GHC/Using rules

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Using rules in GHC

GHC's rewrite rules (invoked by the RULES pragma) offer a powerful way to optimise your program. This page is a place for people who use rewrite rules to collect thoughts about how to use them.

If you aren't already familiar with RULES, read this stuff first:

Advice about using rewrite rules

  • Remember to use the flag -fglasgow-exts and the optimisation flag -O
  • Use the flag -ddump-simpl-stats to see how many rules actually fired.
  • For even more detail use -ddump-simpl-stats -ddump-simpl-iterations to see the core code at each iteration of the simplifer. Note that this produces lots of output so you'll want to direct the output to a file or pipe it to less. Looking at the output of this can help you figure out why rules are not firing when you expect them to do so.
  • Another tip for discovering why rules do not fire, is to use the flag -dverbose-core2core, which (amongst other things) produces the AST after every rule is fired. This can help you to examine whether one rule is creating an expression that thereby prevents another rule from firing, for example.
  • You need to be careful that your identifiers aren't inlined before your RULES have a chance to fire. Consider
{-# INLINE nonFusable #-}
{-# RULES "fusable/aux" forall x y.
      fusable x (aux y) = faux x y ; #-}
nonFusable x y = fusable x (aux y)
You are possibly surprised when the rule for fusable does not fire. It may well be that fusable was inlined before rules were applied.
To control this we add an NOINLINE or an INLINE [1] pragma to identifiers we want to match in rules, to ensure they haven't disappeared by the time the rule matching comes around.

Example: map

(This example code is taken from GHC's base/GHC/Base.lhs module.) 

map :: (a -> b) -> [a] -> [b]
map _ []     = []
map f (x:xs) = f x : map f xs

mapFB ::  (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst
{-# INLINE [0] mapFB #-}
mapFB c f x ys = c (f x) ys

The rules for map work like this.

Up to (but not including) phase 1, we use the "map" rule to rewrite all saturated applications of map with its build/fold form, hoping for fusion to happen. In phase 1 and 0, we switch off that rule, inline build, and switch on the "mapList" rule, which rewrites the foldr/mapFB thing back into plain map.

It's important that these two rules aren't both active at once (along with build's unfolding) else we'd get an infinite loop in the rules. Hence the activation control below.

The "mapFB" rule optimises compositions of map.

This same pattern is followed by many other functions: e.g. append, filter, iterate, repeat, etc. 

{-# RULES
"map"       [~1] forall f xs.   map f xs                = build (\c n -> foldr (mapFB c f) n xs)
"mapList"   [1]  forall f.      foldr (mapFB (:) f) []  = map f
"mapFB"     forall c f g.       mapFB (mapFB c f) g     = mapFB c (f.g)
#-}

Questions

Order of rule-matching

For example, let's say we have two rules 

   "f->g" forall x y .    f x (h y) = g x y
   "h->g" forall x   .    h x = g 0 x

and a fragment of the AST corresponding to 

   f a (h b)

Which rule will fire? "f->g" or "h->g"? (Each rule disables the other.)

Answer: rules are matched against the AST for expressions basically bottom-up rather than top-down. In this example, "h->g" is the rule that fires. But due to the nature of inlining and so on, there are absolutely no guarantees about this kind of behaviour. If you really need to control the order of matching, phase control is the only reliable mechanism.

Pair rules

It is often useful to provide two implementations of a function, and have rewrite rules pick which version to use depending on context. In both GHC's foldr/build fusion, and more extensively in Data.ByteString's stream fusion system, pair rules are used to allow the compiler to choose between two implementations of a function.

Consider the rules: 

    "FPS length -> fused"  [~1]
        length = F.strConsumerBi F.lengthS

    "FPS length -> unfused" [1]
        F.strConsumerBi F.lengthS = length

This rule pair tells the compiler to rewrite occurences of length to a stream-fusible form in early simplifications phases, hoping for fusion to happen. However, if by phase 1 (remember that phases count down from 4), the fusible form remains unfused, it is better to rewrite it back to the unfused-but-fast implementation of length. A similar trick is used for map in the base libraries.

As we want to match length in the rules, we need to ensure that it isn't inlined too soon: 

    length :: ByteString -> Int
    length (PS _ _ l) = assert (l >= 0) $ l
    {-# INLINE [1] length #-}

and we need strConsumerBi to stick around for even longer: 

    strConsumerBi :: (Stream -> a) -> (ByteString -> a)
    strConsumerBi f = f . readStrUp
    {-# INLINE [0] strConsumerBi        #-}

    lengthS :: Stream -> Int 
    lengthS  ...
    {-# INLINE [0] lengthS #-}

Pair rules thus provide a useful mechanism to allow a library to provide multiple implementations of a function, picking the best one to use based on context.

Custom specialisation rules

Another use for rules is to replace a particular use of a slow, polymorphic function with a custom monomorhpic implementation.

Consider: 

    zipWith :: (Word8 -> Word8 -> a) -> ByteString -> ByteString -> [a]

This is a bit slow, but useful. It's often used to zip ByteStrings into a new ByteString, that is: 

    pack (zipWith f p q)

We'd like to spot this, and throw away the intermediate [a] created. And also use a specialised implementation of: 

    zipWith :: (Word8 -> Word8 -> Word8) -> ByteString -> ByteString -> ByteString

We can use rules for this: 

    "FPS specialise pack.zipWith" forall (f :: Word8 -> Word8 -> Word8) p q .
        pack (zipWith f p q) = zipWith' f p q

This rule spots the specific use of zipWith we're looking for, and replaces it with a fast, specialised version.

Rules and sections

This is useful for higher order functions as well. As of ghc 6.6, the rule LHS syntax has been relaxed, allowing for sections and lambda abstractions to appear. Previously, only applications of the following form were valid: 

    "FPS specialise break (x==)" forall x.
        break ((==) x) = breakByte x

That is, replace occurences of: break (x==) with the optimised breakByte function.

This code illustrates how higher order functions can be rewritten to optimised first order equivalents, for special cases like (==). In the case of Data.ByteString, functions using (==) or (/=) are much faster when implemented with memchr(3), and we can use rules to do this, as long as it is possible to match sections. In ghc 6.6 we can now write: 

    "FPS specialise break (==x)" forall x.
        break (==x) = breakByte x

    "FPS specialise break (x==)" forall x.
        break (x==) = breakByte x

Some fragility remains in this rule though, as described below.

Literals, dictionaries and sections

Consider: 

    break (== 10)

Hopefully, this can be rewritten to a breakByte 10 call, however, the combination of sections, literals and dictionaries for Eq makes this rather fragile.

The rule for break ends up translated by GHC as; 

     forall ($dEq :: base:GHC.Base.Eq base:GHC.Word.Word8) 
            (x :: base:GHC.Word.Word8)

        break (base:GHC.Base.== @ base:GHC.Word.Word8 $dEq x) = 
        breakByte x

Notice the LHS: an application of the selector to a (suitably-typed) Eq dictionary. GHC does very little simplification on LHSs, because if it does too much, the LHS doesn't look like you thought it did. Here it might perhaps be better to simplify to GHC.Word.Word8.==, by selecting from the dictionary, but GHC does not do that.

When this rules works, GHC generates exactly that pattern; we get 

        eq = (==) deq
        main = ... break (\x. eq x y) ...

GHC is anxious about substituting eq inside the lambda, but it does it because (==) is just a record selector, and hence is very cheap.

But when we put a literal inline, we get an (Eq a) constraint and a (Num a) constraint (from the literal). Ultimately, 'a' turns out to be Int, by defaulting, but we don't know that yet. So GHC picks the Eq dictionary from the Num dictionary: 

        eq = (==) ($p1 dnum)
        main = ... break (\x. eq x y) ...

Now the 'eq' doesn't look quite so cheap, and it isn't inlined, so the rule does not fire. However, GHC 6.6 has been modified to believe that nested selection is also cheap, so that makes the rule fire.

The underlying lesson is this: the only robust way to make rules fire is if the LHS is a normal form. Otherwise GHC may miss the fleeting moment at which (an instance of) the rule LHS appears in the program. The way you ensure this is with inline phases: don't inline LHS stuff until later, so that the LHS stuff appears in the program more than fleetingly.

But in this case you have (==) on the LHS, and you have no phase control there. So it gets inlined right away, so the rule doesn't match any more. The only way the rule "works" is because GHC catches the pattern right away, before (==) is inlined. Not very robust.

To make this robust, you'd have to say something like 

    instance Eq Word 8 where
      (==) = eqWord8

    eqWord8 = ..
    {-# NOINLINE [1] eqWord8 #-}

    {-# RULES
     "FPS specialise break (x==)" forall x.
        break (x`eqWord8`) = breakByte x
      #-}

Rules and method sharing

GHC by default instantiates overloaded methods by partially applying the original overloaded identifier. This facilitates sharing of multiple method instances with one global definition. However, since a new function name is created during this process, rules matching the original names will not fire. Here is an example from Control.Arrow: 

    class Arrow a where
      arr :: (b -> c) -> a b c
      first :: a b c -> a (b,d) (c,d)
      (>>>) :: a b c -> a c d -> a b d

    {-# RULES
    "compose/arr"   forall f g . arr f >>> arr g = arr (f >>> g)
    "first/arr"     forall f . first (arr f) = arr (first f)
    ...
     -#}

Consider an instance of an arrow and some code on which the rules above should fire: 

    newtype SF a b = SF ([a] -> [b])

    instance Arrow SF where
      arr f = SF (map f)
      ...

    foo :: SF (Int,Int) (Int,Int)
    foo = first (arr (+1)) >>> first (arr (+2) >>> arr (+3))

GHC would generate intermediate code like: 

    dsf :: Arrow SF
    dsf = ...

    first_1 = Control.Arrow.first SF dsf
    arr_1 = Control.Arrow.arr SF dsf

    foo = first_1 (arr_1 (+1)) ...etc...

Due to the introduction of first_1 and arr_1, the rules no longer match since the names have changed.

The solution is to switch off sharing with the -fno-method-sharing flag.

Coexistence of fusion frameworks

I like to use my own fusion framework on an existing data structure because I want to experiment with it or because I have a specific application and I want to optimize the fusion framework for it. How can I disable the fusion rules shipped with that data structure - or at least defer them until the optimizer is finished with my rules?

Answer: Second part of the question first: Asserting that your rules are used before the standard rules is not possible with GHC up to version 6.8. The current system is quite monolithic in this respect. It would be a nice application of a more sophisticated rule control system that allows any number of simplifier phases with explicit statements which phase shall be entered after which other phase.

First part of the question: You may wrap the data structure in a newtype or, to be entirely safe, redefine the data structure. This means that several functions have to be lifted to the wrapped data type. This is tedious, but given that you make an application specific fusion framework, the set of basic functions will be different from that of the general data structure. You might have planned to make your data type distinct anyway, may it be for the Arbitrary class of QuickCheck. Remember to attach a NOINLINE pragma to the wrapped functions, otherwise the compiler may unpack the wrappers and starts fusion on the underlying data structure.

Future of rules in GHC

GHC has much too rigid a notion of phases up to version 6.8. There are precisely 3, namely 2 then 1 then 0, and that does not give enough control. Really we should let you give arbitrary names to phases, express constraints (A must be before B), and run a constraint solver to map phase names to a linear ordering. The current system is horribly non-modular. (See Haskell-Cafe on Properties of optimizer rule application?)

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