Online Lex And Yacc Compiler

Contents • • • • • • • • • • History [ ] The idea of describing the structure of language using rewriting rules can be traced back to at least the work of (ancient Indian Sanskrit grammarian and a revered scholar in Hinduism who lived sometime between the 7th and 4th century ). His notation to describe word structure notation is equivalent in power to that of Backus and has many similar properties. In Western society, grammar was long regarded as a subject for teaching, rather than scientific study; descriptions were informal and targeted at practical usage. In the first half of the 20th century, such as and started attempts to formalize the description of language, including phrase structure.

Meanwhile, string rewriting rules as were introduced and studied by mathematicians such as (in 1914), (1920s–40s) and (1936)., teaching linguistics to students of at, combined linguistics and mathematics by taking what is essentially Thue's formalism as the basis for the description of the syntax of. He also introduced a clear distinction between generative rules (those of ) and transformation rules (1956)., a programming language designer at, proposed a of 'metalinguistic formulas' to describe the syntax of the new programming language IAL, known today as (1959). His notation was first used in the ALGOL 60 report. BNF is a notation for Chomsky's context-free grammars.

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Apparently, Backus was familiar with Chomsky's work. As proposed by Backus, the formula defined 'classes' whose names are enclosed in angle brackets. For example,. Each of these names denotes a class of basic symbols. Further development of led to. In the committee's 1963 report, called Backus's notation Backus normal form. Argued that BNF should rather be read as Backus–Naur form, as it is 'not a in the conventional sense', unlike, for instance,.

The name Pāṇini Backus form was also once suggested in view of the fact that the expansion Backus normal form may not be accurate, and that had independently developed a similar notation earlier. BNF, as described by Peter Naur in the ALGOL 60 report is metalinguistic formula. ' Sequences of characters enclosed in the brackets represent metalinguistic variables whose values are sequences of symbols. The marks '::=' and ' ' (the latter with the meaning of 'or') are metalinguistic connectives. Any mark in a formula, which is not a variable or a connective, denotes itself. Juxtaposition of marks or variables in a formula signifies juxtaposition of the sequence denoted.'

Another example from the ALGOL 60 report illustrates a major difference between the BNF metalanguage and a Chomsky context-free grammar. Metalingustic variables do not require a rule defining their formation. Their formation may simply be described in natural language within the brackets. The following ALGOL 60 report section 2.3 comments specification, exemplifies how this works: For the purpose of including text among the symbols of a program the following 'comment' conventions hold: The sequence of basic symbols: is equivalent to; comment;; begin comment; begin end end By equivalence is here meant that any of the three structures shown in the left column may be replaced, in any occurrence outside of strings, by the symbol shown in the same line in the right column without any effect on the action of the program. Naur changed two of Backus's symbols to commonly available characters.

The '::=' symbol was originally a ':≡'. The ' ' symbol was originally the word ' or' (with a bar over it).: 14 [ ] Working for IBM, Backus would have had a non-disclosure agreement and couldn't have talked about his source if it came from an IBM proprietary project. BNF is very similar to equations that are, and were at the time, used in logic-circuit design. Backus was a mathematician and the designer of the FORTRAN programming language. Studies of boolean algebra is commonly part of a mathematics. What we do know is that neither Backus nor Naur described the names enclosed in as non-terminals.

Chomsky terminology was not originally used in describing BNF. Naur later described them as classes in ALGOL course materials.