Generics.POSable.POSable

Exports the POSable class, which has a generic implementation GPOSable. Also re-exports Generic.SOP, which is needed to derive POSable.

Documentation

class KnownNat (Choices x) => POSable x where

POSable, the base of this library. Provide a compact memory representation for a type and a function to get back to the original type. This memory representation consist of choices, that represent all constructor choices in the type in a single Finite integer, and fields which represents all values in the type as a Product of Sums, which can be mapped to a struct-of-arrays representation for use in array-based languages like Accelerate.

Minimal complete definition

Nothing

Associated Types

type Choices x :: Nat

type Choices x = GChoices (SOP I (Code x))

type Fields x :: [[Type]]

type Fields x = GFields (SOP I (Code x))

Methods

choices :: x -> Finite (Choices x)

default choices :: (Generic x, GPOSable (SOP I (Code x)), GChoices (SOP I (Code x)) ~ Choices x) => x -> Finite (Choices x)

tags :: [Integer]

The tags function returns the range of each constructor. A few examples: >>> tags Bool [1,1] >>> tags (Either Float Float) [1,1] >>> tags (Bool, Bool) [4] >>> tags (Either Bool Bool) [2,2]

default tags :: GPOSable (SOP I (Code x)) => [Integer]

fromPOSable :: Finite (Choices x) -> Product (Fields x) -> x

default fromPOSable :: (Generic x, GPOSable (SOP I (Code x)), Fields x ~ GFields (SOP I (Code x)), Choices x ~ GChoices (SOP I (Code x))) => Finite (Choices x) -> Product (Fields x) -> x

fields :: x -> Product (Fields x)

default fields :: (Generic x, Fields x ~ GFields (SOP I (Code x)), GPOSable (SOP I (Code x))) => x -> Product (Fields x)

emptyFields :: ProductType (Fields x)

default emptyFields :: (GPOSable (SOP I (Code x)), Fields x ~ GFields (SOP I (Code x))) => ProductType (Fields x)

Instances

POSable Bool

Defined in Generics.POSable.Instances

Associated Types

type Choices Bool :: Nat

type Fields Bool :: [[Type]]

Methods

choices :: Bool -> Finite (Choices Bool)

tags :: [Integer]

fromPOSable :: Finite (Choices Bool) -> Product (Fields Bool) -> Bool

fields :: Bool -> Product (Fields Bool)

emptyFields :: ProductType (Fields Bool)

POSable Double

Defined in Examples

Associated Types

type Choices Double :: Nat

type Fields Double :: [[Type]]

Methods

choices :: Double -> Finite (Choices Double)

tags :: [Integer]

fromPOSable :: Finite (Choices Double) -> Product (Fields Double) -> Double

fields :: Double -> Product (Fields Double)

emptyFields :: ProductType (Fields Double)

POSable Float

Defined in Examples

Associated Types

type Choices Float :: Nat

type Fields Float :: [[Type]]

Methods

choices :: Float -> Finite (Choices Float)

tags :: [Integer]

fromPOSable :: Finite (Choices Float) -> Product (Fields Float) -> Float

fields :: Float -> Product (Fields Float)

emptyFields :: ProductType (Fields Float)

POSable Ordering

Defined in Generics.POSable.Instances

Associated Types

type Choices Ordering :: Nat

type Fields Ordering :: [[Type]]

Methods

choices :: Ordering -> Finite (Choices Ordering)

tags :: [Integer]

fromPOSable :: Finite (Choices Ordering) -> Product (Fields Ordering) -> Ordering

fields :: Ordering -> Product (Fields Ordering)

emptyFields :: ProductType (Fields Ordering)

POSable ()

Defined in Generics.POSable.Instances

Associated Types

type Choices () :: Nat

type Fields () :: [[Type]]

Methods

choices :: () -> Finite (Choices ())

tags :: [Integer]

fromPOSable :: Finite (Choices ()) -> Product (Fields ()) -> ()

fields :: () -> Product (Fields ())

emptyFields :: ProductType (Fields ())

POSable Undef

Defined in Generics.POSable.Instances

Associated Types

type Choices Undef :: Nat

type Fields Undef :: [[Type]]

Methods

choices :: Undef -> Finite (Choices Undef)

tags :: [Integer]

fromPOSable :: Finite (Choices Undef) -> Product (Fields Undef) -> Undef

fields :: Undef -> Product (Fields Undef)

emptyFields :: ProductType (Fields Undef)

POSable x => POSable (Maybe x)

Defined in Generics.POSable.Instances

Associated Types

type Choices (Maybe x) :: Nat

type Fields (Maybe x) :: [[Type]]

Methods

choices :: Maybe x -> Finite (Choices (Maybe x))

tags :: [Integer]

fromPOSable :: Finite (Choices (Maybe x)) -> Product (Fields (Maybe x)) -> Maybe x

fields :: Maybe x -> Product (Fields (Maybe x))

emptyFields :: ProductType (Fields (Maybe x))

(POSable l, POSable r) => POSable (Either l r)

Defined in Generics.POSable.Instances

Associated Types

type Choices (Either l r) :: Nat

type Fields (Either l r) :: [[Type]]

Methods

choices :: Either l r -> Finite (Choices (Either l r))

tags :: [Integer]

fromPOSable :: Finite (Choices (Either l r)) -> Product (Fields (Either l r)) -> Either l r

fields :: Either l r -> Product (Fields (Either l r))

emptyFields :: ProductType (Fields (Either l r))

(POSable x0, POSable x1) => POSable (x0, x1)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1) :: Nat

type Fields (x0, x1) :: [[Type]]

Methods

choices :: (x0, x1) -> Finite (Choices (x0, x1))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1)) -> Product (Fields (x0, x1)) -> (x0, x1)

fields :: (x0, x1) -> Product (Fields (x0, x1))

emptyFields :: ProductType (Fields (x0, x1))

(POSable x0, POSable x1, POSable x2) => POSable (x0, x1, x2)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2) :: Nat

type Fields (x0, x1, x2) :: [[Type]]

Methods

choices :: (x0, x1, x2) -> Finite (Choices (x0, x1, x2))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2)) -> Product (Fields (x0, x1, x2)) -> (x0, x1, x2)

fields :: (x0, x1, x2) -> Product (Fields (x0, x1, x2))

emptyFields :: ProductType (Fields (x0, x1, x2))

(POSable x0, POSable x1, POSable x2, POSable x3) => POSable (x0, x1, x2, x3)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3) :: Nat

type Fields (x0, x1, x2, x3) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3) -> Finite (Choices (x0, x1, x2, x3))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3)) -> Product (Fields (x0, x1, x2, x3)) -> (x0, x1, x2, x3)

fields :: (x0, x1, x2, x3) -> Product (Fields (x0, x1, x2, x3))

emptyFields :: ProductType (Fields (x0, x1, x2, x3))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4) => POSable (x0, x1, x2, x3, x4)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4) :: Nat

type Fields (x0, x1, x2, x3, x4) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4) -> Finite (Choices (x0, x1, x2, x3, x4))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4)) -> Product (Fields (x0, x1, x2, x3, x4)) -> (x0, x1, x2, x3, x4)

fields :: (x0, x1, x2, x3, x4) -> Product (Fields (x0, x1, x2, x3, x4))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5) => POSable (x0, x1, x2, x3, x4, x5)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5) :: Nat

type Fields (x0, x1, x2, x3, x4, x5) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5) -> Finite (Choices (x0, x1, x2, x3, x4, x5))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5)) -> Product (Fields (x0, x1, x2, x3, x4, x5)) -> (x0, x1, x2, x3, x4, x5)

fields :: (x0, x1, x2, x3, x4, x5) -> Product (Fields (x0, x1, x2, x3, x4, x5))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6) => POSable (x0, x1, x2, x3, x4, x5, x6)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6)) -> (x0, x1, x2, x3, x4, x5, x6)

fields :: (x0, x1, x2, x3, x4, x5, x6) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7) => POSable (x0, x1, x2, x3, x4, x5, x6, x7)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7)) -> (x0, x1, x2, x3, x4, x5, x6, x7)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8, POSable x9) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8, POSable x9, POSable x10) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8, POSable x9, POSable x10, POSable x11) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8, POSable x9, POSable x10, POSable x11, POSable x12) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8, POSable x9, POSable x10, POSable x11, POSable x12, POSable x13) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8, POSable x9, POSable x10, POSable x11, POSable x12, POSable x13, POSable x14) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14))

(POSable x0, POSable x1, POSable x2, POSable x3, POSable x4, POSable x5, POSable x6, POSable x7, POSable x8, POSable x9, POSable x10, POSable x11, POSable x12, POSable x13, POSable x14, POSable x15) => POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)

Defined in Generics.POSable.Instances

Associated Types

type Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) :: Nat

type Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) :: [[Type]]

Methods

choices :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15))

tags :: [Integer]

fromPOSable :: Finite (Choices (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) -> (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)

fields :: (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15) -> Product (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15))

emptyFields :: ProductType (Fields (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15))

class All (SListI :: [Type] -> Constraint) (Code a) => Generic a

The class of representable datatypes.

The SOP approach to generic programming is based on viewing datatypes as a representation (Rep) built from the sum of products of its components. The components of a datatype are specified using the Code type family.

The isomorphism between the original Haskell datatype and its representation is witnessed by the methods of this class, from and to. So for instances of this class, the following laws should (in general) hold:

to . from === id :: a -> a
from . to === id :: Rep a -> Rep a

You typically don't define instances of this class by hand, but rather derive the class instance automatically.

Option 1: Derive via the built-in GHC-generics. For this, you need to use the DeriveGeneric extension to first derive an instance of the Generic class from module GHC.Generics. With this, you can then give an empty instance for Generic, and the default definitions will just work. The pattern looks as follows:

import qualified GHC.Generics as GHC
import Generics.SOP

...

data T = ... deriving (GHC.Generic, ...)

instance Generic T -- empty
instance HasDatatypeInfo T -- empty, if you want/need metadata

Option 2: Derive via Template Haskell. For this, you need to enable the TemplateHaskell extension. You can then use deriveGeneric from module Generics.SOP.TH to have the instance generated for you. The pattern looks as follows:

import Generics.SOP
import Generics.SOP.TH

...

data T = ...

deriveGeneric ''T -- derives HasDatatypeInfo as well

Tradeoffs: Whether to use Option 1 or 2 is mainly a matter of personal taste. The version based on Template Haskell probably has less run-time overhead.

Non-standard instances: It is possible to give Generic instances manually that deviate from the standard scheme, as long as at least

to . from === id :: a -> a

still holds.

Instances

Generic Undef

Defined in Generics.POSable.Representation

Associated Types

type Code Undef :: [[Type]]

Methods

from :: Undef -> Rep Undef

to :: Rep Undef -> Undef

data Finite (n :: Nat)

Finite number type. Finite n is inhabited by exactly n values. Invariants:

getFinite x < natVal x

getFinite x >= 0

Instances

KnownNat n => Bounded (Finite n)

Throws an error for Finite 0

Defined in Data.Finite.Internal

Methods

minBound :: Finite n

maxBound :: Finite n

KnownNat n => Enum (Finite n)

Defined in Data.Finite.Internal

Methods

succ :: Finite n -> Finite n

pred :: Finite n -> Finite n

toEnum :: Int -> Finite n

fromEnum :: Finite n -> Int

enumFrom :: Finite n -> [Finite n]

enumFromThen :: Finite n -> Finite n -> [Finite n]

enumFromTo :: Finite n -> Finite n -> [Finite n]

enumFromThenTo :: Finite n -> Finite n -> Finite n -> [Finite n]

Eq (Finite n)

Defined in Data.Finite.Internal

Methods

(==) :: Finite n -> Finite n -> Bool

(/=) :: Finite n -> Finite n -> Bool

KnownNat n => Integral (Finite n)

Not modular arithmetic.

Defined in Data.Finite.Internal

Methods

quot :: Finite n -> Finite n -> Finite n

rem :: Finite n -> Finite n -> Finite n

div :: Finite n -> Finite n -> Finite n

mod :: Finite n -> Finite n -> Finite n

quotRem :: Finite n -> Finite n -> (Finite n, Finite n)

divMod :: Finite n -> Finite n -> (Finite n, Finite n)

toInteger :: Finite n -> Integer

KnownNat n => Num (Finite n)

Modular arithmetic. Only the fromInteger function is supposed to be useful.

Defined in Data.Finite.Internal

Methods

(+) :: Finite n -> Finite n -> Finite n

(-) :: Finite n -> Finite n -> Finite n

(*) :: Finite n -> Finite n -> Finite n

negate :: Finite n -> Finite n

abs :: Finite n -> Finite n

signum :: Finite n -> Finite n

fromInteger :: Integer -> Finite n

Ord (Finite n)

Defined in Data.Finite.Internal

Methods

compare :: Finite n -> Finite n -> Ordering

(<) :: Finite n -> Finite n -> Bool

(<=) :: Finite n -> Finite n -> Bool

(>) :: Finite n -> Finite n -> Bool

(>=) :: Finite n -> Finite n -> Bool

max :: Finite n -> Finite n -> Finite n

min :: Finite n -> Finite n -> Finite n

KnownNat n => Read (Finite n)

Defined in Data.Finite.Internal

Methods

readsPrec :: Int -> ReadS (Finite n)

readList :: ReadS [Finite n]

readPrec :: ReadPrec (Finite n)

readListPrec :: ReadPrec [Finite n]

KnownNat n => Real (Finite n)

Defined in Data.Finite.Internal

Methods

toRational :: Finite n -> Rational

Show (Finite n)

Defined in Data.Finite.Internal

Methods

showsPrec :: Int -> Finite n -> ShowS

show :: Finite n -> String

showList :: [Finite n] -> ShowS

Generic (Finite n)

Defined in Data.Finite.Internal

Associated Types

type Rep (Finite n) :: Type -> Type

Methods

from :: Finite n -> Rep (Finite n) x

to :: Rep (Finite n) x -> Finite n

NFData (Finite n)

Defined in Data.Finite.Internal

Methods

rnf :: Finite n -> ()

type Rep (Finite n)

Defined in Data.Finite.Internal

type Rep (Finite n) = D1 ('MetaData "Finite" "Data.Finite.Internal" "finite-typelits-0.1.4.2-5H6I7DpI5LO7unHaqoEAep" 'True) (C1 ('MetaCons "Finite" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Integer)))