Safe Haskell	Safe
Language	Haskell2010

Fcf.Class.Ord

Contents

Order
Equality

Description

Equality and ordering.

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

Synopsis

data Compare :: a -> a -> Exp Ordering
data (<=) :: a -> a -> Exp Bool
data (>=) :: a -> a -> Exp Bool
data (<) :: a -> a -> Exp Bool
data (>) :: a -> a -> Exp Bool
data TyEq :: a -> b -> Exp Bool

Order

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

Type-level compare for totally ordered data types.

Example

Expand

>>> :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 False True) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare False True) = GT
type Eval (Compare True False) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare True False) = GT
type Eval (Compare a a :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare a a :: Ordering -> Type) = EQ
type Eval (Compare (_x ': _xs) ([] :: [a]) :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare (_x ': _xs) ([] :: [a]) :: Ordering -> Type) = GT
type Eval (Compare ([] :: [k]) (_y ': _ys) :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare ([] :: [k]) (_y ': _ys) :: Ordering -> Type) = LT
type Eval (Compare (x ': xs) (y ': ys) :: Ordering -> Type) Source #
Instance details 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]) ([] :: [k]) :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare ([] :: [k]) ([] :: [k]) :: Ordering -> Type) = EQ
type Eval (Compare (Just _a) (Nothing :: Maybe a) :: Ordering -> Type) Source #
Instance details 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) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare (Nothing :: Maybe a) (Just _b) :: Ordering -> Type) = LT
type Eval (Compare (Just a2) (Just b) :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare (Just a2) (Just b) :: Ordering -> Type) = Eval (Compare a2 b)
type Eval (Compare (Nothing :: Maybe a) (Nothing :: Maybe a) :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare (Nothing :: Maybe a) (Nothing :: Maybe a) :: Ordering -> Type) = EQ
type Eval (Compare LT EQ) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare LT EQ) = LT
type Eval (Compare LT GT) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare LT GT) = LT
type Eval (Compare EQ LT) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare EQ LT) = GT
type Eval (Compare EQ GT) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare EQ GT) = LT
type Eval (Compare GT LT) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare GT LT) = GT
type Eval (Compare GT EQ) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare GT EQ) = GT
type Eval (Compare a a :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare a a :: Ordering -> Type) = EQ
type Eval (Compare (Right _a :: Either a b) (Left _b :: Either a b) :: Ordering -> Type) Source #
Instance details 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 _a :: Either a b) (Right _b :: Either a b) :: Ordering -> Type) Source #
Instance details 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 a3 :: Either a2 a1) (Right b :: Either a2 a1) :: Ordering -> Type) Source #
Instance details 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 (Left a2 :: Either a1 b1) (Left b2 :: Either a1 b1) :: Ordering -> Type) Source #
Instance details 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 a b :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare a b :: Ordering -> Type) = CmpNat a b
type Eval (Compare a b :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare a b :: Ordering -> Type) = CmpSymbol a b
type Eval (Compare a b :: Ordering -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (Compare a b :: Ordering -> Type) = EQ
type Eval (Compare ((,) a3 a4) ((,) b1 b2) :: Ordering -> Type) Source #
Instance details 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) Source #
Instance details 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)

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

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

Example

Expand

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

Instances

type Eval (a2 <= b :: Bool -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (a2 <= b :: Bool -> Type)

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

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

Example

Expand

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

Instances

type Eval (a2 >= b :: Bool -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (a2 >= b :: Bool -> Type)

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

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

Example

Expand

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

Instances

type Eval (a2 < b :: Bool -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (a2 < b :: Bool -> Type)

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

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

Example

Expand

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

Instances

type Eval (a2 > b :: Bool -> Type) Source #
Instance details Defined in Fcf.Class.Ord type Eval (a2 > b :: Bool -> Type)

Equality

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

Type equality.

Details

Expand

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) Source #
Instance details Defined in Fcf.Utils type Eval (TyEq a b :: Bool -> Type)