singletons-2.3.1: A framework for generating singleton types

Copyright(C) 2013 Richard Eisenberg
LicenseBSD-style (see LICENSE)
MaintainerRichard Eisenberg (rae@cs.brynmawr.edu)
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Singletons.Decide

Contents

Description

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

Synopsis

The SDecide class

class SDecide k where Source #

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.

Minimal complete definition

(%~)

Methods

(%~) :: forall (a :: k) (b :: k). Sing a -> Sing b -> Decision (a :~: b) Source #

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

Supporting definitions

data (k :~: (a :: k)) (b :: k) :: forall k. k -> 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: 4.7.0.0

Constructors

Refl :: (:~:) k a a 

Instances

TestCoercion k ((:~:) k a)

Since: 4.7.0.0

Methods

testCoercion :: f a -> f b -> Maybe (Coercion (k :~: a) a b) #

TestEquality k ((:~:) k a)

Since: 4.7.0.0

Methods

testEquality :: f a -> f b -> Maybe (((k :~: a) :~: a) b) #

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

Since: 4.7.0.0

Methods

minBound :: (k :~: a) b #

maxBound :: (k :~: a) b #

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

Since: 4.7.0.0

Methods

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

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

toEnum :: Int -> (k :~: a) b #

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

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

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

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

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

Eq ((:~:) k a b) 

Methods

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

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

((~) * a b, Data a) => Data ((:~:) * a b)

Since: 4.7.0.0

Methods

gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> (* :~: a) b -> c ((* :~: a) b) #

gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ((* :~: a) b) #

toConstr :: (* :~: a) b -> Constr #

dataTypeOf :: (* :~: a) b -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c ((* :~: a) b)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ((* :~: a) b)) #

gmapT :: (forall c. Data c => c -> c) -> (* :~: a) b -> (* :~: a) b #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (* :~: a) b -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (* :~: a) b -> r #

gmapQ :: (forall d. Data d => d -> u) -> (* :~: a) b -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> (* :~: a) b -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> (* :~: a) b -> m ((* :~: a) b) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (* :~: a) b -> m ((* :~: a) b) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (* :~: a) b -> m ((* :~: a) b) #

Ord ((:~:) k a b) 

Methods

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

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

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

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

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

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

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

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

Since: 4.7.0.0

Methods

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

readList :: ReadS [(k :~: a) b] #

readPrec :: ReadPrec ((k :~: a) b) #

readListPrec :: ReadPrec [(k :~: a) b] #

Show ((:~:) k a b) 

Methods

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

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

showList :: [(k :~: a) b] -> ShowS #

data Void :: * #

Uninhabited data type

Since: 4.8.0.0

Instances

Eq Void

Since: 4.8.0.0

Methods

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

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

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 :: (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: 4.8.0.0

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 4.8.0.0

Show Void

Since: 4.8.0.0

Methods

showsPrec :: Int -> Void -> ShowS #

show :: Void -> String #

showList :: [Void] -> ShowS #

Ix Void

Since: 4.8.0.0

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 

Associated Types

type Rep Void :: * -> * #

Methods

from :: Void -> Rep Void x #

to :: Rep Void x -> Void #

Semigroup Void

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty Void -> Void #

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

Exception Void

Since: 4.8.0.0

type Rep Void 
type Rep Void = D1 * (MetaData "Void" "Data.Void" "base" False) (V1 *)

type Refuted a = a -> Void Source #

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 Source #

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

Orphan instances

SDecide k3 => TestEquality k3 (Sing k3) Source # 

Methods

testEquality :: f a -> f b -> Maybe ((Sing k3 :~: a) b) #