The syntax of C in Backus-Naur form

C语言语法精要
<translation-unit> ::= {<external-declaration>}*

<external-declaration> ::= <function-definition>
| <declaration>

<function-definition> ::= {<declaration-specifier>}* <declarator> {<declaration>}* <compound-statement>

<declaration-specifier> ::= <storage-class-specifier>
| <type-specifier>
| <type-qualifier>

<storage-class-specifier> ::= auto
| register
| static
| extern
| typedef

<type-specifier> ::= void
| char
| short
| int
| long
| float
| double
| signed
| unsigned
| <struct-or-union-specifier>
| <enum-specifier>
| <typedef-name>

<struct-or-union-specifier> ::= <struct-or-union> <identifier> { {<struct-declaration>}+ }
| <struct-or-union> { {<struct-declaration>}+ }
| <struct-or-union> <identifier>

<struct-or-union> ::= struct
| union

<struct-declaration> ::= {<specifier-qualifier>}* <struct-declarator-list>

<specifier-qualifier> ::= <type-specifier>
| <type-qualifier>

<struct-declarator-list> ::= <struct-declarator>
| <struct-declarator-list> , <struct-declarator>

<struct-declarator> ::= <declarator>
| <declarator> : <constant-expression>
| : <constant-expression>

<declarator> ::= {<pointer>}? <direct-declarator>

<pointer> ::= * {<type-qualifier>}* {<pointer>}?

<type-qualifier> ::= const
| volatile

<direct-declarator> ::= <identifier>
| ( <declarator> )
| <direct-declarator> [ {<constant-expression>}? ]
| <direct-declarator> ( <parameter-type-list> )
| <direct-declarator> ( {<identifier>}* )

<constant-expression> ::= <conditional-expression>

<conditional-expression> ::= <logical-or-expression>
| <logical-or-expression> ? <expression> : <conditional-expression>

<logical-or-expression> ::= <logical-and-expression>
| <logical-or-expression || <logical-and-expression>

<logical-and-expression> ::= <inclusive-or-expression>
| <logical-and-expression && <inclusive-or-expression>

<inclusive-or-expression> ::= <exclusive-or-expression>
| <inclusive-or-expression> | <exclusive-or-expression>

<exclusive-or-expression> ::= <and-expression>
| <exclusive-or-expression> ^ <and-expression>

<and-expression> ::= <equality-expression>
| <and-expression> & <equality-expression>

<equality-expression> ::= <relational-expression>
| <equality-expression> == <relational-expression>
| <equality-expression> != <relational-expression>

<relational-expression> ::= <shift-expression>
| <relational-expression> < <shift-expression>
| <relational-expression> > <shift-expression>
| <relational-expression> <= <shift-expression>
| <relational-expression> >= <shift-expression>

<shift-expression> ::= <additive-expression>
| <shift-expression> << <additive-expression>
| <shift-expression> >> <additive-expression>

<additive-expression> ::= <multiplicative-expression>
| <additive-expression> + <multiplicative-expression>
| <additive-expression> - <multiplicative-expression>

<multiplicative-expression> ::= <cast-expression>
| <multiplicative-expression> * <cast-expression>
| <multiplicative-expression> / <cast-expression>
| <multiplicative-expression> % <cast-expression>

<cast-expression> ::= <unary-expression>
| ( <type-name> ) <cast-expression>

<unary-expression> ::= <postfix-expression>
| ++ <unary-expression>
| -- <unary-expression>
| <unary-operator> <cast-expression>
| sizeof <unary-expression>
| sizeof <type-name>

<postfix-expression> ::= <primary-expression>
| <postfix-expression> [ <expression> ]
| <postfix-expression> ( {<assignment-expression>}* )
| <postfix-expression> . <identifier>
| <postfix-expression> -> <identifier>
| <postfix-expression> ++
| <postfix-expression> --

<primary-expression> ::= <identifier>
| <constant>
| <string>
| ( <expression> )

<constant> ::= <integer-constant>
| <character-constant>
| <floating-constant>
| <enumeration-constant>

<expression> ::= <assignment-expression>
| <expression> , <assignment-expression>

<assignment-expression> ::= <conditional-expression>
| <unary-expression> <assignment-operator> <assignment-expression>

<assignment-operator> ::= =
| *=
| /=
| %=
| +=
| -=
| <<=
| >>=
| &=
| ^=
| |=

<unary-operator> ::= &
| *
| +
| -
| ~
| !

<type-name> ::= {<specifier-qualifier>}+ {<abstract-declarator>}?

<parameter-type-list> ::= <parameter-list>
| <parameter-list> , ...

<parameter-list> ::= <parameter-declaration>
| <parameter-list> , <parameter-declaration>

<parameter-declaration> ::= {<declaration-specifier>}+ <declarator>
| {<declaration-specifier>}+ <abstract-declarator>
| {<declaration-specifier>}+

<abstract-declarator> ::= <pointer>
| <pointer> <direct-abstract-declarator>
| <direct-abstract-declarator>

<direct-abstract-declarator> ::= ( <abstract-declarator> )
| {<direct-abstract-declarator>}? [ {<constant-expression>}? ]
| {<direct-abstract-declarator>}? ( {<parameter-type-list>|? )

<enum-specifier> ::= enum <identifier> { <enumerator-list> }
| enum { <enumerator-list> }
| enum <identifier>

<enumerator-list> ::= <enumerator>
| <enumerator-list> , <enumerator>

<enumerator> ::= <identifier>
| <identifier> = <constant-expression>

<typedef-name> ::= <identifier>

<declaration> ::= {<declaration-specifier>}+ {<init-declarator>}*

<init-declarator> ::= <declarator>
| <declarator> = <initializer>

<initializer> ::= <assignment-expression>
| { <initializer-list> }
| { <initializer-list> , }

<initializer-list> ::= <initializer>
| <initializer-list> , <initializer>

<compound-statement> ::= { {<declaration>}* {<statement>}* }

<statement> ::= <labeled-statement>
| <expression-statement>
| <compound-statement>
| <selection-statement>
| <iteration-statement>
| <jump-statement>

<labeled-statement> ::= <identifier> : <statement>
| case <constant-expression> : <statement>
| default : <statement>

<expression-statement> ::= {<expression>}? ;

<selection-statement> ::= if ( <expression> ) <statement>
| if ( <expression> ) <statement> else <statement>
| switch ( <expression> ) <statement>

<iteration-statement> ::= while ( <expression> ) <statement>
| do <statement> while ( <expression> ) ;
| for ( {<expression>}? ; {<expression>}? ; {<expression>}? ) <statement>

<jump-statement> ::= goto <identifier> ;
| continue ;
| break ;
| return {<expression>}? ;
### Formal Language Theory in Text-Based Natural Language Processing Formal language theory plays a foundational role in the development and implementation of text-based natural language processing (NLP) systems. This branch of theoretical computer science provides a rigorous mathematical framework for defining, analyzing, and manipulating languages, which is essential for modeling human language computationally. One of the primary applications of formal language theory in NLP is in the design of grammars that describe the syntactic structure of natural languages. Context-free grammars (CFGs), for instance, are widely used in parsing algorithms to analyze sentence structures. These grammars enable NLP systems to break down sentences into hierarchical representations such as parse trees, which are crucial for understanding the relationships between words and phrases [^1]. Moreover, finite-state automata and regular expressions derived from formal language theory are extensively applied in tasks like tokenization, part-of-speech tagging, and named entity recognition. These models efficiently handle pattern matching and sequence labeling tasks by representing linguistic patterns as state machines or regular expressions [^1]. In more advanced NLP applications, formal language theory contributes to the development of probabilistic grammars such as Probabilistic Context-Free Grammars (PCFGs). These grammars combine statistical methods with formal grammar rules to model uncertainty and ambiguity in natural language. PCFGs are particularly useful in machine translation and speech recognition systems where disambiguation is critical for accurate interpretation [^1]. Another significant application lies in the area of formal verification of NLP components. By treating language models as formal systems, researchers can apply techniques from automata theory and logic to verify properties of NLP pipelines, ensuring consistency and correctness in processing workflows . Here is an example of how a simple context-free grammar might be defined using Backus-Naur Form (BNF): ```bnf <sentence> ::= <noun_phrase> <verb_phrase> <noun_phrase> ::= <determiner> <noun> <verb_phrase> ::= <verb> <noun_phrase> <determiner> ::= "the" | "a" <noun> ::= "cat" | "dog" <verb> ::= "chased" | "saw" ``` This BNF representation defines a small subset of English syntax and can be used to generate valid sentences or parse input strings according to these rules. Formal language theory also underpins the development of formal semantics in NLP, where logical frameworks such as Montague grammar are employed to map syntactic structures to semantic representations. This mapping enables NLP systems to reason about meaning in a structured way, facilitating tasks like question answering and logical inference over textual data .
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