GHC.Generics

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.

Since: 4.6.0.0

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 D 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.
2. 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)

Methods

(==) :: U1 p -> U1 p -> Bool

(/=) :: U1 p -> U1 p -> Bool

Ord (U1 p)

Methods

compare :: U1 p -> U1 p -> Ordering

(<) :: U1 p -> U1 p -> Bool

(<=) :: U1 p -> U1 p -> Bool

(>) :: U1 p -> U1 p -> Bool

(>=) :: U1 p -> U1 p -> Bool

max :: U1 p -> U1 p -> U1 p

min :: U1 p -> U1 p -> U1 p

Read (U1 p)

Methods

readsPrec :: Int -> ReadS (U1 p)

readList :: ReadS [U1 p]

readPrec :: ReadPrec (U1 p)

readListPrec :: ReadPrec [U1 p]

Show (U1 p)

Methods

showsPrec :: Int -> U1 p -> ShowS

show :: U1 p -> String

showList :: [U1 p] -> ShowS

Generic (U1 p)

Associated Types

type Rep (U1 p) :: * -> *

Methods

from :: U1 p -> Rep (U1 p) x

to :: Rep (U1 p) x -> 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)

Methods

(==) :: Par1 p -> Par1 p -> Bool

(/=) :: Par1 p -> Par1 p -> Bool

Ord p => Ord (Par1 p)

Methods

compare :: Par1 p -> Par1 p -> Ordering

(<) :: Par1 p -> Par1 p -> Bool

(<=) :: Par1 p -> Par1 p -> Bool

(>) :: Par1 p -> Par1 p -> Bool

(>=) :: Par1 p -> Par1 p -> Bool

max :: Par1 p -> Par1 p -> Par1 p

min :: Par1 p -> Par1 p -> Par1 p

Read p => Read (Par1 p)

Methods

readsPrec :: Int -> ReadS (Par1 p)

readList :: ReadS [Par1 p]

readPrec :: ReadPrec (Par1 p)

readListPrec :: ReadPrec [Par1 p]

Show p => Show (Par1 p)

Methods

showsPrec :: Int -> Par1 p -> ShowS

show :: Par1 p -> String

showList :: [Par1 p] -> ShowS

Generic (Par1 p)

Associated Types

type Rep (Par1 p) :: * -> *

Methods

from :: Par1 p -> Rep (Par1 p) x

to :: Rep (Par1 p) x -> 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)

Methods

(==) :: Rec1 f p -> Rec1 f p -> Bool

(/=) :: Rec1 f p -> Rec1 f p -> Bool

Ord (f p) => Ord (Rec1 f p)

Methods

compare :: Rec1 f p -> Rec1 f p -> Ordering

(<) :: Rec1 f p -> Rec1 f p -> Bool

(<=) :: Rec1 f p -> Rec1 f p -> Bool

(>) :: Rec1 f p -> Rec1 f p -> Bool

(>=) :: Rec1 f p -> Rec1 f p -> Bool

max :: Rec1 f p -> Rec1 f p -> Rec1 f p

min :: Rec1 f p -> Rec1 f p -> Rec1 f p

Read (f p) => Read (Rec1 f p)

Methods

readsPrec :: Int -> ReadS (Rec1 f p)

readList :: ReadS [Rec1 f p]

readPrec :: ReadPrec (Rec1 f p)

readListPrec :: ReadPrec [Rec1 f p]

Show (f p) => Show (Rec1 f p)

Methods

showsPrec :: Int -> Rec1 f p -> ShowS

show :: Rec1 f p -> String

showList :: [Rec1 f p] -> ShowS

Generic (Rec1 f p)

Associated Types

type Rep (Rec1 f p) :: * -> *

Methods

from :: Rec1 f p -> Rep (Rec1 f p) x

to :: Rep (Rec1 f p) x -> 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)

Methods

(==) :: K1 i c p -> K1 i c p -> Bool

(/=) :: K1 i c p -> K1 i c p -> Bool

Ord c => Ord (K1 i c p)

Methods

compare :: K1 i c p -> K1 i c p -> Ordering

(<) :: K1 i c p -> K1 i c p -> Bool

(<=) :: K1 i c p -> K1 i c p -> Bool

(>) :: K1 i c p -> K1 i c p -> Bool

(>=) :: K1 i c p -> K1 i c p -> Bool

max :: K1 i c p -> K1 i c p -> K1 i c p

min :: K1 i c p -> K1 i c p -> K1 i c p

Read c => Read (K1 i c p)

Methods

readsPrec :: Int -> ReadS (K1 i c p)

readList :: ReadS [K1 i c p]

readPrec :: ReadPrec (K1 i c p)

readListPrec :: ReadPrec [K1 i c p]

Show c => Show (K1 i c p)

Methods

showsPrec :: Int -> K1 i c p -> ShowS

show :: K1 i c p -> String

showList :: [K1 i c p] -> ShowS

Generic (K1 i c p)

Associated Types

type Rep (K1 i c p) :: * -> *

Methods

from :: K1 i c p -> Rep (K1 i c p) x

to :: Rep (K1 i c p) x -> 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)

Methods

(==) :: M1 i c f p -> M1 i c f p -> Bool

(/=) :: M1 i c f p -> M1 i c f p -> Bool

Ord (f p) => Ord (M1 i c f p)

Methods

compare :: M1 i c f p -> M1 i c f p -> Ordering

(<) :: M1 i c f p -> M1 i c f p -> Bool

(<=) :: M1 i c f p -> M1 i c f p -> Bool

(>) :: M1 i c f p -> M1 i c f p -> Bool

(>=) :: M1 i c f p -> M1 i c f p -> Bool

max :: M1 i c f p -> M1 i c f p -> M1 i c f p

min :: M1 i c f p -> M1 i c f p -> M1 i c f p

Read (f p) => Read (M1 i c f p)

Methods

readsPrec :: Int -> ReadS (M1 i c f p)

readList :: ReadS [M1 i c f p]

readPrec :: ReadPrec (M1 i c f p)

readListPrec :: ReadPrec [M1 i c f p]

Show (f p) => Show (M1 i c f p)

Methods

showsPrec :: Int -> M1 i c f p -> ShowS

show :: M1 i c f p -> String

showList :: [M1 i c f p] -> ShowS

Generic (M1 i c f p)

Associated Types

type Rep (M1 i c f p) :: * -> *

Methods

from :: M1 i c f p -> Rep (M1 i c f p) x

to :: Rep (M1 i c f p) x -> 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)

Methods

(==) :: (f :+: g) p -> (f :+: g) p -> Bool

(/=) :: (f :+: g) p -> (f :+: g) p -> Bool

(Ord (f p), Ord (g p)) => Ord ((:+:) f g p)

Methods

compare :: (f :+: g) p -> (f :+: g) p -> Ordering

(<) :: (f :+: g) p -> (f :+: g) p -> Bool

(<=) :: (f :+: g) p -> (f :+: g) p -> Bool

(>) :: (f :+: g) p -> (f :+: g) p -> Bool

(>=) :: (f :+: g) p -> (f :+: g) p -> Bool

max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p

min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p

(Read (f p), Read (g p)) => Read ((:+:) f g p)

Methods

readsPrec :: Int -> ReadS ((f :+: g) p)

readList :: ReadS [(f :+: g) p]

readPrec :: ReadPrec ((f :+: g) p)

readListPrec :: ReadPrec [(f :+: g) p]

(Show (f p), Show (g p)) => Show ((:+:) f g p)

Methods

showsPrec :: Int -> (f :+: g) p -> ShowS

show :: (f :+: g) p -> String

showList :: [(f :+: g) p] -> ShowS

Generic ((:+:) f g p)

Associated Types

type Rep ((:+:) f g p) :: * -> *

Methods

from :: (f :+: g) p -> Rep ((f :+: g) p) x

to :: Rep ((f :+: g) p) x -> (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)

Methods

(==) :: (f :*: g) p -> (f :*: g) p -> Bool

(/=) :: (f :*: g) p -> (f :*: g) p -> Bool

(Ord (f p), Ord (g p)) => Ord ((:*:) f g p)

Methods

compare :: (f :*: g) p -> (f :*: g) p -> Ordering

(<) :: (f :*: g) p -> (f :*: g) p -> Bool

(<=) :: (f :*: g) p -> (f :*: g) p -> Bool

(>) :: (f :*: g) p -> (f :*: g) p -> Bool

(>=) :: (f :*: g) p -> (f :*: g) p -> Bool

max :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

min :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

(Read (f p), Read (g p)) => Read ((:*:) f g p)

Methods

readsPrec :: Int -> ReadS ((f :*: g) p)

readList :: ReadS [(f :*: g) p]

readPrec :: ReadPrec ((f :*: g) p)

readListPrec :: ReadPrec [(f :*: g) p]

(Show (f p), Show (g p)) => Show ((:*:) f g p)

Methods

showsPrec :: Int -> (f :*: g) p -> ShowS

show :: (f :*: g) p -> String

showList :: [(f :*: g) p] -> ShowS

Generic ((:*:) f g p)

Associated Types

type Rep ((:*:) f g p) :: * -> *

Methods

from :: (f :*: g) p -> Rep ((f :*: g) p) x

to :: Rep ((f :*: g) p) x -> (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)

Methods

(==) :: (f :.: g) p -> (f :.: g) p -> Bool

(/=) :: (f :.: g) p -> (f :.: g) p -> Bool

Ord (f (g p)) => Ord ((:.:) f g p)

Methods

compare :: (f :.: g) p -> (f :.: g) p -> Ordering

(<) :: (f :.: g) p -> (f :.: g) p -> Bool

(<=) :: (f :.: g) p -> (f :.: g) p -> Bool

(>) :: (f :.: g) p -> (f :.: g) p -> Bool

(>=) :: (f :.: g) p -> (f :.: g) p -> Bool

max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p

min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p

Read (f (g p)) => Read ((:.:) f g p)

Methods

readsPrec :: Int -> ReadS ((f :.: g) p)

readList :: ReadS [(f :.: g) p]

readPrec :: ReadPrec ((f :.: g) p)

readListPrec :: ReadPrec [(f :.: g) p]

Show (f (g p)) => Show ((:.:) f g p)

Methods

showsPrec :: Int -> (f :.: g) p -> ShowS

show :: (f :.: g) p -> String

showList :: [(f :.: g) p] -> ShowS

Generic ((:.:) f g p)

Associated Types

type Rep ((:.:) f g p) :: * -> *

Methods

from :: (f :.: g) p -> Rep ((f :.: g) p) x

to :: Rep ((f :.: g) p) x -> (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

Methods

selName :: t NoSelector f a -> [Char]

data NoSelector

Used for constructor fields without a name

Instances

Selector NoSelector

Methods

selName :: t NoSelector f a -> [Char]

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

Methods

(==) :: Fixity -> Fixity -> Bool

(/=) :: Fixity -> Fixity -> Bool

Ord Fixity

Methods

compare :: Fixity -> Fixity -> Ordering

(<) :: Fixity -> Fixity -> Bool

(<=) :: Fixity -> Fixity -> Bool

(>) :: Fixity -> Fixity -> Bool

(>=) :: Fixity -> Fixity -> Bool

max :: Fixity -> Fixity -> Fixity

min :: Fixity -> Fixity -> Fixity

Read Fixity

Methods

readsPrec :: Int -> ReadS Fixity

readList :: ReadS [Fixity]

readPrec :: ReadPrec Fixity

readListPrec :: ReadPrec [Fixity]

Show Fixity

Methods

showsPrec :: Int -> Fixity -> ShowS

show :: Fixity -> String

showList :: [Fixity] -> ShowS

Generic Fixity

Associated Types

type Rep Fixity :: * -> *

Methods

from :: Fixity -> Rep Fixity x

to :: Rep Fixity x -> Fixity

type Rep Fixity

data Associativity

Datatype to represent the associativity of a constructor

Constructors

LeftAssociative

RightAssociative

NotAssociative

Instances

Eq Associativity

Methods

(==) :: Associativity -> Associativity -> Bool

(/=) :: Associativity -> Associativity -> Bool

Ord Associativity

Methods

compare :: Associativity -> Associativity -> Ordering

(<) :: Associativity -> Associativity -> Bool

(<=) :: Associativity -> Associativity -> Bool

(>) :: Associativity -> Associativity -> Bool

(>=) :: Associativity -> Associativity -> Bool

max :: Associativity -> Associativity -> Associativity

min :: Associativity -> Associativity -> Associativity

Read Associativity

Methods

readsPrec :: Int -> ReadS Associativity

readList :: ReadS [Associativity]

readPrec :: ReadPrec Associativity

readListPrec :: ReadPrec [Associativity]

Show Associativity

Methods

showsPrec :: Int -> Associativity -> ShowS

show :: Associativity -> String

showList :: [Associativity] -> ShowS

Generic Associativity

Associated Types

type Rep Associativity :: * -> *

Methods

from :: Associativity -> Rep Associativity x

to :: Rep Associativity x -> Associativity

type Rep Associativity

data Arity

Datatype to represent the arity of a tuple.

Constructors

NoArity

Arity Int

Instances

Eq Arity

Methods

(==) :: Arity -> Arity -> Bool

(/=) :: Arity -> Arity -> Bool

Ord Arity

Methods

compare :: Arity -> Arity -> Ordering

(<) :: Arity -> Arity -> Bool

(<=) :: Arity -> Arity -> Bool

(>) :: Arity -> Arity -> Bool

(>=) :: Arity -> Arity -> Bool

max :: Arity -> Arity -> Arity

min :: Arity -> Arity -> Arity

Read Arity

Methods

readsPrec :: Int -> ReadS Arity

readList :: ReadS [Arity]

readPrec :: ReadPrec Arity

readListPrec :: ReadPrec [Arity]

Show Arity

Methods

showsPrec :: Int -> Arity -> ShowS

show :: Arity -> String

showList :: [Arity] -> ShowS

Generic Arity

Associated Types

type Rep Arity :: * -> *

Methods

from :: Arity -> Rep Arity x

to :: Rep Arity x -> 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

Associated Types

type Rep Bool :: * -> *

Methods

from :: Bool -> Rep Bool x

to :: Rep Bool x -> Bool

Generic Char

Associated Types

type Rep Char :: * -> *

Methods

from :: Char -> Rep Char x

to :: Rep Char x -> Char

Generic Double

Associated Types

type Rep Double :: * -> *

Methods

from :: Double -> Rep Double x

to :: Rep Double x -> Double

Generic Float

Associated Types

type Rep Float :: * -> *

Methods

from :: Float -> Rep Float x

to :: Rep Float x -> Float

Generic Int

Associated Types

type Rep Int :: * -> *

Methods

from :: Int -> Rep Int x

to :: Rep Int x -> Int

Generic Ordering

Associated Types

type Rep Ordering :: * -> *

Methods

from :: Ordering -> Rep Ordering x

to :: Rep Ordering x -> Ordering

Generic ()

Associated Types

type Rep () :: * -> *

Methods

from :: () -> Rep () x

to :: Rep () x -> ()

Generic Associativity

Associated Types

type Rep Associativity :: * -> *

Methods

from :: Associativity -> Rep Associativity x

to :: Rep Associativity x -> Associativity

Generic Fixity

Associated Types

type Rep Fixity :: * -> *

Methods

from :: Fixity -> Rep Fixity x

to :: Rep Fixity x -> Fixity

Generic Arity

Associated Types

type Rep Arity :: * -> *

Methods

from :: Arity -> Rep Arity x

to :: Rep Arity x -> Arity

Generic Any

Associated Types

type Rep Any :: * -> *

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Generic All

Associated Types

type Rep All :: * -> *

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Generic Void

Associated Types

type Rep Void :: * -> *

Methods

from :: Void -> Rep Void x

to :: Rep Void x -> Void

Generic [a]

Associated Types

type Rep [a] :: * -> *

Methods

from :: [a] -> Rep [a] x

to :: Rep [a] x -> [a]

Generic (U1 p)

Associated Types

type Rep (U1 p) :: * -> *

Methods

from :: U1 p -> Rep (U1 p) x

to :: Rep (U1 p) x -> U1 p

Generic (Par1 p)

Associated Types

type Rep (Par1 p) :: * -> *

Methods

from :: Par1 p -> Rep (Par1 p) x

to :: Rep (Par1 p) x -> Par1 p

Generic (Maybe a)

Associated Types

type Rep (Maybe a) :: * -> *

Methods

from :: Maybe a -> Rep (Maybe a) x

to :: Rep (Maybe a) x -> Maybe a

Generic (Last a)

Associated Types

type Rep (Last a) :: * -> *

Methods

from :: Last a -> Rep (Last a) x

to :: Rep (Last a) x -> Last a

Generic (First a)

Associated Types

type Rep (First a) :: * -> *

Methods

from :: First a -> Rep (First a) x

to :: Rep (First a) x -> First a

Generic (Product a)

Associated Types

type Rep (Product a) :: * -> *

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Generic (Sum a)

Associated Types

type Rep (Sum a) :: * -> *

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

Generic (Endo a)

Associated Types

type Rep (Endo a) :: * -> *

Methods

from :: Endo a -> Rep (Endo a) x

to :: Rep (Endo a) x -> Endo a

Generic (Dual a)

Associated Types

type Rep (Dual a) :: * -> *

Methods

from :: Dual a -> Rep (Dual a) x

to :: Rep (Dual a) x -> Dual a

Generic (ZipList a)

Associated Types

type Rep (ZipList a) :: * -> *

Methods

from :: ZipList a -> Rep (ZipList a) x

to :: Rep (ZipList a) x -> ZipList a

Generic (Identity a)

Associated Types

type Rep (Identity a) :: * -> *

Methods

from :: Identity a -> Rep (Identity a) x

to :: Rep (Identity a) x -> Identity a

Generic (Either a b)

Associated Types

type Rep (Either a b) :: * -> *

Methods

from :: Either a b -> Rep (Either a b) x

to :: Rep (Either a b) x -> Either a b

Generic (Rec1 f p)

Associated Types

type Rep (Rec1 f p) :: * -> *

Methods

from :: Rec1 f p -> Rep (Rec1 f p) x

to :: Rep (Rec1 f p) x -> Rec1 f p

Generic (a, b)

Associated Types

type Rep (a, b) :: * -> *

Methods

from :: (a, b) -> Rep (a, b) x

to :: Rep (a, b) x -> (a, b)

Generic (Proxy * t)

Associated Types

type Rep (Proxy * t) :: * -> *

Methods

from :: Proxy * t -> Rep (Proxy * t) x

to :: Rep (Proxy * t) x -> Proxy * t

Generic (WrappedMonad m a)

Associated Types

type Rep (WrappedMonad m a) :: * -> *

Methods

from :: WrappedMonad m a -> Rep (WrappedMonad m a) x

to :: Rep (WrappedMonad m a) x -> WrappedMonad m a

Generic (Const a b)

Associated Types

type Rep (Const a b) :: * -> *

Methods

from :: Const a b -> Rep (Const a b) x

to :: Rep (Const a b) x -> Const a b

Generic (K1 i c p)

Associated Types

type Rep (K1 i c p) :: * -> *

Methods

from :: K1 i c p -> Rep (K1 i c p) x

to :: Rep (K1 i c p) x -> K1 i c p

Generic ((:+:) f g p)

Associated Types

type Rep ((:+:) f g p) :: * -> *

Methods

from :: (f :+: g) p -> Rep ((f :+: g) p) x

to :: Rep ((f :+: g) p) x -> (f :+: g) p

Generic ((:*:) f g p)

Associated Types

type Rep ((:*:) f g p) :: * -> *

Methods

from :: (f :*: g) p -> Rep ((f :*: g) p) x

to :: Rep ((f :*: g) p) x -> (f :*: g) p

Generic ((:.:) f g p)

Associated Types

type Rep ((:.:) f g p) :: * -> *

Methods

from :: (f :.: g) p -> Rep ((f :.: g) p) x

to :: Rep ((f :.: g) p) x -> (f :.: g) p

Generic (a, b, c)

Associated Types

type Rep (a, b, c) :: * -> *

Methods

from :: (a, b, c) -> Rep (a, b, c) x

to :: Rep (a, b, c) x -> (a, b, c)

Generic (Alt k f a)

Associated Types

type Rep (Alt k f a) :: * -> *

Methods

from :: Alt k f a -> Rep (Alt k f a) x

to :: Rep (Alt k f a) x -> Alt k f a

Generic (WrappedArrow a b c)

Associated Types

type Rep (WrappedArrow a b c) :: * -> *

Methods

from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x

to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c

Generic (M1 i c f p)

Associated Types

type Rep (M1 i c f p) :: * -> *

Methods

from :: M1 i c f p -> Rep (M1 i c f p) x

to :: Rep (M1 i c f p) x -> M1 i c f p

Generic (a, b, c, d)

Associated Types

type Rep (a, b, c, d) :: * -> *

Methods

from :: (a, b, c, d) -> Rep (a, b, c, d) x

to :: Rep (a, b, c, d) x -> (a, b, c, d)

Generic (a, b, c, d, e)

Associated Types

type Rep (a, b, c, d, e) :: * -> *

Methods

from :: (a, b, c, d, e) -> Rep (a, b, c, d, e) x

to :: Rep (a, b, c, d, e) x -> (a, b, c, d, e)

Generic (a, b, c, d, e, f)

Associated Types

type Rep (a, b, c, d, e, f) :: * -> *

Methods

from :: (a, b, c, d, e, f) -> Rep (a, b, c, d, e, f) x

to :: Rep (a, b, c, d, e, f) x -> (a, b, c, d, e, f)

Generic (a, b, c, d, e, f, g)

Associated Types

type Rep (a, b, c, d, e, f, g) :: * -> *

Methods

from :: (a, b, c, d, e, f, g) -> Rep (a, b, c, d, e, f, g) x

to :: Rep (a, b, c, d, e, f, g) x -> (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 []

Associated Types

type Rep1 ([] :: * -> *) :: * -> *

Methods

from1 :: [a] -> Rep1 [] a

to1 :: Rep1 [] a -> [a]

Generic1 Maybe

Associated Types

type Rep1 (Maybe :: * -> *) :: * -> *

Methods

from1 :: Maybe a -> Rep1 Maybe a

to1 :: Rep1 Maybe a -> Maybe a

Generic1 Last

Associated Types

type Rep1 (Last :: * -> *) :: * -> *

Methods

from1 :: Last a -> Rep1 Last a

to1 :: Rep1 Last a -> Last a

Generic1 First

Associated Types

type Rep1 (First :: * -> *) :: * -> *

Methods

from1 :: First a -> Rep1 First a

to1 :: Rep1 First a -> First a

Generic1 Product

Associated Types

type Rep1 (Product :: * -> *) :: * -> *

Methods

from1 :: Product a -> Rep1 Product a

to1 :: Rep1 Product a -> Product a

Generic1 Sum

Associated Types

type Rep1 (Sum :: * -> *) :: * -> *

Methods

from1 :: Sum a -> Rep1 Sum a

to1 :: Rep1 Sum a -> Sum a

Generic1 Dual

Associated Types

type Rep1 (Dual :: * -> *) :: * -> *

Methods

from1 :: Dual a -> Rep1 Dual a

to1 :: Rep1 Dual a -> Dual a

Generic1 ZipList

Associated Types

type Rep1 (ZipList :: * -> *) :: * -> *

Methods

from1 :: ZipList a -> Rep1 ZipList a

to1 :: Rep1 ZipList a -> ZipList a

Generic1 Identity

Associated Types

type Rep1 (Identity :: * -> *) :: * -> *

Methods

from1 :: Identity a -> Rep1 Identity a

to1 :: Rep1 Identity a -> Identity a

Generic1 (Either a)

Associated Types

type Rep1 (Either a :: * -> *) :: * -> *

Methods

from1 :: Either a b -> Rep1 (Either a) b

to1 :: Rep1 (Either a) b -> Either a b

Generic1 ((,) a)

Associated Types

type Rep1 ((,) a :: * -> *) :: * -> *

Methods

from1 :: (a, b) -> Rep1 ((,) a) b

to1 :: Rep1 ((,) a) b -> (a, b)

Generic1 (WrappedMonad m)

Associated Types

type Rep1 (WrappedMonad m :: * -> *) :: * -> *

Methods

from1 :: WrappedMonad m a -> Rep1 (WrappedMonad m) a

to1 :: Rep1 (WrappedMonad m) a -> WrappedMonad m a

Generic1 (Const a)

Associated Types

type Rep1 (Const a :: * -> *) :: * -> *

Methods

from1 :: Const a b -> Rep1 (Const a) b

to1 :: Rep1 (Const a) b -> Const a b

Generic1 ((,,) a b)

Associated Types

type Rep1 ((,,) a b :: * -> *) :: * -> *

Methods

from1 :: (a, b, c) -> Rep1 ((,,) a b) c

to1 :: Rep1 ((,,) a b) c -> (a, b, c)

Generic1 (Alt * f)

Associated Types

type Rep1 (Alt * f :: * -> *) :: * -> *

Methods

from1 :: Alt * f a -> Rep1 (Alt * f) a

to1 :: Rep1 (Alt * f) a -> Alt * f a

Generic1 (WrappedArrow a b)

Associated Types

type Rep1 (WrappedArrow a b :: * -> *) :: * -> *

Methods

from1 :: WrappedArrow a b c -> Rep1 (WrappedArrow a b) c

to1 :: Rep1 (WrappedArrow a b) c -> WrappedArrow a b c

Generic1 ((,,,) a b c)

Associated Types

type Rep1 ((,,,) a b c :: * -> *) :: * -> *

Methods

from1 :: (a, b, c, d) -> Rep1 ((,,,) a b c) d

to1 :: Rep1 ((,,,) a b c) d -> (a, b, c, d)

Generic1 ((,,,,) a b c d)

Associated Types

type Rep1 ((,,,,) a b c d :: * -> *) :: * -> *

Methods

from1 :: (a, b, c, d, e) -> Rep1 ((,,,,) a b c d) e

to1 :: Rep1 ((,,,,) a b c d) e -> (a, b, c, d, e)

Generic1 ((,,,,,) a b c d e)

Associated Types

type Rep1 ((,,,,,) a b c d e :: * -> *) :: * -> *

Methods

from1 :: (a, b, c, d, e, f) -> Rep1 ((,,,,,) a b c d e) f

to1 :: Rep1 ((,,,,,) a b c d e) f -> (a, b, c, d, e, f)

Generic1 ((,,,,,,) a b c d e f)

Associated Types

type Rep1 ((,,,,,,) a b c d e f :: * -> *) :: * -> *

Methods

from1 :: (a, b, c, d, e, f, g) -> Rep1 ((,,,,,,) a b c d e f) g

to1 :: Rep1 ((,,,,,,) a b c d e f) g -> (a, b, c, d, e, f, g)