[Haskell-cafe] Eta Reduction

John Lato jwlato at gmail.com
Tue Apr 1 21:26:39 UTC 2014

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 (lazily!).

And if somebody were to suggest that on a different day, +1 from me.

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
>>> operationally
>>> sound currently. The problem is that seq is capable of telling the
>>> difference
>>> between the following two expressions:
>>>     undefined
>>>     \x -> undefined x
>>> The former causes seq to throw an exception, while the latter is
>>> considered
>>> defined enough to not do so. So, if we eta reduce, we can cause
>>> terminating
>>> 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,
>>> simply
>>> 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 for
>>> 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
>>> operationally
>>> 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
>>> versions.
>>> Everyone learns about this type of thing in university computer science
>>> 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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