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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.
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
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.
Besides advocating for string instrument study at all age and proficiency levels in various frameworks, ASTA provides professional development, online and print resources for pedagogical content, scholarly publications, music advocate resources, student-level competitions and evaluation programs, a career center, community connections through ...
The Orff Approach of music education uses very rudimentary forms of everyday activity for the purpose of music creation by music students. The Orff Approach is a "child-centered way of learning" music education that treats music as a basic system like language and believes that just as every child can learn language without formal instruction so can every child learn music by a gentle and ...
Concatenation theory, also called string theory, character-string theory, or theoretical syntax, studies character strings over finite alphabets of characters, signs, symbols, or marks.