Concatenation in the context of Computer programming

In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".

The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called well-formed words. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar.

Concatenation theory, also called string theory, character-string theory, or theoretical syntax, studies character strings over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory. A generative grammar can be seen as a recursive definition in string theory.

The most basic operation on strings is concatenation; connect two strings to form a longer string whose length is the sum of the lengths of those two strings. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. Strings, and concatenation of strings can be treated as an algebraic system with some properties resembling those of the addition of integers; in modern mathematics, this system is called a free monoid.

In music, the terms additive and divisive are used to distinguish two types of both rhythm and meter:

• A divisive (or, alternately, multiplicative) rhythm is a rhythm in which a larger period of time is divided into smaller rhythmic units or, conversely, some integer unit is regularly multiplied into larger, equal units.
• This can be contrasted with additive rhythm, in which larger periods of time are constructed by concatenating (joining end to end) a series of units into larger units of unequal length, such as a
  ₈ meter produced by the regular alternation of
  ₈ and
  ₈.

When applied to meters, the terms perfect and imperfect are sometimes used as the equivalents of divisive and additive, respectively .

SNOBOL (StriNg Oriented and symBOlic Language) is a series of programming languages developed between 1962 and 1967 at AT&T Bell Laboratories by David J. Farber, Ralph Griswold and Ivan P. Polonsky, culminating in SNOBOL4. It was one of a number of text-string-oriented languages developed during the 1950s and 1960s; others included COMIT and TRAC. Despite the similar name, it is entirely unlike COBOL.

SNOBOL4 stands apart from most programming languages of its era by having patterns as a first-class data type, a data type whose values can be manipulated in all ways permitted to any other data type in the programming language, and by providing operators for pattern concatenation and alternation. SNOBOL4 patterns are a type of object and admit various manipulations, much like later object-oriented languages such as JavaScript whose patterns are known as regular expressions. In addition SNOBOL4 strings generated during execution can be treated as programs and either interpreted or compiled and executed (as in the eval function of other languages).

In formal language theory, the Kleene star (or Kleene operator or Kleene closure) refer to two related unary operations, that can be applied either to an alphabet of symbols or to a formal language, a set of strings (finite sequences of symbols).

The Kleene star operator on an alphabet V generates the set V* of all finite-length strings over V, that is, finite sequences whose elements belong to V; in mathematics, it is more commonly known as the free monoid construction. The Kleene star operator on a language L generates another language L*, the set of all strings that can be obtained as a concatenation of zero or more members of L. In both cases, repetitions are allowed.