reduction

(Or "contraction") The process of transforming an expression according to certain reduction rules. The most important forms are beta reduction (application of a lambda abstraction to one or more argument expressions) and delta reduction (application of a mathematical function to the required number of arguments).

An evaluation strategy (or reduction strategy), determines which part of an expression (which redex) to reduce first. There are many such strategies.

See graph reduction, string reduction, normal order reduction, applicative order reduction, parallel reduction, alpha conversion, beta conversion, delta conversion, eta conversion.

(1995-02-21)

Source: The Free On-line Dictionary of Computing (27 SEP 03)
 

Reduction \Re*duc"tion\ (r[-e]*d[u^]k"sh[u^]n), n. [F. r['e]duction, L. reductio. See Reduce.]

1. The act of reducing, or state of being reduced; conversion to a given state or condition; diminution; conquest; as, the reduction of a body to powder; the reduction of things to order; the reduction of the expenses of government; the reduction of a rebellious province. [1913 Webster]

2. (Arith. & Alg.) The act or process of reducing. See Reduce, v. t., 6. and To reduce an equation, To reduce an expression, under Reduce, v. t.

13 Webster]

3. (Astron.)
   (a) The correction of observations for known errors of instruments, etc.
   (b) The preparation of the facts and measurements of observations in order to deduce a general result. [1913 Webster]

4. The process of making a copy of something, as a figure, design, or draught, on a smaller scale, preserving the proper proportions. --Fairholt. [1913 Webster]

5. (Logic) The bringing of a syllogism in one of the so-called imperfect modes into a mode in the first figure. [1913 Webster]

6. (Chem. & Metal.) The act, process, or result of reducing[7]; as, the reduction of iron from its ores; the reduction of an aldehyde into an alcohol. [1913 Webster]

7. (Med.) The operation of restoring a dislocated or fractured part to its former place. [1913 Webster]

Reduction ascending (Arith.), the operation of changing numbers of a lower into others of a higher denomination, as cents to dollars.

Reduction descending (Arith.), the operation of changing numbers of a higher into others of a lower denomination, as dollars to cents. [1913 Webster]

Syn: Diminution; decrease; abatement; curtailment; subjugation; conquest; subjection. [1913 Webster]

Source: The Collaborative International Dictionary of English v.0.48
 

290 Moby Thesaurus words for "reduction": abasement, abatement, abbreviation, about-face, abridgment, abstract, acetification, acidification, acidulation, addition, agio, alchemy, alkalization, allayment, alleviation, allowance, analgesia, anesthesia, anesthetizing, apocope, appeasement, approximation, assimilation, assuagement, assumption, astriction, astringency, attenuation, attrition, bank discount, becoming, blunting, bottleneck, break, breakage, breaking, bump, bust, calming, carbonation, cash discount, casting down, catalysis, cervix, chain discount, change, change-over, charge-off, cheapening, chemicalization, circumscription, coarctation, compactedness, compaction, compression, compressure, concavity, concentration, concession, condensation, conquering, consolidation, conspectus, constriction, constringency, contraction, contracture, conversion, crushing, curtailment, cut, cutting, dampening, damping, de-escalation, deadening, debasement, debilitation, decline, decrease, decrement, decrescence, deduction, deflation, degradation, degrading, demotion, demulsion, depletion, depluming, depreciation, depression, derogation, descent, detraction, detrusion, devaluation, devitalization, differentiation, dilution, diminishment, diminuendo, diminution, dip, discount, disgrading, disparagement, displuming, dive, division, domestication, downgrading, drawback, ducking, dulcification, dulling, dying, dying off, ease, easement, easing, effemination, electrolysis, elision, ellipsis, enervation, enfeeblement, epitome, equation, evisceration, evolution, exhaustion, extenuation, extraction, extrapolation, fade-out, falling-off, fatigue, ferment, fermentation, flip-flop, foreshortening, growth, hauling down, hollowness, hourglass, hourglass figure, humbling, humiliation, hushing, hydrogenation, impairment, inanition, integration, interpolation, inversion, involution, isomerism, isthmus, kickback, knitting, languishment, lapse, leniency, lessening, letdown, letup, lightening, loosening, lowering, lulling, markdown, metamerism, metamerization, miniaturization, mitigation, modulation, mollification, multiplication, narrow place, narrowing, naturalization, neck, nitration, nose dive, notation, numbing, oxidation, oxidization, pacification, palliation, passage, penalty, penalty clause, percentage, phosphatization, plummet, plummeting, plunge, polymerism, polymerization, position isomerism, practice, precis, premium, price cut, price fall, price reduction, price-cut, progress, proportion, puckering, pursing, quelling, quietening, quieting, re-formation, rebate, rebatement, recap, recapitulation, reconversion, refund, relaxation, relief, remedy, remission, resolution, retraction, retrenchment, reversal, rollback, sag, sagging, salvage, salving, saturization, scaling down, setoff, shift, shortening, shrinkage, simplicity, sinking, slackening, slash, slump, softening, solidification, soothing, stranglement, strangulation, striction, stricture, stripping of rank, subdual, subduement, submergence, subtraction, summary, summation, suppression, switch, switch-over, syncope, synopsis, systole, taming, tare, telescoping, tempering, thinning, thrusting under, time discount, trade discount, tranquilization, transformation, transit, transition, treading down, tret, truncation, turning into, underselling, volte-face, wasp waist, weakening, working, wrinkling, write-off

Source: Moby Thesaurus II by Grady Ward, 1.0
 

reduction

Source: WordNet (r) 2.0
 

Reduction \Re*duc"tion\ (r?*d?k"sh?n), n. [F. r['e]duction, L. reductio. See Reduce.]

1. The act of reducing, or state of being reduced; conversion to a given state or condition; diminution; conquest; as, the reduction of a body to powder; the reduction of things to order; the reduction of the expenses of government; the reduction of a rebellious province.

2. (Arith. & Alq.) The act or process of reducing. See Reduce, v. t., 6. and To reduce an equation, To reduce an expression, under Reduce, v. t.

3. (Astron.)
   (a) The correction of observations for known errors of instruments, etc.
   (b) The preparation of the facts and measurements of observations in order to deduce a general result.

4. The process of making a copy of something, as a figure, design, or draught, on a smaller scale, preserving the proper proportions. --Fairholt.

5. (Logic) The bringing of a syllogism in one of the so-called imperfect modes into a mode in the first figure.

6. (Chem. & Metal.) The act, process, or result of reducing; as, the reduction of iron from its ores; the reduction of aldehyde from alcohol.

7. (Med.) The operation of restoring a dislocated or fractured part to its former place.

Reduction ascending (Arith.), the operation of changing numbers of a lower into others of a higher denomination, as cents to dollars.

Reduction descending (Arith.), the operation of changing numbers of a higher into others of a lower denomination, as dollars to cents.

Syn: Diminution; decrease; abatement; curtailment; subjugation; conquest; subjection.

Source: Webster's Revised Unabridged Dictionary (1913)