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The strings over an alphabet, with the concatenation operation, form an associative algebraic structure with identity element the null string—a free monoid. Sets of strings with concatenation and alternation form a semiring, with concatenation (*) distributing over alternation (+); 0 is the empty set and 1 the set consisting of just the null ...
Rexx uses this syntax for concatenation including an intervening space. C (along with Python) allows juxtaposition for string literals, however, for strings stored as character arrays, the strcat function must be used. COBOL uses the STRING statement to concatenate string variables. MATLAB and Octave use the syntax "[x y]" to concatenate x and y.
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.
If is a set of strings, then is defined as the smallest superset of that contains the empty string and is closed under the string concatenation operation. If V {\\displaystyle V} is a set of symbols or characters, then V ∗ {\\displaystyle V^{*}} is the set of all strings over symbols in V {\\displaystyle V} , including the empty string ε ...
Python uses the + operator for string concatenation. Python uses the * operator for duplicating a string a specified number of times. The @ infix operator is intended to be used by libraries such as NumPy for matrix multiplication. [104] [105] The syntax :=, called the "walrus operator", was introduced in Python 3.8. It assigns values to ...
In functional and list-based languages a string is represented as a list (of character codes), therefore all list-manipulation procedures could be considered string functions. However such languages may implement a subset of explicit string-specific functions as well.
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
The definition of a generator appears identical to that of a function, except the keyword yield is used in place of return. However, a generator is an object with persistent state, which can repeatedly enter and leave the same scope. A generator call can then be used in place of a list, or other structure whose elements will be iterated over.