Fwd: EvTerms and how they are used
Iavor Diatchki
iavor.diatchki at gmail.com
Mon Mar 2 21:35:21 UTC 2015
Hello,
I've seen instances of this problem show up over and over again, and I
think that there is a more principled solution, based on the idea of
`improvement`.
The idea is to allow programmers to specify custom improvements.
Functional dependencies are one way to do this, but there is no reason why
this
should be the only way. The details of this idea are explained in this
paper: "Simplifying and Improving Qualified Types" (
http://web.cecs.pdx.edu/~mpj/pubs/RR-1040.pdf).
In concrete Haskell syntax, this might work like this:
1. Add a new declaration:
improve CS using EQs
Here the `CS` are a collection of constraints, and the `EQs` are a
collection of equations.
2. Modify the constraint solver, so that when it sees `CS` in the inert
set, it will emit the `EQs` as derived constraints.
This is all.
So now you can write things like this:
improve PolyMonad a b Identity using (a ~ Identity, b ~ Identity)
This tells GHC that it is OK to assume that if the final result is
`Identity`,
then the first two arguments will also be in the identity monad.
This is a fairly conservative extension, in that it is only used to
instantiate variables,
and it never needs to produce new equality proofs. This is pretty much
exactly how FDs work
in the current implementation of GHC. For example, the declaration:
class C a b | a -> b where ...
with GHC's current implementation, is exactly equivalent to:
class C a b where ...
improve (C a b, C a c) using (b ~ c)
Aside: GHC actually checks that all instances are consistent with the FD
declarations,
so GHC *could* use them to actually generate new evidence, but it does not
do so at the moment.
Anyway, implementing something like this should not be too hard, and it
seems that it could be
used not just for the PolyMonads work, but also for other cases where one
wants to write
specific improvements.
-Iavor
PS: with GHC's current approach to resolving instances, you could also
avoid some of the
ambiguities for the `Identity` instance by writing it like this:
instance (a ~ Identity, b ~ Idnetity) => PolyMonad a b Identity where
...
On Mon, Mar 2, 2015 at 8:38 AM, Jan Bracker <jan.bracker at googlemail.com>
wrote:
> Hi Adam,
>
> again thank you for your extensive and patient answer!
>
> It's a bit hard to know exactly what is going on without the full code,
>> but I think what is happening is this: you have an unsolved constraint
>> `Polymonad Identity n_abpq Identity` and your plugin provides an
>> evidence term of type `Polymonad Identity Identity Identity`, but of
>> course this is ill-typed, because `n_abpq` is not `Identity`. Hence Core
>> Lint quite reasonably complains.
>>
>
> I would have thought the constraint solver would derive that 'obviously'
> `n_abpq` needs to be unified with `Identity` and substitutes.
>
>
>> I'm not sure exactly what you are trying to do, but I think the right
>> way to approach this problem is to simulate a functional dependency on
>> Polymonad (in fact, can you use an actual functional dependency)?
>
>
> That is exactly what I _don't_ want to do. I am trying to achieve a more
> general version of monads, called polymonads as it was introduced here [1].
>
>
>> When confronted with the constraint `Polymonad Identity n_abpq Identity`,
>> do
>> not try to solve it directly, but instead notice that you must have
>> `n_abpq ~ Identity`. Your plugin can emit this as an additional derived
>> constraint, which will allow GHC's built-in solver to instantiate the
>> unification variable `n_abpq` and then solve the original constraint
>> using the existing instance. No manual evidence generation needed!
>>
>
> Yes, that makes perfect sense! I was so gridlocked, I did not see this as a
> possibility to solve the problem.
>
> Out of interest, can you say anything about your aims here? I'm keen to
>> find out about the range of applications of typechecker plugins.
>>
>
> I want to make Polymonads as proposed in [1] usable in Haskell. They
> generalize
> the bind operator to a more general signature `M a -> (a -> N b) -> P b`.
> Polymonads
> subsume the standard Monad as well as indexed or parameterized monad,
> without
> relying on functional dependencies, which can be limiting (there may be
> different
> requirement depending on the monad being implemented).
> Currently I am providing a type class for this:
>
> class Polymonad m n p where
> (>>=) :: m a -> (a -> n b) -> p b
>
> As the paper points out in section 4.2 (Ambiguity), type inference breaks
> down,
> because the constraint solver is not able to solve the ambiguity. Here a
> small example:
>
> -- Return operator for the IO polymonad
> instance Polymonad Identity Identity IO where
> -- ...
>
> -- Identity polymonad
> instance Polymonad Identity Identity Identity where
> -- ...
>
> return :: (Polymonad Identity Identity m) => a -> m a
> return x = Identity x >>= Identity
>
> test :: Identity Bool
> test = do
> x <- return True
> return x
>
> For this example GHC already gives the following ambiguity errors:
>
> Main.hs:134:3:
> No instance for (Polymonad m0 n0 Identity)
> arising from a do statement
> The type variables ‘m0’, ‘n0’ are ambiguous
> Note: there is a potential instance available:
> instance Polymonad Identity Identity Identity
> -- Defined in ‘Polymonad’
> In a stmt of a 'do' block: x <- return True
> In the expression:
> do { x <- return True;
> return x }
> In an equation for ‘test’:
> test
> = do { x <- return True;
> return x }
>
> Main.hs:134:8:
> No instance for (Polymonad Identity Identity m0)
> arising from a use of ‘return’
> The type variable ‘m0’ is ambiguous
> Note: there are several potential instances:
> instance Polymonad Identity Identity Identity
> -- Defined in ‘Polymonad’
> instance Polymonad Identity Identity IO -- Defined at Main.hs:85:10
> In a stmt of a 'do' block: x <- return True
> In the expression:
> do { x <- return True;
> return x }
> In an equation for ‘test’:
> test
> = do { x <- return True;
> return x }
>
> Main.hs:135:3:
> No instance for (Polymonad Identity Identity n0)
> arising from a use of ‘return’
> The type variable ‘n0’ is ambiguous
> Note: there are several potential instances:
> instance Polymonad Identity Identity Identity
> -- Defined in ‘Polymonad’
> instance Polymonad Identity Identity IO -- Defined at Main.hs:85:10
> In a stmt of a 'do' block: return x
> In the expression:
> do { x <- return True;
> return x }
> In an equation for ‘test’:
> test
> = do { x <- return True;
> return x }
>
> Of course, in the given example we can fix the ambiguity by adding type
> annotations.
> But as soon as the examples become bigger that is not possible anymore.
>
> Using the approach of the paper [1] these constraints are solvable
> unambiguously.
> That's what I am working on.
>
> All the best,
> Jan
>
> [1]: http://arxiv.org/pdf/1406.2060v1.pdf
>
> On 26/02/15 10:07, Jan Bracker wrote:
>> > Hi Adam,
>> >
>> > thank you for your quick and detailed answer! I think I understand how
>> > to construct evidence for typeclass constraints now. But trying to apply
>> > this, I still have some problems.
>> >
>> > I have something along the following lines:
>> >
>> > class Polymonad m n p where
>> > -- Functions
>> >
>> > instance Polymonad Identity Identity Identity where
>> > -- Implementation
>> >
>> > -- Further instances and some small chunk of code involving them:
>> >
>> > The code implies the following constraint:
>> > Polymonad Identity n_abpq Identity
>> >
>> > As the ambiguity error I get says, when trying to compile this: There is
>> > only one matching instance (the one above, lets call
>> > it $fPolymonadIdentityIdentityIdentity).
>> >
>> > So my plugin tries to tell GHC to use that instance. As far as I
>> > understand it, since the parameters
>> > of $fPolymonadIdentityIdentityIdentity are no type variables and there
>> > is no superclass it should be as easy as saying:
>> > EvDFunApp $fPolymonadIdentityIdentityIdentity [] []
>> >
>> > But when I run this with -dcore-lint I get the following error message:
>> >
>> > *** Core Lint errors : in result of Desugar (after optimization) ***
>> > <no location info>: Warning:
>> > In the expression: >>
>> > @ Identity
>> > @ Any
>> > @ Identity
>> > $fPolymonadIdentityIdentityIdentity
>> > @ ()
>> > @ ()
>> > (idOp @ Bool True)
>> > (>>=
>> > @ Identity
>> > @ Identity
>> > @ Any
>> > $fPolymonadIdentityIdentityIdentity
>> > @ Char
>> > @ ()
>> > (return
>> > @ Char @ Identity
>> > $fPolymonadIdentityIdentityIdentity (C# 'a'))
>> > (\ _ [Occ=Dead] ->
>> > return @ () @ Identity
>> > $fPolymonadIdentityIdentityIdentity ()))
>> > Argument value doesn't match argument type:
>> > Fun type:
>> > Polymonad Identity Any Identity =>
>> > forall a_abdV[sk] b_abdW[sk].
>> > Identity a_abdV[sk] -> Any b_abdW[sk] -> Identity b_abdW[sk]
>> > Arg type: Polymonad Identity Identity Identity
>> > Arg: $fPolymonadIdentityIdentityIdentity
>> >
>> > What am I missing? Why doesn't the argument type "Polymonad Identity
>> > Identity Identity" match the first argument of the function type
>> > "Polymonad Identity Any Identity => forall a_abdV[sk] b_abdW[sk].
>> > Identity a_abdV[sk] -> Any b_abdW[sk] -> Identity b_abdW[sk]". Why is
>> > the type variable translated to "Any"?
>> >
>> > Best,
>> > Jan
>>
>> --
>> Adam Gundry, Haskell Consultant
>> Well-Typed LLP, http://www.well-typed.com/
>>
>
>
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