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 a6989586621679496884. (~>) a6989586621679496884 ((~>) a6989586621679496884 a6989586621679496884)
data (+@#@$$) (arg6989586621679496904 :: a6989586621679496884) :: (~>) a6989586621679496884 a6989586621679496884
type (+@#@$$$) (arg6989586621679496904 :: a6989586621679496884) (arg6989586621679496905 :: a6989586621679496884) = (+) arg6989586621679496904 arg6989586621679496905
data (-@#@$) :: forall a6989586621679496884. (~>) a6989586621679496884 ((~>) a6989586621679496884 a6989586621679496884)
data (-@#@$$) (arg6989586621679496908 :: a6989586621679496884) :: (~>) a6989586621679496884 a6989586621679496884
type (-@#@$$$) (arg6989586621679496908 :: a6989586621679496884) (arg6989586621679496909 :: a6989586621679496884) = (-) arg6989586621679496908 arg6989586621679496909
data (*@#@$) :: forall a6989586621679496884. (~>) a6989586621679496884 ((~>) a6989586621679496884 a6989586621679496884)
data (*@#@$$) (arg6989586621679496912 :: a6989586621679496884) :: (~>) a6989586621679496884 a6989586621679496884
type (*@#@$$$) (arg6989586621679496912 :: a6989586621679496884) (arg6989586621679496913 :: a6989586621679496884) = * arg6989586621679496912 arg6989586621679496913
data NegateSym0 :: forall a6989586621679496884. (~>) a6989586621679496884 a6989586621679496884
type NegateSym1 (arg6989586621679496916 :: a6989586621679496884) = Negate arg6989586621679496916
data AbsSym0 :: forall a6989586621679496884. (~>) a6989586621679496884 a6989586621679496884
type AbsSym1 (arg6989586621679496918 :: a6989586621679496884) = Abs arg6989586621679496918
data SignumSym0 :: forall a6989586621679496884. (~>) a6989586621679496884 a6989586621679496884
type SignumSym1 (arg6989586621679496920 :: a6989586621679496884) = Signum arg6989586621679496920
data FromIntegerSym0 :: forall a6989586621679496884. (~>) Nat a6989586621679496884
type FromIntegerSym1 (arg6989586621679496922 :: Nat) = FromInteger arg6989586621679496922
data SubtractSym0 :: forall a6989586621679502341. (~>) a6989586621679502341 ((~>) a6989586621679502341 a6989586621679502341)
data SubtractSym1 (a6989586621679502345 :: a6989586621679502341) :: (~>) a6989586621679502341 a6989586621679502341
type SubtractSym2 (a6989586621679502345 :: a6989586621679502341) (a6989586621679502346 :: a6989586621679502341) = Subtract a6989586621679502345 a6989586621679502346

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 (-@#@$) t) t :: a) ~ Apply (Apply TFHelper_6989586621679496932Sym0 t) t => Sing t -> Sing t -> Sing (Apply (Apply (-@#@$) t) t :: a) infixl 6 Source #

sNegate :: forall (t :: a). (Apply NegateSym0 t :: a) ~ Apply Negate_6989586621679496940Sym0 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 a6989586621679496884. (~>) a6989586621679496884 ((~>) a6989586621679496884 a6989586621679496884) 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 ((+@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((+@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) (arg6989586621679496904 :: a6989586621679496884) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((+@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) (arg6989586621679496904 :: a6989586621679496884) = (+@#@$$) arg6989586621679496904

data (+@#@$$) (arg6989586621679496904 :: a6989586621679496884) :: (~>) a6989586621679496884 a6989586621679496884 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 ((+@#@$$) arg6989586621679496904 :: TyFun a6989586621679496884 a6989586621679496884 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((+@#@$$) arg6989586621679496904 :: TyFun a a -> Type) (arg6989586621679496905 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((+@#@$$) arg6989586621679496904 :: TyFun a a -> Type) (arg6989586621679496905 :: a) = arg6989586621679496904 + arg6989586621679496905

type (+@#@$$$) (arg6989586621679496904 :: a6989586621679496884) (arg6989586621679496905 :: a6989586621679496884) = (+) arg6989586621679496904 arg6989586621679496905 Source #

data (-@#@$) :: forall a6989586621679496884. (~>) a6989586621679496884 ((~>) a6989586621679496884 a6989586621679496884) 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 ((-@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((-@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) (arg6989586621679496908 :: a6989586621679496884) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((-@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) (arg6989586621679496908 :: a6989586621679496884) = (-@#@$$) arg6989586621679496908

data (-@#@$$) (arg6989586621679496908 :: a6989586621679496884) :: (~>) a6989586621679496884 a6989586621679496884 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 ((-@#@$$) arg6989586621679496908 :: TyFun a6989586621679496884 a6989586621679496884 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((-@#@$$) arg6989586621679496908 :: TyFun a a -> Type) (arg6989586621679496909 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((-@#@$$) arg6989586621679496908 :: TyFun a a -> Type) (arg6989586621679496909 :: a) = arg6989586621679496908 - arg6989586621679496909

type (-@#@$$$) (arg6989586621679496908 :: a6989586621679496884) (arg6989586621679496909 :: a6989586621679496884) = (-) arg6989586621679496908 arg6989586621679496909 Source #

data (*@#@$) :: forall a6989586621679496884. (~>) a6989586621679496884 ((~>) a6989586621679496884 a6989586621679496884) 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 ((*@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((*@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) (arg6989586621679496912 :: a6989586621679496884) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((@#@$) :: TyFun a6989586621679496884 (a6989586621679496884 ~> a6989586621679496884) -> Type) (arg6989586621679496912 :: a6989586621679496884) = (@#@$$) arg6989586621679496912

data (*@#@$$) (arg6989586621679496912 :: a6989586621679496884) :: (~>) a6989586621679496884 a6989586621679496884 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 ((*@#@$$) arg6989586621679496912 :: TyFun a6989586621679496884 a6989586621679496884 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply ((*@#@$$) arg6989586621679496912 :: TyFun a a -> Type) (arg6989586621679496913 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply ((@#@$$) arg6989586621679496912 :: TyFun a a -> Type) (arg6989586621679496913 :: a) = arg6989586621679496912 arg6989586621679496913

type (*@#@$$$) (arg6989586621679496912 :: a6989586621679496884) (arg6989586621679496913 :: a6989586621679496884) = * arg6989586621679496912 arg6989586621679496913 Source #

data NegateSym0 :: forall a6989586621679496884. (~>) a6989586621679496884 a6989586621679496884 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 a6989586621679496884 a6989586621679496884 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (NegateSym0 :: TyFun a a -> Type) (arg6989586621679496916 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (NegateSym0 :: TyFun a a -> Type) (arg6989586621679496916 :: a) = Negate arg6989586621679496916

type NegateSym1 (arg6989586621679496916 :: a6989586621679496884) = Negate arg6989586621679496916 Source #

data AbsSym0 :: forall a6989586621679496884. (~>) a6989586621679496884 a6989586621679496884 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 a6989586621679496884 a6989586621679496884 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (AbsSym0 :: TyFun a a -> Type) (arg6989586621679496918 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (AbsSym0 :: TyFun a a -> Type) (arg6989586621679496918 :: a) = Abs arg6989586621679496918

type AbsSym1 (arg6989586621679496918 :: a6989586621679496884) = Abs arg6989586621679496918 Source #

data SignumSym0 :: forall a6989586621679496884. (~>) a6989586621679496884 a6989586621679496884 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 a6989586621679496884 a6989586621679496884 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (SignumSym0 :: TyFun a a -> Type) (arg6989586621679496920 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (SignumSym0 :: TyFun a a -> Type) (arg6989586621679496920 :: a) = Signum arg6989586621679496920

type SignumSym1 (arg6989586621679496920 :: a6989586621679496884) = Signum arg6989586621679496920 Source #

data FromIntegerSym0 :: forall a6989586621679496884. (~>) Nat a6989586621679496884 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 a6989586621679496884 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (FromIntegerSym0 :: TyFun Nat k2 -> Type) (arg6989586621679496922 :: Nat) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (FromIntegerSym0 :: TyFun Nat k2 -> Type) (arg6989586621679496922 :: Nat) = (FromInteger arg6989586621679496922 :: k2)

type FromIntegerSym1 (arg6989586621679496922 :: Nat) = FromInteger arg6989586621679496922 Source #

data SubtractSym0 :: forall a6989586621679502341. (~>) a6989586621679502341 ((~>) a6989586621679502341 a6989586621679502341) 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 a6989586621679502341 (a6989586621679502341 ~> a6989586621679502341) -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (SubtractSym0 :: TyFun a6989586621679502341 (a6989586621679502341 ~> a6989586621679502341) -> Type) (a6989586621679502345 :: a6989586621679502341) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (SubtractSym0 :: TyFun a6989586621679502341 (a6989586621679502341 ~> a6989586621679502341) -> Type) (a6989586621679502345 :: a6989586621679502341) = SubtractSym1 a6989586621679502345

data SubtractSym1 (a6989586621679502345 :: a6989586621679502341) :: (~>) a6989586621679502341 a6989586621679502341 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 a6989586621679502345 :: TyFun a6989586621679502341 a6989586621679502341 -> Type) Source #
Instance details Defined in Data.Singletons.Prelude.Num Methods suppressUnusedWarnings :: () Source #
type Apply (SubtractSym1 a6989586621679502345 :: TyFun a a -> Type) (a6989586621679502346 :: a) Source #
Instance details Defined in Data.Singletons.Prelude.Num type Apply (SubtractSym1 a6989586621679502345 :: TyFun a a -> Type) (a6989586621679502346 :: a) = Subtract a6989586621679502345 a6989586621679502346

type SubtractSym2 (a6989586621679502345 :: a6989586621679502341) (a6989586621679502346 :: a6989586621679502341) = Subtract a6989586621679502345 a6989586621679502346 Source #