Ranged-sets-0.3.0: Ranged sets for Haskell

Portability | portable
Stability | experimental
Maintainer | paul@cogito.org.uk
Safe Haskell | None

Data.Ranged.Boundaries

Description

Synopsis

- class Ord a => DiscreteOrdered a where
  - adjacent :: a -> a -> Bool
  - adjacentBelow :: a -> Maybe a
- enumAdjacent :: (Ord a, Enum a) => a -> a -> Bool
- boundedAdjacent :: (Ord a, Enum a) => a -> a -> Bool
- boundedBelow :: (Eq a, Enum a, Bounded a) => a -> Maybe a
- data Boundary a
  - = BoundaryAbove a
  - | BoundaryBelow a
  - | BoundaryAboveAll
  - | BoundaryBelowAll
- above :: Ord v => Boundary v -> v -> Bool
- (/>/) :: Ord v => v -> Boundary v -> Bool

# Documentation

class Ord a => DiscreteOrdered a where Source

Distinguish between dense and sparse ordered types. A dense type is one in which any two values `v1 < v2` have a third value `v3` such that `v1 < v3 < v2`.

In theory the floating types are dense, although in practice they can only have finitely many values. This class treats them as dense.

Tuples up to 4 members are declared as instances. Larger tuples may be added if necessary.

Most values of sparse types have an `adjacentBelow`, such that, for all x:

     case adjacentBelow x of
        Just x1 -> adjacent x1 x
        Nothing -> True

The exception is for bounded types when `x == lowerBound`. For dense types `adjacentBelow` always returns `Nothing`.

This approach was suggested by Ben Rudiak-Gould on comp.lang.functional.

Methods

adjacent :: a -> a -> Bool Source

Two values `x` and `y` are adjacent if `x < y` and there does not exist a third value between them. Always `False` for dense types.

adjacentBelow :: a -> Maybe aSource

The value immediately below the argument, if it can be determined.

Instances

DiscreteOrdered Bool |
DiscreteOrdered Char |
DiscreteOrdered Double |
DiscreteOrdered Float |
DiscreteOrdered Int |
DiscreteOrdered Integer |
DiscreteOrdered Ordering |
Ord a => DiscreteOrdered [a] |
Integral a => DiscreteOrdered (Ratio a) |
(Ord a, DiscreteOrdered b) => DiscreteOrdered (a, b) |
(Ord a, Ord b, DiscreteOrdered c) => DiscreteOrdered (a, b, c) |
(Ord a, Ord b, Ord c, DiscreteOrdered d) => DiscreteOrdered (a, b, c, d) |

enumAdjacent :: (Ord a, Enum a) => a -> a -> Bool Source

Check adjacency for sparse enumerated types (i.e. where there is no value between `x` and `succ x`).

boundedAdjacent :: (Ord a, Enum a) => a -> a -> Bool Source

Check adjacency, allowing for case where x = maxBound. Use as the definition of adjacent for bounded enumerated types such as Int and Char.

boundedBelow :: (Eq a, Enum a, Bounded a) => a -> Maybe aSource

The usual implementation of `adjacentBelow` for bounded enumerated types.

data Boundary a Source

A Boundary is a division of an ordered type into values above and below the boundary. No value can sit on a boundary.

Known bug: for Bounded types

-     BoundaryAbove maxBound < BoundaryAboveAll

-     BoundaryBelow minBound > BoundaryBelowAll

This is incorrect because there are no possible values in between the left and right sides of these inequalities.

Constructors

BoundaryAbove a | The argument is the highest value below the boundary.
BoundaryBelow a | The argument is the lowest value above the boundary.
BoundaryAboveAll | The boundary above all values.
BoundaryBelowAll | The boundary below all values.

Instances

DiscreteOrdered a => Eq (Boundary a) |
DiscreteOrdered a => Ord (Boundary a) |
Show a => Show (Boundary a) |
Arbitrary a => Arbitrary (Boundary a) |
CoArbitrary a => CoArbitrary (Boundary a) |

above :: Ord v => Boundary v -> v -> Bool Source

True if the value is above the boundary, false otherwise.

(/>/) :: Ord v => v -> Boundary v -> Bool Source

Same as `above`, but with the arguments reversed for more intuitive infix usage.