singletons-2.6: A framework for generating singleton types
Copyright(C) 2014 Richard Eisenberg
LicenseBSD-style (see LICENSE)
MaintainerRyan Scott
Stabilityexperimental
Portabilitynon-portable
Safe HaskellNone
LanguageHaskell2010

Data.Singletons.TypeLits

Description

Defines and exports singletons useful for the Nat and Symbol kinds.

Synopsis

Documentation

data Nat #

Instances

Instances details
Enum Nat 
Instance details

Defined in Data.Singletons.TypeLits

Methods

succ :: Nat -> Nat

pred :: Nat -> Nat

toEnum :: Int -> Nat

fromEnum :: Nat -> Int

enumFrom :: Nat -> [Nat]

enumFromThen :: Nat -> Nat -> [Nat]

enumFromTo :: Nat -> Nat -> [Nat]

enumFromThenTo :: Nat -> Nat -> Nat -> [Nat]

Eq Nat 
Instance details

Defined in Data.Singletons.TypeLits

Methods

(==) :: Nat -> Nat -> Bool

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

Num Nat

This bogus Num instance is helpful for people who want to define functions over Nats that will only be used at the type level or as singletons. A correct SNum instance for Nat singletons exists.

Instance details

Defined in Data.Singletons.TypeLits

Methods

(+) :: Nat -> Nat -> Nat

(-) :: Nat -> Nat -> Nat

(*) :: Nat -> Nat -> Nat

negate :: Nat -> Nat

abs :: Nat -> Nat

signum :: Nat -> Nat

fromInteger :: Integer -> Nat

Ord Nat 
Instance details

Defined in Data.Singletons.TypeLits

Methods

compare :: Nat -> Nat -> Ordering

(<) :: Nat -> Nat -> Bool

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

(>) :: Nat -> Nat -> Bool

(>=) :: Nat -> Nat -> Bool

max :: Nat -> Nat -> Nat

min :: Nat -> Nat -> Nat

Show Nat 
Instance details

Defined in Data.Singletons.TypeLits

Methods

showsPrec :: Int -> Nat -> ShowS

show :: Nat -> String

showList :: [Nat] -> ShowS

SingKind Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

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

Methods

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

toSing :: Demote Nat -> SomeSing Nat 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 #

PEq Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool 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 #

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 #

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 #

SNum Nat Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

Methods

(%+) :: 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 #

sNegate :: forall (t :: Nat). Sing t -> Sing (Apply NegateSym0 t) Source #

sAbs :: forall (t :: Nat). Sing t -> Sing (Apply AbsSym0 t) Source #

sSignum :: forall (t :: Nat). Sing t -> Sing (Apply SignumSym0 t) Source #

sFromInteger :: forall (t :: Nat). Sing t -> Sing (Apply FromIntegerSym0 t) Source #

PNum Nat Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

Associated Types

type arg + arg :: a Source #

type arg - arg :: a Source #

type arg * arg :: a Source #

type Negate arg :: a Source #

type Abs arg :: a Source #

type Signum arg :: a Source #

type FromInteger arg :: a Source #

SEnum Nat Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

Methods

sSucc :: forall (t :: Nat). Sing t -> Sing (Apply SuccSym0 t) Source #

sPred :: forall (t :: Nat). Sing t -> Sing (Apply PredSym0 t) Source #

sToEnum :: forall (t :: Nat). Sing t -> Sing (Apply ToEnumSym0 t) Source #

sFromEnum :: forall (t :: Nat). Sing t -> Sing (Apply FromEnumSym0 t) Source #

sEnumFromTo :: forall (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing (Apply (Apply EnumFromToSym0 t) t) Source #

sEnumFromThenTo :: forall (t :: Nat) (t :: Nat) (t :: Nat). Sing t -> Sing t -> Sing t -> Sing (Apply (Apply (Apply EnumFromThenToSym0 t) t) t) 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 #

SShow Nat Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

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

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

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

PShow Nat 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 #

KnownNat n => SingI (n :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sing :: Sing n Source #

SingI Log2Sym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SingI (<=?@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SingI (^@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SingI DivSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SingI ModSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings KnownNatSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings Log2Sym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings (<=?@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings (^@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings DivSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings ModSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings QuotSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings RemSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings DivModSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings QuotRemSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SingI x => SingI ((<=?@#@$$) x :: TyFun Nat Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sing :: Sing ((<=?@#@$$) x) Source #

SingI x => SingI ((^@#@$$) x :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sing :: Sing ((^@#@$$) x) Source #

SingI x => SingI (DivSym1 x :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

Methods

sing :: Sing (DivSym1 x) Source #

SingI x => SingI (ModSym1 x :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

Methods

sing :: Sing (ModSym1 x) Source #

SingI ((!!@#@$) :: TyFun [a] (Nat ~> a) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SNum a => SingI (FromIntegerSym0 :: TyFun Nat a -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

SEnum a => SingI (ToEnumSym0 :: TyFun Nat a -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SingI (SplitAtSym0 :: TyFun Nat ([a] ~> ([a], [a])) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI (DropSym0 :: TyFun Nat ([a] ~> [a]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI (TakeSym0 :: TyFun Nat ([a] ~> [a]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI (ReplicateSym0 :: TyFun Nat (a ~> [a]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SShow a => SingI (ShowsPrecSym0 :: TyFun Nat (a ~> (Symbol ~> Symbol)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI (SplitAtSym0 :: TyFun Nat (NonEmpty a ~> ([a], [a])) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SingI (DropSym0 :: TyFun Nat (NonEmpty a ~> [a]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SingI (TakeSym0 :: TyFun Nat (NonEmpty a ~> [a]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SEnum a => SingI (FromEnumSym0 :: TyFun a Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SEq a => SingI (ElemIndicesSym0 :: TyFun a ([a] ~> [Nat]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SEq a => SingI (ElemIndexSym0 :: TyFun a ([a] ~> Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI ((!!@#@$) :: TyFun (NonEmpty a) (Nat ~> a) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SingI (LengthSym0 :: TyFun (NonEmpty a) Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SingI (FindIndicesSym0 :: TyFun (a ~> Bool) ([a] ~> [Nat]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI (FindIndexSym0 :: TyFun (a ~> Bool) ([a] ~> Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings ((!!@#@$) :: TyFun [a6989586621679970188] (Nat ~> a6989586621679970188) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings ((<=?@#@$$) a3530822107858468865 :: TyFun Nat Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings ((^@#@$$) a3530822107858468865 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings (DivSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings (ModSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings (QuotSym1 a6989586621679504200 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings (RemSym1 a6989586621679504190 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings (DivModSym1 a6989586621679504216 :: TyFun Nat (Nat, Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings (QuotRemSym1 a6989586621679504210 :: TyFun Nat (Nat, Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings (FromIntegerSym0 :: TyFun Nat a6989586621679525469 -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

SuppressUnusedWarnings (ToEnumSym0 :: TyFun Nat a6989586621679763161 -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SuppressUnusedWarnings (DropSym0 :: TyFun Nat ([a6989586621679970205] ~> [a6989586621679970205]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (TakeSym0 :: TyFun Nat ([a6989586621679970206] ~> [a6989586621679970206]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (SplitAtSym0 :: TyFun Nat ([a6989586621679970204] ~> ([a6989586621679970204], [a6989586621679970204])) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (ReplicateSym0 :: TyFun Nat (a6989586621679970190 ~> [a6989586621679970190]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (ShowsPrecSym0 :: TyFun Nat (a6989586621680290747 ~> (Symbol ~> Symbol)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (TakeSym0 :: TyFun Nat (NonEmpty a6989586621681159661 ~> [a6989586621681159661]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SuppressUnusedWarnings (DropSym0 :: TyFun Nat (NonEmpty a6989586621681159660 ~> [a6989586621681159660]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SuppressUnusedWarnings (SplitAtSym0 :: TyFun Nat (NonEmpty a6989586621681159659 ~> ([a6989586621681159659], [a6989586621681159659])) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SuppressUnusedWarnings (FromEnumSym0 :: TyFun a6989586621679763161 Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

SuppressUnusedWarnings (ElemIndicesSym0 :: TyFun a6989586621679970216 ([a6989586621679970216] ~> [Nat]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (ElemIndexSym0 :: TyFun a6989586621679970217 ([a6989586621679970217] ~> Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings ((!!@#@$) :: TyFun (NonEmpty a6989586621681159639) (Nat ~> a6989586621681159639) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SuppressUnusedWarnings (LengthSym0 :: TyFun (NonEmpty a6989586621681159692) Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SuppressUnusedWarnings (FindIndicesSym0 :: TyFun (a6989586621679970214 ~> Bool) ([a6989586621679970214] ~> [Nat]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (FindIndexSym0 :: TyFun (a6989586621679970215 ~> Bool) ([a6989586621679970215] ~> Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI d => SingI (FindIndicesSym1 d :: TyFun [a] [Nat] -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI d => SingI (FindIndexSym1 d :: TyFun [a] (Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

(SEq a, SingI d) => SingI (ElemIndicesSym1 d :: TyFun [a] [Nat] -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

(SEq a, SingI d) => SingI (ElemIndexSym1 d :: TyFun [a] (Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI d => SingI ((!!@#@$$) d :: TyFun Nat a -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

Methods

sing :: Sing ((!!@#@$$) d) Source #

SingI d => SingI ((!!@#@$$) d :: TyFun Nat a -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

Methods

sing :: Sing ((!!@#@$$) d) Source #

SApplicative m => SingI (ReplicateM_Sym0 :: TyFun Nat (m a ~> m ()) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monad

SApplicative m => SingI (ReplicateMSym0 :: TyFun Nat (m a ~> m [a]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monad

SuppressUnusedWarnings (FindIndicesSym1 a6989586621679974716 :: TyFun [a6989586621679970214] [Nat] -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (ElemIndicesSym1 a6989586621679974750 :: TyFun [a6989586621679970216] [Nat] -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (FindIndexSym1 a6989586621679974742 :: TyFun [a6989586621679970215] (Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings (ElemIndexSym1 a6989586621679974758 :: TyFun [a6989586621679970217] (Maybe Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings ((!!@#@$$) a6989586621679974335 :: TyFun Nat a6989586621679970188 -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings ((!!@#@$$) a6989586621681160999 :: TyFun Nat a6989586621681159639 -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

SuppressUnusedWarnings (ReplicateM_Sym0 :: TyFun Nat (m6989586621681271012 a6989586621681271013 ~> m6989586621681271012 ()) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monad

SuppressUnusedWarnings (ReplicateMSym0 :: TyFun Nat (m6989586621681271014 a6989586621681271015 ~> m6989586621681271014 [a6989586621681271015]) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monad

SFoldable t => SingI (LengthSym0 :: TyFun (t a) Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Foldable

SuppressUnusedWarnings (LengthSym0 :: TyFun (t6989586621680486628 a6989586621680486644) Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Foldable

type Demote Nat Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Demote Nat = Natural
type Sing Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Sing = SNat
type Negate (a :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type Negate (a :: Nat) = Error "Cannot negate a natural number" :: Nat
type Abs (a :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type Abs (a :: Nat) = a
type Signum (a :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type Signum (a :: Nat)
type FromInteger a Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type FromInteger a = a
type Succ (a :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type Succ (a :: Nat)
type Pred (a :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type Pred (a :: Nat)
type ToEnum a Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type ToEnum a
type FromEnum (a :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type FromEnum (a :: Nat)
type Show_ (arg0 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Show_ (arg0 :: Nat)
type (x :: Nat) == (y :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type (x :: Nat) == (y :: Nat) = DefaultEq x y
type (x :: Nat) /= (y :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type (x :: Nat) /= (y :: Nat) = Not (x == y)
type Compare (a :: Nat) (b :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Compare (a :: Nat) (b :: Nat) = CmpNat a b
type (arg1 :: Nat) < (arg2 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

type Min (arg1 :: Nat) (arg2 :: Nat)
type (a :: Nat) + (b :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type (a :: Nat) + (b :: Nat) = a + b
type (a :: Nat) - (b :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type (a :: Nat) - (b :: Nat) = a - b
type (a :: Nat) * (b :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type (a :: Nat) * (b :: Nat) = a * b
type EnumFromTo (a1 :: Nat) (a2 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type EnumFromTo (a1 :: Nat) (a2 :: Nat)
type ShowList (arg1 :: [Nat]) arg2 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type ShowList (arg1 :: [Nat]) arg2
type Apply KnownNatSym0 (n6989586621679482086 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply KnownNatSym0 (n6989586621679482086 :: Nat) = KnownNat n6989586621679482086
type Apply Log2Sym0 (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply Log2Sym0 (a3530822107858468865 :: Nat) = Log2 a3530822107858468865
type EnumFromThenTo (a1 :: Nat) (a2 :: Nat) (a3 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type EnumFromThenTo (a1 :: Nat) (a2 :: Nat) (a3 :: Nat)
type ShowsPrec _1 (n :: Nat) x Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type ShowsPrec _1 (n :: Nat) x
type Apply ((<=?@#@$$) a3530822107858468865 :: TyFun Nat Bool -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply ((<=?@#@$$) a3530822107858468865 :: TyFun Nat Bool -> Type) (b3530822107858468866 :: Nat) = a3530822107858468865 <=? b3530822107858468866
type Apply ((^@#@$$) a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply ((^@#@$$) a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) = a3530822107858468865 ^ b3530822107858468866
type Apply (DivSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (DivSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) = Div a3530822107858468865 b3530822107858468866
type Apply (ModSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (ModSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) = Mod a3530822107858468865 b3530822107858468866
type Apply (QuotSym1 a6989586621679504200 :: TyFun Nat Nat -> Type) (a6989586621679504201 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (QuotSym1 a6989586621679504200 :: TyFun Nat Nat -> Type) (a6989586621679504201 :: Nat) = Quot a6989586621679504200 a6989586621679504201
type Apply (RemSym1 a6989586621679504190 :: TyFun Nat Nat -> Type) (a6989586621679504191 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (RemSym1 a6989586621679504190 :: TyFun Nat Nat -> Type) (a6989586621679504191 :: Nat) = Rem a6989586621679504190 a6989586621679504191
type Apply (FromIntegerSym0 :: TyFun Nat k2 -> Type) (arg6989586621679525506 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Num

type Apply (FromIntegerSym0 :: TyFun Nat k2 -> Type) (arg6989586621679525506 :: Nat) = FromInteger arg6989586621679525506 :: k2
type Apply (ToEnumSym0 :: TyFun Nat k2 -> Type) (arg6989586621679763449 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type Apply (ToEnumSym0 :: TyFun Nat k2 -> Type) (arg6989586621679763449 :: Nat) = ToEnum arg6989586621679763449 :: k2
type Apply (FromEnumSym0 :: TyFun a Nat -> Type) (arg6989586621679763451 :: a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Enum

type Apply (FromEnumSym0 :: TyFun a Nat -> Type) (arg6989586621679763451 :: a) = FromEnum arg6989586621679763451
type Apply ((!!@#@$$) a6989586621679974335 :: TyFun Nat a -> Type) (a6989586621679974336 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply ((!!@#@$$) a6989586621679974335 :: TyFun Nat a -> Type) (a6989586621679974336 :: Nat) = a6989586621679974335 !! a6989586621679974336
type Apply ((!!@#@$$) a6989586621681160999 :: TyFun Nat a -> Type) (a6989586621681161000 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

type Apply ((!!@#@$$) a6989586621681160999 :: TyFun Nat a -> Type) (a6989586621681161000 :: Nat) = a6989586621681160999 !! a6989586621681161000
type Apply (<=?@#@$) (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (<=?@#@$) (a3530822107858468865 :: Nat) = (<=?@#@$$) a3530822107858468865
type Apply (^@#@$) (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (^@#@$) (a3530822107858468865 :: Nat) = (^@#@$$) a3530822107858468865
type Apply DivSym0 (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply DivSym0 (a3530822107858468865 :: Nat) = DivSym1 a3530822107858468865
type Apply ModSym0 (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply ModSym0 (a3530822107858468865 :: Nat) = ModSym1 a3530822107858468865
type Apply QuotSym0 (a6989586621679504200 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply QuotSym0 (a6989586621679504200 :: Nat) = QuotSym1 a6989586621679504200
type Apply RemSym0 (a6989586621679504190 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply RemSym0 (a6989586621679504190 :: Nat) = RemSym1 a6989586621679504190
type Apply DivModSym0 (a6989586621679504216 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply DivModSym0 (a6989586621679504216 :: Nat) = DivModSym1 a6989586621679504216
type Apply QuotRemSym0 (a6989586621679504210 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply QuotRemSym0 (a6989586621679504210 :: Nat) = QuotRemSym1 a6989586621679504210
type Apply (DivModSym1 a6989586621679504216 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504217 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (DivModSym1 a6989586621679504216 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504217 :: Nat) = DivMod a6989586621679504216 a6989586621679504217
type Apply (QuotRemSym1 a6989586621679504210 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504211 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (QuotRemSym1 a6989586621679504210 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504211 :: Nat) = QuotRem a6989586621679504210 a6989586621679504211
type Apply (DropSym0 :: TyFun Nat ([a6989586621679970205] ~> [a6989586621679970205]) -> Type) (a6989586621679974502 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (DropSym0 :: TyFun Nat ([a6989586621679970205] ~> [a6989586621679970205]) -> Type) (a6989586621679974502 :: Nat) = DropSym1 a6989586621679974502 a6989586621679970205 :: TyFun [a6989586621679970205] [a6989586621679970205] -> Type
type Apply (TakeSym0 :: TyFun Nat ([a6989586621679970206] ~> [a6989586621679970206]) -> Type) (a6989586621679974516 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (TakeSym0 :: TyFun Nat ([a6989586621679970206] ~> [a6989586621679970206]) -> Type) (a6989586621679974516 :: Nat) = TakeSym1 a6989586621679974516 a6989586621679970206 :: TyFun [a6989586621679970206] [a6989586621679970206] -> Type
type Apply (SplitAtSym0 :: TyFun Nat ([a6989586621679970204] ~> ([a6989586621679970204], [a6989586621679970204])) -> Type) (a6989586621679974496 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (SplitAtSym0 :: TyFun Nat ([a6989586621679970204] ~> ([a6989586621679970204], [a6989586621679970204])) -> Type) (a6989586621679974496 :: Nat) = SplitAtSym1 a6989586621679974496 a6989586621679970204 :: TyFun [a6989586621679970204] ([a6989586621679970204], [a6989586621679970204]) -> Type
type Apply (ReplicateSym0 :: TyFun Nat (a6989586621679970190 ~> [a6989586621679970190]) -> Type) (a6989586621679974355 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (ReplicateSym0 :: TyFun Nat (a6989586621679970190 ~> [a6989586621679970190]) -> Type) (a6989586621679974355 :: Nat) = ReplicateSym1 a6989586621679974355 a6989586621679970190 :: TyFun a6989586621679970190 [a6989586621679970190] -> Type
type Apply (ShowsPrecSym0 :: TyFun Nat (a6989586621680290747 ~> (Symbol ~> Symbol)) -> Type) (arg6989586621680291185 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowsPrecSym0 :: TyFun Nat (a6989586621680290747 ~> (Symbol ~> Symbol)) -> Type) (arg6989586621680291185 :: Nat) = ShowsPrecSym1 arg6989586621680291185 a6989586621680290747 :: TyFun a6989586621680290747 (Symbol ~> Symbol) -> Type
type Apply (TakeSym0 :: TyFun Nat (NonEmpty a6989586621681159661 ~> [a6989586621681159661]) -> Type) (a6989586621681161210 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

type Apply (TakeSym0 :: TyFun Nat (NonEmpty a6989586621681159661 ~> [a6989586621681159661]) -> Type) (a6989586621681161210 :: Nat) = TakeSym1 a6989586621681161210 a6989586621681159661 :: TyFun (NonEmpty a6989586621681159661) [a6989586621681159661] -> Type
type Apply (DropSym0 :: TyFun Nat (NonEmpty a6989586621681159660 ~> [a6989586621681159660]) -> Type) (a6989586621681161202 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

type Apply (DropSym0 :: TyFun Nat (NonEmpty a6989586621681159660 ~> [a6989586621681159660]) -> Type) (a6989586621681161202 :: Nat) = DropSym1 a6989586621681161202 a6989586621681159660 :: TyFun (NonEmpty a6989586621681159660) [a6989586621681159660] -> Type
type Apply (SplitAtSym0 :: TyFun Nat (NonEmpty a6989586621681159659 ~> ([a6989586621681159659], [a6989586621681159659])) -> Type) (a6989586621681161194 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

type Apply (SplitAtSym0 :: TyFun Nat (NonEmpty a6989586621681159659 ~> ([a6989586621681159659], [a6989586621681159659])) -> Type) (a6989586621681161194 :: Nat) = SplitAtSym1 a6989586621681161194 a6989586621681159659 :: TyFun (NonEmpty a6989586621681159659) ([a6989586621681159659], [a6989586621681159659]) -> Type
type Apply (ElemIndicesSym0 :: TyFun a6989586621679970216 ([a6989586621679970216] ~> [Nat]) -> Type) (a6989586621679974750 :: a6989586621679970216) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (ElemIndicesSym0 :: TyFun a6989586621679970216 ([a6989586621679970216] ~> [Nat]) -> Type) (a6989586621679974750 :: a6989586621679970216) = ElemIndicesSym1 a6989586621679974750
type Apply (ElemIndexSym0 :: TyFun a6989586621679970217 ([a6989586621679970217] ~> Maybe Nat) -> Type) (a6989586621679974758 :: a6989586621679970217) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (ElemIndexSym0 :: TyFun a6989586621679970217 ([a6989586621679970217] ~> Maybe Nat) -> Type) (a6989586621679974758 :: a6989586621679970217) = ElemIndexSym1 a6989586621679974758
type Apply (ReplicateM_Sym0 :: TyFun Nat (m6989586621681271012 a6989586621681271013 ~> m6989586621681271012 ()) -> Type) (a6989586621681271372 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monad

type Apply (ReplicateM_Sym0 :: TyFun Nat (m6989586621681271012 a6989586621681271013 ~> m6989586621681271012 ()) -> Type) (a6989586621681271372 :: Nat) = ReplicateM_Sym1 a6989586621681271372 m6989586621681271012 a6989586621681271013 :: TyFun (m6989586621681271012 a6989586621681271013) (m6989586621681271012 ()) -> Type
type Apply (ReplicateMSym0 :: TyFun Nat (m6989586621681271014 a6989586621681271015 ~> m6989586621681271014 [a6989586621681271015]) -> Type) (a6989586621681271391 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monad

type Apply (ReplicateMSym0 :: TyFun Nat (m6989586621681271014 a6989586621681271015 ~> m6989586621681271014 [a6989586621681271015]) -> Type) (a6989586621681271391 :: Nat) = ReplicateMSym1 a6989586621681271391 m6989586621681271014 a6989586621681271015 :: TyFun (m6989586621681271014 a6989586621681271015) (m6989586621681271014 [a6989586621681271015]) -> Type
type Apply (LengthSym0 :: TyFun (NonEmpty a) Nat -> Type) (a6989586621681161411 :: NonEmpty a) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

type Apply (LengthSym0 :: TyFun (NonEmpty a) Nat -> Type) (a6989586621681161411 :: NonEmpty a) = Length a6989586621681161411
type Apply (LengthSym0 :: TyFun (t a) Nat -> Type) (arg6989586621680487289 :: t a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Foldable

type Apply (LengthSym0 :: TyFun (t a) Nat -> Type) (arg6989586621680487289 :: t a) = Length arg6989586621680487289
type Apply (FindIndicesSym1 a6989586621679974716 :: TyFun [a] [Nat] -> Type) (a6989586621679974717 :: [a]) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (FindIndicesSym1 a6989586621679974716 :: TyFun [a] [Nat] -> Type) (a6989586621679974717 :: [a]) = FindIndices a6989586621679974716 a6989586621679974717
type Apply (ElemIndicesSym1 a6989586621679974750 :: TyFun [a] [Nat] -> Type) (a6989586621679974751 :: [a]) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (ElemIndicesSym1 a6989586621679974750 :: TyFun [a] [Nat] -> Type) (a6989586621679974751 :: [a]) = ElemIndices a6989586621679974750 a6989586621679974751
type Apply (FindIndexSym1 a6989586621679974742 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621679974743 :: [a]) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (FindIndexSym1 a6989586621679974742 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621679974743 :: [a]) = FindIndex a6989586621679974742 a6989586621679974743
type Apply (ElemIndexSym1 a6989586621679974758 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621679974759 :: [a]) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (ElemIndexSym1 a6989586621679974758 :: TyFun [a] (Maybe Nat) -> Type) (a6989586621679974759 :: [a]) = ElemIndex a6989586621679974758 a6989586621679974759
type Apply ((!!@#@$) :: TyFun [a6989586621679970188] (Nat ~> a6989586621679970188) -> Type) (a6989586621679974335 :: [a6989586621679970188]) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply ((!!@#@$) :: TyFun [a6989586621679970188] (Nat ~> a6989586621679970188) -> Type) (a6989586621679974335 :: [a6989586621679970188]) = (!!@#@$$) a6989586621679974335
type Apply ((!!@#@$) :: TyFun (NonEmpty a6989586621681159639) (Nat ~> a6989586621681159639) -> Type) (a6989586621681160999 :: NonEmpty a6989586621681159639) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.NonEmpty

type Apply ((!!@#@$) :: TyFun (NonEmpty a6989586621681159639) (Nat ~> a6989586621681159639) -> Type) (a6989586621681160999 :: NonEmpty a6989586621681159639) = (!!@#@$$) a6989586621681160999
type Apply (FindIndicesSym0 :: TyFun (a6989586621679970214 ~> Bool) ([a6989586621679970214] ~> [Nat]) -> Type) (a6989586621679974716 :: a6989586621679970214 ~> Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (FindIndicesSym0 :: TyFun (a6989586621679970214 ~> Bool) ([a6989586621679970214] ~> [Nat]) -> Type) (a6989586621679974716 :: a6989586621679970214 ~> Bool) = FindIndicesSym1 a6989586621679974716
type Apply (FindIndexSym0 :: TyFun (a6989586621679970215 ~> Bool) ([a6989586621679970215] ~> Maybe Nat) -> Type) (a6989586621679974742 :: a6989586621679970215 ~> Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply (FindIndexSym0 :: TyFun (a6989586621679970215 ~> Bool) ([a6989586621679970215] ~> Maybe Nat) -> Type) (a6989586621679974742 :: a6989586621679970215 ~> Bool) = FindIndexSym1 a6989586621679974742

data Symbol #

Instances

Instances details
Eq Symbol

This bogus instance is helpful for people who want to define functions over Symbols that will only be used at the type level or as singletons.

Instance details

Defined in Data.Singletons.TypeLits

Methods

(==) :: Symbol -> Symbol -> Bool

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

Ord Symbol 
Instance details

Defined in Data.Singletons.TypeLits

Methods

compare :: Symbol -> Symbol -> Ordering

(<) :: Symbol -> Symbol -> Bool

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

(>) :: Symbol -> Symbol -> Bool

(>=) :: Symbol -> Symbol -> Bool

max :: Symbol -> Symbol -> Symbol

min :: Symbol -> Symbol -> Symbol

Show Symbol 
Instance details

Defined in Data.Singletons.TypeLits

Methods

showsPrec :: Int -> Symbol -> ShowS

show :: Symbol -> String

showList :: [Symbol] -> ShowS

IsString Symbol 
Instance details

Defined in Data.Singletons.TypeLits

Methods

fromString :: String -> Symbol

Semigroup Symbol 
Instance details

Defined in Data.Singletons.TypeLits

Methods

(<>) :: Symbol -> Symbol -> Symbol

sconcat :: NonEmpty Symbol -> Symbol

stimes :: Integral b => b -> Symbol -> Symbol

Monoid Symbol 
Instance details

Defined in Data.Singletons.TypeLits

SingKind Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

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

SingKind PErrorMessage Source # 
Instance details

Defined in Data.Singletons.TypeError

Associated Types

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

SingKind Symbol 
Instance details

Defined in GHC.Generics

Associated Types

type DemoteRep Symbol

Methods

fromSing :: forall (a :: Symbol). Sing a -> DemoteRep Symbol

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 #

PEq Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Associated Types

type x == y :: Bool Source #

type x /= y :: Bool 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 #

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 #

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 #

SSemigroup Symbol Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Methods

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

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

PSemigroup Symbol Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

Associated Types

type arg <> arg :: a Source #

type Sconcat arg :: a Source #

SShow Symbol Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

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

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

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

PShow Symbol 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 #

SMonoid Symbol Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Methods

sMempty :: Sing MemptySym0 Source #

sMappend :: forall (t :: Symbol) (t :: Symbol). Sing t -> Sing t -> Sing (Apply (Apply MappendSym0 t) t) Source #

sMconcat :: forall (t :: [Symbol]). Sing t -> Sing (Apply MconcatSym0 t) Source #

PMonoid Symbol Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

Associated Types

type Mempty :: a Source #

type Mappend arg arg :: a Source #

type Mconcat arg :: a Source #

SIsString Symbol Source # 
Instance details

Defined in Data.Singletons.Prelude.IsString

Methods

sFromString :: forall (t :: Symbol). Sing t -> Sing (Apply FromStringSym0 t) Source #

PIsString Symbol Source # 
Instance details

Defined in Data.Singletons.Prelude.IsString

Associated Types

type FromString arg :: a Source #

KnownSymbol n => SingI (n :: Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sing :: Sing n Source #

KnownSymbol a => SingI (a :: Symbol) 
Instance details

Defined in GHC.Generics

Methods

sing :: Sing a

SingI t => SingI ('Text t :: ErrorMessage' Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeError

Methods

sing :: Sing ('Text t) Source #

SingI ty => SingI ('ShowType ty :: ErrorMessage' Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeError

Methods

sing :: Sing ('ShowType ty) Source #

(SingI e1, SingI e2) => SingI (e1 :<>: e2 :: ErrorMessage' Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeError

Methods

sing :: Sing (e1 :<>: e2) Source #

(SingI e1, SingI e2) => SingI (e1 :$$: e2 :: ErrorMessage' Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeError

Methods

sing :: Sing (e1 :$$: e2) Source #

SingI ShowParenSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI UnlinesSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI UnwordsSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SingI ShowSpaceSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI ShowCommaSpaceSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI ShowCharSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI ShowStringSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings ShowParenSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings UnlinesSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings UnwordsSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

SuppressUnusedWarnings KnownSymbolSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings ShowSpaceSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings ShowCommaSpaceSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings ShowCharSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings ShowStringSym0 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI (TypeErrorSym0 :: TyFun PErrorMessage b6989586621681327363 -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

SShow a => SingI (ShowListSym0 :: TyFun [a] (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SShow a => SingI (ShowsPrecSym0 :: TyFun Nat (a ~> (Symbol ~> Symbol)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI d => SingI (ShowCharSym1 d :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sing :: Sing (ShowCharSym1 d) Source #

SingI d => SingI (ShowStringSym1 d :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SIsString a => SingI (FromStringSym0 :: TyFun Symbol a -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.IsString

SingI (TextSym0 :: TyFun Symbol (ErrorMessage' Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

SShow a => SingI (ShowsSym0 :: TyFun a (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SShow a => SingI (Show_Sym0 :: TyFun a Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI d => SingI (ShowParenSym1 d :: TyFun (Symbol ~> Symbol) (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI (ShowListWithSym0 :: TyFun (a ~> (Symbol ~> Symbol)) ([a] ~> (Symbol ~> Symbol)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SingI ((:$$:@#@$) :: TyFun (ErrorMessage' Symbol) (ErrorMessage' Symbol ~> ErrorMessage' Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

SingI ((:<>:@#@$) :: TyFun (ErrorMessage' Symbol) (ErrorMessage' Symbol ~> ErrorMessage' Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

SuppressUnusedWarnings (ShowListSym0 :: TyFun [a6989586621680290747] (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowsPrecSym0 :: TyFun Nat (a6989586621680290747 ~> (Symbol ~> Symbol)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowCharSym1 a6989586621680291151 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowStringSym1 a6989586621680291141 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (FromStringSym0 :: TyFun Symbol a6989586621681259525 -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.IsString

SuppressUnusedWarnings (Show_Sym0 :: TyFun a6989586621680290747 Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowsSym0 :: TyFun a6989586621680290732 (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowParenSym1 a6989586621680291123 :: TyFun (Symbol ~> Symbol) (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowListWithSym0 :: TyFun (a6989586621680290731 ~> (Symbol ~> Symbol)) ([a6989586621680290731] ~> (Symbol ~> Symbol)) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (TypeErrorSym0 :: TyFun PErrorMessage b6989586621681327363 -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

SingI d => SingI (ShowListWithSym1 d :: TyFun [a] (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

(SShow a, SingI d) => SingI (ShowListSym1 d :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sing :: Sing (ShowListSym1 d) Source #

(SShow a, SingI d) => SingI (ShowsSym1 d :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sing :: Sing (ShowsSym1 d) Source #

(SingI d1, SingI d2) => SingI (ShowParenSym2 d1 d2 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sing :: Sing (ShowParenSym2 d1 d2) Source #

SingI (ErrorSym0 :: TyFun Symbol a -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SingI (ErrorWithoutStackTraceSym0 :: TyFun Symbol a -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

(SShow a, SingI d) => SingI (ShowsPrecSym1 d a :: TyFun a (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sing :: Sing (ShowsPrecSym1 d a) Source #

SingI (ShowTypeSym0 :: TyFun t (ErrorMessage' Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

SingI x => SingI ((:$$:@#@$$) x :: TyFun (ErrorMessage' Symbol) (ErrorMessage' Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

Methods

sing :: Sing ((:$$:@#@$$) x) Source #

SingI x => SingI ((:<>:@#@$$) x :: TyFun (ErrorMessage' Symbol) (ErrorMessage' Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeError

Methods

sing :: Sing ((:<>:@#@$$) x) Source #

SuppressUnusedWarnings (ShowListWithSym1 a6989586621680291157 :: TyFun [a6989586621680290731] (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowListSym1 arg6989586621680291193 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowsSym1 a6989586621680291177 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowParenSym2 a6989586621680291124 a6989586621680291123 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowsPrecSym1 arg6989586621680291185 a6989586621680290747 :: TyFun a6989586621680290747 (Symbol ~> Symbol) -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

(SShow a, SingI d1, SingI d2) => SingI (ShowsPrecSym2 d1 d2 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sing :: Sing (ShowsPrecSym2 d1 d2) Source #

(SingI d1, SingI d2) => SingI (ShowListWithSym2 d1 d2 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

Methods

sing :: Sing (ShowListWithSym2 d1 d2) Source #

SuppressUnusedWarnings (ShowsPrecSym2 arg6989586621680291186 arg6989586621680291185 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

SuppressUnusedWarnings (ShowListWithSym2 a6989586621680291158 a6989586621680291157 :: TyFun Symbol Symbol -> Type) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Demote Symbol Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Demote Symbol = Text
type Demote PErrorMessage Source # 
Instance details

Defined in Data.Singletons.TypeError

type Sing Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Sing = SSymbol
type Sing Source # 
Instance details

Defined in Data.Singletons.TypeError

type DemoteRep Symbol 
Instance details

Defined in GHC.Generics

type DemoteRep Symbol = String
data Sing (s :: Symbol) 
Instance details

Defined in GHC.Generics

data Sing (s :: Symbol) where
type Mempty Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

type Mempty
type Sconcat (arg0 :: NonEmpty Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

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

Defined in Data.Singletons.Prelude.Show

type Show_ (arg0 :: Symbol)
type Mconcat (arg0 :: [Symbol]) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

type Mconcat (arg0 :: [Symbol])
type FromString a Source # 
Instance details

Defined in Data.Singletons.Prelude.IsString

type FromString a = a
type (x :: Symbol) == (y :: Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type (x :: Symbol) == (y :: Symbol) = DefaultEq x y
type (x :: Symbol) /= (y :: Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type (x :: Symbol) /= (y :: Symbol) = Not (x == y)
type Compare (a :: Symbol) (b :: Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Compare (a :: Symbol) (b :: Symbol) = CmpSymbol a b
type (arg1 :: Symbol) < (arg2 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

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

Defined in Data.Singletons.TypeLits.Internal

type Min (arg1 :: Symbol) (arg2 :: Symbol)
type (a :: Symbol) <> (b :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type (a :: Symbol) <> (b :: Symbol) = AppendSymbol a b
type ShowList (arg1 :: [Symbol]) arg2 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type ShowList (arg1 :: [Symbol]) arg2
type Mappend (arg1 :: Symbol) (arg2 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

type Mappend (arg1 :: Symbol) (arg2 :: Symbol)
type Apply KnownSymbolSym0 (n6989586621679482152 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply KnownSymbolSym0 (n6989586621679482152 :: Symbol) = KnownSymbol n6989586621679482152
type Apply ShowSpaceSym0 (a6989586621680291114 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply ShowSpaceSym0 (a6989586621680291114 :: Symbol) = ShowSpace a6989586621680291114
type Apply ShowCommaSpaceSym0 (a6989586621680291109 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply ShowCommaSpaceSym0 (a6989586621680291109 :: Symbol) = ShowCommaSpace a6989586621680291109
type ShowsPrec a1 (a2 :: Symbol) a3 Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type ShowsPrec a1 (a2 :: Symbol) a3
type Apply (ShowCharSym1 a6989586621680291151 :: TyFun Symbol Symbol -> Type) (a6989586621680291152 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowCharSym1 a6989586621680291151 :: TyFun Symbol Symbol -> Type) (a6989586621680291152 :: Symbol) = ShowChar a6989586621680291151 a6989586621680291152
type Apply (ShowStringSym1 a6989586621680291141 :: TyFun Symbol Symbol -> Type) (a6989586621680291142 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowStringSym1 a6989586621680291141 :: TyFun Symbol Symbol -> Type) (a6989586621680291142 :: Symbol) = ShowString a6989586621680291141 a6989586621680291142
type Apply (FromStringSym0 :: TyFun Symbol k2 -> Type) (arg6989586621681259551 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.IsString

type Apply (FromStringSym0 :: TyFun Symbol k2 -> Type) (arg6989586621681259551 :: Symbol) = FromString arg6989586621681259551 :: k2
type Apply (Show_Sym0 :: TyFun a Symbol -> Type) (arg6989586621680291191 :: a) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (Show_Sym0 :: TyFun a Symbol -> Type) (arg6989586621680291191 :: a) = Show_ arg6989586621680291191
type Apply (TypeErrorSym0 :: TyFun PErrorMessage k2 -> Type) (a6989586621681327364 :: PErrorMessage) Source # 
Instance details

Defined in Data.Singletons.TypeError

type Apply (TypeErrorSym0 :: TyFun PErrorMessage k2 -> Type) (a6989586621681327364 :: PErrorMessage) = TypeError a6989586621681327364 :: k2
type Apply (ShowListSym1 arg6989586621680291193 :: TyFun Symbol Symbol -> Type) (arg6989586621680291194 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowListSym1 arg6989586621680291193 :: TyFun Symbol Symbol -> Type) (arg6989586621680291194 :: Symbol) = ShowList arg6989586621680291193 arg6989586621680291194
type Apply (ShowsSym1 a6989586621680291177 :: TyFun Symbol Symbol -> Type) (a6989586621680291178 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowsSym1 a6989586621680291177 :: TyFun Symbol Symbol -> Type) (a6989586621680291178 :: Symbol) = Shows a6989586621680291177 a6989586621680291178
type Apply (ShowParenSym2 a6989586621680291124 a6989586621680291123 :: TyFun Symbol Symbol -> Type) (a6989586621680291125 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowParenSym2 a6989586621680291124 a6989586621680291123 :: TyFun Symbol Symbol -> Type) (a6989586621680291125 :: Symbol) = ShowParen a6989586621680291124 a6989586621680291123 a6989586621680291125
type Apply (ShowsPrecSym2 arg6989586621680291186 arg6989586621680291185 :: TyFun Symbol Symbol -> Type) (arg6989586621680291187 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowsPrecSym2 arg6989586621680291186 arg6989586621680291185 :: TyFun Symbol Symbol -> Type) (arg6989586621680291187 :: Symbol) = ShowsPrec arg6989586621680291186 arg6989586621680291185 arg6989586621680291187
type Apply (ShowListWithSym2 a6989586621680291158 a6989586621680291157 :: TyFun Symbol Symbol -> Type) (a6989586621680291159 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowListWithSym2 a6989586621680291158 a6989586621680291157 :: TyFun Symbol Symbol -> Type) (a6989586621680291159 :: Symbol) = ShowListWith a6989586621680291158 a6989586621680291157 a6989586621680291159
type Apply ShowParenSym0 (a6989586621680291123 :: Bool) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply ShowParenSym0 (a6989586621680291123 :: Bool) = ShowParenSym1 a6989586621680291123
type Apply ShowCharSym0 (a6989586621680291151 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply ShowCharSym0 (a6989586621680291151 :: Symbol) = ShowCharSym1 a6989586621680291151
type Apply ShowStringSym0 (a6989586621680291141 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply ShowStringSym0 (a6989586621680291141 :: Symbol) = ShowStringSym1 a6989586621680291141
type Apply (ShowsPrecSym0 :: TyFun Nat (a6989586621680290747 ~> (Symbol ~> Symbol)) -> Type) (arg6989586621680291185 :: Nat) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowsPrecSym0 :: TyFun Nat (a6989586621680290747 ~> (Symbol ~> Symbol)) -> Type) (arg6989586621680291185 :: Nat) = ShowsPrecSym1 arg6989586621680291185 a6989586621680290747 :: TyFun a6989586621680290747 (Symbol ~> Symbol) -> Type
type Apply (ShowsSym0 :: TyFun a6989586621680290732 (Symbol ~> Symbol) -> Type) (a6989586621680291177 :: a6989586621680290732) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowsSym0 :: TyFun a6989586621680290732 (Symbol ~> Symbol) -> Type) (a6989586621680291177 :: a6989586621680290732) = ShowsSym1 a6989586621680291177
type Apply (ShowsPrecSym1 arg6989586621680291185 a6989586621680290747 :: TyFun a6989586621680290747 (Symbol ~> Symbol) -> Type) (arg6989586621680291186 :: a6989586621680290747) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowsPrecSym1 arg6989586621680291185 a6989586621680290747 :: TyFun a6989586621680290747 (Symbol ~> Symbol) -> Type) (arg6989586621680291186 :: a6989586621680290747) = ShowsPrecSym2 arg6989586621680291185 arg6989586621680291186
type Apply UnlinesSym0 (a6989586621679974943 :: [Symbol]) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply UnlinesSym0 (a6989586621679974943 :: [Symbol]) = Unlines a6989586621679974943
type Apply UnwordsSym0 (a6989586621679974932 :: [Symbol]) Source # 
Instance details

Defined in Data.Singletons.Prelude.List.Internal

type Apply UnwordsSym0 (a6989586621679974932 :: [Symbol]) = Unwords a6989586621679974932
type Apply (ShowListSym0 :: TyFun [a6989586621680290747] (Symbol ~> Symbol) -> Type) (arg6989586621680291193 :: [a6989586621680290747]) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowListSym0 :: TyFun [a6989586621680290747] (Symbol ~> Symbol) -> Type) (arg6989586621680291193 :: [a6989586621680290747]) = ShowListSym1 arg6989586621680291193
type Apply (ShowListWithSym1 a6989586621680291157 :: TyFun [a6989586621680290731] (Symbol ~> Symbol) -> Type) (a6989586621680291158 :: [a6989586621680290731]) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowListWithSym1 a6989586621680291157 :: TyFun [a6989586621680290731] (Symbol ~> Symbol) -> Type) (a6989586621680291158 :: [a6989586621680290731]) = ShowListWithSym2 a6989586621680291157 a6989586621680291158
type Apply (ShowParenSym1 a6989586621680291123 :: TyFun (Symbol ~> Symbol) (Symbol ~> Symbol) -> Type) (a6989586621680291124 :: Symbol ~> Symbol) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowParenSym1 a6989586621680291123 :: TyFun (Symbol ~> Symbol) (Symbol ~> Symbol) -> Type) (a6989586621680291124 :: Symbol ~> Symbol) = ShowParenSym2 a6989586621680291123 a6989586621680291124
type Apply (ShowListWithSym0 :: TyFun (a6989586621680290731 ~> (Symbol ~> Symbol)) ([a6989586621680290731] ~> (Symbol ~> Symbol)) -> Type) (a6989586621680291157 :: a6989586621680290731 ~> (Symbol ~> Symbol)) Source # 
Instance details

Defined in Data.Singletons.Prelude.Show

type Apply (ShowListWithSym0 :: TyFun (a6989586621680290731 ~> (Symbol ~> Symbol)) ([a6989586621680290731] ~> (Symbol ~> Symbol)) -> Type) (a6989586621680291157 :: a6989586621680290731 ~> (Symbol ~> Symbol)) = ShowListWithSym1 a6989586621680291157

type family Sing :: k -> Type Source #

The singleton kind-indexed type family.

Instances

Instances details
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SBool
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Sing = SNat
type Sing Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Sing = SSymbol
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple0
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SVoid
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAll
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SAny
type Sing Source # 
Instance details

Defined in Data.Singletons.TypeError

type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SList :: [a] -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SMaybe :: Maybe a -> Type
type Sing Source #

A choice of singleton for the kind TYPE rep (for some RuntimeRep rep), an instantiation of which is the famous kind Type.

Conceivably, one could generalize this instance to `Sing @k` for any kind k, and remove all other Sing instances. We don't adopt this design, however, since it is far more convenient in practice to work with explicit singleton values than TypeReps (for instance, TypeReps are more difficult to pattern match on, and require extra runtime checks).

We cannot produce explicit singleton values for everything in TYPE rep, however, since it is an open kind, so we reach for TypeRep in this one particular case.

Instance details

Defined in Data.Singletons.TypeRepTYPE

type Sing = TypeRep :: TYPE rep -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SNonEmpty :: NonEmpty a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Ord

type Sing = SDown :: Down a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SIdentity :: Identity a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SFirst :: First a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SLast :: Last a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMax :: Max a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SMin :: Min a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SOption :: Option a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SWrappedMonoid :: WrappedMonoid m -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SDual :: Dual a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SProduct :: Product a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup.Internal

type Sing = SSum :: Sum a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

type Sing = SFirst :: First a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Monoid

type Sing = SLast :: Last a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = SEither :: Either a b -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple2 :: (a, b) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Internal

type Sing = SLambda :: (k1 ~> k2) -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Internal

type Sing = SWrappedSing :: WrappedSing a -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Semigroup

type Sing = SArg :: Arg a b -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Sigma

type Sing = SSigma :: Sigma s t -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Const

type Sing = SConst :: Const a b -> Type
type Sing Source # 
Instance details

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Instances

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

Defined in Data.Singletons.Prelude.Instances

type Sing = STuple7 :: (a, b, c, d, e, f, g) -> Type

data SNat (n :: Nat) Source #

Constructors

KnownNat n => SNat 

Instances

Instances details
Show (SNat n) 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SNat n -> ShowS

show :: SNat n -> String

showList :: [SNat n] -> ShowS

data SSymbol (n :: Symbol) Source #

Constructors

KnownSymbol n => SSym 

Instances

Instances details
Show (SSymbol s) 
Instance details

Defined in Data.Singletons.ShowSing

Methods

showsPrec :: Int -> SSymbol s -> ShowS

show :: SSymbol s -> String

showList :: [SSymbol s] -> ShowS

withKnownNat :: Sing n -> (KnownNat n => r) -> r Source #

Given a singleton for Nat, call something requiring a KnownNat instance.

withKnownSymbol :: Sing n -> (KnownSymbol n => r) -> r Source #

Given a singleton for Symbol, call something requiring a KnownSymbol instance.

type family Error (str :: k0) :: k where ... Source #

The promotion of error. This version is more poly-kinded for easier use.

sError :: HasCallStack => Sing (str :: Symbol) -> a Source #

The singleton for error

type family ErrorWithoutStackTrace (str :: k0) :: k where ... Source #

The promotion of errorWithoutStackTrace. This version is more poly-kinded for easier use.

sErrorWithoutStackTrace :: Sing (str :: Symbol) -> a Source #

The singleton for errorWithoutStackTrace.

type family Undefined :: k where ... Source #

The promotion of undefined.

sUndefined :: HasCallStack => a Source #

The singleton for undefined.

class KnownNat (n :: Nat) #

Minimal complete definition

natSing

natVal :: forall (n :: Nat) proxy. KnownNat n => proxy n -> Natural #

class KnownSymbol (n :: Symbol) #

Minimal complete definition

symbolSing

symbolVal :: forall (n :: Symbol) proxy. KnownSymbol n => proxy n -> String #

type family (a :: Nat) ^ (b :: Nat) :: Nat where ... #

(%^) :: Sing a -> Sing b -> Sing (a ^ b) infixr 8 Source #

The singleton analogue of (^) for Nats.

type family (a :: Nat) <=? (b :: Nat) :: Bool where ... #

(%<=?) :: Sing a -> Sing b -> Sing (a <=? b) infix 4 Source #

The singleton analogue of <=?

Note that, because of historical reasons in GHC's Nat API, <=? is incompatible (unification-wise) with <= and the PEq, SEq, POrd, and SOrd instances for Nat. (a <=? b) ~ 'True does not imply anything about a <= b or any other PEq / POrd relationships.

(Be aware that <= in the paragraph above refers to <= from the POrd typeclass, exported from Data.Singletons.Prelude.Ord, and not the <= from GHC.TypeNats. The latter is simply a type alias for (a <=? b) ~ 'True.)

This is provided here for the sake of completeness and for compatibility with libraries with APIs built around <=?. New code should use CmpNat, exposed through this library through the POrd and SOrd instances for Nat.

type family Log2 (a :: Nat) :: Nat where ... #

sLog2 :: Sing x -> Sing (Log2 x) Source #

type family Div (a :: Nat) (b :: Nat) :: Nat where ... #

sDiv :: Sing x -> Sing y -> Sing (Div x y) infixl 7 Source #

type family Mod (a :: Nat) (b :: Nat) :: Nat where ... #

sMod :: Sing x -> Sing y -> Sing (Mod x y) infixl 7 Source #

type family DivMod (a :: Nat) (a :: Nat) :: (Nat, Nat) where ... Source #

Equations

DivMod x y = Apply (Apply Tuple2Sym0 (Apply (Apply DivSym0 x) y)) (Apply (Apply ModSym0 x) y) 

sDivMod :: Sing x -> Sing y -> Sing (DivMod x y) Source #

type family Quot (a :: Nat) (a :: Nat) :: Nat where ... infixl 7 Source #

Equations

Quot a_6989586621679504196 a_6989586621679504198 = Apply (Apply DivSym0 a_6989586621679504196) a_6989586621679504198 

sQuot :: Sing x -> Sing y -> Sing (Quot x y) infixl 7 Source #

type family Rem (a :: Nat) (a :: Nat) :: Nat where ... infixl 7 Source #

Equations

Rem a_6989586621679504186 a_6989586621679504188 = Apply (Apply ModSym0 a_6989586621679504186) a_6989586621679504188 

sRem :: Sing x -> Sing y -> Sing (Rem x y) infixl 7 Source #

type family QuotRem (a :: Nat) (a :: Nat) :: (Nat, Nat) where ... Source #

Equations

QuotRem a_6989586621679504206 a_6989586621679504208 = Apply (Apply DivModSym0 a_6989586621679504206) a_6989586621679504208 

sQuotRem :: Sing x -> Sing y -> Sing (QuotRem x y) Source #

Defunctionalization symbols

data ErrorSym0 :: forall k06989586621679481929 k6989586621679481930. (~>) k06989586621679481929 k6989586621679481930 Source #

Instances

Instances details
SingI (ErrorSym0 :: TyFun Symbol a -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings (ErrorSym0 :: TyFun k06989586621679481929 k6989586621679481930 -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (ErrorSym0 :: TyFun k0 k2 -> Type) (str6989586621679481931 :: k0) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (ErrorSym0 :: TyFun k0 k2 -> Type) (str6989586621679481931 :: k0) = Error str6989586621679481931 :: k2

type ErrorSym1 (str6989586621679481931 :: k06989586621679481929) = Error str6989586621679481931 Source #

data ErrorWithoutStackTraceSym0 :: forall k06989586621679483019 k6989586621679483020. (~>) k06989586621679483019 k6989586621679483020 Source #

Instances

Instances details
SingI (ErrorWithoutStackTraceSym0 :: TyFun Symbol a -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings (ErrorWithoutStackTraceSym0 :: TyFun k06989586621679483019 k6989586621679483020 -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (ErrorWithoutStackTraceSym0 :: TyFun k0 k2 -> Type) (str6989586621679483021 :: k0) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (ErrorWithoutStackTraceSym0 :: TyFun k0 k2 -> Type) (str6989586621679483021 :: k0) = ErrorWithoutStackTrace str6989586621679483021 :: k2

type ErrorWithoutStackTraceSym1 (str6989586621679483021 :: k06989586621679483019) = ErrorWithoutStackTrace str6989586621679483021 Source #

data KnownNatSym0 :: (~>) Nat Constraint Source #

Instances

Instances details
SuppressUnusedWarnings KnownNatSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply KnownNatSym0 (n6989586621679482086 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply KnownNatSym0 (n6989586621679482086 :: Nat) = KnownNat n6989586621679482086

type KnownNatSym1 (n6989586621679482086 :: Nat) = KnownNat n6989586621679482086 Source #

data KnownSymbolSym0 :: (~>) Symbol Constraint Source #

Instances

Instances details
SuppressUnusedWarnings KnownSymbolSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply KnownSymbolSym0 (n6989586621679482152 :: Symbol) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply KnownSymbolSym0 (n6989586621679482152 :: Symbol) = KnownSymbol n6989586621679482152

type KnownSymbolSym1 (n6989586621679482152 :: Symbol) = KnownSymbol n6989586621679482152 Source #

data (^@#@$) :: (~>) Nat ((~>) Nat Nat) infixr 8 Source #

Instances

Instances details
SingI (^@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings (^@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (^@#@$) (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (^@#@$) (a3530822107858468865 :: Nat) = (^@#@$$) a3530822107858468865

data (^@#@$$) (a3530822107858468865 :: Nat) :: (~>) Nat Nat infixr 8 Source #

Instances

Instances details
SingI x => SingI ((^@#@$$) x :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sing :: Sing ((^@#@$$) x) Source #

SuppressUnusedWarnings ((^@#@$$) a3530822107858468865 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply ((^@#@$$) a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply ((^@#@$$) a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) = a3530822107858468865 ^ b3530822107858468866

type (^@#@$$$) (a3530822107858468865 :: Nat) (b3530822107858468866 :: Nat) = (^) a3530822107858468865 b3530822107858468866 Source #

data (<=?@#@$) :: (~>) Nat ((~>) Nat Bool) infix 4 Source #

Instances

Instances details
SingI (<=?@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

SuppressUnusedWarnings (<=?@#@$) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (<=?@#@$) (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply (<=?@#@$) (a3530822107858468865 :: Nat) = (<=?@#@$$) a3530822107858468865

data (<=?@#@$$) (a3530822107858468865 :: Nat) :: (~>) Nat Bool infix 4 Source #

Instances

Instances details
SingI x => SingI ((<=?@#@$$) x :: TyFun Nat Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

Methods

sing :: Sing ((<=?@#@$$) x) Source #

SuppressUnusedWarnings ((<=?@#@$$) a3530822107858468865 :: TyFun Nat Bool -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply ((<=?@#@$$) a3530822107858468865 :: TyFun Nat Bool -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits.Internal

type Apply ((<=?@#@$$) a3530822107858468865 :: TyFun Nat Bool -> Type) (b3530822107858468866 :: Nat) = a3530822107858468865 <=? b3530822107858468866

type (<=?@#@$$$) (a3530822107858468865 :: Nat) (b3530822107858468866 :: Nat) = (<=?) a3530822107858468865 b3530822107858468866 Source #

data Log2Sym0 :: (~>) Nat Nat Source #

Instances

Instances details
SingI Log2Sym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings Log2Sym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply Log2Sym0 (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply Log2Sym0 (a3530822107858468865 :: Nat) = Log2 a3530822107858468865

type Log2Sym1 (a3530822107858468865 :: Nat) = Log2 a3530822107858468865 Source #

data DivSym0 :: (~>) Nat ((~>) Nat Nat) infixl 7 Source #

Instances

Instances details
SingI DivSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings DivSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply DivSym0 (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply DivSym0 (a3530822107858468865 :: Nat) = DivSym1 a3530822107858468865

data DivSym1 (a3530822107858468865 :: Nat) :: (~>) Nat Nat infixl 7 Source #

Instances

Instances details
SingI x => SingI (DivSym1 x :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

Methods

sing :: Sing (DivSym1 x) Source #

SuppressUnusedWarnings (DivSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (DivSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (DivSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) = Div a3530822107858468865 b3530822107858468866

type DivSym2 (a3530822107858468865 :: Nat) (b3530822107858468866 :: Nat) = Div a3530822107858468865 b3530822107858468866 Source #

data ModSym0 :: (~>) Nat ((~>) Nat Nat) infixl 7 Source #

Instances

Instances details
SingI ModSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

SuppressUnusedWarnings ModSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply ModSym0 (a3530822107858468865 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply ModSym0 (a3530822107858468865 :: Nat) = ModSym1 a3530822107858468865

data ModSym1 (a3530822107858468865 :: Nat) :: (~>) Nat Nat infixl 7 Source #

Instances

Instances details
SingI x => SingI (ModSym1 x :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

Methods

sing :: Sing (ModSym1 x) Source #

SuppressUnusedWarnings (ModSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (ModSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (ModSym1 a3530822107858468865 :: TyFun Nat Nat -> Type) (b3530822107858468866 :: Nat) = Mod a3530822107858468865 b3530822107858468866

type ModSym2 (a3530822107858468865 :: Nat) (b3530822107858468866 :: Nat) = Mod a3530822107858468865 b3530822107858468866 Source #

data DivModSym0 :: (~>) Nat ((~>) Nat (Nat, Nat)) Source #

Instances

Instances details
SuppressUnusedWarnings DivModSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply DivModSym0 (a6989586621679504216 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply DivModSym0 (a6989586621679504216 :: Nat) = DivModSym1 a6989586621679504216

data DivModSym1 (a6989586621679504216 :: Nat) :: (~>) Nat (Nat, Nat) Source #

Instances

Instances details
SuppressUnusedWarnings (DivModSym1 a6989586621679504216 :: TyFun Nat (Nat, Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (DivModSym1 a6989586621679504216 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504217 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (DivModSym1 a6989586621679504216 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504217 :: Nat) = DivMod a6989586621679504216 a6989586621679504217

type DivModSym2 (a6989586621679504216 :: Nat) (a6989586621679504217 :: Nat) = DivMod a6989586621679504216 a6989586621679504217 Source #

data QuotSym0 :: (~>) Nat ((~>) Nat Nat) infixl 7 Source #

Instances

Instances details
SuppressUnusedWarnings QuotSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply QuotSym0 (a6989586621679504200 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply QuotSym0 (a6989586621679504200 :: Nat) = QuotSym1 a6989586621679504200

data QuotSym1 (a6989586621679504200 :: Nat) :: (~>) Nat Nat infixl 7 Source #

Instances

Instances details
SuppressUnusedWarnings (QuotSym1 a6989586621679504200 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (QuotSym1 a6989586621679504200 :: TyFun Nat Nat -> Type) (a6989586621679504201 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (QuotSym1 a6989586621679504200 :: TyFun Nat Nat -> Type) (a6989586621679504201 :: Nat) = Quot a6989586621679504200 a6989586621679504201

type QuotSym2 (a6989586621679504200 :: Nat) (a6989586621679504201 :: Nat) = Quot a6989586621679504200 a6989586621679504201 Source #

data RemSym0 :: (~>) Nat ((~>) Nat Nat) infixl 7 Source #

Instances

Instances details
SuppressUnusedWarnings RemSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply RemSym0 (a6989586621679504190 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply RemSym0 (a6989586621679504190 :: Nat) = RemSym1 a6989586621679504190

data RemSym1 (a6989586621679504190 :: Nat) :: (~>) Nat Nat infixl 7 Source #

Instances

Instances details
SuppressUnusedWarnings (RemSym1 a6989586621679504190 :: TyFun Nat Nat -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (RemSym1 a6989586621679504190 :: TyFun Nat Nat -> Type) (a6989586621679504191 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (RemSym1 a6989586621679504190 :: TyFun Nat Nat -> Type) (a6989586621679504191 :: Nat) = Rem a6989586621679504190 a6989586621679504191

type RemSym2 (a6989586621679504190 :: Nat) (a6989586621679504191 :: Nat) = Rem a6989586621679504190 a6989586621679504191 Source #

data QuotRemSym0 :: (~>) Nat ((~>) Nat (Nat, Nat)) Source #

Instances

Instances details
SuppressUnusedWarnings QuotRemSym0 Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply QuotRemSym0 (a6989586621679504210 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply QuotRemSym0 (a6989586621679504210 :: Nat) = QuotRemSym1 a6989586621679504210

data QuotRemSym1 (a6989586621679504210 :: Nat) :: (~>) Nat (Nat, Nat) Source #

Instances

Instances details
SuppressUnusedWarnings (QuotRemSym1 a6989586621679504210 :: TyFun Nat (Nat, Nat) -> Type) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (QuotRemSym1 a6989586621679504210 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504211 :: Nat) Source # 
Instance details

Defined in Data.Singletons.TypeLits

type Apply (QuotRemSym1 a6989586621679504210 :: TyFun Nat (Nat, Nat) -> Type) (a6989586621679504211 :: Nat) = QuotRem a6989586621679504210 a6989586621679504211

type QuotRemSym2 (a6989586621679504210 :: Nat) (a6989586621679504211 :: Nat) = QuotRem a6989586621679504210 a6989586621679504211 Source #

Orphan instances

Enum Nat Source # 
Instance details

Methods

succ :: Nat -> Nat

pred :: Nat -> Nat

toEnum :: Int -> Nat

fromEnum :: Nat -> Int

enumFrom :: Nat -> [Nat]

enumFromThen :: Nat -> Nat -> [Nat]

enumFromTo :: Nat -> Nat -> [Nat]

enumFromThenTo :: Nat -> Nat -> Nat -> [Nat]

Eq Nat Source # 
Instance details

Methods

(==) :: Nat -> Nat -> Bool

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

Eq Symbol Source #

This bogus instance is helpful for people who want to define functions over Symbols that will only be used at the type level or as singletons.

Instance details

Methods

(==) :: Symbol -> Symbol -> Bool

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

Num Nat Source #

This bogus Num instance is helpful for people who want to define functions over Nats that will only be used at the type level or as singletons. A correct SNum instance for Nat singletons exists.

Instance details

Methods

(+) :: Nat -> Nat -> Nat

(-) :: Nat -> Nat -> Nat

(*) :: Nat -> Nat -> Nat

negate :: Nat -> Nat

abs :: Nat -> Nat

signum :: Nat -> Nat

fromInteger :: Integer -> Nat

Ord Nat Source # 
Instance details

Methods

compare :: Nat -> Nat -> Ordering

(<) :: Nat -> Nat -> Bool

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

(>) :: Nat -> Nat -> Bool

(>=) :: Nat -> Nat -> Bool

max :: Nat -> Nat -> Nat

min :: Nat -> Nat -> Nat

Ord Symbol Source # 
Instance details

Methods

compare :: Symbol -> Symbol -> Ordering

(<) :: Symbol -> Symbol -> Bool

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

(>) :: Symbol -> Symbol -> Bool

(>=) :: Symbol -> Symbol -> Bool

max :: Symbol -> Symbol -> Symbol

min :: Symbol -> Symbol -> Symbol

Show Nat Source # 
Instance details

Methods

showsPrec :: Int -> Nat -> ShowS

show :: Nat -> String

showList :: [Nat] -> ShowS

Show Symbol Source # 
Instance details

Methods

showsPrec :: Int -> Symbol -> ShowS

show :: Symbol -> String

showList :: [Symbol] -> ShowS

IsString Symbol Source # 
Instance details

Methods

fromString :: String -> Symbol

Semigroup Symbol Source # 
Instance details

Methods

(<>) :: Symbol -> Symbol -> Symbol

sconcat :: NonEmpty Symbol -> Symbol

stimes :: Integral b => b -> Symbol -> Symbol

Monoid Symbol Source # 
Instance details