How to define association on rule without tokens?

Question

I have the following minimized grammar

Exp : let var '=' Exp in Exp end                     { App (Fn $2 $6) $4 }
    | Exp Exp                                        { App $1 $2 }
    | Exp OpCode Exp                                 { Op $1 Add $3 }
    | '(' Exp ')'                                    { $2 }
    | num                                            { Num $1 }
    | var                                            { Ident $1 }
    | '\\' var '.' Exp                               { Fn $2 $4 }

The Exp Exp rule is used to apply a function in a value. But if I have something like myFunc 1 2 it defaults to precendence myFunc (1 2), which is not what I want. I want (myFunc 1) 2, for currying.

But how can I define the association if I don't have a non-terminal symbol? Trying to do %left Exp don't seems to help.

score 1 · Accepted Answer · answered May 19 '15 at 05:02

You can't really apply precedence or associativity unless you have a terminal to shift, because precedence and associativity rules are used to resolve shift/reduce conflicts. You don't necessarily need a terminal in the reduction, so you could use a fake terminal and write:

Exp: Exp Exp %prec CURRY

But that won't help you because there is no terminal to compare precedence with. Precedence relations are always a comparison between the precedence of the lookahead symbol (a terminal) and possible reductions (by default, the precedence of a reduction is based on the rightmost terminal in the rule, but as above you can explicitly specify).

Since you can't do it the short-hand way, you need to fallback to the old-fashioned style where you write an unambiguous grammar with explicit precedence rules:

Curry: Term
     | Curry Term

(That's left-associative, by the away. If func 1 2 is parsed as ((func 1) 2), then application is associating to the left.)

Assuming that infix binds tighter than application, you'd then have:

Term: Value
    | Term Opcode Value

Value: '(' Exp ')'
     | num
     | var

Exp: Curry

(You'll have to figure out how to integrate lambdas into that. It depends on how you expect them to group, but hopefully the model above is clear.)

Why do you use Term, Value and Exp? Can you point me something to read to help me organize better my grammar? — fotanus, May 19 '15 at 05:20
@fotanus: Because I wasn't planning ahead. The names are really irrelevant: in complex grammars, I just number them. But they are essentially different precedence levels. Here's an example of a C grammar with precedence fully written out: http://www.lysator.liu.se/%28nobg%29/c/ANSI-C-grammar-y.html — rici, May 19 '15 at 05:41

How to define association on rule without tokens?

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