Data.Singletons.Prelude.Ord

Defines the promoted version of Ord, POrd, and the singleton version, SOrd.

Documentation

class (PEq (KProxy :: KProxy a), kproxy ~ KProxy) => POrd kproxy

Associated Types

type Compare arg arg :: Ordering

type arg :< arg :: Bool infix 4

type arg :<= arg :: Bool infix 4

type arg :> arg :: Bool infix 4

type arg :>= arg :: Bool infix 4

type Max arg arg :: a

type Min arg arg :: a

Instances

POrd Bool (KProxy Bool)

POrd Ordering (KProxy Ordering)

POrd () (KProxy ())

POrd [a] (KProxy [a])

POrd (Maybe a) (KProxy (Maybe a))

POrd (Either a b) (KProxy (Either a b))

POrd ((,) a b) (KProxy ((,) a b))

POrd ((,,) a b c) (KProxy ((,,) a b c))

POrd ((,,,) a b c d) (KProxy ((,,,) a b c d))

POrd ((,,,,) a b c d e) (KProxy ((,,,,) a b c d e))

POrd ((,,,,,) a b c d e f) (KProxy ((,,,,,) a b c d e f))

POrd ((,,,,,,) a b c d e f g) (KProxy ((,,,,,,) a b c d e f g))

class (SEq (KProxy :: KProxy a), kproxy ~ KProxy) => SOrd kproxy where

Minimal complete definition

Nothing

Methods

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

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

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

(%:>) :: forall t t. Sing t -> Sing t -> Sing (Apply (Apply (:>$) t) t :: Bool) infix 4

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

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

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

Instances

SOrd Bool (KProxy Bool)

SOrd Ordering (KProxy Ordering)

SOrd () (KProxy ())

(SOrd a0 (KProxy a0), SOrd [a0] (KProxy [a0])) => SOrd [a] (KProxy [a])

SOrd a0 (KProxy a0) => SOrd (Maybe a) (KProxy (Maybe a))

(SOrd a0 (KProxy a0), SOrd b0 (KProxy b0)) => SOrd (Either a b) (KProxy (Either a b))

(SOrd a0 (KProxy a0), SOrd b0 (KProxy b0)) => SOrd ((,) a b) (KProxy ((,) a b))

(SOrd a0 (KProxy a0), SOrd b0 (KProxy b0), SOrd c0 (KProxy c0)) => SOrd ((,,) a b c) (KProxy ((,,) a b c))

(SOrd a0 (KProxy a0), SOrd b0 (KProxy b0), SOrd c0 (KProxy c0), SOrd d0 (KProxy d0)) => SOrd ((,,,) a b c d) (KProxy ((,,,) a b c d))

(SOrd a0 (KProxy a0), SOrd b0 (KProxy b0), SOrd c0 (KProxy c0), SOrd d0 (KProxy d0), SOrd e0 (KProxy e0)) => SOrd ((,,,,) a b c d e) (KProxy ((,,,,) a b c d e))

(SOrd a0 (KProxy a0), SOrd b0 (KProxy b0), SOrd c0 (KProxy c0), SOrd d0 (KProxy d0), SOrd e0 (KProxy e0), SOrd f0 (KProxy f0)) => SOrd ((,,,,,) a b c d e f) (KProxy ((,,,,,) a b c d e f))

(SOrd a0 (KProxy a0), SOrd b0 (KProxy b0), SOrd c0 (KProxy c0), SOrd d0 (KProxy d0), SOrd e0 (KProxy e0), SOrd f0 (KProxy f0), SOrd g0 (KProxy g0)) => SOrd ((,,,,,,) a b c d e f g) (KProxy ((,,,,,,) a b c d e f g))

thenCmp returns its second argument if its first is EQ; otherwise, it returns its first argument.

thenCmp :: Ordering -> Ordering -> Ordering

type family ThenCmp a a :: Ordering

Equations

ThenCmp EQ x = x

ThenCmp LT _z_1627669159 = LTSym0

ThenCmp GT _z_1627669162 = GTSym0

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

data family Sing a

The singleton kind-indexed data family.

Instances

data Sing Bool where

• SFalse :: (~) Bool z False => Sing Bool z
• STrue :: (~) Bool z True => Sing Bool z

data Sing Ordering where

• SLT :: (~) Ordering z LT => Sing Ordering z
• SEQ :: (~) Ordering z EQ => Sing Ordering z
• SGT :: (~) Ordering z GT => Sing Ordering z

data Sing * where

• STypeRep :: Typeable * a => Sing * a

data Sing Nat where

• SNat :: KnownNat n => Sing Nat n

data Sing Symbol where

• SSym :: KnownSymbol n => Sing Symbol n

data Sing () where

• STuple0 :: (~) () z () => Sing () z

data Sing [a0] where

• SNil :: (~) [a] z ([] a) => Sing [a] z
• SCons :: (~) [a] z ((:) a n n) => Sing a n -> Sing [a] n -> Sing [a] z

data Sing (Maybe a0) where

• SNothing :: (~) (Maybe a) z (Nothing a) => Sing (Maybe a) z
• SJust :: (~) (Maybe a) z (Just a n) => Sing a n -> Sing (Maybe a) z

data Sing (TyFun k1 k2 -> *) = SLambda {

• applySing :: forall t. Sing k1 t -> Sing k2 ((@@) k2 k1 f t)

}

data Sing (Either a0 b0) where

• SLeft :: (~) (Either a b) z (Left a b n) => Sing a n -> Sing (Either a b) z
• SRight :: (~) (Either a b) z (Right a b n) => Sing b n -> Sing (Either a b) z

data Sing ((,) a0 b0) where

• STuple2 :: (~) ((,) a b) z ((,) a b n n) => Sing a n -> Sing b n -> Sing ((,) a b) z

data Sing ((,,) a0 b0 c0) where

• STuple3 :: (~) ((,,) a b c) z ((,,) a b c n n n) => Sing a n -> Sing b n -> Sing c n -> Sing ((,,) a b c) z

data Sing ((,,,) a0 b0 c0 d0) where

• STuple4 :: (~) ((,,,) a b c d) z ((,,,) a b c d n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing ((,,,) a b c d) z

data Sing ((,,,,) a0 b0 c0 d0 e0) where

• STuple5 :: (~) ((,,,,) a b c d e) z ((,,,,) a b c d e n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing ((,,,,) a b c d e) z

data Sing ((,,,,,) a0 b0 c0 d0 e0 f0) where

• STuple6 :: (~) ((,,,,,) a b c d e f) z ((,,,,,) a b c d e f n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing ((,,,,,) a b c d e f) z

data Sing ((,,,,,,) a0 b0 c0 d0 e0 f0 g0) where

• STuple7 :: (~) ((,,,,,,) a b c d e f g) z ((,,,,,,) a b c d e f g n n n n n n n) => Sing a n -> Sing b n -> Sing c n -> Sing d n -> Sing e n -> Sing f n -> Sing g n -> Sing ((,,,,,,) a b c d e f g) z

Defunctionalization symbols

data ThenCmpSym0 l

Instances

SuppressUnusedWarnings (TyFun Ordering (TyFun Ordering Ordering -> *) -> *) ThenCmpSym0

type Apply (TyFun Ordering Ordering -> *) Ordering ThenCmpSym0 l0 = ThenCmpSym1 l0

data ThenCmpSym1 l l

Instances

SuppressUnusedWarnings (Ordering -> TyFun Ordering Ordering -> *) ThenCmpSym1

type Apply Ordering Ordering (ThenCmpSym1 l1) l0 = ThenCmpSym2 l1 l0

type ThenCmpSym2 t t = ThenCmp t t

type LTSym0 = LT

type EQSym0 = EQ

type GTSym0 = GT

data CompareSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k Ordering -> *) -> *) (CompareSym0 k)

type Apply (TyFun k Ordering -> *) k (CompareSym0 k) l0 = CompareSym1 k l0

data CompareSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k Ordering -> *) (CompareSym1 k)

type Apply Ordering k (CompareSym1 k l1) l0 = CompareSym2 k l1 l0

type CompareSym2 t t = Compare t t

data (:<$) l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k Bool -> *) -> *) ((:<$) k)

type Apply (TyFun k Bool -> *) k ((:<$) k) l0 = (:<$$) k l0

data l :<$$ l

Instances

SuppressUnusedWarnings (k -> TyFun k Bool -> *) ((:<$$) k)

type Apply Bool k ((:<$$) k l1) l0 = (:<$$$) k l1 l0

type (:<$$$) t t = (:<) t t

data (:<=$) l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k Bool -> *) -> *) ((:<=$) k)

type Apply (TyFun k Bool -> *) k ((:<=$) k) l0 = (:<=$$) k l0

data l :<=$$ l

Instances

SuppressUnusedWarnings (k -> TyFun k Bool -> *) ((:<=$$) k)

type Apply Bool k ((:<=$$) k l1) l0 = (:<=$$$) k l1 l0

type (:<=$$$) t t = (:<=) t t

data (:>$) l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k Bool -> *) -> *) ((:>$) k)

type Apply (TyFun k Bool -> *) k ((:>$) k) l0 = (:>$$) k l0

data l :>$$ l

Instances

SuppressUnusedWarnings (k -> TyFun k Bool -> *) ((:>$$) k)

type Apply Bool k ((:>$$) k l1) l0 = (:>$$$) k l1 l0

type (:>$$$) t t = (:>) t t

data (:>=$) l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k Bool -> *) -> *) ((:>=$) k)

type Apply (TyFun k Bool -> *) k ((:>=$) k) l0 = (:>=$$) k l0

data l :>=$$ l

Instances

SuppressUnusedWarnings (k -> TyFun k Bool -> *) ((:>=$$) k)

type Apply Bool k ((:>=$$) k l1) l0 = (:>=$$$) k l1 l0

type (:>=$$$) t t = (:>=) t t

data MaxSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k k -> *) -> *) (MaxSym0 k)

type Apply (TyFun k k -> *) k (MaxSym0 k) l0 = MaxSym1 k l0

data MaxSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (MaxSym1 k)

type Apply k k (MaxSym1 k l1) l0 = MaxSym2 k l1 l0

type MaxSym2 t t = Max t t

data MinSym0 l

Instances

SuppressUnusedWarnings (TyFun k (TyFun k k -> *) -> *) (MinSym0 k)

type Apply (TyFun k k -> *) k (MinSym0 k) l0 = MinSym1 k l0

data MinSym1 l l

Instances

SuppressUnusedWarnings (k -> TyFun k k -> *) (MinSym1 k)

type Apply k k (MinSym1 k l1) l0 = MinSym2 k l1 l0

type MinSym2 t t = Min t t