Search results
Results From The WOW.Com Content Network
A spreadsheet's concatenate ("&") function is used to assemble a complex text string—in this example, XML code for an SVG "circle" element. In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball".
The multiplicative identity is often called unity in the latter context ... Strings, lists: Concatenation: Empty string, empty list A Boolean algebra: ∧ (logical and)
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
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. [ 1 ]
The set of all finite strings over some fixed alphabet Σ forms a monoid with string concatenation as the operation. The empty string serves as the identity element. This monoid is denoted Σ ∗ and is called the free monoid over Σ. It is not commutative if Σ has at least two elements.
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 ...
A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. String may also denote more general arrays or other sequence (or list) data types and structures.
Observe that the right syntactic equivalence is a left congruence with respect to string concatenation and vice versa; i.e., for all . The syntactic congruence or Myhill congruence [1] is defined as [2]