Regarding inference, the place that comes to mind is Vytiniotis et al.
OutsideIn(X):
Thanks Adam for the references. Hmm That OutsideIn paper is formidable in so many senses ...
I'm not sure I grok your response on my specific q; to adapt your example slightly, without a signature
foo2 x@(_: _) = x
GHC infers `foo2 :: [a] -> [a]`. That's not general enough. So I give a signature with bare `b` as the return type, using the (~) to improve it:
foo2 :: [a] ~ b => [a] -> b
... and GHC infers `foo2 :: [a] -> [a]`. Oh. Is that what I should expect?
I'm chiefly concerned about improving bare tyvars under a FunDep. So to take the time-worn example, I want instances morally equivalent to
data TTrue = TTrue; data TFalse = TFalse
class TEq a b r | a b -> r where tEq :: a -> b -> r
instance TEq a a TTrue where tEq _ _ = TTrue
instance TEq a b TFalse where tEq _ _ = TFalse
The FunDeps via CHRs 2006 paper tells me that first instance is supposed to be as if
instance (r ~ TTrue) => TEq a a r where ...
but it isn't
tEq 'a' 'a' :: TFalse -- returns TFalse, using the first pair of instances
tEq 'a' 'a' :: TFalse -- rejected, using the (~) instance: 'Couldn't match type TFalse with TTrue ...'
The 'happily' returning the 'wrong' answer in the first case has caused consternation amongst beginners, and a few Trac tickets.
So what magic is happening with (~) that it can eagerly improve `foo2` but semi-lazily hold back for `tEq`?
Of course I lied about the first-given two instances for TEq: instances are not consistent with Functional Dependency. So I need to resort to overlaps and a (~) and exploit GHC's bogus consistency check:
instance {-# OVERLAPPABLE #-} (r ~ TFalse) => TEq a b r where ...
> ... like automatically inferring where `typeCast` needs to be placed
Yes the non-automatic `TypeCast` version
instance (TypeCast TTrue r) => TEq a a r where
tEq _ _ = TTrue -- rejected 'Couldn't match expected type 'r' with actual type 'TTrue' ...'
tEq _ _ = typeCast TTrue -- accepted
Even though `typeCast` is really `id` (after it's jumped through the devious indirection hoops I talked about).
So what I'm trying to understand is not just "where" to place `typeCast` but also "when" in inference it unmasks the unification.
AntC
About your specific question, if a wanted constraint `a ~ b` can be
solved by unifying `a` with `b`, then GHC is free to do so (in a sense,
either parameter of (~) can be improved from the other). The real
difference with `TypeCast` arises when local equality assumptions (given
constraints) are involved, because then there may be wanted constraints
that cannot be solved by unification but can be solved by exploiting the
local assumptions.
For example, consider this function:
foo :: forall a b . a ~ b => [a] -> [b]
foo x = x
When checking the RHS of `foo`, a wanted constraint `[a] ~ [b]` arises
(because `x` has type `[a]` and is used in a place where `[b]` is
expected). Since `a` and `b` are universally quantified variables, this
cannot be solved by unification. However, the local assumption (given
constraint) `a ~ b` can be used to solve this wanted.
This is rather like automatically inferring where `typeCast` needs to be
placed (indeed, at the Core level there is a construct for casting by an
equality proof, which plays much the same role).
Hope this helps,
Adam
On 06/12/2018 12:01, Anthony Clayden wrote:
> The (~) constraint syntax is enabled by either `GADTs` or `TypeFamilies`
> language extension.
>
> GADTs/Assoc Data Types/Assoc Type Synonyms/Type Families arrived in a
> series of papers 2005 to 2008, and IIRC the development wasn't finished
> in full in GHC until after that. (Superclass constraints took up to
> about 2010.)
>
> Suppose I wanted just the (~) parts of those implementations. Which
> would be the best place to look? (The Users Guide doesn't give a
> reference.) ICFP 2008 'Type Checking with Open Type Functions' shows
> uses of (~) in user-written code, but doesn't explain it or motivate it
> as a separate feature.
>
> My specific question is: long before (~), it was possible to write a
> TypeCast class, with bidirectional FunDeps to improve each type
> parameter from the other. But for the compiler to see the type
> improvement at term level, typically you also need a typeCast method and
> to explicitly wrap a term in it. If you just wrote a term of type `a` in
> a place where `b` was wanted, the compiler would either fail to see your
> `TypeCast a b`, or unify the two too eagerly, then infer an overall type
> that wasn't general enough.
>
> (For that reason, the instance for TypeCast goes through some
> devious/indirect other classes/instances or exploits separate
> compilation, to hide what's going on from the compiler's enthusiasm.)
>
> But (~) does some sort of magic: it's a kinda typeclass but without a
> method. How does it mesh with type improvement in the goldilocks zone:
> neither too eager nor too lazy?
>
>
> AntC