Safe Haskell | Safe-Inferred |
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- module GHC.Generics
Introduction
Datatype-generic functions are are based on the idea of converting values of
a datatype T
into corresponding values of a (nearly) isomorphic type
.
The type Rep
T
is
built from a limited set of type constructors, all provided by this module. A
datatype-generic function is then an overloaded function with instances
for most of these type constructors, together with a wrapper that performs
the mapping between Rep
TT
and
. By using this technique, we merely need
a few generic instances in order to implement functionality that works for any
representable type.
Rep
T
Representable types are collected in the Generic
class, which defines the
associated type Rep
as well as conversion functions from
and to
.
Typically, you will not define Generic
instances by hand, but have the compiler
derive them for you.
Representing datatypes
The key to defining your own datatype-generic functions is to understand how to represent datatypes using the given set of type constructors.
Let us look at an example first:
data Tree a = Leaf a | Node (Tree a) (Tree a)
deriving Generic
The above declaration (which requires the language pragma DeriveGeneric
)
causes the following representation to be generated:
classGeneric
(Tree a) where typeRep
(Tree a) =D1
D1Tree (C1
C1_0Tree (S1
NoSelector
(Par0
a)):+:
C1
C1_1Tree (S1
NoSelector
(Rec0
(Tree a)):*:
S1
NoSelector
(Rec0
(Tree a)))) ...
Hint: You can obtain information about the code being generated from GHC by passing
the -ddump-deriv
flag. In GHCi, you can expand a type family such as Rep
using
the :kind!
command.
Derived and fundamental representation types
There are many datatype-generic functions that do not distinguish between positions that are parameters or positions that are recursive calls. There are also many datatype-generic functions that do not care about the names of datatypes and constructors at all. To keep the number of cases to consider in generic functions in such a situation to a minimum, it turns out that many of the type constructors introduced above are actually synonyms, defining them to be variants of a smaller set of constructors.
Individual fields of constructors: K1
The type constructors Par0
and Rec0
are variants of K1
:
typePar0
=K1
P
typeRec0
=K1
R
Here, P
and R
are type-level proxies again that do not have any associated values.
Meta information: M1
The type constructors S1
, C1
and D1
are all variants of M1
:
typeS1
=M1
S
typeC1
=M1
C
typeD1
=M1
D
The types S
, C
and R
are once again type-level proxies, just used to create
several variants of M1
.
Additional generic representation type constructors
Next to K1
, M1
, :+:
and :*:
there are a few more type constructors that occur
in the representations of other datatypes.
Empty datatypes: V1
For empty datatypes, V1
is used as a representation. For example,
data Empty deriving Generic
yields
instanceGeneric
Empty where typeRep
Empty =D1
D1EmptyV1
Constructors without fields: U1
If a constructor has no arguments, then U1
is used as its representation. For example
the representation of Bool
is
instanceGeneric
Bool where typeRep
Bool =D1
D1Bool (C1
C1_0BoolU1
:+:
C1
C1_1BoolU1
)
Representation of types with many constructors or many fields
As :+:
and :*:
are just binary operators, one might ask what happens if the
datatype has more than two constructors, or a constructor with more than two
fields. The answer is simple: the operators are used several times, to combine
all the constructors and fields as needed. However, users /should not rely on
a specific nesting strategy/ for :+:
and :*:
being used. The compiler is
free to choose any nesting it prefers. (In practice, the current implementation
tries to produce a more or less balanced nesting, so that the traversal of the
structure of the datatype from the root to a particular component can be performed
in logarithmic rather than linear time.)
Defining datatype-generic functions
A datatype-generic function comprises two parts:
- Generic instances for the function, implementing it for most of the representation type constructors introduced above.
- A wrapper that for any datatype that is in
Generic
, performs the conversion between the original value and itsRep
-based representation and then invokes the generic instances.
As an example, let us look at a function encode
that produces a naive, but lossless
bit encoding of values of various datatypes. So we are aiming to define a function
encode :: Generic
a => a -> [Bool]
where we use Bool
as our datatype for bits.
For part 1, we define a class Encode'
. Perhaps surprisingly, this class is parameterized
over a type constructor f
of kind * -> *
. This is a technicality: all the representation
type constructors operate with kind * -> *
as base kind. But the type argument is never
being used. This may be changed at some point in the future. The class has a single method,
and we use the type we want our final function to have, but we replace the occurrences of
the generic type argument a
with f p
(where the p
is any argument; it will not be used).
class Encode' f where encode' :: f p -> [Bool]
With the goal in mind to make encode
work on Tree
and other datatypes, we now define
instances for the representation type constructors V1
, U1
, :+:
, :*:
, K1
, and M1
.
Definition of the generic representation types
In order to be able to do this, we need to know the actual definitions of these types:
dataV1
p -- lifted version of Empty dataU1
p =U1
-- lifted version of () data (:+:
) f g p =L1
(f p) |R1
(g p) -- lifted version ofEither
data (:*:
) f g p = (f p):*:
(g p) -- lifted version of (,) newtypeK1
i c p =K1
{unK1
:: c } -- a container for a c newtypeM1
i t f p =M1
{unM1
:: f p } -- a wrapper
So, U1
is just the unit type, :+:
is just a binary choice like Either
,
:*:
is a binary pair like the pair constructor (,)
, and K1
is a value
of a specific type c
, and M1
wraps a value of the generic type argument,
which in the lifted world is an f p
(where we do not care about p
).
Generic instances
The instance for V1
is slightly awkward (but also rarely used):
instance Encode' V1
where
encode' x = undefined
There are no values of type V1 p
to pass (except undefined), so this is
actually impossible. One can ask why it is useful to define an instance for
V1
at all in this case? Well, an empty type can be used as an argument to
a non-empty type, and you might still want to encode the resulting type.
As a somewhat contrived example, consider [Empty]
, which is not an empty
type, but contains just the empty list. The V1
instance ensures that we
can call the generic function on such types.
There is exactly one value of type U1
, so encoding it requires no
knowledge, and we can use zero bits:
instance Encode'U1
where encode'U1
= []
In the case for :+:
, we produce False
or True
depending on whether
the constructor of the value provided is located on the left or on the right:
instance (Encode' f, Encode' g) => Encode' (f:+:
g) where encode' (L1
x) = False : encode' x encode' (R1
x) = True : encode' x
In the case for :*:
, we append the encodings of the two subcomponents:
instance (Encode' f, Encode' g) => Encode' (f:*:
g) where encode' (x:*:
y) = encode' x ++ encode' y
The case for K1
is rather interesting. Here, we call the final function
encode
that we yet have to define, recursively. We will use another type
class Encode
for that function:
instance (Encode c) => Encode' (K1
i c) where encode' (K1
x) = encode x
Note how Par0
and Rec0
both being mapped to K1
allows us to define
a uniform instance here.
Similarly, we can define a uniform instance for M1
, because we completely
disregard all meta-information:
instance (Encode' f) => Encode' (M1
i t f) where encode' (M1
x) = encode' x
Unlike in K1
, the instance for M1
refers to encode'
, not encode
.
The wrapper and generic default
We now define class Encode
for the actual encode
function:
class Encode a where encode :: a -> [Bool] default encode :: (Generic
a) => a -> [Bool] encode x = encode' (from
x)
The incoming x
is converted using from
, then we dispatch to the
generic instances using encode'
. We use this as a default definition
for encode
. We need the 'default encode' signature because ordinary
Haskell default methods must not introduce additional class constraints,
but our generic default does.
Defining a particular instance is now as simple as saying
instance (Encode a) => Encode (Tree a)
Omitting generic instances
It is not always required to provide instances for all the generic representation types, but omitting instances restricts the set of datatypes the functions will work for:
- If no
:+:
instance is given, the function may still work for empty datatypes or datatypes that have a single constructor, but will fail on datatypes with more than one constructor. - If no
:*:
instance is given, the function may still work for datatypes where each constructor has just zero or one field, in particular for enumeration types. - If no
K1
instance is given, the function may still work for enumeration types, where no constructor has any fields. - If no
V1
instance is given, the function may still work for any datatype that is not empty. - If no
U1
instance is given, the function may still work for any datatype where each constructor has at least one field.
An M1
instance is always required (but it can just ignore the
meta-information, as is the case for encode
above).
Generic constructor classes
Datatype-generic functions as defined above work for a large class
of datatypes, including parameterized datatypes. (We have used Tree
as our example above, which is of kind * -> *
.) However, the
Generic
class ranges over types of kind *
, and therefore, the
resulting generic functions (such as encode
) must be parameterized
by a generic type argument of kind *
.
What if we want to define generic classes that range over type
constructors (such as Functor
, Traversable
, or Foldable
)?
The Generic1
class
Like Generic
, there is a class Generic1
that defines a
representation Rep1
and conversion functions from1
and to1
,
only that Generic1
ranges over types of kind * -> *
.
The Generic1
class is also derivable.
The representation Rep1
is ever so slightly different from Rep
.
Let us look at Tree
as an example again:
data Tree a = Leaf a | Node (Tree a) (Tree a)
deriving Generic1
The above declaration causes the following representation to be generated:
class Generic1
Tree where
type Rep1
Tree =
D1
D1Tree
(C1
C1_0Tree
(S1
NoSelector
Par1
)
:+:
C1
C1_1Tree
(S1
NoSelector
(Rec1
Tree)
:*:
S1
NoSelector
(Rec1
Tree)))
...
The representation reuses D1
, C1
, S1
(and thereby M1
) as well
as :+:
and :*:
from Rep
. (This reusability is the reason that we
carry around the dummy type argument for kind-*
-types, but there are
already enough different names involved without duplicating each of
these.)
What's different is that we now use Par1
to refer to the parameter
(and that parameter, which used to be a
), is not mentioned explicitly
by name anywhere; and we use Rec1
to refer to a recursive use of Tree a
.
Representation of * -> *
types
Unlike Par0
and Rec0
, the Par1
and Rec1
type constructors do not
map to K1
. They are defined directly, as follows:
newtypePar1
p =Par1
{unPar1
:: p } -- gives access to parameter p newtypeRec1
f p =Rec1
{unRec1
:: f p } -- a wrapper
In Par1
, the parameter p
is used for the first time, whereas Rec1
simply
wraps an application of f
to p
.
Note that K1
(in the guise of Rec0
) can still occur in a Rep1
representation,
namely when the datatype has a field that does not mention the parameter.
The declaration
data WithInt a = WithInt Int a
deriving Generic1
yields
classRep1
WithInt where typeRep1
WithInt =D1
D1WithInt (C1
C1_0WithInt (S1
NoSelector
(Rec0
Int):*:
S1
NoSelector
Par1
))
If the parameter a
appears underneath a composition of other type constructors,
then the representation involves composition, too:
data Rose a = Fork a [Rose a]
yields
classRep1
Rose where typeRep1
Rose =D1
D1Rose (C1
C1_0Rose (S1
NoSelector
Par1
:*:
S1
NoSelector
([]:.:
Rec1
Rose)
where
newtype (:.:
) f g p =Comp1
{unComp1
:: f (g p) }
module GHC.Generics