The resulting call by let calculus is observationally equivalent to call by value; the translation, ....

....Our first presentation reported incorrectly that the translation is complete for general reduction sequences, which we have corrected here. The standard reduction results for Lin and Aff, as well as the present proof of conservative extension of Val to Let, are from the first author s thesis [24]. Our results now also apply to translations of the equality and observational equivalence relations of the various calculi, and to extended translations from the usual recursive extensions of call by name and call by value into a similarly extended recursive linear calculus. We have expanded the ....

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J. Maraist, Comparing Reduction Strategies in Resource-Conscious Lambda Calculi (Doctoral Thesis, University of Karlsruhe, Germany, 1997).

....encompass term reduction became clear later. Both translations preserve typability of terms: The standard translation is sound and complete for mapping general reduction sequences from call by name, and the steadfast translation is sound for mapping general reduction sequences from call by value [18, 20, 22]. The steadfast translation can also address call by need [2, 3, 21] Call by need is a more suitable basis for the analysis of lazy functional languages than call by name. Although call by need uses a different notion of reduction than call by name, their observational equivalence theories are ....

.... lambda calculus have been presented, including (but not exhaustively) comments in Girard s original paper on linear logic [13] the work of Abramsky [1] Barber [4] Benton, Bierman, de Paiva and Hyland [6 9] Brauner [10] della Rocca and Roversi [26] and Wadler [28, 29] and our previous work [20, 22], which is the basis for the present work. All of these approaches have used a single mode for enabling both weakening and contraction. In the three substructural lambda calculi I [11] A and L [16] any use, explicit or implicit, of (respectively) weakening, contraction or both are simply banned. ....

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J. Maraist, Comparing Reduction Strategies in Resource-Conscious Lambda Calculi (Doctoral thesis, University of Karlsruhe, 1997).

....of developments is equivalent to strong normalisation of marked reduction need 0 0 . The technique is standard, based on a positive integer measure of a decoration of marked terms which is decreased by reduction. We give only a summary of the proof; full details are available elsewhere (Maraist, 1997). We construct weighted terms by giving every variable occurrence x or V x a weight of some positive integer, written x i or V x i . We let M ; N and so forth range over weighted terms, V range over weighted values, and define the norm k : k on weighted terms (ignoring marks) as ....

....2 and so on. The manipulation made explicit by our (C) rule is implicit in Nederpelt s rule, appearing only when necessary for a beta like contraction to occur, but Nederpelt does not address all of call by need reduction, and some massaging of , is necessary to capture reduction by (A) as well (Maraist, 1997). On types and logic. It is straightforward to assign simple types to call by need terms; in addition to the usual rules for terms we have Gamma M : A Gamma; x : A N : B Gamma let x = M in N : B Let : It is easy to verify that call by need reduction satisfies the subject reduction ....

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Maraist, J. (1997). Comparing Reduction Strategies in Resource-Conscious Lambda Calculi. Doctoral thesis, University of Karlsruhe.

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