Data.Singletons.Decide

Defines the class SDecide, allowing for decidable equality over singletons.

The SDecide class

class SDecide k where

Members of the SDecide "kind" class support decidable equality. Instances of this class are generated alongside singleton definitions for datatypes that derive an Eq instance.

Methods

(%~) :: forall (a :: k) (b :: k). Sing a -> Sing b -> Decision (a :~: b) infix 4

Compute a proof or disproof of equality, given two singletons.

Supporting definitions

data (a :: k) :~: (b :: k) where infix 4

Propositional equality. If a :~: b is inhabited by some terminating value, then the type a is the same as the type b. To use this equality in practice, pattern-match on the a :~: b to get out the Refl constructor; in the body of the pattern-match, the compiler knows that a ~ b.

Since: base-4.7.0.0

Constructors

Refl :: forall k (a :: k). a :~: a

Instances

TestCoercion ((:~:) a :: k -> Type)

Since: base-4.7.0.0

Defined in Data.Type.Coercion

Methods

testCoercion :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (Coercion a0 b)

TestEquality ((:~:) a :: k -> Type)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

testEquality :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (a0 :~: b)

a ~ b => Bounded (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

minBound :: a :~: b

maxBound :: a :~: b

a ~ b => Enum (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

succ :: (a :~: b) -> a :~: b

pred :: (a :~: b) -> a :~: b

toEnum :: Int -> a :~: b

fromEnum :: (a :~: b) -> Int

enumFrom :: (a :~: b) -> [a :~: b]

enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b]

enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b]

enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b]

Eq (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

(==) :: (a :~: b) -> (a :~: b) -> Bool

(/=) :: (a :~: b) -> (a :~: b) -> Bool

Ord (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

compare :: (a :~: b) -> (a :~: b) -> Ordering

(<) :: (a :~: b) -> (a :~: b) -> Bool

(<=) :: (a :~: b) -> (a :~: b) -> Bool

(>) :: (a :~: b) -> (a :~: b) -> Bool

(>=) :: (a :~: b) -> (a :~: b) -> Bool

max :: (a :~: b) -> (a :~: b) -> a :~: b

min :: (a :~: b) -> (a :~: b) -> a :~: b

a ~ b => Read (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

readsPrec :: Int -> ReadS (a :~: b)

readList :: ReadS [a :~: b]

readPrec :: ReadPrec (a :~: b)

readListPrec :: ReadPrec [a :~: b]

Show (a :~: b)

Since: base-4.7.0.0

Defined in Data.Type.Equality

Methods

showsPrec :: Int -> (a :~: b) -> ShowS

show :: (a :~: b) -> String

showList :: [a :~: b] -> ShowS

data Void

Uninhabited data type

Since: base-4.8.0.0

Instances

Eq Void

Since: base-4.8.0.0

Defined in Data.Void

Methods

(==) :: Void -> Void -> Bool

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

Data Void

Since: base-4.8.0.0

Defined in Data.Void

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Void -> c Void

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Void

toConstr :: Void -> Constr

dataTypeOf :: Void -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Void)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Void)

gmapT :: (forall b. Data b => b -> b) -> Void -> Void

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Void -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Void -> r

gmapQ :: (forall d. Data d => d -> u) -> Void -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Void -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Void -> m Void

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Void -> m Void

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Void -> m Void

Ord Void

Since: base-4.8.0.0

Defined in Data.Void

Methods

compare :: Void -> Void -> Ordering

(<) :: Void -> Void -> Bool

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

(>) :: Void -> Void -> Bool

(>=) :: Void -> Void -> Bool

max :: Void -> Void -> Void

min :: Void -> Void -> Void

Read Void

Reading a Void value is always a parse error, considering Void as a data type with no constructors.

Since: base-4.8.0.0

Defined in Data.Void

Methods

readsPrec :: Int -> ReadS Void

readList :: ReadS [Void]

readPrec :: ReadPrec Void

readListPrec :: ReadPrec [Void]

Show Void

Since: base-4.8.0.0

Defined in Data.Void

Methods

showsPrec :: Int -> Void -> ShowS

show :: Void -> String

showList :: [Void] -> ShowS

Ix Void

Since: base-4.8.0.0

Defined in Data.Void

Methods

range :: (Void, Void) -> [Void]

index :: (Void, Void) -> Void -> Int

unsafeIndex :: (Void, Void) -> Void -> Int

inRange :: (Void, Void) -> Void -> Bool

rangeSize :: (Void, Void) -> Int

unsafeRangeSize :: (Void, Void) -> Int

Generic Void

Since: base-4.8.0.0

Defined in Data.Void

Associated Types

type Rep Void :: Type -> Type

Methods

from :: Void -> Rep Void x

to :: Rep Void x -> Void

Semigroup Void

Since: base-4.9.0.0

Defined in Data.Void

Methods

(<>) :: Void -> Void -> Void

sconcat :: NonEmpty Void -> Void

stimes :: Integral b => b -> Void -> Void

Exception Void

Since: base-4.8.0.0

Defined in Data.Void

Methods

toException :: Void -> SomeException

fromException :: SomeException -> Maybe Void

displayException :: Void -> String

type Rep Void

Defined in Data.Void

type Rep Void = D1 ('MetaData "Void" "Data.Void" "base" 'False) (V1 :: Type -> Type)

type Refuted a = a -> Void

Because we can never create a value of type Void, a function that type-checks at a -> Void shows that objects of type a can never exist. Thus, we say that a is Refuted

data Decision a

A Decision about a type a is either a proof of existence or a proof that a cannot exist.

Constructors

Proved a

Witness for a

Disproved (Refuted a)

Proof that no a exists

decideEquality :: forall k (a :: k) (b :: k). SDecide k => Sing a -> Sing b -> Maybe (a :~: b)

A suitable default implementation for testEquality that leverages SDecide.

decideCoercion :: forall k (a :: k) (b :: k). SDecide k => Sing a -> Sing b -> Maybe (Coercion a b)

A suitable default implementation for testCoercion that leverages SDecide.

Orphan instances

SDecide k => TestCoercion (WrappedSing :: k -> Type)

Methods

testCoercion :: forall (a :: k0) (b :: k0). WrappedSing a -> WrappedSing b -> Maybe (Coercion a b)

SDecide k => TestEquality (WrappedSing :: k -> Type)

Methods

testEquality :: forall (a :: k0) (b :: k0). WrappedSing a -> WrappedSing b -> Maybe (a :~: b)