Formal language

https://en.wikipedia.org/wiki/Formal_language

• formal language

• formal language theory

• symbols

• alphabet

• strings

• well-formed words

• words

• formal language

  • set of symbols, from the alphabet

  • set of strings, well-formed words/formulas

  • set of formation rules

Formal language

https://en.wikipedia.org/wiki/Formal_language

In mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules.

• An alphabet of a formal language is a set of symbols (letters).

• Symbols are joined to produce strings or words but not all are valid.

• Well-formed formulas (words) is a set of valid words belonging to a lang.

• Not all well-formed formulas are meaningful (area of semantics)

• A formal language is often defined by means of a formal grammar

• A formal grammar may be a regular grammar or context-free grammar

• A context-free grammar is a set of formation rules for lang words

Symbols are the most basic element of a language, formal or natural. A symbol may be spoken or written, although the latter is usually meant more often, especially with formal languages, since they only have a written form.

There's a sort of a feedback loop relation between a language and the symbols that make up the language's alphabet. A naisant language in

Since the set of concievable symbols is infinite, each language recognizes just a finite subset of symbols, called the alphabet of the language. So, each (at least, written) language is identified by its alphabet (which is a set of recognized symbols together with an ordering), by its strings (which are the valid concatenations of symbols from its alphabet; valid according to that particular language), and by its dictionary (which is a set of all possible valid strings of language), and by a set of (other) syntactic, grammatic and semantic rules.

Joining togher

Each formal language

On the atomic level, there is a plethora of symbols

(characters, glyphs, letters)

A formal language has

• symbols (characters, glyphs, letters) as the most basic units

• a set of symbols together with an order is the alphabet of the language

• strings are concatenating symbols

• strings are formed by concatenating symbols according to the lang rules

• Set of finite strings of atomic symbols

• Set of symbols is called the alphabet

• Strings of symbols are written one symbol after another

• Empty string is denoted by ""

• Some strings belong to a particular language, the others (if any) do not

• The strings that belong to the language are sometimes called "words"

symbols (characters, glyphs) ↓ symbols that comprise an alphabet of a formal lang ↓ alphabet of a formal lang is a set of its symbols and an ordering ↓ strings of a formal lang are comprised of symbols from the alphabet of the language, formed according to the language rules.

An alphabet is a set of symbols from which the strings of the language may be formed. An alphabet of a formal language is denoted by Σ.

A string is a finite sequence consisting of concatenated symbols.

A string of a formal language is composed of symbols which are that language's alphabet.

A formal language is a set of strings (of symbols) from an alphabet, along with a set of rules. In other words, a formal language consists of strings, which are composed of symbols in that language's alphabet, called words or formulas and are well-formed according to a particular set of rules.

Well-formed formulas (wff) or well-formed words (or just words in less formal settings), are the well-formed strings built from the well-drawn symbols of an well-defined alphabet.

All this wellness is just to ensure that not any old sequence of items (strokes making up the symbols, symbols making up the words, particular sequence of words) is admitted to the language without previous consideration and consensus.

A formal language is often defined by means of a formal grammar, also called formation rule, such as regular or context-free grammar.

Formal syntax of a language consists of 2 layers:

• lexical

• grammar

Syntax encompasses form, format, well-formedness, compositional structure.

Semantics concerns meaning and interpretation of the language.

Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas.

A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules.

The field of formal language theory studies primarily the purely syntactical aspects of such languages i.e their internal structural patterns.

Formal language theory sprang out of linguistics, as a way of understanding the syntactic regularities of natural languages.

In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics.

In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power.

In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems. Mathematical formalism is the philosophy that all of mathematics can be reduced to the syntactic manipulation of formal languages in this way.