Re: Fwd: EvTerms and how they are used

[Iavor Diatchki]

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 exampl

Re: Fwd: EvTerms and how they are used

[Jan Bracker]

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 alon

Re: Fwd: EvTerms and how they are used

[Adam Gundry]

Hi Jan,

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.

The `Any` type is used by GHC to instantiate type variables
whose values are irrelevant, because they do not occur in the type. The
classic example is `null []`, where the type of the list is unimportant:
rather than having an unsolved unification variable, GHC solves it with
`Any`.

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)? 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!

Emitting this extra derived constraint is essentially what happens if
you specify the functional dependency

class Polymonad m n p | m p -> n where

but the plugin approach allows more fine-grained control over exactly
when this applies.

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.

All the best,

Adam


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) ***
> : 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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Fwd: EvTerms and how they are used

[Jan Bracker]

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) ***
: 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

2015-02-25 13:35 GMT+00:00 Adam Gundry :

> Hi Jan,
>
> Yes, unfortunately the meaning of EvTerm is a weak point of the current
> typechecker plugins story; it rather requires one to understand how
> GHC's constraint solver produces evidence. There are lots of papers on
> evidence for equality constraints in System FC, but typeclass
> constraints are generally ignored as they are just datatypes at the FC
> level.
>
> Let me try to give you some idea of what EvDFunApp means, then hopefully
> those with more knowledge of the GHC internals can correct me...
>
> If you write a class instance, e.g.
>
> instance (Show a, Show b) => Show (T a b) where ...
>
> then GHC generates a dfun (short for "dictionary function", I guess)
>
> $fShowT :: forall a b . (Show a, Show b) => Show (T a b)
>
> where Show is treated as a record data type containing a dictionary of
> methods for the class. At the core level, this is a normal term-level
> function (albeit with a strange name).
>
> Now when the typechecker has a constraint to solve, say
>
> Show (T Int Bool),
>
> it produces evidence for this by applying $fShowT to the appropriate
> types and to evidence for the superclass constraints, in this case
> something like
>
> $fShowT @Int @Bool $fShowInt $fShowBool
>
> where I'm using @ for type application. This is represented in EvTerm as
>
> EvDFunApp $fShowT [Int, Bool] [ EvDFunApp $fShowInt [] []
>   , EvDFunApp $fShowBool [] [] ]
>
> Thus the [Type] is the list of kinds/types at which to instantiate the
> dfun, and the [EvTerm] is the list of evidence terms to which it must be
> applied. Obviously this application should be well-typed, and
> -dcore-lint will complain if it is not.
>
> For typechecker plugins, it would be nice if we could write arbitrary
> core expressions as evidence, but this hasn't yet been implemented
> (partially because most of the examples so far solve equality
> constraints, rather than typeclass constraints).
>
> Hope this helps,
>
> Adam
>
>
> On 25/02/15 10:55, Jan Bracker wrote:
> > Hello,
> >
> > I am trying to use the new type checker plugins [1] that are implemented
> > in head.
> >
> > When successful a plugin has to return a [(EvTerm, Ct)] for the solved
> > constraints. The documentation on EvTerms is scarce [2,3,4] and I could
> > not find papers that explain them (many talk about 'evidence', but they
> > never get concret