}

On Thu, Oct 30, 2008 at 1:05 PM, Todd O'Bryan <toddobr...@gmail.com> wrote:
> I've assigned my high school programming students a symbolic algebra
> project and provided them an ANTLR parser so they could translate
> Strings to values easily. I used an AST, so the translation is pretty
> easy. The basic idea is a mapping like this:

> "sin(x ^ 2)" --> new Sin(new Exp(new Var(), new Number(2.0))

> Everything was working great, until... I wanted exponentiation to have
> higher precedence than unary operators, so

> "~x^3" ---> new Neg(new Exp(new Var(), new Number(2.0)))
> "sin x ^ 2" ---> new Sin(new Exp(new Var(), new Number(2.0)))

> But a student tried this:

> "sin(x) ^ 2"

> Clearly this SHOULD be new Exp(new Sin(new Var()), new Number(2.0)),
> but since ^ has higher precedence than sin, it doesn't work.

> I can't figure out how to fix it, however, because sin(...) should
> have the same precedence as a parenthesized expression (higher than
> ^), but sin ... should have lower precedence. I tried a syntactic
> predicate, but since the sin rule is in two rules, I can't get rid of
> the ambiguity. Here's my grammar that doesn't work. Can anybody help?

> grammar Expression;
> options {
>  output = AST;
>  ASTLabelType=CommonTree;
> }

> expr : addExpr EOF!
>  ;

> addExpr : multExpr (('+'^|'-'^) multExpr)*
>  ;

> multExpr : unaryExpr (('*'^|'/'^) unaryExpr)*
>  ;

> unaryExpr : ('sin'^|'cos'^|'ln'^|'~'^) expExpr
>  | expExpr
>  ;

> expExpr : atom ('^'^ atom)*
>  ;

> parenExpr : ('sin'^|'cos'^|'ln'^|'~'^)? '('! addExpr ')'!
>  ;

> atom : parenExpr
>  | NUMBER
>  | VAR
>  ;

> NUMBER : '-'? '0'..'9'+ ('.' '0'..'9'*)? ;
> VAR : 'x' ;
> WHITESPACE : (' '|'\t'|'\n'|'\r')+ { skip(); } ;

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