base-4.7.0.0: Basic libraries

Copyright | (c) Universiteit Utrecht 2010-2011, University of Oxford 2012-2013
License | see libraries/base/LICENSE
Maintainer | libraries@haskell.org
Stability | internal
Portability | non-portable
Safe Haskell | Trustworthy
Language | Haskell2010

GHC.Generics

Contents

- Introduction
  - Representing datatypes
  - Derived and fundamental representation types
    - Individual fields of constructors: `K1`
    - Meta information: `M1`
    - Additional generic representation type constructors
      - Empty datatypes: `V1`
      - Constructors without fields: `U1`
    - Representation of types with many constructors or many fields
  - Defining datatype-generic functions
    - Definition of the generic representation types
    - Generic instances
    - The wrapper and generic default
    - Omitting generic instances
  - Generic constructor classes
    - The `Generic1` class
    - Representation of `* -> *` types
- Generic representation types
  - Synonyms for convenience
- Meta-information
- Generic type classes

Description

Since: 4.6.0.0

If you're using `GHC.Generics`, you should consider using the http://hackage.haskell.org/package/generic-deriving package, which contains many useful generic functions.

Synopsis

- data V1 p
- data U1 p = U1
- newtype Par1 p = Par1 {
  - unPar1 :: p
  }
- newtype Rec1 f p = Rec1 {
  - unRec1 :: f p
  }
- newtype K1 i c p = K1 {
  - unK1 :: c
  }
- newtype M1 i c f p = M1 {
  - unM1 :: f p
  }
- data (f :+: g) p
  - = L1 (f p)
  - | R1 (g p)
- data (f :*: g) p = (f p) :*: (g p)
- newtype (f :.: g) p = Comp1 {
  - unComp1 :: f (g p)
  }
- type Rec0 = K1 R
- type Par0 = K1 P
- data R
- data P
- type D1 = M1 D
- type C1 = M1 C
- type S1 = M1 S
- data D
- data C
- data S
- class Datatype d where
  - datatypeName :: t d (f :: * -> *) a -> [Char]
  - moduleName :: t d (f :: * -> *) a -> [Char]
  - isNewtype :: t d (f :: * -> *) a -> Bool
- class Constructor c where
  - conName :: t c (f :: * -> *) a -> [Char]
  - conFixity :: t c (f :: * -> *) a -> Fixity
  - conIsRecord :: t c (f :: * -> *) a -> Bool
- class Selector s where
  - selName :: t s (f :: * -> *) a -> [Char]
- data NoSelector
- data Fixity
  - = Prefix
  - | Infix Associativity Int
- data Associativity
  - = LeftAssociative
  - | RightAssociative
  - | NotAssociative
- data Arity
  - = NoArity
  - | Arity Int
- prec :: Fixity -> Int
- class Generic a where
  - type Rep a :: * -> *
  - from :: a -> Rep a x
  - to :: Rep a x -> a
- class Generic1 f where
  - type Rep1 f :: * -> *
  - from1 :: f a -> Rep1 f a
  - to1 :: Rep1 f a -> f a

# 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 ``Rep` T`. 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 `T` and ``Rep` T`. By using this technique, we merely need a few generic instances in order to implement functionality that works for any representable type.

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:

    instance Generic (Tree a) where
      type Rep (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`:

    type Par0 = K1 P
    type Rec0 = 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`:

    type S1 = M1 S
    type C1 = M1 C
    type D1 = 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

    instance Generic Empty where
      type Rep Empty = D1 D1Empty V1

#### Constructors without fields: `U1`

If a constructor has no arguments, then `U1` is used as its representation. For example the representation of `Bool` is

    instance Generic Bool where
      type Rep Bool =
        D1 D1Bool
          (C1 C1_0Bool U1 :+: C1 C1_1Bool U1)

### 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:

1. Generic instances for the function, implementing it for most of the representation type constructors introduced above.
   1. A wrapper that for any datatype that is in `Generic`, performs the conversion between the original value and its `Rep`-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:

    data    V1        p                       -- lifted version of Empty
    data    U1        p = U1                  -- lifted version of ()
    data    (:+:) f g p = L1 (f p) | R1 (g p) -- lifted version of Either
    data    (:*:) f g p = (f p) :*: (g p)     -- lifted version of (,)
    newtype K1    i c p = K1 { unK1 :: c }    -- a container for a c
    newtype M1  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:

instance `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:

    newtype Par1   p = Par1 { unPar1 ::   p } -- gives access to parameter p
    newtype Rec1 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

    class Rep1 WithInt where
      type Rep1 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

    class Rep1 Rose where
      type Rep1 Rose =
        D1 D1Rose
          (C1 C1_0Rose
            (S1 NoSelector Par1
             :*:
             S1 NoSelector ([] :.: Rec1 Rose)

where

    newtype (:.:) f g p = Comp1 { unComp1 :: f (g p) }

# Generic representation types

data V1 p

Void: used for datatypes without constructors

data U1 p

Unit: used for constructors without arguments

Constructors

U1 |

Instances

Eq (U1 p) |
Ord (U1 p) |
Read (U1 p) |
Show (U1 p) |
Generic (U1 p) |
type Rep (U1 p) |

newtype Par1 p

Used for marking occurrences of the parameter

Constructors

Par1 |
Fields unPar1 :: p

Instances

Eq p => Eq (Par1 p) |
Ord p => Ord (Par1 p) |
Read p => Read (Par1 p) |
Show p => Show (Par1 p) |
Generic (Par1 p) |
type Rep (Par1 p) |

newtype Rec1 f p

Recursive calls of kind * -> *

Constructors

Rec1 |
Fields unRec1 :: f p

Instances

Eq (f p) => Eq (Rec1 f p) |
Ord (f p) => Ord (Rec1 f p) |
Read (f p) => Read (Rec1 f p) |
Show (f p) => Show (Rec1 f p) |
Generic (Rec1 f p) |
type Rep (Rec1 f p) |

newtype K1 i c p

Constants, additional parameters and recursion of kind *

Constructors

K1 |
Fields unK1 :: c

Instances

Eq c => Eq (K1 i c p) |
Ord c => Ord (K1 i c p) |
Read c => Read (K1 i c p) |
Show c => Show (K1 i c p) |
Generic (K1 i c p) |
type Rep (K1 i c p) |

newtype M1 i c f p

Meta-information (constructor names, etc.)

Constructors

M1 |
Fields unM1 :: f p

Instances

Eq (f p) => Eq (M1 i c f p) |
Ord (f p) => Ord (M1 i c f p) |
Read (f p) => Read (M1 i c f p) |
Show (f p) => Show (M1 i c f p) |
Generic (M1 i c f p) |
type Rep (M1 i c f p) |

data (f :+: g) p infixr 5

Sums: encode choice between constructors

Constructors

L1 (f p) |
R1 (g p) |

Instances

(Eq (f p), Eq (g p)) => Eq ((:+:) f g p) |
(Ord (f p), Ord (g p)) => Ord ((:+:) f g p) |
(Read (f p), Read (g p)) => Read ((:+:) f g p) |
(Show (f p), Show (g p)) => Show ((:+:) f g p) |
Generic ((:+:) f g p) |
type Rep ((:+:) f g p) |

data (f :*: g) p infixr 6

Products: encode multiple arguments to constructors

Constructors

(f p) :*: (g p) infixr 6 |

Instances

(Eq (f p), Eq (g p)) => Eq ((:*:) f g p) |
(Ord (f p), Ord (g p)) => Ord ((:*:) f g p) |
(Read (f p), Read (g p)) => Read ((:*:) f g p) |
(Show (f p), Show (g p)) => Show ((:*:) f g p) |
Generic ((:*:) f g p) |
type Rep ((:*:) f g p) |

newtype (f :.: g) p infixr 7

Composition of functors

Constructors

Comp1 |
Fields unComp1 :: f (g p)

Instances

Eq (f (g p)) => Eq ((:.:) f g p) |
Ord (f (g p)) => Ord ((:.:) f g p) |
Read (f (g p)) => Read ((:.:) f g p) |
Show (f (g p)) => Show ((:.:) f g p) |
Generic ((:.:) f g p) |
type Rep ((:.:) f g p) |

## Synonyms for convenience

type Rec0 = K1 R

Type synonym for encoding recursion (of kind *)

type Par0 = K1 P

Deprecated: `Par0` is no longer used; use `Rec0` instead

Type synonym for encoding parameters (other than the last)

data R

Tag for K1: recursion (of kind *)

data P

Deprecated: `P` is no longer used; use `R` instead

Tag for K1: parameters (other than the last)

type D1 = M1 D

Type synonym for encoding meta-information for datatypes

type C1 = M1 C

Type synonym for encoding meta-information for constructors

type S1 = M1 S

Type synonym for encoding meta-information for record selectors

data D

Tag for M1: datatype

data C

Tag for M1: constructor

data S

Tag for M1: record selector

# Meta-information

class Datatype d where

Class for datatypes that represent datatypes

Minimal complete definition

datatypeName, moduleName

Methods

datatypeName :: t d (f :: * -> *) a -> [Char]

The name of the datatype (unqualified)

moduleName :: t d (f :: * -> *) a -> [Char]

The fully-qualified name of the module where the type is declared

isNewtype :: t d (f :: * -> *) a -> Bool

Marks if the datatype is actually a newtype

class Constructor c where

Class for datatypes that represent data constructors

Minimal complete definition

conName

Methods

conName :: t c (f :: * -> *) a -> [Char]

The name of the constructor

conFixity :: t c (f :: * -> *) a -> Fixity

The fixity of the constructor

conIsRecord :: t c (f :: * -> *) a -> Bool

Marks if this constructor is a record

class Selector s where

Class for datatypes that represent records

Methods

selName :: t s (f :: * -> *) a -> [Char]

The name of the selector

Instances

Selector NoSelector |

data NoSelector

Used for constructor fields without a name

Instances

Selector NoSelector |

data Fixity

Datatype to represent the fixity of a constructor. An infix | declaration directly corresponds to an application of `Infix`.

Constructors

Prefix |
Infix Associativity Int |

Instances

Eq Fixity |
Ord Fixity |
Read Fixity |
Show Fixity |
Generic Fixity |
type Rep Fixity |

data Associativity

Datatype to represent the associativity of a constructor

Constructors

LeftAssociative |
RightAssociative |
NotAssociative |

Instances

Eq Associativity |
Ord Associativity |
Read Associativity |
Show Associativity |
Generic Associativity |
type Rep Associativity |

data Arity

Datatype to represent the arity of a tuple.

Constructors

NoArity |
Arity Int |

Instances

Eq Arity |
Ord Arity |
Read Arity |
Show Arity |
Generic Arity |
type Rep Arity |

prec :: Fixity -> Int

Get the precedence of a fixity value.

# Generic type classes

class Generic a where

Representable types of kind *. This class is derivable in GHC with the DeriveGeneric flag on.

Associated Types

type Rep a :: * -> *

Generic representation type

Methods

from :: a -> Rep a x

Convert from the datatype to its representation

to :: Rep a x -> a

Convert from the representation to the datatype

Instances

Generic Bool |
Generic Char |
Generic Double |
Generic Float |
Generic Int |
Generic Ordering |
Generic () |
Generic Associativity |
Generic Fixity |
Generic Arity |
Generic Any |
Generic All |
Generic [a] |
Generic (U1 p) |
Generic (Par1 p) |
Generic (Maybe a) |
Generic (Last a) |
Generic (First a) |
Generic (Product a) |
Generic (Sum a) |
Generic (Endo a) |
Generic (Dual a) |
Generic (ZipList a) |
Generic (Either a b) |
Generic (Rec1 f p) |
Generic (a, b) |
Generic (Proxy * t) |
Generic (WrappedMonad m a) |
Generic (Const a b) |
Generic (K1 i c p) |
Generic ((:+:) f g p) |
Generic ((:*:) f g p) |
Generic ((:.:) f g p) |
Generic (a, b, c) |
Generic (WrappedArrow a b c) |
Generic (M1 i c f p) |
Generic (a, b, c, d) |
Generic (a, b, c, d, e) |
Generic (a, b, c, d, e, f) |
Generic (a, b, c, d, e, f, g) |

class Generic1 f where

Representable types of kind * -> *. This class is derivable in GHC with the DeriveGeneric flag on.

Associated Types

type Rep1 f :: * -> *

Generic representation type

Methods

from1 :: f a -> Rep1 f a

Convert from the datatype to its representation

to1 :: Rep1 f a -> f a

Convert from the representation to the datatype

Instances

Generic1 [] |
Generic1 Maybe |
Generic1 Last |
Generic1 First |
Generic1 Product |
Generic1 Sum |
Generic1 Dual |
Generic1 ZipList |
Generic1 (Either a) |
Generic1 ((,) a) |
Generic1 (WrappedMonad m) |
Generic1 (Const a) |
Generic1 ((,,) a b) |
Generic1 (WrappedArrow a b) |
Generic1 ((,,,) a b c) |
Generic1 ((,,,,) a b c d) |
Generic1 ((,,,,,) a b c d e) |
Generic1 ((,,,,,,) a b c d e f) |