Strings are such an important and useful datatype that they are implemented in nearly every programming language. See also: Comparison of programming languages (string functions)Ī string datatype is a datatype modeled on the idea of a formal string. These are given in the article on string operations. See Shortlex for an alternative string ordering that preserves well-foundedness.Ī number of additional operations on strings commonly occur in the formal theory. The lexicographical order is total if the alphabetical order is, but isn't well-founded for any nontrivial alphabet, even if the alphabetical order is. For example, if Σ = and 0 < 1, then the lexicographical order on Σ * includes the relationships ε < 0 < 00 < 000 <. A string (or word) over Σ is any finite sequence of symbols from Σ. No assumption is made about the nature of the symbols. Let Σ be a non-empty finite set of symbols (alternatively called characters), called the alphabet. In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set called an alphabet. When a string appears literally in source code, it is known as a string literal or an anonymous string. String may also denote more general arrays or other sequence (or list) data types and structures.ĭepending on programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. A string is generally considered 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. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. in Bioinformatics to describe DNA strands composed of nitrogenous bases. As Tarski himself noted using other terminology, serious difficulties arise if strings are construed as tokens rather than types in the sense of Pierce's type-token distinction, not to be confused with similar distinctions underlying other type-token distinctions.Strings are applied e.g. Coincidentally, the first English presentation of Tarski's 1933 axiomatic foundations of string theory appeared in 1956 – the same year that Church called for such axiomatizations. Church was evidently unaware that string theory already had two axiomatizations from the 1930s: one by Hans Hermes and one by Alfred Tarski. In 1956 Alonzo Church wrote: "Like any branch of mathematics, theoretical syntax may, and ultimately must, be studied by the axiomatic method". 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. ABCDE is the concatenation of AB with CDE, in symbols ABCDE = AB ^ CDE. 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. A generative grammar can be seen as a recursive definition in string theory. String theory is foundational for formal linguistics, computer science, logic, and metamathematics especially proof theory. For the theory of strings in physics, see String theory.Ĭoncatenation theory, also called string theory, character-string theory, or theoretical syntax, studies character strings over finite alphabets of characters, signs, symbols, or marks.
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