Fcf.Class.Ord

Equality and ordering.

Note that equality doesn't really require a class, it can be defined uniformly as TyEq.

Order

data Compare :: a -> a -> Exp Ordering

Type-level compare for totally ordered data types.

Example

>>> :kind! Eval (Compare "a" "b")
Eval (Compare "a" "b") :: Ordering
= LT

>>> :kind! Eval (Compare '[1, 2, 3] '[1, 2, 3])
Eval (Compare '[1, 2, 3] '[1, 2, 3]) :: Ordering
= EQ

>>> :kind! Eval (Compare '[1, 3] '[1, 2])
Eval (Compare '[1, 3] '[1, 2]) :: Ordering
= GT

Instances

type Eval (Compare ('Left _a :: Either a b) ('Right _b :: Either a b) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Left _a :: Either a b) ('Right _b :: Either a b) :: Ordering -> Type) = 'LT

type Eval (Compare ('Right _a :: Either a b) ('Left _b :: Either a b) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Right _a :: Either a b) ('Left _b :: Either a b) :: Ordering -> Type) = 'GT

type Eval (Compare ('Left a2 :: Either a1 b1) ('Left b2 :: Either a1 b1) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Left a2 :: Either a1 b1) ('Left b2 :: Either a1 b1) :: Ordering -> Type) = Eval (Compare a2 b2)

type Eval (Compare ('Right a3 :: Either a2 a1) ('Right b :: Either a2 a1) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Right a3 :: Either a2 a1) ('Right b :: Either a2 a1) :: Ordering -> Type) = Eval (Compare a3 b)

type Eval (Compare 'EQ 'GT)

Defined in Fcf.Class.Ord

type Eval (Compare 'EQ 'GT) = 'LT

type Eval (Compare 'EQ 'LT)

Defined in Fcf.Class.Ord

type Eval (Compare 'EQ 'LT) = 'GT

type Eval (Compare 'GT 'EQ)

Defined in Fcf.Class.Ord

type Eval (Compare 'GT 'EQ) = 'GT

type Eval (Compare 'GT 'LT)

Defined in Fcf.Class.Ord

type Eval (Compare 'GT 'LT) = 'GT

type Eval (Compare 'LT 'EQ)

Defined in Fcf.Class.Ord

type Eval (Compare 'LT 'EQ) = 'LT

type Eval (Compare 'LT 'GT)

Defined in Fcf.Class.Ord

type Eval (Compare 'LT 'GT) = 'LT

type Eval (Compare a a :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare a a :: Ordering -> Type) = 'EQ

type Eval (Compare ('Just _a) ('Nothing :: Maybe a) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Just _a) ('Nothing :: Maybe a) :: Ordering -> Type) = 'GT

type Eval (Compare ('Nothing :: Maybe a) ('Just _b) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Nothing :: Maybe a) ('Just _b) :: Ordering -> Type) = 'LT

type Eval (Compare ('Nothing :: Maybe a) ('Nothing :: Maybe a) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Nothing :: Maybe a) ('Nothing :: Maybe a) :: Ordering -> Type) = 'EQ

type Eval (Compare ('Just a2) ('Just b) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('Just a2) ('Just b) :: Ordering -> Type) = Eval (Compare a2 b)

type Eval (Compare a b :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare a b :: Ordering -> Type) = CmpNat a b

type Eval (Compare a b :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare a b :: Ordering -> Type) = 'EQ

type Eval (Compare '(a3, a4) '(b1, b2) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare '(a3, a4) '(b1, b2) :: Ordering -> Type) = Eval (Compare a3 b1) <> Eval (Compare a4 b2)

type Eval (Compare '(a4, a5, a6) '(b1, b2, b3) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare '(a4, a5, a6) '(b1, b2, b3) :: Ordering -> Type) = (Eval (Compare a4 b1) <> Eval (Compare a5 b2)) <> Eval (Compare a6 b3)

type Eval (Compare 'False 'True)

Defined in Fcf.Class.Ord

type Eval (Compare 'False 'True) = 'GT

type Eval (Compare 'True 'False)

Defined in Fcf.Class.Ord

type Eval (Compare 'True 'False) = 'GT

type Eval (Compare a a :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare a a :: Ordering -> Type) = 'EQ

type Eval (Compare (_x ': _xs) ('[] :: [a]) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare (_x ': _xs) ('[] :: [a]) :: Ordering -> Type) = 'GT

type Eval (Compare (x ': xs) (y ': ys) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare (x ': xs) (y ': ys) :: Ordering -> Type) = Eval (Compare x y) <> Eval (Compare xs ys)

type Eval (Compare ('[] :: [k]) (_y ': _ys) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('[] :: [k]) (_y ': _ys) :: Ordering -> Type) = 'LT

type Eval (Compare ('[] :: [k]) ('[] :: [k]) :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare ('[] :: [k]) ('[] :: [k]) :: Ordering -> Type) = 'EQ

type Eval (Compare a b :: Ordering -> Type)

Defined in Fcf.Class.Ord

type Eval (Compare a b :: Ordering -> Type) = CmpSymbol a b

data (<=) :: a -> a -> Exp Bool

"Smaller than or equal to". Type-level version of (<=).

Example

>>> :kind! Eval ("b" <= "a")
Eval ("b" <= "a") :: Bool
= False

Instances

type Eval (a2 <= b :: Bool -> Type)

Defined in Fcf.Class.Ord

type Eval (a2 <= b :: Bool -> Type)

data (>=) :: a -> a -> Exp Bool

"Greater than or equal to". Type-level version of (>=).

Example

>>> :kind! Eval ("b" >= "a")
Eval ("b" >= "a") :: Bool
= True

Instances

type Eval (a2 >= b :: Bool -> Type)

Defined in Fcf.Class.Ord

type Eval (a2 >= b :: Bool -> Type)

data (<) :: a -> a -> Exp Bool

"Smaller than". Type-level version of (<).

Example

>>> :kind! Eval ("a" < "b")
Eval ("a" < "b") :: Bool
= True

Instances

type Eval (a2 < b :: Bool -> Type)

Defined in Fcf.Class.Ord

type Eval (a2 < b :: Bool -> Type)

data (>) :: a -> a -> Exp Bool

"Greater than". Type-level version of (>).

Example

>>> :kind! Eval ("b" > "a")
Eval ("b" > "a") :: Bool
= True

Instances

type Eval (a2 > b :: Bool -> Type)

Defined in Fcf.Class.Ord

type Eval (a2 > b :: Bool -> Type)

Equality

data TyEq :: a -> b -> Exp Bool

Type equality.

Details

The base library also defines a similar (==); it differs from TyEq in the following ways:

• TyEq is heterogeneous: its arguments may have different kinds;
• TyEq is reflexive: TyEq a a always reduces to True even if a is a variable.

Instances

type Eval (TyEq a b :: Bool -> Type)

Defined in Fcf.Utils

type Eval (TyEq a b :: Bool -> Type)