Re: Fwd: EvTerms and how they are used

2 Mar 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 
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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Re: Fwd: EvTerms and how they are used

Iavor Diatchki