Opened 3 years ago
Last modified 11 months ago
#12564 new bug
Type family in type pattern kind
Reported by: | int-index | Owned by: | goldfire |
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Priority: | high | Milestone: | 8.4.1 |
Component: | Compiler (Type checker) | Version: | 8.0.1 |
Keywords: | TypeInType, TypeFamilies | Cc: | goldfire, int-index, RyanGlScott |
Operating System: | Unknown/Multiple | Architecture: | Unknown/Multiple |
Type of failure: | GHC rejects valid program | Test Case: | |
Blocked By: | #14119 | Blocking: | |
Related Tickets: | Differential Rev(s): | ||
Wiki Page: |
Description
I want to write a type family that is analogous to !!
for lists but requires the index to be no bigger than the length of the list. Usually, in dependently typed languages finite sets are used for this purpose, here's an attempt to do so in Haskell:
{-# LANGUAGE TypeInType, TypeFamilies, GADTs, TypeOperators #-} import Data.Kind data N = Z | S N type family Len (xs :: [a]) :: N where Len '[] = Z Len (_ ': xs) = S (Len xs) data Fin :: N -> Type where FZ :: Fin (S n) FS :: Fin n -> Fin (S n) type family At (xs :: [a]) (i :: Fin (Len xs)) :: a where At (x ': _) FZ = x At (_ ': xs) (FS i) = At xs i
It fails to compile with this error:
FinAt.hs:16:3: error: • Illegal type synonym family application in instance: 'FZ • In the equations for closed type family ‘At’ In the type family declaration for ‘At’
That's because the kind of the FZ
pattern (first clause of At
) has the kind Fin (Len xs)
and the application of Len
cannot reduce completely. checkValidTypePat
then disallows the pattern, as it contains a type family application.
I tried to suppress checkValidTypePat
and the definition of At
has compiled; however, it's of little use, since At
doesn't reduce:
x :: At '[Bool] FZ x = True
results in
FinAt.hs:20:5: error: • Couldn't match expected type ‘At * ((':) * Bool ('[] *)) ('FZ 'Z)’ with actual type ‘Bool’ • In the expression: True In an equation for ‘x’: x = True
Change History (19)
comment:1 Changed 3 years ago by
Owner: | set to goldfire |
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comment:2 Changed 3 years ago by
Priority: | normal → high |
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comment:4 Changed 3 years ago by
ummm... Maybe :)
In reality, probably not. It depends on how my levity polymorphism stuff evolves.
comment:5 Changed 3 years ago by
In reality, probably not
:(
I'd love to see a fix for this in 8.2 - tell me if I can assist.
comment:6 Changed 3 years ago by
Milestone: | 8.2.1 → 8.4.1 |
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In that case I'll bump this off to 8.4. Do feel free to bump it back if things change, however.
comment:7 Changed 3 years ago by
Cc: | RyanGlScott added |
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comment:8 Changed 2 years ago by
Blocked By: | 14119 added |
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comment:9 Changed 2 years ago by
I've made a new ticket #14119 discussing a refactoring of type patterns. That ticket would solve this one.
comment:10 Changed 18 months ago by
Blocking: | 15515 added |
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comment:11 Changed 17 months ago by
Blocking: | 15515 removed |
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comment:12 Changed 13 months ago by
Current error message is a bit better
T12564.hs:18:3: error: • Illegal type synonym family application ‘Len @a _1’ in instance: At @a ((':) @a x _1) ('FZ @(Len @a _1)) • In the equations for closed type family ‘At’ In the type family declaration for ‘At’ | 18 | At (x ': _) FZ = x | ^^^^^^^^^^^^^^^^^^
comment:13 Changed 13 months ago by
I have an approach here worth documenting. In brief: flatten equations' left-hand sides, emitting constraints during reduction.
Here is how the example in the OP would work. Original equation:
At (x ': _) FZ = x
with implicit things made explicit:
At @a ((:) @a x _1) (FZ @(Len @a _1)) = x
But now, we flatten. By this, I mean we take all type family applications on the LHS and convert them into variables, and assert equality constraints that the variables equal the original type family applications. To wit:
(m ~ Len @a _1) => At @a ((:) @a x _1) (FZ @m) = x
This yields a constrained type family equation. (Note: this is mostly unrelated to Constrained Type Families) During reduction, this equation would match a target regardless of the (implicit) argument to FZ
, but the matcher would then emit a constraint asserting that this argument equals Len @a _1
. It's quite like how class instance matching works: we match against the head, emitting any instance constraints.
Type family equations give rise to axioms in Core. To keep type safety, we would need these axioms to take the evidence of the equality match as arguments. Continuing our example, we would get this axiom:
axAt :: forall (a :: Type) (x :: a) (_1 :: [a]) (m :: Nat). forall (cv :: m ~ Len @a _1). At @a ((:) @a x _1) (FZ @m) ~ x
Note that there are two forall
s: the first binds type variables and the second binds coercion variables. In this case, the coercion variable cv
is unused in the RHS, but it might potentially be mentioned.
This equation could be used to reduce At ["a", "b", "c"] FZ
to "a"
. We would use the instantiated axiom
axAt Symbol "a" ["b", "c"] 2 coLen :: At ["a", "b", "c"] FZ ~ "a"
where coLen :: 2 ~ Len ["b", "c"]
is built from the axioms that describe the behavior of Len
.
Note that there is already some infrastructure for this: the cvs
in CoAxBranch
(and a few other places nearby) are exactly these coercion variables. What's remaining to do is to perform the flattening pass that inserts the cvs and to teach the type-family reduction mechanism (in TcFlatten
) to emit the constraints. One challenge is that sometimes (normaliseType
) we reduce type families without the ability to solve constraints, so some care must be taken there. However, these cases are outside our usual pipeline and can be special-cased. (While implementing -XTypeInType
, I did this once upon a time, so I know it's possible.)
comment:14 Changed 13 months ago by
Generally I like this. But:
- We'd need to update the dynamic semantics and subject-reduction proof for FC to show that the resulting system is sound.
- I'm very troubled by the fact that the evidence is not used. It's all very similar to class instances, except that in class instances we use the evidence.
- You way that the "evidence may potentially be mentioned" but how might that happen?
- In the example here we know for certain that the evidence is redundant. The
(Len @a _1)
was not written by the user; it was inferred. GHC never guesses, so it must be uniquely determined. So it's really a waste of time to construct and pass that evidence at every call site.
Surely there must be a solid criterion for what components of the type are fully determined, and hence redundant and don't need to be matched?
comment:15 Changed 13 months ago by
- Bizarrely, I don't think we need to do much proving. The type safety proof depends on the non-overlap of axiom LHSs. That's unchanged here -- the overlap check must treat any type family application on an LHS just like it would a variable. The equality constraints serve only to reduce the applicability of axioms, never to increase it. Thus, no threats to safety.
- But the evidence is used: it's passed to the coercion axiom. The evidence is the
coLen
in my example above.
- I take back the "evidence may be mentioned" comment.
- GHC passes loads of redundant information at every call site (e.g.
id @Bool True
). This is not new. The uniquely-determined check would help those other places too. I think, in the end, that idea is orthogonal to the plan here, which would work forF x (G x) = True
, should we ever want to support that.
comment:16 Changed 13 months ago by
A fix for this ticket may also fix #15905. Well, at least the older plan, before comment:12.
comment:17 Changed 12 months ago by
For anyone reading this ticket who is searching for a workaround:
While I haven't found a general-purpose way to avoid this bug, in limited situations it's often possible to rewrite your type families in a way that shifts applications of type families from the left-hand side to the right-hand side. For example, GHC does accept this formulation of At
:
{-# LANGUAGE DataKinds #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE UndecidableInstances #-} import Data.Kind import Data.Type.Equality data N = Z | S N type family Len (xs :: [a]) :: N where Len '[] = Z Len (_ ': xs) = S (Len xs) data Vec :: N -> Type -> Type where VNil :: Vec Z a (:>) :: a -> Vec n a -> Vec (S n) a type family ListToVec (l :: [a]) :: Vec (Len l) a where ListToVec '[] = VNil ListToVec (x:xs) = x :> ListToVec xs data Fin :: N -> Type where FZ :: Fin (S n) FS :: Fin n -> Fin (S n) type family At (xs :: [a]) (i :: Fin (Len xs)) :: a where At xs i = At' (ListToVec xs) i type family At' (xs :: Vec n a) (i :: Fin n) :: a where At' (x :> _) FZ = x At' (_ :> xs) (FS i) = At' xs i -- Unit tests test1 :: At '[True] FZ :~: True test1 = Refl test2 :: At [True, False] FZ :~: True test2 = Refl test3 :: At [True, False] (FS FZ) :~: False test3 = Refl
If you inspect the definition of At
, you'll see why this works:
λ> :info At type family At @a (xs :: [a]) (i :: Fin (Len @a xs)) :: a where forall a (xs :: [a]) (i :: Fin (Len @a xs)). At @a xs i = At' @(Len @a xs) @a (ListToVec @a xs) i
Note that the left-hand side, At @a xs i
, does not contain any immediate uses of Len
. (The kind of i
does, but thankfully, GHC doesn't consider that to be an illegal type synonym family application.) The other uses of Len
and ListToVec
have been quarantined off on the right-hand side, where GHC can't complain about them.
comment:18 Changed 11 months ago by
The trick from comment:17 can be further generalized to a pseudo-algorithm that (I think) would work for any closed type family that suffers from this problem. Here is what you have to do:
- Identity any "problematic" type families that cause the
Illegal type synonym family application in instance
error. In the original example, the only problematic type family isLen
. - Encode each problematic type families as an inductive proposition. In the particular case of
Len
, this would look this like:
data LenProp :: forall a. [a] -> N -> Type where LenNil :: LenProp '[] Z LenCons :: LenProp xs n -> LenProp (x:xs) (S n)
The type family's argument kinds (e.g.,
[a]
) as well as the return kind (e.g.,N
) become part of the proposition's kind. Each constructor encodes a single equation of the type family. TheLenNil
constructor encodes theLen '[] = Z
equation, and its return type ofLenProp '[] Z
encodes the fact that this equation takes'[]
as an argument and returnsZ
. Similarly, theLenCons
constructor encodes theLen (_ ': xs) = S (Len xs)
equation, and the field of typeLenProp xs n
encodes the recursive call toLen
on the right-hand side of the equation. Notice that we "bind" the result of this recursive call ton
and useS n
in the return type, since the equation appliesS
to the recursiveLen
call.
- Take all type families that were rejected previously due to occurrences of problematic type families and define "internal" versions of them using the newly defined proposition types. In the particular case of
At
, this would look this:
type family At' (xs :: [a]) (lp :: LenProp xs r) (i :: Fin r) :: a where At' (x:_) (LenCons _) FZ = x At' (_:xs) (LenCons lp) (FS i) = At' xs lp i
Note that
Len
does not appear anywhere in this definition. Where we previously hadFin (Len xs)
we now haveFin r
, where ther
is bound by a new argument of kindLenProp xs r
. In general, you'll need to introduce as many new arguments with proposition kinds as is necessary to replace all occurrences of problematic type families.
- For each proposition-encoded type family, define another type family that translates the arguments of the original type family to the corresponding proposition. For example, the following type family translates a list to a
LenProp
:
type family EncodeLenProp (xs :: [a]) :: LenProp xs (Len xs) where EncodeLenProp '[] = LenNil EncodeLenProp (_:xs) = LenCons (EncodeLenProp xs)
Note the return kind of
LenProp xs (Len xs)
. This is important, since this is how we are going to "sneak in" a use ofLen
intoAt
in the next step. Note thatLen
is not problematic inEncodeLenProp
itself sinceLen
never worms its way into a left-hand-side argument.
- Finally, redefine type families in terms of the "internal" ones created in step (3). In the particular case of
At
, it would become:
type family At (xs :: [a]) (i :: Fin (Len xs)) :: a where At xs i = At' xs (EncodeLenProp xs) i
This uses
EncodeLenProp
to sneak a use ofLen
intoAt'
. Critically, this definition avoids pattern-matching oni
(since that would trigger theIllegal type synonym family application in instance
error). All thatAt
does now is pass its arguments along toAt'
, which does the real work on the proposition created byEncodeLenProp
. In this version ofAt
, the only place whereLen
occurs on the left-hand side is in the kind ofi
, which GHC deems acceptable.
My program in comment:17 essentially follows the algorithm above, except it uses a slightly more complicated type, Vec
, instead of LenProp
.
This seems to work for all of the closed type families that I've encountered that suffer from this issue. That being said, this trick doesn't really work well in the setting of open type families, as it's not always possible to know a priori which kind arguments in an open type family might end up being instantiated with type families. If you figure out a general workaround for that, let me know :)
comment:19 Changed 11 months ago by
After reading comment:13, I'm left wondering about how this idea would work in practice. I've wanted to define instances like these before:
type family Sing :: k -> Type type instance Sing @Type = TypeRep type instance Sing @(Sing a) = Sing
Currently, GHC prevents me from writing the Sing @(Sing a)
instance since its argument mentions the Sing
type family. If I understand the plan in comment:13, then GHC would turn this instance into something that looks roughly like this:
type instance (x ~ Sing a) => Sing @x = Sing
However, this might be a problem. We have both a Sing @x
and a Sing @Type
instance defined—wouldn't these instances conflict?
Yes. This is a known (but perhaps undocumented) infelicity. I am hoping to fix for 8.2.