Copyright	(C) 2014 Richard Eisenberg
License	BSD-style (see LICENSE)
Maintainer	Ryan Scott
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Singletons.Prelude.Num

Contents

Defunctionalization symbols

Description

Defines and exports promoted and singleton versions of definitions from GHC.Num.

Be warned that some of the associated type families in the PNum class ((+), (-), and (*)) clash with their counterparts for Nat in the GHC.TypeLits module.

Synopsis

class PNum (a :: Type) where
- type (arg :: a) + (arg :: a) :: a
- type (arg :: a) - (arg :: a) :: a
- type (arg :: a) * (arg :: a) :: a
- type Negate (arg :: a) :: a
- type Abs (arg :: a) :: a
- type Signum (arg :: a) :: a
- type FromInteger (arg :: Nat) :: a
class SNum a where
- (%+) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t :: a)
- (%-) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t :: a)
- (%*) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (*@#@$) t) t :: a)
- sNegate :: forall (t :: a). Sing t -> Sing (Apply NegateSym0 t :: a)
- sAbs :: forall (t :: a). Sing t -> Sing (Apply AbsSym0 t :: a)
- sSignum :: forall (t :: a). Sing t -> Sing (Apply SignumSym0 t :: a)
- sFromInteger :: forall (t :: Nat). Sing t -> Sing (Apply FromIntegerSym0 t :: a)
type family Subtract (a :: a) (a :: a) :: a where ...
sSubtract :: forall a (t :: a) (t :: a). SNum a => Sing t -> Sing t -> Sing (Apply (Apply SubtractSym0 t) t :: a)
data (+@#@$) :: forall a6989586621679506009. (~>) a6989586621679506009 ((~>) a6989586621679506009 a6989586621679506009)
data (+@#@$$) (arg6989586621679506029 :: a6989586621679506009) :: (~>) a6989586621679506009 a6989586621679506009
type (+@#@$$$) (arg6989586621679506029 :: a6989586621679506009) (arg6989586621679506030 :: a6989586621679506009) = (+) arg6989586621679506029 arg6989586621679506030
data (-@#@$) :: forall a6989586621679506009. (~>) a6989586621679506009 ((~>) a6989586621679506009 a6989586621679506009)
data (-@#@$$) (arg6989586621679506033 :: a6989586621679506009) :: (~>) a6989586621679506009 a6989586621679506009
type (-@#@$$$) (arg6989586621679506033 :: a6989586621679506009) (arg6989586621679506034 :: a6989586621679506009) = (-) arg6989586621679506033 arg6989586621679506034
data (*@#@$) :: forall a6989586621679506009. (~>) a6989586621679506009 ((~>) a6989586621679506009 a6989586621679506009)
data (*@#@$$) (arg6989586621679506037 :: a6989586621679506009) :: (~>) a6989586621679506009 a6989586621679506009
type (*@#@$$$) (arg6989586621679506037 :: a6989586621679506009) (arg6989586621679506038 :: a6989586621679506009) = * arg6989586621679506037 arg6989586621679506038
data NegateSym0 :: forall a6989586621679506009. (~>) a6989586621679506009 a6989586621679506009
type NegateSym1 (arg6989586621679506041 :: a6989586621679506009) = Negate arg6989586621679506041
data AbsSym0 :: forall a6989586621679506009. (~>) a6989586621679506009 a6989586621679506009
type AbsSym1 (arg6989586621679506043 :: a6989586621679506009) = Abs arg6989586621679506043
data SignumSym0 :: forall a6989586621679506009. (~>) a6989586621679506009 a6989586621679506009
type SignumSym1 (arg6989586621679506045 :: a6989586621679506009) = Signum arg6989586621679506045
data FromIntegerSym0 :: forall a6989586621679506009. (~>) Nat a6989586621679506009
type FromIntegerSym1 (arg6989586621679506047 :: Nat) = FromInteger arg6989586621679506047
data SubtractSym0 :: forall a6989586621679511466. (~>) a6989586621679511466 ((~>) a6989586621679511466 a6989586621679511466)
data SubtractSym1 (a6989586621679511470 :: a6989586621679511466) :: (~>) a6989586621679511466 a6989586621679511466
type SubtractSym2 (a6989586621679511470 :: a6989586621679511466) (a6989586621679511471 :: a6989586621679511466) = Subtract a6989586621679511470 a6989586621679511471

Documentation

class PNum (a :: Type) Source #

Associated Types

type (arg :: a) + (arg :: a) :: a infixl 6 Source #

type (arg :: a) - (arg :: a) :: a infixl 6 Source #

type (arg :: a) * (arg :: a) :: a infixl 7 Source #

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

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

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

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

Instances

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 #
PNum (Min a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup 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 #
PNum (Max a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup 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 #
PNum (Identity a) Source #
Instance details Defined in Data.Singletons.Prelude.Identity 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 #
PNum (Sum a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal 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 #
PNum (Product a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal 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 #
PNum (Down a) 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 #
PNum (Const a b) Source #
Instance details Defined in Data.Singletons.Prelude.Const 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 #

class SNum a where Source #

Minimal complete definition

(%+), (%*), sAbs, sSignum, sFromInteger

Methods

(%+) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t :: a) infixl 6 Source #

(%-) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t :: a) infixl 6 Source #

(%*) :: forall (t :: a) (t :: a). Sing t -> Sing t -> Sing (Apply (Apply (*@#@$) t) t :: a) infixl 7 Source #

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

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

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

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

(%-) :: forall (t :: a) (t :: a). (Apply (Apply (-@#@$) t) t :: a) ~ Apply (Apply TFHelper_6989586621679506057Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t :: a) infixl 6 Source #

sNegate :: forall (t :: a). (Apply NegateSym0 t :: a) ~ Apply Negate_6989586621679506065Sym0 t => Sing t -> Sing (Apply NegateSym0 t :: a) Source #

Instances

SNum Nat Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #
SNum a => SNum (Min a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #
SNum a => SNum (Max a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #
SNum a => SNum (Identity a) Source #
Instance details Defined in Data.Singletons.Prelude.Identity Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #
SNum a => SNum (Sum a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #
SNum a => SNum (Product a) Source #
Instance details Defined in Data.Singletons.Prelude.Semigroup.Internal Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #
SNum a => SNum (Down a) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #
SNum a => SNum (Const a b) Source #
Instance details Defined in Data.Singletons.Prelude.Const Methods (%+) :: Sing t -> Sing t -> Sing (Apply (Apply (+@#@$) t) t) Source # (%-) :: Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t) Source # (%) :: Sing t -> Sing t -> Sing (Apply (Apply (@#@$) t) t) Source # sNegate :: Sing t -> Sing (Apply NegateSym0 t) Source # sAbs :: Sing t -> Sing (Apply AbsSym0 t) Source # sSignum :: Sing t -> Sing (Apply SignumSym0 t) Source # sFromInteger :: Sing t -> Sing (Apply FromIntegerSym0 t) Source #

type family Subtract (a :: a) (a :: a) :: a where ... Source #

Equations

Subtract x y = Apply (Apply (-@#@$) y) x

sSubtract :: forall a (t :: a) (t :: a). SNum a => Sing t -> Sing t -> Sing (Apply (Apply SubtractSym0 t) t :: a) Source #

Defunctionalization symbols

data (+@#@$) :: forall a6989586621679506009. (~>) a6989586621679506009 ((~>) a6989586621679506009 a6989586621679506009) infixl 6 Source #

Instances

SNum a => SingI ((+@#@$) :: TyFun a (a ~> a) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing (+@#@$) Source #
SuppressUnusedWarnings ((+@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((+@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) (arg6989586621679506029 :: a6989586621679506009) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((+@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) (arg6989586621679506029 :: a6989586621679506009) = (+@#@$$) arg6989586621679506029

data (+@#@$$) (arg6989586621679506029 :: a6989586621679506009) :: (~>) a6989586621679506009 a6989586621679506009 infixl 6 Source #

Instances

(SNum a, SingI d) => SingI ((+@#@$$) d :: TyFun a a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing ((+@#@$$) d) Source #
SuppressUnusedWarnings ((+@#@$$) arg6989586621679506029 :: TyFun a6989586621679506009 a6989586621679506009 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((+@#@$$) arg6989586621679506029 :: TyFun a a -> Type) (arg6989586621679506030 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((+@#@$$) arg6989586621679506029 :: TyFun a a -> Type) (arg6989586621679506030 :: a) = arg6989586621679506029 + arg6989586621679506030

type (+@#@$$$) (arg6989586621679506029 :: a6989586621679506009) (arg6989586621679506030 :: a6989586621679506009) = (+) arg6989586621679506029 arg6989586621679506030 Source #

data (-@#@$) :: forall a6989586621679506009. (~>) a6989586621679506009 ((~>) a6989586621679506009 a6989586621679506009) infixl 6 Source #

Instances

SNum a => SingI ((-@#@$) :: TyFun a (a ~> a) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing (-@#@$) Source #
SuppressUnusedWarnings ((-@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((-@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) (arg6989586621679506033 :: a6989586621679506009) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((-@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) (arg6989586621679506033 :: a6989586621679506009) = (-@#@$$) arg6989586621679506033

data (-@#@$$) (arg6989586621679506033 :: a6989586621679506009) :: (~>) a6989586621679506009 a6989586621679506009 infixl 6 Source #

Instances

(SNum a, SingI d) => SingI ((-@#@$$) d :: TyFun a a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing ((-@#@$$) d) Source #
SuppressUnusedWarnings ((-@#@$$) arg6989586621679506033 :: TyFun a6989586621679506009 a6989586621679506009 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((-@#@$$) arg6989586621679506033 :: TyFun a a -> Type) (arg6989586621679506034 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((-@#@$$) arg6989586621679506033 :: TyFun a a -> Type) (arg6989586621679506034 :: a) = arg6989586621679506033 - arg6989586621679506034

type (-@#@$$$) (arg6989586621679506033 :: a6989586621679506009) (arg6989586621679506034 :: a6989586621679506009) = (-) arg6989586621679506033 arg6989586621679506034 Source #

data (*@#@$) :: forall a6989586621679506009. (~>) a6989586621679506009 ((~>) a6989586621679506009 a6989586621679506009) infixl 7 Source #

Instances

SNum a => SingI ((*@#@$) :: TyFun a (a ~> a) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing (*@#@$) Source #
SuppressUnusedWarnings ((*@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((*@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) (arg6989586621679506037 :: a6989586621679506009) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((@#@$) :: TyFun a6989586621679506009 (a6989586621679506009 ~> a6989586621679506009) -> Type) (arg6989586621679506037 :: a6989586621679506009) = (@#@$$) arg6989586621679506037

data (*@#@$$) (arg6989586621679506037 :: a6989586621679506009) :: (~>) a6989586621679506009 a6989586621679506009 infixl 7 Source #

Instances

(SNum a, SingI d) => SingI ((*@#@$$) d :: TyFun a a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing ((*@#@$$) d) Source #
SuppressUnusedWarnings ((*@#@$$) arg6989586621679506037 :: TyFun a6989586621679506009 a6989586621679506009 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((*@#@$$) arg6989586621679506037 :: TyFun a a -> Type) (arg6989586621679506038 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((@#@$$) arg6989586621679506037 :: TyFun a a -> Type) (arg6989586621679506038 :: a) = arg6989586621679506037 arg6989586621679506038

type (*@#@$$$) (arg6989586621679506037 :: a6989586621679506009) (arg6989586621679506038 :: a6989586621679506009) = * arg6989586621679506037 arg6989586621679506038 Source #

data NegateSym0 :: forall a6989586621679506009. (~>) a6989586621679506009 a6989586621679506009 Source #

Instances

SNum a => SingI (NegateSym0 :: TyFun a a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing NegateSym0 Source #
SuppressUnusedWarnings (NegateSym0 :: TyFun a6989586621679506009 a6989586621679506009 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (NegateSym0 :: TyFun a a -> Type) (arg6989586621679506041 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (NegateSym0 :: TyFun a a -> Type) (arg6989586621679506041 :: a) = Negate arg6989586621679506041

type NegateSym1 (arg6989586621679506041 :: a6989586621679506009) = Negate arg6989586621679506041 Source #

data AbsSym0 :: forall a6989586621679506009. (~>) a6989586621679506009 a6989586621679506009 Source #

Instances

SNum a => SingI (AbsSym0 :: TyFun a a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing AbsSym0 Source #
SuppressUnusedWarnings (AbsSym0 :: TyFun a6989586621679506009 a6989586621679506009 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (AbsSym0 :: TyFun a a -> Type) (arg6989586621679506043 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (AbsSym0 :: TyFun a a -> Type) (arg6989586621679506043 :: a) = Abs arg6989586621679506043

type AbsSym1 (arg6989586621679506043 :: a6989586621679506009) = Abs arg6989586621679506043 Source #

data SignumSym0 :: forall a6989586621679506009. (~>) a6989586621679506009 a6989586621679506009 Source #

Instances

SNum a => SingI (SignumSym0 :: TyFun a a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing SignumSym0 Source #
SuppressUnusedWarnings (SignumSym0 :: TyFun a6989586621679506009 a6989586621679506009 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (SignumSym0 :: TyFun a a -> Type) (arg6989586621679506045 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (SignumSym0 :: TyFun a a -> Type) (arg6989586621679506045 :: a) = Signum arg6989586621679506045

type SignumSym1 (arg6989586621679506045 :: a6989586621679506009) = Signum arg6989586621679506045 Source #

data FromIntegerSym0 :: forall a6989586621679506009. (~>) Nat a6989586621679506009 Source #

Instances

SNum a => SingI (FromIntegerSym0 :: TyFun Nat a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing FromIntegerSym0 Source #
SuppressUnusedWarnings (FromIntegerSym0 :: TyFun Nat a6989586621679506009 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (FromIntegerSym0 :: TyFun Nat k2 -> Type) (arg6989586621679506047 :: Nat) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (FromIntegerSym0 :: TyFun Nat k2 -> Type) (arg6989586621679506047 :: Nat) = (FromInteger arg6989586621679506047 :: k2)

type FromIntegerSym1 (arg6989586621679506047 :: Nat) = FromInteger arg6989586621679506047 Source #

data SubtractSym0 :: forall a6989586621679511466. (~>) a6989586621679511466 ((~>) a6989586621679511466 a6989586621679511466) Source #

Instances

SNum a => SingI (SubtractSym0 :: TyFun a (a ~> a) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing SubtractSym0 Source #
SuppressUnusedWarnings (SubtractSym0 :: TyFun a6989586621679511466 (a6989586621679511466 ~> a6989586621679511466) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (SubtractSym0 :: TyFun a6989586621679511466 (a6989586621679511466 ~> a6989586621679511466) -> Type) (a6989586621679511470 :: a6989586621679511466) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (SubtractSym0 :: TyFun a6989586621679511466 (a6989586621679511466 ~> a6989586621679511466) -> Type) (a6989586621679511470 :: a6989586621679511466) = SubtractSym1 a6989586621679511470

data SubtractSym1 (a6989586621679511470 :: a6989586621679511466) :: (~>) a6989586621679511466 a6989586621679511466 Source #

Instances

(SNum a, SingI d) => SingI (SubtractSym1 d :: TyFun a a -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods sing :: Sing (SubtractSym1 d) Source #
SuppressUnusedWarnings (SubtractSym1 a6989586621679511470 :: TyFun a6989586621679511466 a6989586621679511466 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (SubtractSym1 a6989586621679511470 :: TyFun a a -> Type) (a6989586621679511471 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (SubtractSym1 a6989586621679511470 :: TyFun a a -> Type) (a6989586621679511471 :: a) = Subtract a6989586621679511470 a6989586621679511471

type SubtractSym2 (a6989586621679511470 :: a6989586621679511466) (a6989586621679511471 :: a6989586621679511466) = Subtract a6989586621679511470 a6989586621679511471 Source #