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A '''simple precedence grammar''' is a [[context-free]] [[formal grammar]] that can be parsed with a [[simple precedence parser]].<ref>
The Theory of Parsing, Translation, and Compiling: Compiling, Alfred V. Aho, Jeffrey D. Ullman, Prentice-Hall, 1972.</ref>  The concept was first developed by [[Niklaus Wirth]] and [[Helmut Weber]] from the ideas of [[Robert Floyd]] in their paper, ''EULER: a generalization of ALGOL, and its formal definition'', in the [[Communications of the ACM]] in 1966.<ref>{{citation |title=Machines, Languages, and Computation |publisher=[[Prentice-Hall]] |year=1978 |isbn=9780135422588 |quote=Wirth and Weber [1966] generalized Floyd's precedence grammars, obtaining the simple precedence grammars.}}</ref>


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==Formal definition==
 
G = (''N'', Σ, ''P'', ''S'') is a simple precedence grammar if all the production rules in ''P'' comply with the following constraints:
 
* There are no [[erasing rule]]s (ε-productions)
* There are no [[Useless Rules|useless rules]] (unreachable symbols or unproductive rules)
* For each pair of symbols ''X'', ''Y'' (''X'', ''Y'' <math>\in</math> (''N'' ∪ Σ)) there is only one [[Wirth-Weber precedence relationship|Wirth-Weber precedence relation]].
* G is [[Uniquely Inversible Grammar|uniquely inversible]]
 
==Examples==
<math>S \to aSSb | c</math>
 
precedence table:
{|class="wikitable" cellpadding="2" style="background-color:white"
| ||S||a||b||c||$
|-
|S||<math>\dot =</math>|| <math>\lessdot</math> || <math>\dot =</math> || <math>\lessdot</math>||
|-
|a||<math>\dot =</math>||<math>\lessdot</math>||  ||<math>\lessdot</math>||
|-
|b||  ||<math>\gtrdot</math>||  ||<math>\gtrdot</math>||<math>\gtrdot</math>
|-
|c||  ||<math>\gtrdot</math>||<math>\gtrdot</math>||<math>\gtrdot</math>||<math>\gtrdot</math>
|-
|$|| ||<math>\lessdot</math>||  ||<math>\lessdot</math>||
|}
<!--
===Example number 2===
:<math>E \to E + E | id</math>
:precedence table:
:{|border="1" cellpadding="2"
| ||E||+||id|
|-
|E||  ||<math>\dot =</math> <math>\grdot</math> <math>\lessdot</math>|| 
|-
|+||<math>\dot =</math>||  ||<math>\lessdot</math> 
|-
|id||  ||<math>\gtrdot</math>|| 
|}
-->
 
==Notes==
{{reflist}}
 
==References==
* Alfred V. Aho, Jeffrey D. Ullman (1977). ''Principles of Compiler Design''. 1st Edition. Addison-Wesley.
* William A. Barrett, John D. Couch (1979). ''Compiler construction: Theory and Practice''. Science Research Associate.
* Jean-Paul Tremblay, P. G. Sorenson (1985). ''The Theory and Practice of Compiler Writing''. McGraw-Hill.
 
==External links==
* [http://www.cs.clemson.edu/course/cpsc827/material/Simple%20Precedence/Relations.pdf "Simple Precedence Relations"] at Clemson University
 
{{DEFAULTSORT:Simple Precedence Grammar}}
[[Category:Formal languages]]
 
 
{{comp-sci-stub}}
{{Compu-lang-stub}}

Revision as of 04:07, 27 February 2013

A simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser.[1] The concept was first developed by Niklaus Wirth and Helmut Weber from the ideas of Robert Floyd in their paper, EULER: a generalization of ALGOL, and its formal definition, in the Communications of the ACM in 1966.[2]

Formal definition

G = (N, Σ, P, S) is a simple precedence grammar if all the production rules in P comply with the following constraints:

Examples

SaSSb|c

precedence table:

S a b c $
S =˙ =˙
a =˙
b
c
$

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

  • Alfred V. Aho, Jeffrey D. Ullman (1977). Principles of Compiler Design. 1st Edition. Addison-Wesley.
  • William A. Barrett, John D. Couch (1979). Compiler construction: Theory and Practice. Science Research Associate.
  • Jean-Paul Tremblay, P. G. Sorenson (1985). The Theory and Practice of Compiler Writing. McGraw-Hill.

External links


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