[Haskell-cafe] Eta Reduction

John Lato jwlato at gmail.com
Wed Apr 2 03:39:39 UTC 2014

I'm already uneasy using bang patterns on polymorphic data because I don't
know exactly what it will accomplish.  Maybe it adds too much strictness?
Not enough? Simply duplicates work?  Perhaps it's acceptable to remove that
feature entirely (although that may require adding extra strictness in a
lot of other places).

Alternatively, maybe it's enough to simply find a use for that
good-for-nothing syntax we already have?

On Apr 1, 2014 5:32 PM, "Edward Kmett" <ekmett at gmail.com> wrote:
> Unfortunately the old class based solution also carries other baggage,
like the old data type contexts being needed in the language for bang
patterns. :(
> -Edward
> On Apr 1, 2014, at 5:26 PM, John Lato <jwlato at gmail.com> wrote:
>> Hi Edward,
>> Yes, I'm aware of that.  However, I thought Dan's proposal especially
droll given that changing seq to a class-based function would be sufficient
to make eta-reduction sound, given appropriate instances (or lack
thereof).  Meaning we could leave the rest of the proposal unevaluated
>> And if somebody were to suggest that on a different day, +1 from me.
>> John
>> On Apr 1, 2014 10:32 AM, "Edward Kmett" <ekmett at gmail.com> wrote:
>>> John,
>>> Check the date and consider the process necessary to "enumerate all
Haskell programs and check their types".
>>> -Edward
>>> On Tue, Apr 1, 2014 at 9:17 AM, John Lato <jwlato at gmail.com> wrote:
>>>> I think this is a great idea and should become a top priority. I would
probably start by switching to a type-class-based seq, after which perhaps
the next step forward would become more clear.
>>>> John L.
>>>> On Apr 1, 2014 2:54 AM, "Dan Doel" <dan.doel at gmail.com> wrote:
>>>>> In the past year or two, there have been multiple performance
problems in
>>>>> various areas related to the fact that lambda abstraction is not
free, though we
>>>>> tend to think of it as so. A major example of this was deriving of
Functor. If we
>>>>> were to derive Functor for lists, we would end up with something like:
>>>>>     instance Functor [] where
>>>>>       fmap _ [] = []
>>>>>       fmap f (x:xs) = f x : fmap (\y -> f y) xs
>>>>> This definition is O(n^2) when fully evaluated,, because it causes
O(n) eta
>>>>> expansions of f, so we spend time following indirections proportional
to the
>>>>> depth of the element in the list. This has been fixed in 7.8, but
there are
>>>>> other examples. I believe lens, [1] for instance, has some stuff in
it that
>>>>> works very hard to avoid this sort of cost; and it's not always as
easy to avoid
>>>>> as the above example. Composing with a newtype wrapper, for instance,
causes an
>>>>> eta expansion that can only be seen as such at the core level.
>>>>> The obvious solution is: do eta reduction. However, this is not
>>>>> sound currently. The problem is that seq is capable of telling the
>>>>> between the following two expressions:
>>>>>     undefined
>>>>>     \x -> undefined x
>>>>> The former causes seq to throw an exception, while the latter is
>>>>> defined enough to not do so. So, if we eta reduce, we can cause
>>>>> programs to diverge if they make use of this feature.
>>>>> Luckily, there is a solution.
>>>>> Semantically one would usually identify the above two expressions.
While I do
>>>>> believe one could construct a semantics that does distinguish them,
it is not
>>>>> the usual practice. This suggests that there is a way to not
distinguish them,
>>>>> perhaps even including seq. After all, the specification of seq is
monotone and
>>>>> continuous regardless of whether we unify ⊥ with \x -> ⊥ x or insert
an extra
>>>>> element for the latter.
>>>>> The currently problematic case is function spaces, so I'll focus on
it. How
>>>>> should:
>>>>>     seq : (a -> b) -> c -> c
>>>>> act? Well, other than an obvious bottom, we need to emit bottom
whenever our
>>>>> given function is itself bottom at every input. This may first seem
like a
>>>>> problem, but it is actually quite simple. Without loss of generality,
let us
>>>>> assume that we can enumerate the type a. Then, we can feed these
values to the
>>>>> function, and check their results for bottom. Conal Elliot has prior
art for
>>>>> this sort of thing with his unamb [2] package. For each value x :: a,
>>>>> compute 'f x `seq` ()' in parallel, and look for any successes. If we
ever find
>>>>> one, we know the function is non-bottom, and we can return our value
of c. If we
>>>>> never finish searching, then the function must be bottom, and seq
should not
>>>>> terminate, so we have satisfied the specification.
>>>>> Now, some may complain about the enumeration above. But this, too, is
a simple
>>>>> matter. It is well known that Haskell programs are denumerable. So it
is quite
>>>>> easy to enumerate all Haskell programs that produce a value, check
whether that
>>>>> value has the type we're interested in, and compute said value. All
of this can
>>>>> be done in Haskell. Thus, every Haskell type is programatically
enumerable in
>>>>> Haskell, and we can use said enumeration in our implementation of seq
>>>>> function types. I have discussed this with Russell O'Connor [3], and
he assures
>>>>> me that this argument should be sufficient even if we consider
semantic models
>>>>> of Haskell that contain values not denoted by any Haskell program, so
we should
>>>>> be safe there.
>>>>> The one possible caveat is that this implementation of seq is not
>>>>> uniform across all types, so the current fully polymorphic type of
seq may not
>>>>> make sense. But moving back to a type class based approach isn't so
bad, and
>>>>> this time we will have a semantically sound backing, instead of just
having a
>>>>> class with the equivalent of the current magic function in it.
>>>>> Once this machinery is in place, we can eta reduce to our hearts'
content, and
>>>>> not have to worry about breaking semantics. We'd no longer put the
burden on
>>>>> programmers to use potentially unsafe hacks to avoid eta expansions.
I apologize
>>>>> for not sketching an implementation of the above algorithm, but I'm
sure it
>>>>> should be elementary enough to make it into GHC in the next couple
>>>>> Everyone learns about this type of thing in university computer
>>>>> programs, no?
>>>>> Thoughts? Comments? Questions?
>>>>> Cheers,
>>>>> -- Dan
>>>>> [1] http://hackage.haskell.org/package/lens
>>>>> [2] http://hackage.haskell.org/package/unamb
>>>>> [3] http://r6.ca/
>>>>> _______________________________________________
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