Context-free grammars are important in linguistics for describing the structure of sentences and words in natural language, and in computer science for describing the structure of programming languages and other formal languages.

Context-free languages have many applications in programming languages ; for example, the language of all properly matched parentheses is generated by the grammar.

Context-free languages are closed under the following operations.

Context-free languages are not closed under complement, intersection, or difference.

Context-free languages are also not closed under complementation, as for any languages A and B:.

Context-free grammars were originally conceived in an attempt to model natural languages, i. e. those normally spoken by humans.

* Context-free language, a formal language that is a member of the set of languages defined by context-free grammars

The grammars of human languages produce hierarchical tree structures and some linguists argue that human languages are also capable of infinite recursion ( see Context-free grammar ).

Context-free grammars are simple enough to allow the construction of efficient parsing algorithms which, for a given string, determine whether and how it can be generated from the grammar.

Context-free L-systems are thus specified by either a prefix grammar, or a regular grammar.

Context-free grammars are adept at modeling the secondary structure of RNA

Context-free grammars are limited in the extent to which they can express all of the requirements of a language.

Earley parsers in particular have been used in compiler compilers where their ability to parse using arbitrary Context-free grammars eases the task of writing the grammar for a particular language.

Context-free grammars specify programming language syntax.

Context-free grammars specify programming language syntax.

Computer scientists define a language that can be accepted by a pushdown automaton as a Context-free language, which can be specified as a Context-free grammar.

The following is a simple Context-free grammar which can describe a language made up of multiplication and addition of integers.

Such rules have been proved to form a Context-free grammar.

The great majority of present-day linguists fall into one or more of a number of overlapping types: those who are convinced that tone cannot be analysed, those who are personally scared of tone and tone languages generally, those who are convinced that tone is merely an unnecessary marginal feature in those languages where it occurs, those who have no idea how to proceed with tone analysis, those who take a simplistic view of the whole matter.

But no other two phonologic systems are as difficult to disentangle as are tone and intonation in some languages.

There are more stems per item in Athabascan, which expresses the fact that the Athabascan languages have undergone somewhat more change in diverging from proto-Athabascan than the Yokuts languages from proto-Yokuts.

Thus his persistence values for some stem frequencies per meaning are: stem identical in 8 languages, 100% ; ;

The Austro-Asiatic ( Austroasiatic ) languages, in recent classifications synonymous with Mon – Khmer, are a large language family of Southeast Asia, also scattered throughout India and Bangladesh.

The rest of the languages are spoken by minority groups.

Austro-Asiatic languages have a disjunct distribution across India, Bangladesh and Southeast Asia, separated by regions where other languages are spoken.

The Austro-Asiatic languages are well known for having a " sesquisyllabic " pattern, with basic nouns and verbs consisting of a reduced minor syllable plus a full syllable.

Little work has been done on the Munda languages, which are not well documented ; with their demotion from a primary branch, Proto-Mon – Khmer becomes synonymous with Proto-Austro-Asiatic.

Afroasiatic languages are spoken predominantly in the Middle East, North Africa, the Horn of Africa, and parts of the Sahel.

Berber languages are spoken in Morocco, Algeria, Libya and across the rest of North Africa and the Sahara Desert by about 25 to 35 million people.

Other widely spoken Afroasiatic languages are Amharic, the national language of Ethiopia, with 18 million native speakers ; Somali, spoken by around 19 million people in Greater Somalia ; and Hausa, the dominant language of northern Nigeria and southern Niger, spoken by 18. 5 million people and used as a lingua franca in large parts of the Sahel, with some 25 million speakers in total.

* The Omotic language branch is the most controversial member of Afroasiatic, since the grammatical formatives which most linguists have given greatest weight in classifying languages in the family " are either absent or distinctly wobbly " ( Hayward 1995 ).

Afroasiatic languages are today primarily spoken in the Middle East, North Africa, the Horn of Africa, and parts of the Sahel.

At the other extreme are languages such as English, where the spelling of many words simply has to be memorized as they do not correspond to sounds in a consistent way.

Programming languages are primarily intended for expressing algorithms in a form that can be executed by a computer, but are often used as a way to define or document algorithms.

Abstract data types are purely theoretical entities, used ( among other things ) to simplify the description of abstract algorithms, to classify and evaluate data structures, and to formally describe the type systems of programming languages.

It was a theoretical contribution, since the language was not implemented in his lifetime and did not directly influence subsequent early languages.

It is argued that Bloomfield's Indo-European work had two broad implications: " He stated clearly the theoretical bases for Indo-European linguistics ..."; and "... he established the study of Indo-European languages firmly within general linguistics ...."

Halliday contrasts theoretical categories with descriptive categories, defined as ‘ categories set up in the description of particular languages ’.

Another usage regards programming languages as theoretical constructs for programming abstract machines, and computer languages as the subset thereof that runs on physical computers, which have finite hardware resources.

Government Phonology, which originated in the early 1980s as an attempt to unify theoretical notions of syntactic and phonological structures, is based on the notion that all languages necessarily follow a small set of principles and vary according to their selection of certain binary parameters.

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.

Essentials of theoretical computer science A textbook covering the topics of formal languages, automata and grammars.

* Martin Davis, Ron Sigal, Elaine J. Weyuker, Computability, complexity, and languages: fundamentals of theoretical computer science, 2nd ed., Academic Press, 1994, ISBN 0-12-206382-1.

It includes three subdisciplines: qualitative typology, which deals with the issue of comparing languages and within-language variance ; quantitative typology, which deals with the distribution of structural patterns in the world ’ s languages ; and theoretical typology, which explains these distributions.

The broad term Vulgar Latin should not be confused with the more specific term Proto-Romance, which refers specifically to the theoretical common ancestor to the modern Romance languages.

That is one obvious difference from phonology, which concerns the structure and organisation of speech sounds in natural languages, and furthermore has a theoretical and abstract nature.

So for solipsism if we assume there's only one human in the universe, no languages are private unless no theoretical second person can comprehend it.

It was introduced by Moses Schönfinkel and Haskell Curry and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages.

Formal methods are best described as the application of a fairly broad variety of theoretical computer science fundamentals, in particular logic calculi, formal languages, automata theory, and program semantics, but also type systems and algebraic data types to problems in software and hardware specification and verification.

It combines vocational training with theoretical education in languages, mathematics, history, arts and sciences.

Subyping of records can be defined in System F < sub ><:</ sub >, which combines parametric polymorphism with subtyping of record types and is a theoretical basis for many functional programming languages that support both features.

The Communist International published a theoretical magazine in a variety of European languages from 1919 to 1943.

The theoretical framework of Hanslick's criticism is expounded in his book of 1854, Vom Musikalisch-Schönen ( On the Musically Beautiful ), which started as an attack on the Wagnerian aesthetic and established itself as an influential text, subsequently going through many editions and translations in several languages.

The central theoretical journal of the ICL ( FI ) is Spartacist which is published in four languages approximately once a year.

The use of names, as the many different kinds of nouns embedded in different languages, connects nomenclature to theoretical linguistics, while the way we mentally structure the world in relation to word meanings and experience relates to the philosophy of language.