concatenaties

Concatenation is an operation that combines two sequences by placing one after the other. In computing, the most common form is string concatenation: given two strings a and b, the result is the string ab. The concept also applies to lists, arrays, and other sequences, and in mathematics it can refer to combining numbers by writing their digits in sequence.

In formal language theory, the concatenation of two languages L and M is the set {xy | x in L, y in M}. This operation is associative, and the empty string acts as an identity element, making concatenation a monoid on the set of strings. The same idea extends to lists and other sequence types.

From a computational perspective, concatenation typically requires time proportional to the total length of the resulting sequence. When concatenating many pieces in languages with immutable strings, repeated naive concatenation can be inefficient; common remedies include using a string builder, a join operation, or accumulating pieces in a collection and joining once at the end. In databases, concatenation is often provided by a CONCAT function or a || operator, depending on the dialect.

Examples include Python’s "hello" + "world" resulting in "helloworld", and SQL's "A" || "B" yielding "AB" in dialects that support the operator. Concatenating numbers is a matter of digit placement, so 12 and 345 can be interpreted as forming 12345 in decimal representation.

Applications span text processing, data formatting, and the construction of identifiers or composite keys. Variants include Unicode-aware concatenation with normalization considerations, and the use of concatenation within monoid structures in algebra and computer science. See also: join, merge, string processing, monoid.