28 Jan 2006 15:13:25 -0500

Related articles |
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Arithmetic expressions w. recursive descent parser? bmildh@linuxmail.org (2006-01-26) |

Re: Arithmetic expressions w. recursive descent parser? Juergen.Kahrs@vr-web.de (=?ISO-8859-1?Q?J=FCrgen_Kahrs?=) (2006-01-28) |

Re: Arithmetic expressions w. recursive descent parser? torbenm@app-2.diku.dk (2006-01-28) |

Re: Arithmetic expressions w. recursive descent parser? NOSPAMrszeflerNOSPAM@murator.com.pl (RobertSzefler) (2006-01-28) |

From: | torbenm@app-2.diku.dk (=?iso-8859-1?q?Torben_=C6gidius_Mogensen?=) |

Newsgroups: | comp.compilers |

Date: | 28 Jan 2006 15:13:25 -0500 |

Organization: | Department of Computer Science, University of Copenhagen |

References: | 06-01-078 |

Keywords: | arithmetic, parse |

bmildh@linuxmail.org writes:

*> I'm trying to make a simple java program to parse arithmetic*

*> expressions. To keep it simple, only integers are used in the*

*> expression, together with * / + - ( ) as terminals.*

*> I want the parser to be a predictive recursive descent parser, with 1*

*> lookahead.*

*>*

*> The problem is that I cant get the implementation right with +,- in*

*> combination w. numbers starting w. + or -, eg. -45, +3, etc.*

*> I would appreciate any help, pointers, tips, on how to get the + and -*

*> operator correctly implemented with numbers that could start with + or*

*> - .*

*>*

*> Typical expressions that I want to parse:*

*> (12--21)*

*> 5+4-1-2*

*>*

*> A made a grammar but it was left-recursive, but I removed it and this*

*> is the resulting grammar:*

*>*

*> E -> TX | T*

*> X -> +TX | +T | -TX | -T*

*> T -> FY | F*

*> Y -> *FY | /FY | /F | *F*

*> F -> number*

*> F -> (E)*

This doesn't seem like the correct grammar for what you describe.

Initially, we have an ambiguous grammar:

E -> E+E | E-E | E*E | E/E | +E | -E | number | (E)

Next, we have to decide on the precedence of the operators. The usual

decision is:

+, -: lowest priority, left associative when infix, highest priority

when prefix.

*, /: medium priority, left associative.

Note that + and - have different priorities when prefix or infix.

We now rewrite the grammar to get the precedences right:

E -> E+T | E-T | T

T -> T*F | T/F | F

F -> +F | -F | number | (E)

and eliminate left-recursion:

E -> TE'

E' -> +TE' | -TE' | \epsilon

T -> FT'

T' -> *FT' | /FT' | \epsilon

F -> +F | -F | number | (E)

Starting from here, you should have no problem writing a recursive

descent parser.

Torben

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