scholarly journals Superdevelopments for Weak Reduction

2010 ◽  
Vol 15 ◽  
pp. 20-31
Author(s):  
Eduardo Bonelli ◽  
Pablo Barenbaum
Keyword(s):  
Weak Reduction

Tree Rewriting Systems, Combinatory Weak Reduction Systems and Type Free Languages1

1982 ◽  
Vol 5 (3-4) ◽  
pp. 279-299
Author(s):  
Alberto Pettorossi
Keyword(s):  
Combinatory Logic ◽  
Rewriting Systems ◽  
Tree Transducers ◽  
Tree Languages ◽  
One To One ◽  
The One ◽  
Weak Reduction

In this paper we consider combinators as tree transducers: this approach is based on the one-to-one correspondence between terms of Combinatory Logic and trees, and on the fact that combinators may be considered as transformers of terms. Since combinators are terms themselves, we will deal with trees as objects to be transformed and tree transformers as well. Methods for defining and studying tree rewriting systems inside Combinatory Weak Reduction Systems and Weak Combinatory Logic are also analyzed and particular attention is devoted to the problem of finiteness and infinity of the generated tree languages (here defined). This implies the study of the termination of the rewriting process (i.e. reduction) for combinators.

Effect of BaCO3 and Pb3O4 on Properties of BaTiO3-Based PTCR Ceramics

2007 ◽  
Vol 280-283 ◽  
pp. 349-352
Author(s):  
Wei Bing Ma ◽  
Yuan Fang Qu ◽  
Yan Xia Hao
Keyword(s):  
Electrical Properties ◽  
Grain Boundary ◽  
High Performance ◽  
Room Temperature ◽  
Sintering Behavior ◽  
Low Resistivity ◽  
Phase Constituent ◽  
Weak Reduction ◽  
Grain Boundary Resistivity

High-performance PTCR ceramics with low resistivity (8Ω.cm) at room temperature and around four orders magnitude of the PTCR jump were obtained by adding BaCO3 and Pb3O4(B-P) in BaTiO3. The influence of adding B-P on the sintering behavior, the microstructure and the electrical properties of BaTiO3-based PTCR was investigated. The phase constituent in the sintered ceramics was analyzed by XRD and it was shown that the metallic layered Ba3Pb2O7 phase was synthesized during the sintering. Analysis suggested that making the weak reduction atmosphere at the grain boundary may decrease the grain-boundary resistivity.

Weak Reduction Principle and Computable Metric Spaces

2018 ◽  
pp. 234-243 ◽  
Author(s):  
Margarita Korovina ◽  
Oleg Kudinov
Keyword(s):  
Metric Spaces ◽  
Reduction Principle ◽  
Weak Reduction

Weak-reduction graphene oxide membrane for improving water purification performance

2020 ◽  
Vol 39 ◽  
pp. 106-112 ◽  
Author(s):  
Hao Yu ◽  
Yi He ◽  
Guoqing Xiao ◽  
Yi Fan ◽  
Jing Ma ◽  
...  
Keyword(s):  
Graphene Oxide ◽  
Water Purification ◽  
Oxide Membrane ◽  
Weak Reduction

Morphological Changes and Reduction Mechanism for the Weak Reduction of the Preoxidized Panzhihua Ilmenite

2014 ◽  
Vol 45 (3) ◽  
pp. 914-922 ◽  
Author(s):  
Jianbo Zhang ◽  
Gengyu Zhang ◽  
Qingshan Zhu ◽  
Chao Lei ◽  
Zhaohui Xie ◽  
...  
Keyword(s):  
Morphological Changes ◽  
Reduction Mechanism ◽  
Weak Reduction

scholarly journals Modeling, Sharing, and Recursion for Weak Reduction Strategies using Explicit Substitution

1996 ◽  
Vol 3 (56) ◽  
Author(s):  
Zine-El-Abidine Benaissa ◽  
Pierre Lescanne ◽  
Kristoffer H. Rose
Keyword(s):  
Programming Languages ◽  
Data Structures ◽  
Functional Programming ◽  
Explicit Substitution ◽  
Reduction Strategies ◽  
Recursive Data Structures ◽  
Recursive Data ◽  
Parallel Evaluation ◽  
Major Reduction ◽  
Weak Reduction

<p>We present the lambda sigma^a_w calculus, a formal synthesis of the concepts of<br />sharing and explicit substitution for weak reduction. We show how<br />lambda sigma^a_w can be used as a foundation of implementations of functional<br />programming languages by modelling the essential ingredients of such<br />implementations, namely weak reduction strategies, recursion, space<br />leaks, recursive data structures, and parallel evaluation, in a uniform way.<br />First, we give a precise account of the major reduction strategies<br />used in functional programming and the consequences of choosing <br /> lambda-graph-reduction vs. environment-based evaluation. Second, we show<br />how to add constructors and explicit recursion to give a precise account<br />of recursive functions and data structures even with respect to<br />space complexity. Third, we formalize the notion of space leaks in lambda sigma^a_w<br />and use this to define a space leak free calculus; this suggests optimisations<br />for call-by-need reduction that prevent space leaking and enables<br />us to prove that the "trimming" performed by the STG machine does<br />not leak space.<br />In summary we give a formal account of several implementation<br />techniques used by state of the art implementations of functional programming<br />languages.</p><p>Keywords. Implementation of functional programming, lambda<br />calculus, weak reduction, explicit substitution, sharing, recursion, space<br />leaks.</p>

scholarly journals The discrimination theorem holds for combinatory weak reduction

1979 ◽  
Vol 8 (3) ◽  
pp. 393-394 ◽  
Author(s):  
R. Hindley
Keyword(s):  
Weak Reduction

Axioms for strong reduction in combinatory logic

1967 ◽  
Vol 32 (2) ◽  
pp. 224-236 ◽  
Author(s):  
Roger Hindley
Keyword(s):  
Binary Relation ◽  
Equivalence Relation ◽  
Combinatory Logic ◽  
Strong Reduction ◽  
Image Position ◽  
Weak Reduction

In combinatory logic there is a system of objects which intuitively represent functions, and a binary relation between these objects, which represents the process of evaluating the result of applying a function to an argument. (This is explained fully in [1].) From this relation called weak reduction, “≥,” an equivalence relation is defined by saying that X is weakly equivalent to Y if and only if there exist n (with 0 ≤ n) and X0,…,Xη such that It turns out that equivalent objects represent the same function, but two objects representing the same function need not be equivalent.

Surjectivity for finite sets of combinators by weak reduction

1988 ◽  
pp. 27-43 ◽  
Author(s):  
Corrado Böhm ◽  
Adolfo Piperno
Keyword(s):  
Finite Sets ◽  
Weak Reduction

Effect of estrogen and estrogen-progestin replacement regimens on mammographic breast parenchymal density.

1997 ◽  
Vol 15 (10) ◽  
pp. 3201-3207 ◽  
Author(s):  
I Persson ◽  
E Thurfjell ◽  
L Holmberg
Keyword(s):  
Logistic Regression ◽  
Hormone Replacement Therapy ◽  
Mammographic Density ◽  
Hormone Replacement ◽  
Mammographic Screening ◽  
Elevated Risk ◽  
Descriptive Statistics ◽  
Regression Analyses ◽  
Treatment Regimens ◽  
Weak Reduction

PURPOSE Hormone replacement therapy (HRT) may increase the mammographic density with a possible reduction in the sensitivity or specificity. If so, the benefit of mammographic screening in women using HRT could be compromised. We evaluated the hypothesis that HRT regimens have differential effects on the mammographic density depending on treatment regimens or on age. PATIENTS AND METHODS Among 31,498 Swedish women who received mammographic screening, we selected 554 women who started HRT after the first examination and who were current users at the second, and 554 age-matched women who had never received HRT. Mammograms were examined in a blinded review. The changes in density between the two examinations, graded as moderate or weak reduction, no change, or weak, moderate, or substantial increase, were assessed. We studied four HRT regimens-estradiol compounds only, estradiol compounds cyclically or continuously combined with progestins, and weak estrogens-and used descriptive statistics and logistic regression to analyze the association between HRT and density change. RESULTS Density increased in 10% and 28% of women who received estradiol compounds with cyclically or continuously combined progestins, respectively, but in only 3% of unexposed women. Logistic regression analyses showed an elevated risk of a density increase (relative risk [RR] = 3.6; 95% confidence interval [CI], 1.6 to 7.7) in women who received cyclically combined regimens or continuously combined regimens (RR = 12.4; 95% CI, 6.3 to 24.4) compared with unexposed women. Women > or = 50 years of age had even stronger associations; RRs in women on estradiol only, the cyclically combined and the continuously combined regimens were 32.2 (95% CI, 3.9 to 267.5), 21.9 (95% CI, 1.9 to 251.5), and 176.9 (95% CI, 22.8 to 1,372.7), respectively. CONCLUSION HRT with estradiol-progestin regimens, especially continuously combined, may increase the mammographic density in a substantial proportion of women.

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