Is it possible to establish Coercible instances between custom types and standard library ones? - haskell

Question

For a simple example, say I want a type to represent tic-tac-toe marks:
data Mark = Nought | Cross
Which is the same as Bool
Prelude> :info Bool
data Bool = False | True -- Defined in ‘GHC.Types’
But there's no Coercible Bool Mark between them, not even if I import GHC.Types (I first thought maybe GHC needs Bool's defining place to be visible), the only way to have this instance seems to be through newtype.
Probably I could have defined newtype Mark = Mark Bool and define Nought and Cross with bidirectional patterns, I wish there's something simpler than that.

Answer 1

Unfortunately, you're out of luck. As the documentation for Data.Coerce explains, "one can pretend that the following three kinds of instances exist:"
Self-instances, as in instance Coercible a a,
Instances for coercing between two versions of a data type that differ by representational or phantom type parameters, as in instance Coercible a a' => Coercible (Maybe a) (Maybe a'), and
Instances between new types.
Furthermore, "Trying to manually declare an instance of Coercible is an error", so that's all you get. There are no instances between arbitrarily different data types, even if they look similar.
This may seem frustratingly limiting, but consider this: if there were a Coercible instance between Bool and Mark, what's stopping it from coercing Nought to True and Cross to False? It may be that Bool and Mark are represented in memory the same way, but there is no guarantee that they are semantically similar enough to warrant a Coercible instance.
Your solution of using a newtype and pattern synonyms is a great, safe way to get around the problem, even if it is a little annoying.
Another option is to consider using Generic. For instance, check out the idea of genericCoerce from this other question

Answer 2

This isn’t possible yet, and pattern synonyms are a good solution for now. I often use code like this to derive useful instances for a type that happens to be isomorphic to an existing primitive type.
module Mark
( Mark(Nought, Cross)
) where
newtype Mark = Mark Bool
deriving stock (…)
deriving newtype (…)
deriving (…) via Any
…
pattern Nought = Mark False
pattern Cross = Mark True
Coercion between unrelated ADTs is also not on the list of permitted unsafe coercions. Last I knew, in practice in GHC, coercions between Mark and Bool will work only if the values in question are fully evaluated, because they have a small number of constructors, so the constructor index is stored in the tag bits of the pointer at runtime. But an arbitrary thunk of type Mark or Bool can’t be coerced reliably, and the method doesn’t generalise to types with more than {4, 8} constructors (on resp. {32, 64}-bit systems).
Moreover, the code generator and runtime representation of objects both change periodically, so even if this works now (I don’t know), it will probably break in the future anyway.
My hope is that we get a generalised Coercible in the future that can accommodate more coercions than just newtype-of-T ↔ T, or even better, that allows us to specify a stable ABI for a data type. To my knowledge, no one is actively working on that in Haskell, although there is some similar work going on in Rust for safe transmute, so maybe someone will smuggle it back over to functional-land.
(Speaking of ABI, you could use the FFI for this, and I’ve done so in circumstances where I was already writing foreign code and knew the Storable instances matched. alloca a suitably sized buffer, poke a value of type Bool into it, castPtr the Ptr Bool into a Ptr Mark, peek the Mark out of it, and unsafePerformIO the whole shebang.)

Answer 3

Coercible Bool Mark is not required. Mark-instances can be derived via Bool without it.
Generic types whose generic representations (Rep) are Coercible can be converted to each other:
from coerce to
A -----> Rep A () -----> Rep Via () -----> Via
For the datatype Mark this means instances (Eq, ..) can be derived via instances of Bool.
type Mark :: Type
data Mark = Nought | Cross
deriving
stock Generic
deriving Eq
via Bool <-> Mark
How does Bool <-> Mark work?
type (<->) :: Type -> Type -> Type
newtype via <-> a = Via a
First we capture the constraint that we can coerce between the generic representation of two types:
type CoercibleRep :: Type -> Type -> Constraint
type CoercibleRep via a = (Generic via, Generic a, Rep a () `Coercible` Rep via ())
Given this constraint we can move from a to it via type, creating intermediate Reps:
translateTo :: forall b a. CoercibleRep a b => a -> b
translateTo = from #a #() >>> coerce >>> to #b #()
Now we can easily write an Eq instance for this type, we assume an Eq via instance for the via type (Bool in our case)
instance (CoercibleRep via a, Eq via) => Eq (via <-> a) where
(==) :: (via <-> a) -> (via <-> a) -> Bool
Via a1 == Via a2 = translateTo #via a1 == translateTo #via a2
The instance for Semigroup requires translating via back to a
instance (CoercibleRep via a, Semigroup via) => Semigroup (via <-> a) where
(<>) :: (via <-> a) -> (via <-> a) -> (via <-> a)
Via a1 <> Via a2 = Via do
translateTo #a do
translateTo #via a1 <> translateTo #via a2
Now we can derive Eq and Semigroup!
-- >> V3 "a" "b" "c" <> V3 "!" "!" "!"
-- V3 "a!" "b!" "c!"
type V4 :: Type -> Type
data V4 a = V4 a a a a
deriving
stock Generic
deriving (Eq, Semigroup)
via (a, a, a, a) <-> V4 a
Using a newtype from the beginning avoids this boilerplate but once it's up it can be reused. It is simple to write a newtype and use pattern synonyms to cover it up.