[Haskell-cafe] Fixity declaration extension

[Евгений Пермяков]

fixity declaration has form infix(l|r)? [Digit] in haskell. I'm pretty sure, that this is not enough for complicated cases. Ideally, fixity declarations should have form infix(l|r)? [Digit](\.(+|-)[Digit])* , with implied infinitely long repeated (.0) tail. This will allow fine tuning of operator priorities and much easier priority selection. For example, it may be assumed, that bit operations like (.&.) operator have hightest priority and have priorities like 9.0.1 or 9.0.2, anti-lisps like ($) have lowest priority like 0.0.1, control operators have base priority 1.* and logic operations like (&&) have priority of 2.* and it will be possibly to add new operators between or above all (for example) control operators without moving fixity of other ones.

Agda2 language supports wide priority range, but still without 'tails' to my knowledge. Is there any haskell-influenced language or experimental syntactic extension that address the issue?

[Ryan Ingram]

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.

You could write statements like

-- define + and - to have the same precedence
infixl + -

-- define * to have higher precedence than +
infixl * above +

-- define / to have the same precedence as *
infixr / equal *

-- $ is right-associative
infixr $
-- you can also separate precedence from fixity declaration
precedence $ below +

-- function application has higher precedence than all operators by default, but you can override that
infixl . above APP

-- == is non-associative
infix ==

Here's some parses with this system:

a + b - c   =>   (a+b)-c
f.x.y z == g w  => (((f.x).y) z) == (g w)
a == b == c  => parse error (non-associative operator)
a * b / c => parse error (left-associative/right-associative operators with same precedence)
a == b $ c => parse error (no ordering known between == and $)
a $ b + c => a $ (b+c)

I think this is a much cleaner way to solve the problem and I hope something like it makes it into a future version of Haskell.

  -- ryan

On Sun, Aug 12, 2012 at 11:46 AM, Евгений Пермяков <perm...@gmail.com> wrote:

fixity declaration has form infix(l|r)? [Digit] in haskell. I'm pretty sure, that this is not enough for complicated cases. Ideally, fixity declarations should have form infix(l|r)? [Digit](\.(+|-)[Digit])* , with implied infinitely long repeated (.0) tail. This will allow fine tuning of operator priorities and much easier priority selection. For example, it may be assumed, that bit operations like (.&.) operator have hightest priority and have priorities like 9.0.1 or 9.0.2, anti-lisps like ($) have lowest priority like 0.0.1, control operators have base priority 1.* and logic operations like (&&) have priority of 2.* and it will be possibly to add new operators between or above all (for example) control operators without moving fixity of other ones.

Agda2 language supports wide priority range, but still without 'tails' to my knowledge. Is there any haskell-influenced language or experimental syntactic extension that address the issue?

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[AntC]

Ryan Ingram <ryani.spam <at> gmail.com> 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

[Евгений Пермяков]

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.

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.

[Ryan Ingram]

On Tue, Aug 14, 2012 at 1:04 AM, Евгений Пермяков <perm...@gmail.com> 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

[Евгений Пермяков]

On 08/14/2012 02:52 PM, Ryan Ingram wrote:

On Tue, Aug 14, 2012 at 1:04 AM, Евгений Пермяков <perm...@gmail.com> 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:

Yes, I can guess it. This way. however, is linearly dependent in time from number of operators in scope. It is clearly much worse then looking into Map OperatorName Fixity . But changing numeric fixity in Map when adding operator somewhere in between existing stack is also linearly - dependent. Of course, associated penalties are small if few operators are in scope. It is unclear for me, how heavy associated penalties will be for both cases.

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. 

Noway. Monoid, Monad and Functor are absolutely independent typeclasses and defined in different modules. There is, however, type [], which has instances for all three typeclasses, so operators for all three of them have to play together. Thus, when you create typeclass and operator-combinators for it, you should add them to entire set of operators on all hackages, as you never know, which typeclass instances will give some yet unknown types. So, rules for such cases must exists, and leaving priorities undefined is not a good way.

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.

I hate lisp-like syntax.

  -- ryan

[Ketil Malde]

AntC <anthony...@clear.net.nz> 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"?

-k
--
If I haven't seen further, it is by standing in the footprints of giants

[Twan van Laarhoven]

On 14/08/12 13:46, Ketil Malde wrote:
> AntC <anthony...@clear.net.nz> 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