Data.Enum

class (Ord a) <= Enum a  where

Type class for enumerations.

Laws:

• Successor: all (a < _) (succ a)
• Predecessor: all (_ < a) (pred a)
• Succ retracts pred: pred >=> succ >=> pred = pred
• Pred retracts succ: succ >=> pred >=> succ = succ
• Non-skipping succ: b <= a || any (_ <= b) (succ a)
• Non-skipping pred: a <= b || any (b <= _) (pred a)

The retraction laws can intuitively be understood as saying that succ is the opposite of pred; if you apply succ and then pred to something, you should end up with what you started with (although of course this doesn't apply if you tried to succ the last value in an enumeration and therefore got Nothing out).

The non-skipping laws can intuitively be understood as saying that succ shouldn't skip over any elements of your type. For example, without the non-skipping laws, it would be permissible to write an Enum Int instance where succ x = Just (x+2), and similarly pred x = Just (x-2).

Members

• succ :: a -> Maybe a
• pred :: a -> Maybe a

Instances

• Enum Boolean
• Enum Int
• Enum Char
• Enum Unit
• Enum Ordering
• (BoundedEnum a) => Enum (Maybe a)
• (BoundedEnum a, BoundedEnum b) => Enum (Either a b)
• (Enum a, BoundedEnum b) => Enum (Tuple a b)

class (Bounded a, Enum a) <= BoundedEnum a  where

Type class for finite enumerations.

This should not be considered a part of a numeric hierarchy, as in Haskell. Rather, this is a type class for small, ordered sum types with statically-determined cardinality and the ability to easily compute successor and predecessor elements like DayOfWeek.

Laws:

• succ bottom >>= succ >>= succ ... succ [cardinality - 1 times] == top
• pred top >>= pred >>= pred ... pred [cardinality - 1 times] == bottom
• forall a > bottom: pred a >>= succ == Just a
• forall a < top: succ a >>= pred == Just a
• forall a > bottom: fromEnum <$> pred a = pred (fromEnum a)
• forall a < top: fromEnum <$> succ a = succ (fromEnum a)
• e1 `compare` e2 == fromEnum e1 `compare` fromEnum e2
• toEnum (fromEnum a) = Just a

Members

• cardinality :: Cardinality a
• toEnum :: Int -> Maybe a
• fromEnum :: a -> Int

Instances

• BoundedEnum Boolean
• BoundedEnum Char
• BoundedEnum Unit
• BoundedEnum Ordering

toEnumWithDefaults :: forall a. BoundedEnum a => a -> a -> Int -> a

Like toEnum but returns the first argument if x is less than fromEnum bottom and the second argument if x is greater than fromEnum top.

toEnumWithDefaults False True (-1) -- False
toEnumWithDefaults False True 0    -- False
toEnumWithDefaults False True 1    -- True
toEnumWithDefaults False True 2    -- True

newtype Cardinality a

A type for the size of finite enumerations.

Constructors

• Cardinality Int

Instances

• Newtype (Cardinality a) _
• Eq (Cardinality a)
• Ord (Cardinality a)
• Show (Cardinality a)

enumFromTo :: forall a u. Enum a => Unfoldable1 u => a -> a -> u a

Returns a contiguous sequence of elements from the first value to the second value (inclusive).

enumFromTo 0 3 = [0, 1, 2, 3]
enumFromTo 'c' 'a' = ['c', 'b', 'a']

The example shows Array return values, but the result can be any type with an Unfoldable1 instance.

enumFromThenTo :: forall f a. Unfoldable f => Functor f => BoundedEnum a => a -> a -> a -> f a

Returns a sequence of elements from the first value, taking steps according to the difference between the first and second value, up to (but not exceeding) the third value.

enumFromThenTo 0 2 6 = [0, 2, 4, 6]
enumFromThenTo 0 3 5 = [0, 3]

Note that there is no BoundedEnum instance for integers, they're just being used here for illustrative purposes to help clarify the behaviour.

The example shows Array return values, but the result can be any type with an Unfoldable1 instance.

upFrom :: forall a u. Enum a => Unfoldable u => a -> u a

Produces all successors of an Enum value, excluding the start value.

upFromIncluding :: forall a u. Enum a => Unfoldable1 u => a -> u a

Produces all successors of an Enum value, including the start value.

upFromIncluding bottom will return all values in an Enum.

downFrom :: forall a u. Enum a => Unfoldable u => a -> u a

Produces all predecessors of an Enum value, excluding the start value.

downFromIncluding :: forall a u. Enum a => Unfoldable1 u => a -> u a

Produces all predecessors of an Enum value, including the start value.

downFromIncluding top will return all values in an Enum, in reverse order.

defaultSucc :: forall a. (Int -> Maybe a) -> (a -> Int) -> a -> Maybe a

Provides a default implementation for succ, given a function that maps integers to values in the Enum, and a function that maps values in the Enum back to integers. The integer mapping must agree in both directions for this to implement a law-abiding succ.

If a BoundedEnum instance exists for a, the toEnum and fromEnum functions can be used here:

succ = defaultSucc toEnum fromEnum

defaultPred :: forall a. (Int -> Maybe a) -> (a -> Int) -> a -> Maybe a

Provides a default implementation for pred, given a function that maps integers to values in the Enum, and a function that maps values in the Enum back to integers. The integer mapping must agree in both directions for this to implement a law-abiding pred.

If a BoundedEnum instance exists for a, the toEnum and fromEnum functions can be used here:

pred = defaultPred toEnum fromEnum

defaultCardinality :: forall a. Bounded a => Enum a => Cardinality a

Provides a default implementation for cardinality.

Runs in O(n) where n is fromEnum top

defaultToEnum :: forall a. Bounded a => Enum a => Int -> Maybe a

Provides a default implementation for toEnum.

• Assumes fromEnum bottom = 0.
• Cannot be used in conjuction with defaultSucc.

Runs in O(n) where n is fromEnum a.

defaultFromEnum :: forall a. Enum a => a -> Int

Provides a default implementation for fromEnum.

• Assumes toEnum 0 = Just bottom.
• Cannot be used in conjuction with defaultPred.

Runs in O(n) where n is fromEnum a.