A related process is coarticulation where one segment influences another to produce an allophonic variation, such as vowels acquiring the feature nasal before nasal consonants when the velum opens prematurely or /b/ becoming labialised as in "boot". This article will describe both processes under the term, assimilation.
The physiological or psychological mechanisms of coarticulation are unknown, but we often loosely speak of a segment as "triggering" an assimilatory change in another segment. In assimilation, the phonological patterning of the language, discourse styles and accent are some of the factors contributing to changes observed.
There are four configurations found in assimilations: the increase in phonetic similarity may be between adjacent segments, or between segments separated by one or more intervening segments; and the changes may be in reference to a preceding segment, or to a following one. Although all four occur, changes in regard to a following adjacent segment account for virtually all assimilatory changes (and most of the regular ones). Also, assimilations to an adjacent segment are vastly more frequent than assimilations to a non-adjacent one. (These radical asymmetries might contain hints about the mechanisms involved, but they are unobvious.)
If a sound changes with reference to a following segment, it is traditionally called "regressive assimilation"; changes with reference to a preceding segment are traditionally called "progressive". Many find these terms confusing, as they seem to mean the opposite of the intended meaning. Accordingly, a variety of alternative terms have arisen—not all of which avoid the problem of the traditional terms. Regressive assimilation is also known as right-to-left, leading or anticipatory assimilation. Progressive assimilation is also known as left-to-right or perseveratory or preservative, lagging or lag assimilation. The terms anticipatory and lag will be used here.
Very occasionally two sounds (invariably adjacent) may influence one another in reciprocal assimilation. When such a change results in a single segment with some of the features of both components, it is known as coalescence or fusion.
Some authorities distinguish between partial and complete assimilation, i.e., between assimilatory changes in which there remains some phonetic difference between the segments involved, and those in which all differences are obliterated. There is no theoretical advantage to such a classification, as one of the following examples will show.
This is the most common type of assimilation by far, and typically has the character of a conditioned sound change, i.e., it applies to the whole lexicon. Thus in Latin, prefixes ending in a nasal (com- "with" (also marks completive action); in- "in(to)" (also marks "ingression", i.e. the commencement of an action); in- (forms privative adjectives)) all show the following assimilatory changes relative to a following adjacent segment:
All become /m/ before /p/, /b/, and /m/: impendeō "hang over", imbibō "drink in", immēnsus "immeasurable" All become /n/ before /t/, /d/, and /n/: contāminō "render unclean", connīveō "lower the eyes; be complicit', condōnō "give away, present" All become /l/ or /r/ before /l/ and /r/, respectively: corrumpō "break to pieces", irrētiō "entangle in a net", irrāsus "unshaved", illūdō "play with", illīterātus "ignorant, unlettered", colloquor "converse, talk with", collūdō "play with" (but usually "have a secret understanding with"). The assimilation to [ŋ] before /k/ or /ɡ/ is not shown in writing.
Also in Latin, a stop followed by a nasal assimilates to the nasal: Proto-Indo-European *swepnos "sleep" > Lat. somnus [the vowel changes are regular, too], *supmos "highest" > summus, *ad-nec- > annectō "bind to" (cf. annex), sub-moenium "red light district" (lit. "under the walls") > summoenium. (This example also indicates the pointlessness of the division into "partial" and "complete" assimilations: this is plainly a single sound-law—stops become nasals—and whether the output assimilation is "complete" or "partial" hinges inconsequentially on the phonetic details of the input.)
In Italian, voiceless stops assimilate to a following /t/: Latin okto "eight" > It. otto, Latin lectus "bed" > letto, suptus "under" > sotto.
Rare, and usually merely an accident in the history of a specific word. Old French cercher "to chase" /ser.ʧer/ > Modern Fr. chercher /ʃɛʁ.ʃe/. However, the diverse and common assimilations known as umlaut, wherein the phonetics of a vowel are influenced by the phonetics of a vowel in a following syllable, are both commonplace and in the nature of sound laws. Such changes abound in the histories of Germanic Languages, Romanian, Old Irish, and many others. Examples: in the history of English, a back vowel becomes front if a high front vocoid (*i, ī, y) is in the following syllable: Proto-Germanic *mūsiz "mice" > Old English mýs /myːs/ > mice; PGmc *batizōn- "better" > OE bettre; PGmc *fōtiwiz "feet" > OE fét > feet. Contrariwise, Proto-Germanic *i and *u > e, o respectively before *a in the following syllable: PGmc *nistaz > OE nest. Another example of a regular change is the sibilant assimilation of Sanskrit, wherein if there were two different sibilants as the onset of successive syllables, a plain /s/ was always replaced by the palatal /ɕ/: Proto-Indo-European *smeḱru- "beard" > Skt. śmaśru-; *ḱoso- "gray" > Skt. śaśa- "rabbit"; PIE *sweḱru- "husband's mother' > Skt. śvaśrū-.
Tolerably common, and often has the nature of a sound law. Proto-Indo-Eruopean *-ln- > -ll- in both Germanic and Italic. Thus *ḱļnis "hill" > PreLat. *kolnis > Lat. collis; > PGmc *hulniz, *hulliz > OE hyll /hyl/ > hill. The enclitic form of English is, shedding the vowel, becomes voiceless when adjacent to a word-final voiceless non-sibilant.
Rare, and usually sporadic (except when part of something bigger, as in the Skt. śaśa- example, above): Greek leirion > Lat. līlium "lily". Vowel harmony is the reverse of umlaut, namely, a following vowel's phonetics is influenced by that of a preceding vowel. Thus for example most Finnish case markers come in two flavors, with /a/ and /æ/ (written ä) depending on whether the preceding vowel is back or front. However, it's a difficult question to know just where and how in the history of Finnish an actual assimilatory change took place. The distribution of pairs of endings in Finnish is just that, is not in any sense the operation of an assimilatory innovation (though probably the outbirth of such an innovation in the past).
Proto-Italic *dw > Latin b, as in *dwis "twice" > Lat. bis. Proto-Celtic *sw shows up in Old Irish in initial position as s, thus *swesōr "sister" > OIr siur */ʃuɾ/, *spenyo- > *swinea- > *swine "nipple" > sine. But when a vowel preceded, the *sw sequence becomes /f/: má fiur "my sister", bó tri-fne "a cow with three teats". There's also the famous change in P-Celtic of kW -> p. Proto-Celtic also underwent the change gw -> b.