Copyright	(C) 2013 Richard Eisenberg
License	BSD-style (see LICENSE)
Maintainer	Ryan Scott
Stability	experimental
Portability	non-portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Singletons.Decide

Contents

The SDecide class
Supporting definitions
Orphan instances

Description

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

Synopsis

class SDecide k where
- (%~) :: forall (a :: k) (b :: k). Sing a -> Sing b -> Decision (a :~: b)
data (a :: k) :~: (b :: k) where
- Refl :: forall {k} (a :: k). a :~: a
data Void
type Refuted a = a -> Void
data Decision a
- = Proved a
- | Disproved (Refuted a)
decideEquality :: forall k (a :: k) (b :: k). SDecide k => Sing a -> Sing b -> Maybe (a :~: b)
decideCoercion :: forall k (a :: k) (b :: k). SDecide k => Sing a -> Sing b -> Maybe (Coercion a b)

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.

Methods

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

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

Supporting definitions

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

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

Instances details

TestCoercion ((:~:) a :: k -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Coercion Methods testCoercion :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (Coercion a0 b) Source #
TestEquality ((:~:) a :: k -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods testEquality :: forall (a0 :: k0) (b :: k0). (a :~: a0) -> (a :~: b) -> Maybe (a0 :~: b) Source #
a ~ b => Bounded (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods minBound :: a :~: b Source # maxBound :: a :~: b Source #
a ~ b => Enum (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods succ :: (a :~: b) -> a :~: b Source # pred :: (a :~: b) -> a :~: b Source # toEnum :: Int -> a :~: b Source # fromEnum :: (a :~: b) -> Int Source # enumFrom :: (a :~: b) -> [a :~: b] Source # enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] Source # enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] Source # enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] Source #
a ~ b => Read (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods readsPrec :: Int -> ReadS (a :~: b) Source # readList :: ReadS [a :~: b] Source # readPrec :: ReadPrec (a :~: b) Source # readListPrec :: ReadPrec [a :~: b] Source #
Show (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods showsPrec :: Int -> (a :~: b) -> ShowS Source # show :: (a :~: b) -> String Source # showList :: [a :~: b] -> ShowS Source #
Eq (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods (==) :: (a :~: b) -> (a :~: b) -> Bool Source # (/=) :: (a :~: b) -> (a :~: b) -> Bool Source #
Ord (a :~: b)	Since: base-4.7.0.0
Instance details Defined in Data.Type.Equality Methods compare :: (a :~: b) -> (a :~: b) -> Ordering Source # (<) :: (a :~: b) -> (a :~: b) -> Bool Source # (<=) :: (a :~: b) -> (a :~: b) -> Bool Source # (>) :: (a :~: b) -> (a :~: b) -> Bool Source # (>=) :: (a :~: b) -> (a :~: b) -> Bool Source # max :: (a :~: b) -> (a :~: b) -> a :~: b Source # min :: (a :~: b) -> (a :~: b) -> a :~: b Source #

data Void Source #

Uninhabited data type

Since: base-4.8.0.0

Instances

Instances details

Data Void	Since: base-4.8.0.0
Instance details 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 Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Void Source # toConstr :: Void -> Constr Source # dataTypeOf :: Void -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Void) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Void) Source # gmapT :: (forall b. Data b => b -> b) -> Void -> Void Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Void -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Void -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Void -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Void -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Void -> m Void Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Void -> m Void Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Void -> m Void Source #
Semigroup Void	Since: base-4.9.0.0
Instance details Defined in Data.Void Methods (<>) :: Void -> Void -> Void Source # sconcat :: NonEmpty Void -> Void Source # stimes :: Integral b => b -> Void -> Void Source #
Exception Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods toException :: Void -> SomeException Source # fromException :: SomeException -> Maybe Void Source # displayException :: Void -> String Source #
Generic Void
Instance details Defined in Data.Void Associated Types type Rep Void :: Type -> Type Source # Methods from :: Void -> Rep Void x Source # to :: Rep Void x -> Void Source #
Ix Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods range :: (Void, Void) -> [Void] Source # index :: (Void, Void) -> Void -> Int Source # unsafeIndex :: (Void, Void) -> Void -> Int Source # inRange :: (Void, Void) -> Void -> Bool Source # rangeSize :: (Void, Void) -> Int Source # unsafeRangeSize :: (Void, Void) -> Int Source #
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
Instance details Defined in Data.Void Methods readsPrec :: Int -> ReadS Void Source # readList :: ReadS [Void] Source # readPrec :: ReadPrec Void Source # readListPrec :: ReadPrec [Void] Source #
Show Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods showsPrec :: Int -> Void -> ShowS Source # show :: Void -> String Source # showList :: [Void] -> ShowS Source #
Eq Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods (==) :: Void -> Void -> Bool Source # (/=) :: Void -> Void -> Bool Source #
Ord Void	Since: base-4.8.0.0
Instance details Defined in Data.Void Methods compare :: Void -> Void -> Ordering Source # (<) :: Void -> Void -> Bool Source # (<=) :: Void -> Void -> Bool Source # (>) :: Void -> Void -> Bool Source # (>=) :: Void -> Void -> Bool Source # max :: Void -> Void -> Void Source # min :: Void -> Void -> Void Source #
type Rep Void	Since: base-4.8.0.0
Instance details Defined in Data.Void type Rep Void = D1 ('MetaData "Void" "Data.Void" "base" 'False) (V1 :: Type -> Type)

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

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

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) Source #

A suitable default implementation for testCoercion that leverages SDecide.

Orphan instances

SDecide k => TestCoercion (WrappedSing :: k -> Type) Source #
Instance details Methods testCoercion :: forall (a :: k0) (b :: k0). WrappedSing a -> WrappedSing b -> Maybe (Coercion a b) Source #
SDecide k => TestEquality (WrappedSing :: k -> Type) Source #
Instance details Methods testEquality :: forall (a :: k0) (b :: k0). WrappedSing a -> WrappedSing b -> Maybe (a :~: b) Source #