singletons-2.6: A framework for generating singleton types
Copyright(C) 2013 Richard Eisenberg
LicenseBSD-style (see LICENSE)
MaintainerRyan Scott
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Singletons.TH

Description

This module contains everything you need to derive your own singletons via Template Haskell.

TURN ON -XScopedTypeVariables IN YOUR MODULE IF YOU WANT THIS TO WORK.

Synopsis

Primary Template Haskell generation functions

singletons :: DsMonad q => q [Dec] -> q [Dec] Source #

Make promoted and singleton versions of all declarations given, retaining the original declarations. See https://github.com/goldfirere/singletons/blob/master/README.md for further explanation.

singletonsOnly :: DsMonad q => q [Dec] -> q [Dec] Source #

Make promoted and singleton versions of all declarations given, discarding the original declarations. Note that a singleton based on a datatype needs the original datatype, so this will fail if it sees any datatype declarations. Classes, instances, and functions are all fine.

genSingletons :: DsMonad q => [Name] -> q [Dec] Source #

Generate singleton definitions from a type that is already defined. For example, the singletons package itself uses

$(genSingletons [''Bool, ''Maybe, ''Either, ''[]])

to generate singletons for Prelude types.

promote :: DsMonad q => q [Dec] -> q [Dec] Source #

Promote every declaration given to the type level, retaining the originals.

promoteOnly :: DsMonad q => q [Dec] -> q [Dec] Source #

Promote each declaration, discarding the originals. Note that a promoted datatype uses the same definition as an original datatype, so this will not work with datatypes. Classes, instances, and functions are all fine.

genPromotions :: DsMonad q => [Name] -> q [Dec] Source #

Generate promoted definitions from a type that is already defined. This is generally only useful with classes.

Functions to generate equality instances

promoteEqInstances :: DsMonad q => [Name] -> q [Dec] Source #

Produce instances for (==) (type-level equality) from the given types

promoteEqInstance :: DsMonad q => Name -> q [Dec] Source #

Produce an instance for (==) (type-level equality) from the given type

singEqInstances :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of SEq and type-level (==) for each type in the list

singEqInstance :: DsMonad q => Name -> q [Dec] Source #

Create instance of SEq and type-level (==) for the given type

singEqInstancesOnly :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of SEq (only -- no instance for (==), which SEq generally relies on) for each type in the list

singEqInstanceOnly :: DsMonad q => Name -> q [Dec] Source #

Create instances of SEq (only -- no instance for (==), which SEq generally relies on) for the given type

singDecideInstances :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of SDecide, TestEquality, and TestCoercion for each type in the list.

singDecideInstance :: DsMonad q => Name -> q [Dec] Source #

Create instance of SDecide, TestEquality, and TestCoercion for the given type.

Functions to generate Ord instances

promoteOrdInstances :: DsMonad q => [Name] -> q [Dec] Source #

Produce instances for POrd from the given types

promoteOrdInstance :: DsMonad q => Name -> q [Dec] Source #

Produce an instance for POrd from the given type

singOrdInstances :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of SOrd for the given types

singOrdInstance :: DsMonad q => Name -> q [Dec] Source #

Create instance of SOrd for the given type

Functions to generate Bounded instances

promoteBoundedInstances :: DsMonad q => [Name] -> q [Dec] Source #

Produce instances for PBounded from the given types

promoteBoundedInstance :: DsMonad q => Name -> q [Dec] Source #

Produce an instance for PBounded from the given type

singBoundedInstances :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of SBounded for the given types

singBoundedInstance :: DsMonad q => Name -> q [Dec] Source #

Create instance of SBounded for the given type

Functions to generate Enum instances

promoteEnumInstances :: DsMonad q => [Name] -> q [Dec] Source #

Produce instances for PEnum from the given types

promoteEnumInstance :: DsMonad q => Name -> q [Dec] Source #

Produce an instance for PEnum from the given type

singEnumInstances :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of SEnum for the given types

singEnumInstance :: DsMonad q => Name -> q [Dec] Source #

Create instance of SEnum for the given type

Functions to generate Show instances

promoteShowInstances :: DsMonad q => [Name] -> q [Dec] Source #

Produce instances for PShow from the given types

promoteShowInstance :: DsMonad q => Name -> q [Dec] Source #

Produce an instance for PShow from the given type

singShowInstances :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of SShow for the given types

(Not to be confused with showSingInstances.)

singShowInstance :: DsMonad q => Name -> q [Dec] Source #

Create instance of SShow for the given type

(Not to be confused with showShowInstance.)

showSingInstances :: DsMonad q => [Name] -> q [Dec] Source #

Create instances of Show for the given singleton types

(Not to be confused with singShowInstances.)

showSingInstance :: DsMonad q => Name -> q [Dec] Source #

Create instance of Show for the given singleton type

(Not to be confused with singShowInstance.)

Utility functions

singITyConInstances :: DsMonad q => [Int] -> q [Dec] Source #

Create an instance for SingI TyCon{N}, where N is the positive number provided as an argument.

Note that the generated code requires the use of the QuantifiedConstraints language extension.

singITyConInstance :: DsMonad q => Int -> q [Dec] Source #

Create an instance for SingI TyCon{N}, where N is the positive number provided as an argument.

Note that the generated code requires the use of the QuantifiedConstraints language extension.

cases Source #

Arguments

:: DsMonad q 
=> Name

The head of the type of the scrutinee. (Like ''Maybe or ''Bool.)

-> q Exp

The scrutinee, in a Template Haskell quote

-> q Exp

The body, in a Template Haskell quote

-> q Exp 

The function cases generates a case expression where each right-hand side is identical. This may be useful if the type-checker requires knowledge of which constructor is used to satisfy equality or type-class constraints, but where each constructor is treated the same.

sCases Source #

Arguments

:: DsMonad q 
=> Name

The head of the type the scrutinee's type is based on. (Like ''Maybe or ''Bool.)

-> q Exp

The scrutinee, in a Template Haskell quote

-> q Exp

The body, in a Template Haskell quote

-> q Exp 

The function sCases generates a case expression where each right-hand side is identical. This may be useful if the type-checker requires knowledge of which constructor is used to satisfy equality or type-class constraints, but where each constructor is treated the same. For sCases, unlike cases, the scrutinee is a singleton. But make sure to pass in the name of the original datatype, preferring ''Maybe over ''SMaybe.

Basic singleton definitions

data SBool :: Bool -> Type where Source #

Constructors

SFalse :: SBool 'False 
STrue :: SBool 'True 

Instances

Instances details
TestCoercion SBool Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (Coercion a b) #

TestEquality SBool Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a :: k) (b :: k). SBool a -> SBool b -> Maybe (a :~: b) #

Show (SBool z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SBool z -> ShowS #

show :: SBool z -> String #

showList :: [SBool z] -> ShowS #

data STuple0 :: () -> Type where Source #

Constructors

STuple0 :: STuple0 '() 

Instances

Instances details
TestCoercion STuple0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a :: k) (b :: k). STuple0 a -> STuple0 b -> Maybe (Coercion a b) #

TestEquality STuple0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a :: k) (b :: k). STuple0 a -> STuple0 b -> Maybe (a :~: b) #

Show (STuple0 z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> STuple0 z -> ShowS #

show :: STuple0 z -> String #

showList :: [STuple0 z] -> ShowS #

data STuple2 :: forall a b. (a, b) -> Type where Source #

Constructors

STuple2 :: forall a b (n :: a) (n :: b). (Sing (n :: a)) -> (Sing (n :: b)) -> STuple2 '(n, n) 

Instances

Instances details
(SDecide a, SDecide b) => TestCoercion (STuple2 :: (a, b) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a0 :: k) (b0 :: k). STuple2 a0 -> STuple2 b0 -> Maybe (Coercion a0 b0) #

(SDecide a, SDecide b) => TestEquality (STuple2 :: (a, b) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a0 :: k) (b0 :: k). STuple2 a0 -> STuple2 b0 -> Maybe (a0 :~: b0) #

(ShowSing a, ShowSing b) => Show (STuple2 z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> STuple2 z -> ShowS #

show :: STuple2 z -> String #

showList :: [STuple2 z] -> ShowS #

data STuple3 :: forall a b c. (a, b, c) -> Type where Source #

Constructors

STuple3 :: forall a b c (n :: a) (n :: b) (n :: c). (Sing (n :: a)) -> (Sing (n :: b)) -> (Sing (n :: c)) -> STuple3 '(n, n, n) 

Instances

Instances details
(SDecide a, SDecide b, SDecide c) => TestCoercion (STuple3 :: (a, b, c) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a0 :: k) (b0 :: k). STuple3 a0 -> STuple3 b0 -> Maybe (Coercion a0 b0) #

(SDecide a, SDecide b, SDecide c) => TestEquality (STuple3 :: (a, b, c) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a0 :: k) (b0 :: k). STuple3 a0 -> STuple3 b0 -> Maybe (a0 :~: b0) #

(ShowSing a, ShowSing b, ShowSing c) => Show (STuple3 z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> STuple3 z -> ShowS #

show :: STuple3 z -> String #

showList :: [STuple3 z] -> ShowS #

data STuple4 :: forall a b c d. (a, b, c, d) -> Type where Source #

Constructors

STuple4 :: forall a b c d (n :: a) (n :: b) (n :: c) (n :: d). (Sing (n :: a)) -> (Sing (n :: b)) -> (Sing (n :: c)) -> (Sing (n :: d)) -> STuple4 '(n, n, n, n) 

Instances

Instances details
(SDecide a, SDecide b, SDecide c, SDecide d) => TestCoercion (STuple4 :: (a, b, c, d) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a0 :: k) (b0 :: k). STuple4 a0 -> STuple4 b0 -> Maybe (Coercion a0 b0) #

(SDecide a, SDecide b, SDecide c, SDecide d) => TestEquality (STuple4 :: (a, b, c, d) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a0 :: k) (b0 :: k). STuple4 a0 -> STuple4 b0 -> Maybe (a0 :~: b0) #

(ShowSing a, ShowSing b, ShowSing c, ShowSing d) => Show (STuple4 z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> STuple4 z -> ShowS #

show :: STuple4 z -> String #

showList :: [STuple4 z] -> ShowS #

data STuple5 :: forall a b c d e. (a, b, c, d, e) -> Type where Source #

Constructors

STuple5 :: forall a b c d e (n :: a) (n :: b) (n :: c) (n :: d) (n :: e). (Sing (n :: a)) -> (Sing (n :: b)) -> (Sing (n :: c)) -> (Sing (n :: d)) -> (Sing (n :: e)) -> STuple5 '(n, n, n, n, n) 

Instances

Instances details
(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e) => TestCoercion (STuple5 :: (a, b, c, d, e) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a0 :: k) (b0 :: k). STuple5 a0 -> STuple5 b0 -> Maybe (Coercion a0 b0) #

(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e) => TestEquality (STuple5 :: (a, b, c, d, e) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a0 :: k) (b0 :: k). STuple5 a0 -> STuple5 b0 -> Maybe (a0 :~: b0) #

(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e) => Show (STuple5 z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> STuple5 z -> ShowS #

show :: STuple5 z -> String #

showList :: [STuple5 z] -> ShowS #

data STuple6 :: forall a b c d e f. (a, b, c, d, e, f) -> Type where Source #

Constructors

STuple6 :: forall a b c d e f (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f). (Sing (n :: a)) -> (Sing (n :: b)) -> (Sing (n :: c)) -> (Sing (n :: d)) -> (Sing (n :: e)) -> (Sing (n :: f)) -> STuple6 '(n, n, n, n, n, n) 

Instances

Instances details
(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e, SDecide f) => TestCoercion (STuple6 :: (a, b, c, d, e, f) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a0 :: k) (b0 :: k). STuple6 a0 -> STuple6 b0 -> Maybe (Coercion a0 b0) #

(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e, SDecide f) => TestEquality (STuple6 :: (a, b, c, d, e, f) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a0 :: k) (b0 :: k). STuple6 a0 -> STuple6 b0 -> Maybe (a0 :~: b0) #

(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f) => Show (STuple6 z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> STuple6 z -> ShowS #

show :: STuple6 z -> String #

showList :: [STuple6 z] -> ShowS #

data STuple7 :: forall a b c d e f g. (a, b, c, d, e, f, g) -> Type where Source #

Constructors

STuple7 :: forall a b c d e f g (n :: a) (n :: b) (n :: c) (n :: d) (n :: e) (n :: f) (n :: g). (Sing (n :: a)) -> (Sing (n :: b)) -> (Sing (n :: c)) -> (Sing (n :: d)) -> (Sing (n :: e)) -> (Sing (n :: f)) -> (Sing (n :: g)) -> STuple7 '(n, n, n, n, n, n, n) 

Instances

Instances details
(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e, SDecide f, SDecide g) => TestCoercion (STuple7 :: (a, b, c, d, e, f, g) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a0 :: k) (b0 :: k). STuple7 a0 -> STuple7 b0 -> Maybe (Coercion a0 b0) #

(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e, SDecide f, SDecide g) => TestEquality (STuple7 :: (a, b, c, d, e, f, g) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a0 :: k) (b0 :: k). STuple7 a0 -> STuple7 b0 -> Maybe (a0 :~: b0) #

(ShowSing a, ShowSing b, ShowSing c, ShowSing d, ShowSing e, ShowSing f, ShowSing g) => Show (STuple7 z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> STuple7 z -> ShowS #

show :: STuple7 z -> String #

showList :: [STuple7 z] -> ShowS #

data SOrdering :: Ordering -> Type where Source #

Constructors

SLT :: SOrdering 'LT 
SEQ :: SOrdering 'EQ 
SGT :: SOrdering 'GT 

Instances

Instances details
TestCoercion SOrdering Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a :: k) (b :: k). SOrdering a -> SOrdering b -> Maybe (Coercion a b) #

TestEquality SOrdering Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a :: k) (b :: k). SOrdering a -> SOrdering b -> Maybe (a :~: b) #

Show (SOrdering z) Source # 
Instance details

Defined in Data.Singletons.ShowSing

Auxiliary definitions

These definitions might be mentioned in code generated by Template Haskell, so they must be in scope.

class PEq a Source #

The promoted analogue of Eq. If you supply no definition for (==), then it defaults to a use of DefaultEq.

Associated Types

type (x :: a) == (y :: a) :: Bool infix 4 Source #

type (==) (x :: a) (y :: a) = x `DefaultEq` y Source #

type (x :: a) /= (y :: a) :: Bool infix 4 Source #

type (/=) (x :: a) (y :: a) = Not (x == y) Source #

Instances

Instances details
PEq Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq () Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq All Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq Any Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq [a] Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Maybe a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (TYPE rep) Source # 
Instance details

Defined in Data.Singletons.TypeRepTYPE

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (WrappedMonoid m) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Option a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Identity a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Dual a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Sum a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Product a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Down a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (NonEmpty a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Either a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (a, b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Arg a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (a, b, c) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (Const a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (a, b, c, d) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (a, b, c, d, e) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

PEq (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

type family If (cond :: Bool) (tru :: k) (fls :: k) :: k where ... #

Type-level If. If True a b ==> a; If False a b ==> b

Equations

If 'True (tru :: k) (fls :: k) = tru 
If 'False (tru :: k) (fls :: k) = fls 

sIf :: Sing a -> Sing b -> Sing c -> Sing (If a b c) Source #

Conditional over singletons

type family (a :: Bool) && (b :: Bool) :: Bool where ... infixr 3 #

Type-level "and"

Equations

'False && a = 'False 
'True && a = a 
a && 'False = 'False 
a && 'True = a 
a && a = a 

(%&&) :: Sing a -> Sing b -> Sing (a && b) infixr 3 Source #

Conjunction of singletons

class SEq k where Source #

The singleton analogue of Eq. Unlike the definition for Eq, it is required that instances define a body for (%==). You may also supply a body for (%/=).

Minimal complete definition

(%==)

Methods

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

Boolean equality on singletons

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

Boolean disequality on singletons

default (%/=) :: forall (a :: k) (b :: k). (a /= b) ~ Not (a == b) => Sing a -> Sing b -> Sing (a /= b) Source #

Instances

Instances details
SEq Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a :: Bool) (b :: Bool). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: Bool) (b :: Bool). Sing a -> Sing b -> Sing (a /= b) Source #

SEq Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a :: Ordering) (b :: Ordering). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: Ordering) (b :: Ordering). Sing a -> Sing b -> Sing (a /= b) Source #

SEq Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

(%==) :: forall (a :: Nat) (b :: Nat). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: Nat) (b :: Nat). Sing a -> Sing b -> Sing (a /= b) Source #

SEq Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

(%==) :: forall (a :: Symbol) (b :: Symbol). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: Symbol) (b :: Symbol). Sing a -> Sing b -> Sing (a /= b) Source #

SEq () Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a :: ()) (b :: ()). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: ()) (b :: ()). Sing a -> Sing b -> Sing (a /= b) Source #

SEq Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a :: Void) (b :: Void). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: Void) (b :: Void). Sing a -> Sing b -> Sing (a /= b) Source #

SEq Bool => SEq All Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a :: All) (b :: All). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: All) (b :: All). Sing a -> Sing b -> Sing (a /= b) Source #

SEq Bool => SEq Any Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a :: Any) (b :: Any). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: Any) (b :: Any). Sing a -> Sing b -> Sing (a /= b) Source #

(SEq a, SEq [a]) => SEq [a] Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: [a]) (b :: [a]). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: [a]) (b :: [a]). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Maybe a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: Maybe a) (b :: Maybe a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Maybe a) (b :: Maybe a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq (TYPE rep) Source # 
Instance details

Defined in Data.Singletons.TypeRepTYPE

Methods

(%==) :: forall (a :: TYPE rep) (b :: TYPE rep). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: TYPE rep) (b :: TYPE rep). Sing a -> Sing b -> Sing (a /= b) Source #

SEq a => SEq (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: Min a) (b :: Min a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Min a) (b :: Min a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: Max a) (b :: Max a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Max a) (b :: Max a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: First a) (b :: First a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: First a) (b :: First a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: Last a) (b :: Last a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Last a) (b :: Last a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq m => SEq (WrappedMonoid m) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a :: WrappedMonoid m) (b :: WrappedMonoid m). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: WrappedMonoid m) (b :: WrappedMonoid m). Sing a -> Sing b -> Sing (a /= b) Source #

SEq (Maybe a) => SEq (Option a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: Option a) (b :: Option a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Option a) (b :: Option a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Identity a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: Identity a) (b :: Identity a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Identity a) (b :: Identity a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq (Maybe a) => SEq (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Methods

(%==) :: forall (a0 :: First a) (b :: First a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: First a) (b :: First a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq (Maybe a) => SEq (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Methods

(%==) :: forall (a0 :: Last a) (b :: Last a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Last a) (b :: Last a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Dual a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: Dual a) (b :: Dual a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Dual a) (b :: Dual a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Sum a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: Sum a) (b :: Sum a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Sum a) (b :: Sum a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Product a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%==) :: forall (a0 :: Product a) (b :: Product a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Product a) (b :: Product a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

SEq a => SEq (Down a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

(%==) :: forall (a0 :: Down a) (b :: Down a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: Down a) (b :: Down a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

(SEq a, SEq [a]) => SEq (NonEmpty a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: NonEmpty a) (b :: NonEmpty a). Sing a0 -> Sing b -> Sing (a0 == b) Source #

(%/=) :: forall (a0 :: NonEmpty a) (b :: NonEmpty a). Sing a0 -> Sing b -> Sing (a0 /= b) Source #

(SEq a, SEq b) => SEq (Either a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: Either a b) (b0 :: Either a b). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: Either a b) (b0 :: Either a b). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

(SEq a, SEq b) => SEq (a, b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: (a, b)) (b0 :: (a, b)). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: (a, b)) (b0 :: (a, b)). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

SEq a => SEq (Arg a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

Methods

(%==) :: forall (a0 :: Arg a b) (b0 :: Arg a b). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: Arg a b) (b0 :: Arg a b). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

(SEq a, SEq b, SEq c) => SEq (a, b, c) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: (a, b, c)) (b0 :: (a, b, c)). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: (a, b, c)) (b0 :: (a, b, c)). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

SEq a => SEq (Const a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

Methods

(%==) :: forall (a0 :: Const a b) (b0 :: Const a b). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: Const a b) (b0 :: Const a b). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

(SEq a, SEq b, SEq c, SEq d) => SEq (a, b, c, d) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: (a, b, c, d)) (b0 :: (a, b, c, d)). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: (a, b, c, d)) (b0 :: (a, b, c, d)). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

(SEq a, SEq b, SEq c, SEq d, SEq e) => SEq (a, b, c, d, e) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: (a, b, c, d, e)) (b0 :: (a, b, c, d, e)). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: (a, b, c, d, e)) (b0 :: (a, b, c, d, e)). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

(SEq a, SEq b, SEq c, SEq d, SEq e, SEq f) => SEq (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: (a, b, c, d, e, f)) (b0 :: (a, b, c, d, e, f)). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: (a, b, c, d, e, f)) (b0 :: (a, b, c, d, e, f)). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

(SEq a, SEq b, SEq c, SEq d, SEq e, SEq f, SEq g) => SEq (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a0 :: (a, b, c, d, e, f, g)) (b0 :: (a, b, c, d, e, f, g)). Sing a0 -> Sing b0 -> Sing (a0 == b0) Source #

(%/=) :: forall (a0 :: (a, b, c, d, e, f, g)) (b0 :: (a, b, c, d, e, f, g)). Sing a0 -> Sing b0 -> Sing (a0 /= b0) Source #

class POrd (a :: Type) Source #

Associated Types

type Compare (arg :: a) (arg :: a) :: Ordering Source #

type Compare a a = Apply (Apply Compare_6989586621679394057Sym0 a) a Source #

type (arg :: a) < (arg :: a) :: Bool infix 4 Source #

type (<) a a = Apply (Apply TFHelper_6989586621679394081Sym0 a) a Source #

type (arg :: a) <= (arg :: a) :: Bool infix 4 Source #

type (<=) a a = Apply (Apply TFHelper_6989586621679394099Sym0 a) a Source #

type (arg :: a) > (arg :: a) :: Bool infix 4 Source #

type (>) a a = Apply (Apply TFHelper_6989586621679394117Sym0 a) a Source #

type (arg :: a) >= (arg :: a) :: Bool infix 4 Source #

type (>=) a a = Apply (Apply TFHelper_6989586621679394135Sym0 a) a Source #

type Max (arg :: a) (arg :: a) :: a Source #

type Max a a = Apply (Apply Max_6989586621679394153Sym0 a) a Source #

type Min (arg :: a) (arg :: a) :: a Source #

type Min a a = Apply (Apply Min_6989586621679394171Sym0 a) a Source #

Instances

Instances details
POrd Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd () Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd All Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd Any Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd [a] Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Maybe a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (WrappedMonoid m) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Option a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Identity a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Dual a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Sum a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Product a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Down a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (NonEmpty a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Either a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (a, b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Arg a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (a, b, c) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (Const a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (a, b, c, d) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (a, b, c, d, e) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

POrd (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

class SEq a => SOrd a where Source #

Minimal complete definition

Nothing

Methods

sCompare :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t :: Ordering) Source #

default sCompare :: forall (t :: a) (t :: a). (Apply (Apply CompareSym0 t) t :: Ordering) ~ Apply (Apply Compare_6989586621679394057Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t :: Ordering) Source #

(%<) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t :: Bool) infix 4 Source #

default (%<) :: forall (t :: a) (t :: a). (Apply (Apply (<@#@$) t) t :: Bool) ~ Apply (Apply TFHelper_6989586621679394081Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t :: Bool) Source #

(%<=) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t :: Bool) infix 4 Source #

default (%<=) :: forall (t :: a) (t :: a). (Apply (Apply (<=@#@$) t) t :: Bool) ~ Apply (Apply TFHelper_6989586621679394099Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t :: Bool) Source #

(%>) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t :: Bool) infix 4 Source #

default (%>) :: forall (t :: a) (t :: a). (Apply (Apply (>@#@$) t) t :: Bool) ~ Apply (Apply TFHelper_6989586621679394117Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t :: Bool) Source #

(%>=) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t :: Bool) infix 4 Source #

default (%>=) :: forall (t :: a) (t :: a). (Apply (Apply (>=@#@$) t) t :: Bool) ~ Apply (Apply TFHelper_6989586621679394135Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t :: Bool) Source #

sMax :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t :: a) Source #

default sMax :: forall (t :: a) (t :: a). (Apply (Apply MaxSym0 t) t :: a) ~ Apply (Apply Max_6989586621679394153Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t :: a) Source #

sMin :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t :: a) Source #

default sMin :: forall (t :: a) (t :: a). (Apply (Apply MinSym0 t) t :: a) ~ Apply (Apply Min_6989586621679394171Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t :: a) Source #

Instances

Instances details
SOrd Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Bool) (t :: Bool). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sCompare :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sCompare :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd () Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: ()) (t :: ()). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: ()) (t :: ()). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: ()) (t :: ()). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: ()) (t :: ()). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: ()) (t :: ()). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: ()) (t :: ()). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: ()) (t :: ()). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd Bool => SOrd All Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: All) (t :: All). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: All) (t :: All). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: All) (t :: All). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: All) (t :: All). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: All) (t :: All). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: All) (t :: All). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: All) (t :: All). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd Bool => SOrd Any Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Any) (t :: Any). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Any) (t :: Any). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Any) (t :: Any). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Any) (t :: Any). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Any) (t :: Any). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Any) (t :: Any). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Any) (t :: Any). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd [a]) => SOrd [a] Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: [a]) (t :: [a]). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Maybe a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Maybe a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Maybe a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Maybe a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Maybe a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Maybe a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Maybe a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Maybe a) (t :: Maybe a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Min a) (t :: Min a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Min a) (t :: Min a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Min a) (t :: Min a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Min a) (t :: Min a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Min a) (t :: Min a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Min a) (t :: Min a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Min a) (t :: Min a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Max a) (t :: Max a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Max a) (t :: Max a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Max a) (t :: Max a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Max a) (t :: Max a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Max a) (t :: Max a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Max a) (t :: Max a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Max a) (t :: Max a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd m => SOrd (WrappedMonoid m) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: WrappedMonoid m) (t :: WrappedMonoid m). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: WrappedMonoid m) (t :: WrappedMonoid m). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: WrappedMonoid m) (t :: WrappedMonoid m). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: WrappedMonoid m) (t :: WrappedMonoid m). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: WrappedMonoid m) (t :: WrappedMonoid m). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: WrappedMonoid m) (t :: WrappedMonoid m). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: WrappedMonoid m) (t :: WrappedMonoid m). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd (Maybe a) => SOrd (Option a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Option a) (t :: Option a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Option a) (t :: Option a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Option a) (t :: Option a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Option a) (t :: Option a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Option a) (t :: Option a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Option a) (t :: Option a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Option a) (t :: Option a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Identity a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Identity a) (t :: Identity a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd (Maybe a) => SOrd (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Methods

sCompare :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: First a) (t :: First a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd (Maybe a) => SOrd (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Methods

sCompare :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Last a) (t :: Last a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Dual a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Dual a) (t :: Dual a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Dual a) (t :: Dual a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Dual a) (t :: Dual a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Dual a) (t :: Dual a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Dual a) (t :: Dual a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Dual a) (t :: Dual a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Dual a) (t :: Dual a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Sum a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Sum a) (t :: Sum a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Sum a) (t :: Sum a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Sum a) (t :: Sum a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Sum a) (t :: Sum a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Sum a) (t :: Sum a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Sum a) (t :: Sum a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Sum a) (t :: Sum a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Product a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

sCompare :: forall (t :: Product a) (t :: Product a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Product a) (t :: Product a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Product a) (t :: Product a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Product a) (t :: Product a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Product a) (t :: Product a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Product a) (t :: Product a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Product a) (t :: Product a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Down a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Down a) (t :: Down a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Down a) (t :: Down a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Down a) (t :: Down a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Down a) (t :: Down a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Down a) (t :: Down a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Down a) (t :: Down a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Down a) (t :: Down a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd [a]) => SOrd (NonEmpty a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: NonEmpty a) (t :: NonEmpty a). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: NonEmpty a) (t :: NonEmpty a). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: NonEmpty a) (t :: NonEmpty a). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: NonEmpty a) (t :: NonEmpty a). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: NonEmpty a) (t :: NonEmpty a). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: NonEmpty a) (t :: NonEmpty a). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: NonEmpty a) (t :: NonEmpty a). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd b) => SOrd (Either a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Either a b) (t :: Either a b). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Either a b) (t :: Either a b). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Either a b) (t :: Either a b). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Either a b) (t :: Either a b). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Either a b) (t :: Either a b). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Either a b) (t :: Either a b). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Either a b) (t :: Either a b). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd b) => SOrd (a, b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: (a, b)) (t :: (a, b)). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: (a, b)) (t :: (a, b)). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: (a, b)) (t :: (a, b)). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: (a, b)) (t :: (a, b)). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: (a, b)) (t :: (a, b)). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: (a, b)) (t :: (a, b)). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: (a, b)) (t :: (a, b)). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Arg a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

Methods

sCompare :: forall (t :: Arg a b) (t :: Arg a b). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Arg a b) (t :: Arg a b). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Arg a b) (t :: Arg a b). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Arg a b) (t :: Arg a b). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Arg a b) (t :: Arg a b). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Arg a b) (t :: Arg a b). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Arg a b) (t :: Arg a b). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd b, SOrd c) => SOrd (a, b, c) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: (a, b, c)) (t :: (a, b, c)). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: (a, b, c)) (t :: (a, b, c)). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: (a, b, c)) (t :: (a, b, c)). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: (a, b, c)) (t :: (a, b, c)). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: (a, b, c)) (t :: (a, b, c)). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: (a, b, c)) (t :: (a, b, c)). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: (a, b, c)) (t :: (a, b, c)). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

SOrd a => SOrd (Const a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

Methods

sCompare :: forall (t :: Const a b) (t :: Const a b). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Const a b) (t :: Const a b). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Const a b) (t :: Const a b). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Const a b) (t :: Const a b). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Const a b) (t :: Const a b). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Const a b) (t :: Const a b). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Const a b) (t :: Const a b). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd b, SOrd c, SOrd d) => SOrd (a, b, c, d) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: (a, b, c, d)) (t :: (a, b, c, d)). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: (a, b, c, d)) (t :: (a, b, c, d)). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: (a, b, c, d)) (t :: (a, b, c, d)). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: (a, b, c, d)) (t :: (a, b, c, d)). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: (a, b, c, d)) (t :: (a, b, c, d)). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: (a, b, c, d)) (t :: (a, b, c, d)). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: (a, b, c, d)) (t :: (a, b, c, d)). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd b, SOrd c, SOrd d, SOrd e) => SOrd (a, b, c, d, e) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: (a, b, c, d, e)) (t :: (a, b, c, d, e)). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: (a, b, c, d, e)) (t :: (a, b, c, d, e)). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: (a, b, c, d, e)) (t :: (a, b, c, d, e)). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: (a, b, c, d, e)) (t :: (a, b, c, d, e)). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: (a, b, c, d, e)) (t :: (a, b, c, d, e)). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: (a, b, c, d, e)) (t :: (a, b, c, d, e)). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: (a, b, c, d, e)) (t :: (a, b, c, d, e)). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd b, SOrd c, SOrd d, SOrd e, SOrd f) => SOrd (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: (a, b, c, d, e, f)) (t :: (a, b, c, d, e, f)). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: (a, b, c, d, e, f)) (t :: (a, b, c, d, e, f)). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: (a, b, c, d, e, f)) (t :: (a, b, c, d, e, f)). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: (a, b, c, d, e, f)) (t :: (a, b, c, d, e, f)). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: (a, b, c, d, e, f)) (t :: (a, b, c, d, e, f)). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: (a, b, c, d, e, f)) (t :: (a, b, c, d, e, f)). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: (a, b, c, d, e, f)) (t :: (a, b, c, d, e, f)). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

(SOrd a, SOrd b, SOrd c, SOrd d, SOrd e, SOrd f, SOrd g) => SOrd (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: (a, b, c, d, e, f, g)) (t :: (a, b, c, d, e, f, g)). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: (a, b, c, d, e, f, g)) (t :: (a, b, c, d, e, f, g)). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: (a, b, c, d, e, f, g)) (t :: (a, b, c, d, e, f, g)). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: (a, b, c, d, e, f, g)) (t :: (a, b, c, d, e, f, g)). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: (a, b, c, d, e, f, g)) (t :: (a, b, c, d, e, f, g)). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: (a, b, c, d, e, f, g)) (t :: (a, b, c, d, e, f, g)). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: (a, b, c, d, e, f, g)) (t :: (a, b, c, d, e, f, g)). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

type family ThenCmp (a :: Ordering) (a :: Ordering) :: Ordering where ... Source #

Equations

ThenCmp 'EQ x = x 
ThenCmp 'LT _ = LTSym0 
ThenCmp 'GT _ = GTSym0 

sThenCmp :: forall (t :: Ordering) (t :: Ordering). Sing t -> Sing t -> Sing (Apply (Apply ThenCmpSym0 t) t :: Ordering) Source #

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.

Instances

Instances details
SDecide Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

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

SDecide Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

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

SDecide Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

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

SDecide Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

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

SDecide () Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

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

SDecide Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

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

SDecide Bool => SDecide All Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

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

SDecide Bool => SDecide Any Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

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

(SDecide a, SDecide [a]) => SDecide [a] Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: [a]) (b :: [a]). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Maybe a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: Maybe a) (b :: Maybe a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide (TYPE rep) Source # 
Instance details

Defined in Data.Singletons.TypeRepTYPE

Methods

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

SDecide a => SDecide (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: Min a) (b :: Min a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: Max a) (b :: Max a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: First a) (b :: First a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: Last a) (b :: Last a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide m => SDecide (WrappedMonoid m) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

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

SDecide (Maybe a) => SDecide (Option a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: Option a) (b :: Option a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Identity a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: Identity a) (b :: Identity a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide (Maybe a) => SDecide (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Methods

(%~) :: forall (a0 :: First a) (b :: First a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide (Maybe a) => SDecide (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Methods

(%~) :: forall (a0 :: Last a) (b :: Last a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Dual a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: Dual a) (b :: Dual a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Sum a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: Sum a) (b :: Sum a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Product a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%~) :: forall (a0 :: Product a) (b :: Product a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

SDecide a => SDecide (Down a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

(%~) :: forall (a0 :: Down a) (b :: Down a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

(SDecide a, SDecide [a]) => SDecide (NonEmpty a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: NonEmpty a) (b :: NonEmpty a). Sing a0 -> Sing b -> Decision (a0 :~: b) Source #

(SDecide a, SDecide b) => SDecide (Either a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: Either a b) (b0 :: Either a b). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

(SDecide a, SDecide b) => SDecide (a, b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: (a, b)) (b0 :: (a, b)). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

(SDecide a, SDecide b, SDecide c) => SDecide (a, b, c) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: (a, b, c)) (b0 :: (a, b, c)). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

SDecide a => SDecide (Const a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

Methods

(%~) :: forall (a0 :: Const a b) (b0 :: Const a b). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

(SDecide a, SDecide b, SDecide c, SDecide d) => SDecide (a, b, c, d) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: (a, b, c, d)) (b0 :: (a, b, c, d)). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e) => SDecide (a, b, c, d, e) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: (a, b, c, d, e)) (b0 :: (a, b, c, d, e)). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e, SDecide f) => SDecide (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: (a, b, c, d, e, f)) (b0 :: (a, b, c, d, e, f)). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

(SDecide a, SDecide b, SDecide c, SDecide d, SDecide e, SDecide f, SDecide g) => SDecide (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

(%~) :: forall (a0 :: (a, b, c, d, e, f, g)) (b0 :: (a, b, c, d, e, f, g)). Sing a0 -> Sing b0 -> Decision (a0 :~: b0) Source #

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

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) #

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) #

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

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

minBound :: a :~: b #

maxBound :: a :~: b #

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

Since: base-4.7.0.0

Instance details

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

Instance details

Defined in Data.Type.Equality

Methods

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

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

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

Since: base-4.7.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> (a :~: b) -> c (a :~: b) #

gunfold :: (forall b0 r. Data b0 => c (b0 -> 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 b0. Data b0 => b0 -> b0) -> (a :~: b) -> a :~: b #

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

gmapQr :: forall r r'. (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 (a :~: b)

Since: base-4.7.0.0

Instance details

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

Instance details

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

Instance details

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

Instances details
Eq Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Methods

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

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

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 #

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

Instance details

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

Instance details

Defined in Data.Void

Show Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Methods

showsPrec :: Int -> Void -> ShowS #

show :: Void -> String #

showList :: [Void] -> ShowS #

Ix Void

Since: base-4.8.0.0

Instance details

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

Instance details

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

Instance details

Defined in Data.Void

Methods

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

sconcat :: NonEmpty Void -> Void #

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

Lift Void

Since: template-haskell-2.15.0.0

Instance details

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Void -> Q Exp #

Exception Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

SingKind Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Associated Types

type Demote Void = (r :: Type) Source #

Methods

fromSing :: forall (a :: Void). Sing a -> Demote Void Source #

toSing :: Demote Void -> SomeSing Void Source #

SDecide Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

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

PEq Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool Source #

SEq Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

Methods

(%==) :: forall (a :: Void) (b :: Void). Sing a -> Sing b -> Sing (a == b) Source #

(%/=) :: forall (a :: Void) (b :: Void). Sing a -> Sing b -> Sing (a /= b) Source #

SOrd Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Methods

sCompare :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply CompareSym0 t) t) Source #

(%<) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (<@#@$) t) t) Source #

(%<=) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (<=@#@$) t) t) Source #

(%>) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (>@#@$) t) t) Source #

(%>=) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (>=@#@$) t) t) Source #

sMax :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply MaxSym0 t) t) Source #

sMin :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply MinSym0 t) t) Source #

POrd Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

Associated Types

type Compare arg arg :: Ordering Source #

type arg < arg :: Bool Source #

type arg <= arg :: Bool Source #

type arg > arg :: Bool Source #

type arg >= arg :: Bool Source #

type Max arg arg :: a Source #

type Min arg arg :: a Source #

SSemigroup Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

(%<>) :: forall (t :: Void) (t :: Void). Sing t -> Sing t -> Sing (Apply (Apply (<>@#@$) t) t) Source #

sSconcat :: forall (t :: NonEmpty Void). Sing t -> Sing (Apply SconcatSym0 t) Source #

PSemigroup Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type arg <> arg :: a Source #

type Sconcat arg :: a Source #

SShow Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sShowsPrec :: forall (t :: Nat) (t :: Void) (t :: Symbol). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply ShowsPrecSym0 t) t) t) Source #

sShow_ :: forall (t :: Void). Sing t -> Sing (Apply Show_Sym0 t) Source #

sShowList :: forall (t :: [Void]) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply ShowListSym0 t) t) Source #

PShow Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Associated Types

type ShowsPrec arg arg arg :: Symbol Source #

type Show_ arg :: Symbol Source #

type ShowList arg arg :: Symbol Source #

TestCoercion SVoid Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testCoercion :: forall (a :: k) (b :: k). SVoid a -> SVoid b -> Maybe (Coercion a b) #

TestEquality SVoid Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

Methods

testEquality :: forall (a :: k) (b :: k). SVoid a -> SVoid b -> Maybe (a :~: b) #

SingI (AbsurdSym0 :: TyFun Void a -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Void

SuppressUnusedWarnings (AbsurdSym0 :: TyFun Void a6989586621679369444 -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Void

type Rep Void 
Instance details

Defined in Data.Void

type Rep Void = D1 ('MetaData "Void" "Data.Void" "base" 'False) (V1 :: Type -> Type)
type Demote Void Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SVoid
type Sconcat (arg0 :: NonEmpty Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sconcat (arg0 :: NonEmpty Void)
type Show_ (arg0 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Show_ (arg0 :: Void)
type (a :: Void) == (b :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

type (a :: Void) == (b :: Void)
type (x :: Void) /= (y :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Eq

type (x :: Void) /= (y :: Void) = Not (x == y)
type Compare (a1 :: Void) (a2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type Compare (a1 :: Void) (a2 :: Void)
type (arg1 :: Void) < (arg2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type (arg1 :: Void) < (arg2 :: Void)
type (arg1 :: Void) <= (arg2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type (arg1 :: Void) <= (arg2 :: Void)
type (arg1 :: Void) > (arg2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type (arg1 :: Void) > (arg2 :: Void)
type (arg1 :: Void) >= (arg2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type (arg1 :: Void) >= (arg2 :: Void)
type Max (arg1 :: Void) (arg2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type Max (arg1 :: Void) (arg2 :: Void)
type Min (arg1 :: Void) (arg2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type Min (arg1 :: Void) (arg2 :: Void)
type (a1 :: Void) <> (a2 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type (a1 :: Void) <> (a2 :: Void)
type ShowList (arg1 :: [Void]) arg2 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type ShowList (arg1 :: [Void]) arg2
type ShowsPrec a1 (a2 :: Void) a3 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type ShowsPrec a1 (a2 :: Void) a3
type Apply (AbsurdSym0 :: TyFun Void k2 -> Type) (a6989586621679369447 :: Void) Source # 
Instance details

Defined in Data.Singletons.Prelude.Void

type Apply (AbsurdSym0 :: TyFun Void k2 -> Type) (a6989586621679369447 :: Void) = Absurd a6989586621679369447 :: k2

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

class PBounded (a :: Type) Source #

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

Instances

Instances details
PBounded Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded () Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded All Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded Any Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (WrappedMonoid m) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Identity a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Dual a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Sum a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Product a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (a, b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (a, b, c) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (Const a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (a, b, c, d) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (a, b, c, d, e) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

PBounded (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type MinBound :: a Source #

type MaxBound :: a Source #

class SBounded a where Source #

Instances

Instances details
SBounded Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SBounded Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SBounded () Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SBounded Bool => SBounded All Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded Bool => SBounded Any Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded a => SBounded (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded a => SBounded (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded a => SBounded (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded a => SBounded (Last a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded m => SBounded (WrappedMonoid m) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded a => SBounded (Identity a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SBounded a => SBounded (Dual a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded a => SBounded (Sum a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

SBounded a => SBounded (Product a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

(SBounded a, SBounded b) => SBounded (a, b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

(SBounded a, SBounded b, SBounded c) => SBounded (a, b, c) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SBounded a => SBounded (Const a b) Source # 
Instance details

Defined in Data.Singletons.Prelude.Const

(SBounded a, SBounded b, SBounded c, SBounded d) => SBounded (a, b, c, d) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

(SBounded a, SBounded b, SBounded c, SBounded d, SBounded e) => SBounded (a, b, c, d, e) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

(SBounded a, SBounded b, SBounded c, SBounded d, SBounded e, SBounded f) => SBounded (a, b, c, d, e, f) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

(SBounded a, SBounded b, SBounded c, SBounded d, SBounded e, SBounded f, SBounded g) => SBounded (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

class PEnum (a :: Type) Source #

Associated Types

type ToEnum (arg :: Nat) :: a Source #

type FromEnum (arg :: a) :: Nat Source #

Instances

Instances details
PEnum Bool Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type Succ arg :: a Source #

type Pred arg :: a Source #

type ToEnum arg :: a Source #

type FromEnum arg :: Nat Source #

type EnumFromTo arg arg :: [a] Source #

type EnumFromThenTo arg arg arg :: [a] Source #

PEnum Ordering Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type Succ arg :: a Source #

type Pred arg :: a Source #

type ToEnum arg :: a Source #

type FromEnum arg :: Nat Source #

type EnumFromTo arg arg :: [a] Source #

type EnumFromThenTo arg arg arg :: [a] Source #

PEnum Nat Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type Succ arg :: a Source #

type Pred arg :: a Source #

type ToEnum arg :: a Source #

type FromEnum arg :: Nat Source #

type EnumFromTo arg arg :: [a] Source #

type EnumFromThenTo arg arg arg :: [a] Source #

PEnum () Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Associated Types

type Succ arg :: a Source #

type Pred arg :: a Source #

type ToEnum arg :: a Source #

type FromEnum arg :: Nat Source #

type EnumFromTo arg arg :: [a] Source #

type EnumFromThenTo arg arg arg :: [a] Source #

PEnum (Min a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

Associated Types

type Succ arg :: a Source #

type Pred arg :: a Source #

type ToEnum arg :: a Source #

type FromEnum arg :: Nat Source #

type EnumFromTo arg arg :: [a] Source #

type EnumFromThenTo arg arg arg :: [a] Source #

PEnum (Max a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

Associated Types

type Succ arg :: a Source #

type Pred arg :: a Source #

type ToEnum arg :: a Source #

type FromEnum arg :: Nat Source #

type EnumFromTo arg arg :: [a] Source #

type EnumFromThenTo arg arg arg :: [a] Source #

PEnum (First a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

Associated Types

type Succ arg :: a Source #

type Pred arg :: a Source #

type ToEnum arg :: a Source #

type FromEnum arg :: Nat Source #

type EnumFromTo arg arg :: [a] Source #

type EnumFromThenTo arg arg arg :: [a] Source #