Bang patterns
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#76  Bang patterns 

Goal
Our goal is to make it easier to write strict programs in Haskell. Programs that use 'seq' extensively are possible but clumsy, and it's often quite awkward or inconvenient to increase the strictness of a Haskell program. This proposal changes nothing fundamental; but it makes strictness more convenient.
The basic idea
The main idea is to add a single new production to the syntax of patterns
pat ::= !pat
Matching an expression e against a pattern !p is done by first evaluating e (to WHNF) and then matching the result against p.
Example:
f1 !x = True
f1 is strict in x. In this case, it's not so bad to write
f1 x = x `seq` True
but when guards are involved the seq
version becomes horrible:
 Duplicate the seq on y
f2 x y  g x = y `seq` rhs1
 otherwise = y `seq` rhs2
 Have a weird guard
f2 x y  y `seq` False = undefined
 g x = rhs1
 otherwise = rhs2
 Use bang patterns
f2 !x !y  g x = rhs1
 otherwise = rhs2
Bang patterns can be nested of course:
f2 (!x, y) = [x,y]
f2 is strict in x but not in y. A bang only really has an effect if it precedes a variable or wildcard pattern:
f3 !(x,y) = [x,y]
f4 (x,y) = [x,y]
f3 and f4 are identical; putting a bang before a pattern that forces evaluation anyway does nothing.
g5 x = let y = f x in body
g6 x = case f x of { y > body }
g7 x = case f x of { !y > body }
g5 and g6 mean exactly the same thing. But g7 evalutes (f x), binds y to the result, and then evaluates body.
Let and where bindings
In Haskell, let and where bindings can bind patterns. We propose to modify this by allowing an optional bang at the top level of the pattern. Thus for example:
let ![x,y] = e in b
The "!
" should not be regarded as part of the pattern; after all,
in a function argument ![x,y]
means the same as [x,y]
. Rather, the "!
"
is part of the syntax of let
bindings.
The semantics is simple; the above program is equivalent to:
let p@[x,y] = e in p `seq` b
That is, for each bang pattern, invent a variable p
, bind it to the
banged pattern (removing the bang) with an aspattern, and seq
on it
in the body of the let
. (Thanks to Ben RudiakGould for suggesting
this idea.)
A useful special case is when the pattern is a variable: Similarly
let !y = f x in b
means
let y = f x in y `seq` b
which evaluates the (f x)
, thereby giving a strict let
.
A useful law is this. A nonrecursive bangpattern binding
is equivalent to a case
expression:
let !p = <rhs> in <body>
is equivalent to (when the let is nonrecursive)
case <rhs> of !p > <body>
Here is a more realistic example, a strict version of partition:
partitionS p [] = ([], [])
partitionS p (x:xs)
 p x = (x:ys, zs)
 otherwise = (ys, x:zs)
where
!(ys,zs) = partitionS p xs
The bang in the where clause ensures that the recursive call is evaluated eagerly. In Haskell today we are forced to write
partitionS p [] = ([], [])
partitionS p (x:xs)
= case partitionS p xs of
(ys,zs)  p x = (x:ys, zs)
 otherwise = (ys, x:zs)
which is clumsier (especially if there are a bunch of whereclause bindings, all of which should be evaluated strictly), and doesn't provide the opportunity to fall through to the next equation (not needed in this example but often useful).
Changes to the Report
The changes to the Report would be these. (Incomplete.)

Section 3.17, add pat ::= !pat to the syntax of patterns. We would need to take care to make clear whether
f !x = 3
was a definition of the function "!", or of "f". (There is a somewhat similar complication with n+k patterns; see the end of 4.3.3.2 in the Report. However we probably do not want to require parens thus
f (!x) = 3
which are required in n+k patterns.

Section 3.17.2: add new bullet 10, saying "Matching the pattern "!pat" against a value "v" behaves as follows:
 if v is bottom, the match diverges
 otherwise, "pat" is matched against "v".

Fig 3.1, 3.2, add a new case (t):
case v of { !pat > e; _ > e' } = v `seq` case v of { pat > e; _ > e' }

Section 3.12 (let expressions). In the translation box, first apply the following transformation: for each pattern pi that is of form
!qi = ei
, transform it toxi@qi = ei
, and and replacee0
by(xi
seqe0)
. Then, when none of the lefthandside patterns have a bang at the top, apply the rules in the existing box.
Discussion
Recursive let and where bindings
At first you might think that a recursive bang pattern don't make sense: how can you evaluate it strictly if it doesn't exist yet? But consider
let !xs = if funny then 1:xs else 2:xs in ...
Here the binding is recursive, but the translation still makes sense:
let xs = if funny then 1:xs else 2:xs
in xs `seq` ...
Toplevel bangpattern bindings
Does this make sense?
module Foo where
!x = factorial 1000
A toplevel bangpattern binding like this would imply that the binding is evaluated when the program is started; a kind of module initialisation. This makes some kind of sense, since (unlike unrestricted side effects) it doesn't matter in which order the module initialisation is performed.
But it's not clear why it would be necessary or useful. Conservative conclusion: no toplevel bangpatterns.
Tricky point: syntax
What does this mean?
f ! x = True
Is this a definition of (!)
or a banged argument? (Assuming that
space is insignificant.)
Proposal: resolve this ambiguity in favour of the bangpattern. If
you want to define (!)
, use the prefix form
(!) f x = True
Another point that came up in implementation is this. In GHC, at least,
patterns are initially parsed as expressions, because Haskell's syntax
doesn't let you tell the two apart until quite late in the day.
In expressions, the form (! x)
is a right section, and parses fine.
But the form (!x, !y)
is simply illegal. Solution:
in the syntax of expressions, allow sections without the wrapping parens
in explicit lists and tuples. Actually this would make sense generally:
what could (+ 3, + 4)
mean apart from a tuple of two sections?
Tricky point: patternmatching semantics
A bang is part of a pattern; matching a bang forces evaluation. So the exact placement of bangs in equations matters. For example, there is a difference between these two functions:
f1 x True = True
f1 !x False = False
f2 !x True = True
f2 x False = False
Since pattern matching goes toptobottom, lefttoright,
(f1 bottom True)
is True
, whereas (f2 bottom True)
is bottom
.
Tricky point: binding transformations
In Haskell 98, these two bindings are equivalent:
{ p1=e1; p2=e2 } and { (~p1,~p2) = (e1,e2) }
But with bang patterns this transformation only holds if p1
, p2
are
not bangpatterns. Remember, the bang is part of the binding, not the pattern,
Tricky point: exceptions
Consider this program
test = "no exception"
where !_ = error "top down"
!_ = error "bottom up"
eval_order = evaluate test `catch` \e >
case e of
ErrorCall txt > return txt
_ > throw e
Depending on whether the strict bindings induced by the bang patters in test
are evaluated toptobottom or bottomtotop, you'll get different results from eval_order
. But this is exactly the point of of the Imprecise Exceptions paper: the semantics of test
is a set of exception values, rather than a unique one. So this nondeterminism (which can only be observed in the IO monad) is fine.
See this email thread
Tricky point: nested bangs (part 1)
Consider this:
let (x, Just !y) = <rhs> in <body>
Is y
evaluted before <body>
is begun? No, it isn't. That would be
quite wrong. Pattern matching in a let
is lazy; if any of the variables bound
by the pattern is evaluated, then the whole pattern is matched. In this example,
if x
or y
is evaluated, the whole pattern is matched, which in turn forces
evaluation of y
. The binding is equivalent to
let t = <rhs>
x = case t of { (x, Just !y) > x }
y = case t of { (x, Just !y) > y }
in <body>
Tricky point: nested bangs (part 2)
Consider this:
let !(x, Just !y) = <rhs> in <body>
This should be equivalent to
case <rhs> of { (x, Just !y) > <body> }
Notice that this meant that the entire pattern is matched
(as always with Haskell). The Just
may fail; x
is
not evaluated; but y
is evaluated.
This means that you can't give the obvious alternative translation that uses just letbindings and {{{seq}}. For example, we could attempt to translate the example to:
let
t = <rhs>
x = case t of (x, Just !y) > x
y = case t of (x, Just !y) > y
in
t `seq` <body>
This won't work, because using seq
on t
won't force y
.
However, the semantics says that the original code is equivalent to
let p@(x, Just !y) = <rhs> in p `seq` <body>
and we can desugar that in obvious way to
let
t = <rhs>
p = case t of p@(x, Just !y) > p
x = case t of p@(x, Just !y) > x
y = case t of p@(x, Just !y) > y
in
p `seq` <body>
which is fine.
You could also build an intermediate tuple, thus:
let
t = case <rhs> of p@(x, Just !y) > (p,x,y)
p = sel13 t
x = sel23 t
y = sel33 t
in
t `seq` <body>
Indeed GHC does just this for complicated pattern bindings.
Tricky point: polymorphism
Haskell allows this:
let f :: forall a. Num a => a>a
Just f = <rhs>
in (f (1::Int), f (2::Integer))
But if we were to allow a bang pattern, !Just f = <rhs>
,
with the translation to
a case expression given earlier, we would end up with
case <rhs> of { Just f > (f (1::Int), f (2::Integer) }
But if this is Haskell source, then f
won't be polymorphic.
One could say that the translation isn't required to preserve the static semantics, but GHC, at least, translates into System F, and being able to do so is a good sanity check. If we were to do that, then we would need
<rhs> :: Maybe (forall a. Num a => a > a)
so that the case expression works out in System F:
case <rhs> of {
Just (f :: forall a. Num a > a > a)
> (f Int dNumInt (1::Int), f Integer dNumInteger (2::Integer) }
The trouble is that <rhs>
probably has a type more like
<rhs> :: forall a. Num a => Maybe (a > a)
…and now the dictionary lambda may get in the way of forcing the pattern.
This is a swamp. Conservative conclusion: no generalisation (at all) for bangpattern bindings.
Existentials
A strict pattern match could perhaps support existentials (which GHC currently rejects in pattern bindings):
data T where
T :: a > (a>Int) > T
f x = let !(T y f) = x in ...
A more radical proposal
A more radical proposal (from John Hughes) is to make pattern matching
in let
strict. Thus
let (x,y) = e in b
would be equivalent to
case e of (x,y) > b
(in the nonrecursive case) and to
let t = let { x = fst t; y = snd t } in e
in case t of (x,y) > b
(in the recursive case).
To recover Haskell 98 semantics for a pattern binding, use a tilde:
let ~(x,y) = e in b
More precisely, the rules for desugaring binding are these:
 Sort into stronglyconnected components.
 Apply the following rules:
let p1=e1 ; ... ; pn = en in e ==> let (p1,...,pn) = (e1,...,en) in e
let p = e1 in e0 ==> case e1 of p > e0
where no variable in p occurs free in e1
let p = e1 in e0 ==> let p = fix (\ ~p > e1) in e0
otherwise
Why the stronglyconnected component?
Consider this
let (y:ys) = xs
(z:zs) = ys
in ...
There is no real recursion here, but considered all together the second binding does refer to the first. So the desugaring above would use fix, and if you work it out you'll find that all the variables get bound to bottom.
Note that the static semantics already requires a stronglyconneted component analysis.