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String functions common to many languages are listed below, including the different names used. The below list of common functions aims to help programmers find the equivalent function in a language. Note, string concatenation and regular expressions are handled in separate pages.
AWK uses the empty string: two expressions adjacent to each other are concatenated. This is called juxtaposition. Unix shells have a similar syntax. Rexx uses this syntax for concatenation including an intervening space.
Many authors also use concatenation of a string set and a single string, and vice versa, which are defined similarly by S 1 w = { vw : v ∈ S 1} and vS 2 = { vw : w ∈ S 2}. In these definitions, the string vw is the ordinary concatenation of strings v and w as defined in the introductory section.
String concatenation is an associative, but non-commutative operation. The empty string ε serves as the identity element; for any string s, εs = sε = s. Therefore, the set Σ * and the concatenation operation form a monoid, the free monoid generated by Σ.
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String homomorphisms are monoid morphisms on the free monoid, preserving the empty string and the binary operation of string concatenation. Given a language , the set () is called the homomorphic image of . The inverse homomorphic image of a string is defined as