Ryan Ingram writes:

When I was implementing a toy functional languages compiler I did away with

precedence declarations by number and instead allowed the programmer to specify a partial order on declarations; this seems to be a much cleaner solution and avoids arbitrary precedences between otherwise unrelated operators defined in different modules. I agree. I don't declare operators very often, and when I do I always struggle to remember which way round the precedence numbers go. I usually end up hunting for a Prelude operator that works the way I'm aiming for, then copy its definition. It would be much easier to declare the fixity of myop to be same as someotherop (which would presumably have to be already declared/fixed in an imported module). [It's also slightly counterintuitive that the thing being defined comes last in an infix declaration, and that the stand-alone operator isn't in parens.] infixAs !! .$ -- fixing myop (.$) to be fixed as Preludeop (!!) If you wanted to define precedence relative to some other operator(s), it might be clearer to give some model parsings (grabbing some syntax something like Ryan's): infix .$ (x ** y .$ z .$ w) ==> (x ** ((y .$ z) .$ w)) -- === infixl 9 .$ OTOH, I think Евгений's proposal is getting too exotic. Do we really need such fine shades of binding? Will the reader remember how each operator binds relative to the others? Surely a case where explicit parens would be better. (Anything else we can bikeshed about while we're at it?) AntC

On 14/08/12 13:46, Ketil Malde wrote:

AntC writes:

...

I agree. I don't declare operators very often, and when I do I always struggle to remember which way round the precedence numbers go. [...] (Anything else we can bikeshed about while we're at it?)

infixl * before +

Perhaps "before" and "after" clearer than "higher" and "lower"?

I would pick "tighter than" and "looser than", but I suppose that "before" and "after" are also clear enough. Or maybe "inside" and "outside"? I don't think that we really need a new keyword for precedence declarations. The current "infix" would suffice if the default was for operators to be non-fix and of indeterminate precedence. Multiple fixity declarations for the same operator should then be allowed. Or perhaps just require that separate declarations use the same "infix[lr]?" keyword. Twan

On Tue, Aug 14, 2012 at 1:04 AM, Евгений Пермяков wrote:

Your idea looks _much_ better from code clarity point of view, but it's unclear to me, how to deal with it internally and in error messages. I'm not a compiler guy, though.

How to deal with it internally: It's pretty easy, actually. The hardest part is implementing an extensible partial order; once you have that and you can use it to drive comparisons, parsing is not hard. Basically, at each step when you read an operator token, you need to decide to "shift", that is, put it onto a stack of operations, "reduce", that is, apply the operator at the top of the stack (leaving the current token to check again at the next step), or give a parse error. The rules for deciding which of those to do are pretty simple: Given X, the operator at the top of the stack, and Y, the operator you just read: (1) Compare the precedence of X and Y. If they are incomparable, it's a parse error. (2) If Y is higher precedence than X, shift. (3) If Y is lower precedence than X, reduce. (At this point, we know X and Y have equal precedence) (4) If X or Y is non-associative, it's a parse error. (5) If X and Y don't have the same associativity, it's a parse error. (At this point we know X and Y have the same associativity) (6) If X and Y are left associative, reduce. (7) Otherwise they are both right associative, shift. So, for example, reading the expression x * y + x + g w $ z Start with stack [empty x]. The empty operator has lower precedence than anything else (that is, it will never be reduced). When you finish reading an expression, reduce until the empty operator is the only thing on the stack and return its expression. * is higher precedence than empty, shift. [empty x, * y] + is lower precedence than *, reduce. [empty (x*y)] + is higher precedence than empty, shift. [empty (x*y), + x] + is the same precedence as +, and is left associative, reduce. [empty ((x*y)+x)] + is higher precedence than empty, shift [empty ((x*y)+x), + g] function application is higher precedence than +, shift. [empty ((x*y)+x), + g, APP w] $ is lower precedence than function application, reduce. [empty ((x*y)+x), + (g w)] $ is lower precedence than +, reduce. [empty (((x*y)+x) + (g w))] $ is higher precedence than empty, shift. [empty (((x*y)+x) + (g w)), $ z] Done, but the stack isn't empty. Reduce. [empty ((((x*y)+x) + (g w)) $ z)] Done, and the stack is empty. Result: ((((x*y)+x) + (g w)) $ z) Each operator is shifted exactly once and reduced exactly once, so this algorithm runs in a number of steps linear in the expression size. Parentheses start a new sub-stack when parsing the 'thing to apply the operator to' part of the expression. Something like this: simple_exp :: Parser Exp simple_exp = (ExpId <$> identifier) <|> (ExpLit <$> literal) <|> (lparen *> expression <* rparen) expression :: Parser Exp expression = do first <- simple_exp binops [ (Empty, first) ] reduceAll [ (Empty, e) ] = return e reduceAll ((op1, e1) : (op2, e2) : rest) = reduceAll ((op2, (ExpOperator op1 e1 e2)) : rest) binops :: Stack -> Parser Exp binops s = handle_binop <|> handle_application <|> reduceAll s where handle_binop = do op <- operator rhs <- simple_exp reduce_until_shift op rhs s handle_application = do rhs <- simple_exp reduce_until_shift FunctionApplication rhs s reduce_until_shift implements the algorithm above until it eventually shifts the operator onto the stack. identifier parses an identifier, operator parses an operator, literal parses a literal (like 3 or "hello") lparen and rparen parse left and right parentheses. I haven't considered how difficult it would be to expand this algorithm to support unary or more-than-binary operators; I suspect it's not ridiculously difficult, but I don't know. Haskell's support for both of those is pretty weak, however; even the lip service paid to unary - is a source of many problems in parsing Haskell. Worse, it does not allow to set up fixity relative to operator that is not

in scope and it will create unnecessary intermodule dependencies. One should fall back to numeric fixities for such cases, if it is needed.

You can get numeric fixity by just declaring precedence equal to some prelude operator with the desired fixity; this will likely be the common case. I would expect modules to declare locally relative fixities between operators imported from different modules if and only if it was relevant to that module's implementation. In most cases I expect the non-ordering to be resolved by adding parentheses, not by declaring additional precedence directives; for example, even though (a == b == c) would be a parse error due to == being non-associative, both ((a == b) == c) and (a == (b == c)) are not. The same method of 'just add parentheses where you mean it' fixes any parse error due to incomparable precedences. -- ryan