verb (used with object), verb (used without object), unified, unifying.
to make or become a single unit; unite: to unify conflicting theories; to unify a country.

1495–1505; < Late Latin ūnificāre, equivalent to Latin ūni- uni- + -ficāre -fy

unifier, noun
nonunified, adjective
quasi-unified, adjective
reunify, verb (used with object), reunified, reunifying.
ununified, adjective

combine, merge, fuse, coalesce.
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
unify (ˈjuːnɪˌfaɪ)
vb , -fies, -fying, -fied
to make or become one; unite
[C16: from Medieval Latin ūnificāre, from Latin ūnus one + facere to make]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

c.1500, "to make into one," from M.Fr. unifier (14c.), from L.L. unificare "make one," from L. uni- "one" (see uni-) + root of facere "to make" (see factitious). Unification is attested from 1851; the Unification Church was founded 1954 in Korea
by Sun Myung Moon. Unified is attested from 1862. Unified (field) theory in physics is recorded from 1935.
Online Etymology Dictionary, © 2010 Douglas Harper
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Computing Dictionary

unifier definition

The unifier of a set of expressions is a set of substitutions of terms for variables such that the expressions are all equal.
See also most general unifier, unification.

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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