Reduction - Dictionary Definition and Overview

Reduction :  (noun)
1: the act of decreasing or reducing something [syn: decrease, diminution, step-down] [ant: increase]
2: any process in which electrons are added to an atom or ion (as by removing oxygen or adding hydrogen); always occurs accompanied by oxidation of the reducing agent [syn: reducing]
3: the act of reducing complexity [syn: simplification]

Based on WordNet 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.

Based on Webster's Revised Unabridged Dictionary

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)



Based on Webster's Revised Unabridged Dictionary (1913)
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