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# Support for generic programming

- Support for generic programming
- Kind polymorphic overhaul

GHC includes a new (in 2010) mechanism to let you write generic functions. It is described in paper A generic deriving mechanism for Haskell. This page sketches the specifics of the implementation; we assume you have read the paper. The HaskellWiki page gives a more general overview.

This mechanism replaces the previous generic classes implementation. What we describe until the "Kind polymorphic overhaul" section is implemented and released in GHC 7.0.1.

## Main components

`TcDeriv.tcDeriving`

now allows deriving`Generic`

instances.

- The representation types and core functionality of the library live on
`GHC.Generics`

(on the`ghc-prim`

package).

- Many names have been added as known in
`prelude/PrelNames`

- Most of the code generation is handled by
`types/Generics`

## Things that have been removed

- All of the generic classes stuff. In particular, the following have been removed:
`hasGenerics`

field from`TyCon`

;`HsNumTy`

constructor from`HsType`

;`TypePat`

constructor from`Pat`

.

- The
`-XGenerics`

flag is now deprecated.

## What already works

`Generic`

instances can be derived when`-XDeriveGeneric`

is enabled.

- The
`default`

keyword can used for generic default method signatures when`-XDefaultSignatures`

is enabled.

- Generic defaults are properly instantiated when giving an instance without defining the generic default method.

- Base types like
`[]`

,`Maybe`

, tuples, come with Generic instances.

## To be done

- Derive
`Generic1`

instances

## Testing

- Tests are available under the
`generics`

directory of the testsuite.

# Kind polymorphic overhaul

With the new `-XPolyKinds`

functionality we can make the support for generic programming better typed. The basic idea is to define the universe codes (`M1`

, `:+:`

, etc.) as constructors of a datatype. Promotion then lifts these constructors to types, which we can use as before, only that now we have them all classified under a new kind. The overhaul of the main module is explained below; for easier comparison with the current approach, names are kept the same whenever possible.

## Generic representation universe

`m`

is the only real parameter here. `f`

and `x`

are there because we
can't write kinds directly, since `Universe`

is also a datatype (even if
we're only interested in its promoted version). So we pass `f`

and `x`

only to set them to `* -> *`

and `*`

, respectively, in `Interprt`

.
`m`

is different: it stands for the kind of metadata representation types,
and we really want to be polymorphic over that, since each user datatype
will introduce a new metadata kind.

data Universe f x m = -- Void (used for datatypes without constructors) VV -- Unit | UU -- The parameter | PAR -- Recursion into a type of kind * -> * | REC f -- Constants (either other parameters or recursion into types of kind *) | KK Constant x -- Metadata | MM MetaData m (Universe f x m) -- Sum, product, composition | Universe f x m :++: Universe f x m | Universe f x m :**: Universe f x m | f :..: Universe f x m -- Note that we always compose a concrete type on the left (like []) with -- a generic representation on the right infixr 5 :++: infixr 6 :**: infixr 6 :*: infixr 7 :..: -- Some shortcuts data MetaData = CC | DD | SS data Constant = PP | RR data ConstantV (c :: Constant) where P :: ConstantV PP R :: ConstantV RR data MetaDataV (m :: MetaData) where C :: MetaDataV CC D :: MetaDataV DD S :: MetaDataV SS

## Universe interpretation

As promised, we set `f`

to `* -> *`

and `x`

to `*`

.
Unfortunately we don't have explicit kind variable annotations
yet, so we cannot leave `m`

polymorphic! So this code doesn't compile:

data Interprt :: Universe (* -> *) * m -> * -> * where -- No interpretation for VV, as it shouldn't map to any value -- Unit U1 :: Interprt UU p -- The parameter Par1 :: p -> Interprt PAR p -- Recursion into a type of kind * -> * Rec1 :: r p -> Interprt (REC r) p -- Constants K1 :: x -> Interprt (KK c x) p -- Constants shortcuts Par0 :: x -> Interprt (KK PP x) p Rec0 :: x -> Interprt (KK RR x) p -- Metadata M1 :: Interprt x p -> Interprt (MM m c x) p -- Metadata shortcuts D1 :: Interprt x p -> Interprt (MM DD c x) p C1 :: Interprt x p -> Interprt (MM CC c x) p S1 :: Interprt x p -> Interprt (MM SS c x) p -- Sum, product, and composition L1 :: Interprt a r -> Interprt (a :++: b) r R1 :: Interprt b r -> Interprt (a :++: b) r (:*:) :: Interprt a r -> Interprt b r -> Interprt (a :**: b) r Comp1 :: f (Interprt g r) -> Interprt (f :..: g) r

### Names

As an aside, note that we have to come up with names like `UU`

and `KK`

for the `Universe`

even though we really just wanted to use `U1`

and `K1`

, like before. Then we would have
a type and a constructor with the same name, but that's ok. However, `Universe`

defines
both a type (with constructors) and a kind (with types). So if we were to use `U1`

in the
`Universe`

constructors, then we could no longer use that name in the `Interprt`

constructors. It's a bit annoying, because we are never really interested in the type
`Universe`

and its constructors: we're only interested in its promoted variant.
This is a slight annoyance of automatic promotion: when you define a "singleton type"
(like our GADT `Interprt`

for `Universe`

) you cannot reuse the constructor names.

## Metadata representation

data Proxy d = Proxy -- kind polymorphic -- Meta data classes class Datatype d where -- kind polymorphic -- The name of the datatype, fully qualified datatypeName :: Proxy d -> String

There's more of these, but they don't add any new concerns.

## Conversion between user datatypes and generic representation

We now get a more precise kind for `Rep`

:

-- Representable types of kind * class Generic a where type Rep a :: Universe (* -> *) * m from :: a -> Interprt (Rep a) x to :: Interprt (Rep a) x -> a -- Representable types of kind * -> * class Generic1 (f :: * -> *) where type Rep1 f :: Universe (* -> *) * m from1 :: f a -> Interprt (Rep1 f) a to1 :: Interprt (Rep1 f) a -> f a

## Example generic function: `fmap`

(kind `* -> *`

)

User-visible class, exported:

class Functor (f :: * -> *) where fmap :: (a -> b) -> f a -> f b default fmap :: (Generic1 f, GFunctor (Rep1 f)) => (a -> b) -> f a -> f b fmap f = to1 . gfmap f . from1

Defined by the generic programmer, not exported:

class GFunctor (f :: Universe (* -> *) * m) where gfmap :: (a -> b) -> Interprt f a -> Interprt f b instance GFunctor UU where gfmap _ U1 = U1 instance GFunctor PAR where gfmap f (Par1 a) = Par1 (f a) instance GFunctor (KK i c) where gfmap _ (K1 a) = K1 a instance (Functor f) => GFunctor (REC f) where gfmap f (Rec1 a) = Rec1 (fmap f a) instance (GFunctor f) => GFunctor (MM m c f) where gfmap f (M1 a) = M1 (gfmap f a) instance (GFunctor f, GFunctor g) => GFunctor (f :++: g) where gfmap f (L1 a) = L1 (gfmap f a) gfmap f (R1 a) = R1 (gfmap f a) instance (GFunctor f, GFunctor g) => GFunctor (f :**: g) where gfmap f (a :*: b) = gfmap f a :*: gfmap f b instance (Functor f, GFunctor g) => GFunctor (f :..: g) where gfmap f (Comp1 x) = Comp1 (fmap (gfmap f) x)

Note that previously `Functor`

and `GFunctor`

had exactly the same types.
Now we can make clear what the difference between them is.

## Example generic function: `show`

(kind `*`

, uses metadata)

User-visible class, exported:

class Show (a :: *) where show :: a -> String default show :: (Generic a, GShow (Rep a)) => a -> String show = gshow . from

Defined by the generic programmer, not exported:

class GShow (f :: Universe (* -> *) * m) where gshow :: Interprt f x -> String instance GShow UU where gshow U1 = "" instance (P.Show c) => GShow (KK i c) where gshow (K1 a) = P.show a instance (Datatype c, GShow f) => GShow (MM DD c f) where gshow (M1 x) = datatypeName (Proxy :: Proxy c) ++ " " ++ gshow x

The other cases do not add any further complexity.

## Example datatype encoding: lists (derived by the compiler)

instance Generic [a] where type Rep [a] = MM DD DList (MM CC DList_Nil UU :++: MM CC DList_Cons (KK PP a :**: KK RR [a])) from [] = D1 (L1 (C1 U1)) from (h:t) = D1 (R1 (C1 (Par0 h :*: Rec0 t))) to (D1 (L1 (C1 U1))) = [] to (D1 (R1 (C1 (Par0 h :*: Rec0 t)))) = h:t -- Metadata data List_Meta = DList | DList_Nil | DList_Cons

Note that we use only one datatype; more correct would be to use 3, one for
`DList`

, another for the constructors, and yet another for the selectors
(or maybe even n datatypes for the selectors, one for each constructor?)
But we don't do that because `Universe`

is polymorphic only over `m`

, so
a single metadata representation type. If we want a more fine-grained
distinction then we would need more parameters in `Universe`

, and also to
split the `MM`

case.

instance Datatype DList where datatypeName _ = "[]"

### Digression

Even better would be to index the metadata representation types over the type they refer to. Something like:

data family MetaTypes a -- kind polymorphic data instance MetaTypes [] = DList | DList_Nil | DList_Cons

But now we are basically asking for promotion of data families, since we want
to use promoted `DList`

. Also, the case for `MM`

in `Universe`

would then
be something like:

| MM MetaData (MetaTypes m) (Universe f x m)

But I'm not entirely sure about this.