Concatenation

Concatenation is the operation of joining two or more sequences end-to-end to form a new sequence. In computing, strings are the most common sequences concatenated, but concatenation also applies to lists, arrays, and other sequence types. In many programming languages, concatenation is exposed through operators (such as +) or through dedicated functions (such as concat or join). The result preserves the order of the operands, and the length of the result is the sum of the lengths of the operands.

Mathematically, concatenation is a binary operation on sequences. For strings over an alphabet, it is associative: (xy)z = x(yz). The empty string ε acts as the identity element, since xε = εx = x. The concept extends to other sequence-like structures, including lists, arrays, and languages, forming a monoid under concatenation with the appropriate identity element.

In practical computing, the way concatenation is implemented affects performance. When strings are immutable, naive repeated concatenation can create many intermediate copies, leading to inefficient, quadratic-time behavior in the total length. Many languages provide optimized approaches: mutable buffers or string builders that accumulate content before producing a final string, or join operations that allocate the final size once. Functional styles may reduce the number of allocations by folding a collection with a dedicated strategy.

Applications include constructing text from tokens, assembling data records, or combining identifiers. In databases, concatenation is used to merge string fields (for example, to form full names). In formal language theory, concatenation of languages L and M is defined as {xy | x in L, y in M}. Overall, concatenation is a fundamental and widely used operation in programming, data processing, and theory.