range-0.3.0.2: An efficient and versatile range library.

Data.Range

Description

This module provides a simple api to access range functionality. It provides standard set operations on ranges, the ability to merge ranges together and, importantly, the ability to check if a value is within a range. The primary benifit of the Range library is performance and versatility.

Note: It is intended that you will read the documentation in this module from top to bottom.

# Understanding custom range syntax

This library supports five different types of ranges:

• SpanRange: A range starting from a value and ending with another value.
• SingletonRange: This range is really just a shorthand for a range that starts and ends with the same value.
• LowerBoundRange: A range that starts at a value and extends infinitely in the positive direction.
• UpperBoundRange: A range that starts at a value and extends infinitely in the negative direction.
• InfiniteRange: A range that includes all values in your range.

All of these ranges are bounded in an Inclusive or Exclusive manner.

To run through a simple example of what this looks like, let's start with mathematical notation and then move into our own notation.

The bound [1, 5) says "All of the numbers from one to five, including one but excluding 5."

Using the data types directly, you could write this as:

SpanRange (Bound 1 Inclusive) (Bound 5 Exclusive)

This is overly verbose, as a result, this library contains operators and functions for writing this much more succinctly. The above example could be written as:

1 +=* 5

There the + symbol is used to represent the inclusive side of a range and the * symbol is used to represent the exclusive side of a range.

The Show instance of the Range class will actually output these simplified helper functions, for example:

>>> [SingletonRange 5, SpanRange (Bound 1 Inclusive) (Bound 5 Exclusive), InfiniteRange]
[SingletonRange 5,1 +=* 5,inf]


There are lbi, lbe, ubi and ube functions to create lower bound inclusive, lower bound exclusive, upper bound inclusive and upper bound exclusive ranges respectively.

SingletonRange x is equivalent to x +=+ x but is nicer for presentational purposes in a Show.

Now that you know the basic syntax to declare ranges, the following uses cases will be easier to understand.

# Use case 1: Basic Integer Range

The standard use case for this library is efficiently discovering if an integer is within a given range.

For example, if we had the range made up of the inclusive unions of [5, 10] and [20, 30] and [25, Infinity) then we could instantiate, and simplify, such a range like this:

>>> mergeRanges [(5 :: Integer) +=+ 10, 20 +=+ 30, lbi 25]
[5 +=+ 10,lbi 20]


You can then test if elements are within this range:

>>> let ranges = mergeRanges [(5 :: Integer) +=+ 10, 20 +=+ 30, lbi 25]
>>> inRanges ranges 7
True
>>> inRanges ranges 50
True
>>> inRanges ranges 15
False


The other convenience methods in this library will help you perform more range operations.

# Use case 2: Version ranges

All the Range library really needs to work, is the Ord type. If you have a data type that can be ordered, than we can perform range calculations on it. The Data.Version type is an excellent example of this. For example, let's say that you want to say: "I accept a version range of [1.1.0, 1.2.1] or [1.3, 1.4) or [1.4, 1.4.2)" then you can write that as:

>>> :m + Data.Version
>>> let v x = Version x []
>>> let ranges = mergeRanges [v [1, 1, 0] +=+ v [1,2,1], v [1,3] +=* v [1,4], v [1,4] +=* v [1,4,2]]
>>> inRanges ranges (v [1,0])
False
>>> inRanges ranges (v [1,5])
False
>>> inRanges ranges (v [1,1,5])
True
>>> inRanges ranges (v [1,3,5])
True


As you can see, it is almost identical to the previous example, yet you are now comparing if a version is within a version range! Not only that, but so long as your type is orderable, the ranges can be merged together cleanly.

With any luck, you can apply this library to your use case of choice. Good luck!

Synopsis

# Range creation

(+=+) :: a -> a -> Range a Source #

Mathematically equivalent to [x, y].

x +=+ y is the short version of SpanRange (Bound x Inclusive) (Bound y Inclusive)

(+=*) :: a -> a -> Range a Source #

Mathematically equivalent to [x, y).

x +=* y is the short version of SpanRange (Bound x Inclusive) (Bound y Exclusive)

(*=+) :: a -> a -> Range a Source #

Mathematically equivalent to (x, y].

x *=+ y is the short version of SpanRange (Bound x Exclusive) (Bound y Inclusive)

(*=*) :: a -> a -> Range a Source #

Mathematically equivalent to (x, y).

x *=* y is the short version of SpanRange (Bound x Exclusive) (Bound y Exclusive)

lbi :: a -> Range a Source #

Mathematically equivalent to [x, Infinity).

lbi x is the short version of LowerBoundRange (Bound x Inclusive)

lbe :: a -> Range a Source #

Mathematically equivalent to (x, Infinity).

lbe x is the short version of LowerBoundRange (Bound x Exclusive)

ubi :: a -> Range a Source #

Mathematically equivalent to (Infinity, x].

ubi x is the short version of UpperBoundRange (Bound x Inclusive)

ube :: a -> Range a Source #

Mathematically equivalent to (Infinity, x).

ube x is the short version of UpperBoundRange (Bound x Exclusive)

Shorthand for the InfiniteRange

# Comparison functions

inRange :: Ord a => Range a -> a -> Bool Source #

Given a range and a value it will tell you wether or not the value is in the range. Remember that all ranges are inclusive.

The primary value of this library is performance and this method can be used to show this quite clearly. For example, you can try and approximate basic range functionality with "Data.List.elem" so we can generate an apples to apples comparison in GHCi:

>>> :set +s
>>> elem (10000000 :: Integer) [1..10000000]
True
(0.26 secs, 720,556,888 bytes)
>>> inRange (1 +=+ 10000000) (10000000 :: Integer)
True
(0.00 secs, 557,656 bytes)
>>> 


As you can see, this function is significantly more performant, in both speed and memory, than using the elem function.

inRanges :: Ord a => [Range a] -> a -> Bool Source #

Given a list of ranges this function tells you if a value is in any of those ranges. This is especially useful for more complex ranges.

aboveRange :: Ord a => Range a -> a -> Bool Source #

Checks if the value provided is above (or greater than) the biggest value in the given range.

The LowerBoundRange and the InfiniteRange will always cause this method to return False because you can't have a value higher than them since they are both infinite in the positive direction.

>>> aboveRange (SingletonRange 5) (6 :: Integer)
True
>>> aboveRange (1 +=+ 5) (6 :: Integer)
True
>>> aboveRange (1 +=+ 5) (0 :: Integer)
False
>>> aboveRange (lbi 0) (6 :: Integer)
False
>>> aboveRange (ubi 0) (6 :: Integer)
True
>>> aboveRange inf (6 :: Integer)
False


aboveRanges :: Ord a => [Range a] -> a -> Bool Source #

Checks if the value provided is above all of the ranges provided.

belowRange :: Ord a => Range a -> a -> Bool Source #

Checks if the value provided is below (or less than) the smallest value in the given range.

The UpperBoundRange and the InfiniteRange will always cause this method to return False because you can't have a value lower than them since they are both infinite in the negative direction.

>>> belowRange (SingletonRange 5) (4 :: Integer)
True
>>> belowRange (1 +=+ 5) (0 :: Integer)
True
>>> belowRange (1 +=+ 5) (6 :: Integer)
False
>>> belowRange (lbi 6) (0 :: Integer)
True
>>> belowRange (ubi 6) (0 :: Integer)
False
>>> belowRange inf (6 :: Integer)
False


belowRanges :: Ord a => [Range a] -> a -> Bool Source #

Checks if the value provided is below all of the ranges provided.

rangesOverlap :: Ord a => Range a -> Range a -> Bool Source #

A check to see if two ranges overlap. The ranges overlap if at least one value exists within both ranges. If they do overlap then true is returned; false otherwise.

For example:

>>> rangesOverlap (1 +=+ 5) (3 +=+ 7)
True
>>> rangesOverlap (1 +=+ 5) (5 +=+ 7)
True
>>> rangesOverlap (1 +=* 5) (5 +=+ 7)
False


The last case of these three is the primary "gotcha" of this method. With [1, 5) and [5, 7] there is no value that exists within both ranges. Therefore, technically, the ranges do not overlap. If you expected this to return True then it is likely that you would prefer to use rangesAdjoin instead.

rangesAdjoin :: Ord a => Range a -> Range a -> Bool Source #

A check to see if two ranges overlap or adjoin. The ranges adjoin if no values exist between them. If they do overlap or adjoin then true is returned; false otherwise.

For example:

>>> rangesAdjoin (1 +=+ 5) (3 +=+ 7)
True
>>> rangesAdjoin (1 +=+ 5) (5 +=+ 7)
True
>>> rangesAdjoin (1 +=* 5) (5 +=+ 7)
True


The last case of these three is the primary "gotcha" of this method. With [1, 5) and [5, 7] there exist no values between them. Therefore the ranges adjoin. If you expected this to return False then it is likely that you would prefer to use rangesOverlap instead.

# Set operations

mergeRanges :: Ord a => [Range a] -> [Range a] Source #

An array of ranges may have overlaps; this function will collapse that array into as few Ranges as possible. For example:

>>> mergeRanges [lbi 12, 1 +=+ 10, 5 +=+ (15 :: Integer)]
[lbi 1]
(0.01 secs, 588,968 bytes)


As you can see, the mergeRanges method collapsed multiple ranges into a single range that still covers the same surface area.

This may be useful for a few use cases:

• You are hyper concerned about performance and want to have the minimum number of ranges for comparison in the inRanges function.
• You wish to display ranges to a human and want to show the minimum number of ranges to avoid having to make people perform those calculations themselves.

Please note that the use of any of the operations on sets of ranges like invert, union and intersection will have the same behaviour as mergeRanges as a side effect. So, for example, this is redundant:

mergeRanges . union []


union :: Ord a => [Range a] -> [Range a] -> [Range a] Source #

Performs a set union between the two input ranges and returns the resultant set of ranges.

For example:

>>> union [1 +=+ 10] [5 +=+ (15 :: Integer)]
[1 +=+ 15]
(0.00 secs, 587,152 bytes)


intersection :: Ord a => [Range a] -> [Range a] -> [Range a] Source #

Performs a set intersection between the two input ranges and returns the resultant set of ranges.

For example:

>>> intersection [1 +=* 10] [5 +=+ (15 :: Integer)]
[5 +=* 10]
(0.00 secs, 584,616 bytes)


difference :: Ord a => [Range a] -> [Range a] -> [Range a] Source #

Performs a set difference between the two input ranges and returns the resultant set of ranges.

For example:

>>> difference [1 +=+ 10] [5 +=+ (15 :: Integer)]
[1 +=* 5]
(0.00 secs, 590,424 bytes)


invert :: Ord a => [Range a] -> [Range a] Source #

An inversion function, given a set of ranges it returns the inverse set of ranges.

For example:

>>> invert [1 +=* 10, 15 *=+ (20 :: Integer)]
[ube 1,10 +=+ 15,lbe 20]
(0.00 secs, 623,456 bytes)


# Enumerable methods

fromRanges :: (Ord a, Enum a) => [Range a] -> [a] Source #

Instantiate all of the values in a range.

Warning: This method is meant as a convenience method, it is not efficient.

A set of ranges represents a collection of real values without actually instantiating those values. Not instantiating ranges, allows the range library to support infinite ranges and be super performant.

However, sometimes you actually want to get the values that your range represents, or even get a sample set of the values. This function generates as many of the values that belong to your range as you like.

Because ranges can be infinite, it is highly recommended to combine this method with something like "Data.List.take" to avoid an infinite recursion.

This method will attempt to take a sample from all of the ranges that you have provided, however it is not guaranteed that you will get an even sampling. All that is guaranteed is that you will only get back values that are within one or more of the ranges you provide.

## Examples

A simple span:

>>> take 5 . fromRanges $[1 +=+ 10 :: Range Integer, 20 +=+ 30] [1,20,2,21,3] (0.01 secs, 566,016 bytes)  An infinite range: >>> take 5 . fromRanges$ [inf :: Range Integer]
[0,1,-1,2,-2]
(0.00 secs, 566,752 bytes)


joinRanges :: (Ord a, Enum a) => [Range a] -> [Range a] Source #

Joins together ranges that we only know can be joined because of the Enum class.

To make the purpose of this method easier to understand, let's run throuh a simple example:

>>> mergeRanges [1 +=+ 5, 6 +=+ 10] :: [Range Integer]
[1 +=+ 5,6 +=+ 10]


In this example, you know that the values are all of the type Integer. Because of this, you know that there are no values between 5 and 6. You may expect that the mergeRanges function should "just know" that it can merge these together; but it can't because it does not have the required constraints. This becomes more obvious if you modify the example to use Double instead:

>>> mergeRanges [1.5 +=+ 5.5, 6.5 +=+ 10.5] :: [Range Double]
[1.5 +=+ 5.5,6.5 +=+ 10.5]


Now we can see that there are an infinite number of values between 5.5 and 6.5 and thus no such join between the two ranges could occur.

This function, joinRanges, provides the missing piece that you would expect:

>>> joinRanges $mergeRanges [1 +=+ 5, 6 +=+ 10] :: [Range Integer] [1 +=+ 10]  You can use this method to ensure that all ranges for whom the value implements Enum can be compressed to their smallest representation. # Data types data Bound a Source # Represents a bound at a particular value with a BoundType. There is no implicit understanding if this is a lower or upper bound, it could be either. Constructors  Bound FieldsboundValue :: aThe value at the edge of this bound.boundType :: BoundTypeThe type of bound. Should be Inclusive or Exclusive. Instances  Source # Instance detailsDefined in Data.Range.Data Methodsfmap :: (a -> b) -> Bound a -> Bound b #(<$) :: a -> Bound b -> Bound a # Eq a => Eq (Bound a) Source # Instance detailsDefined in Data.Range.Data Methods(==) :: Bound a -> Bound a -> Bool #(/=) :: Bound a -> Bound a -> Bool # Show a => Show (Bound a) Source # Instance detailsDefined in Data.Range.Data MethodsshowsPrec :: Int -> Bound a -> ShowS #show :: Bound a -> String #showList :: [Bound a] -> ShowS #

data BoundType Source #

Represents a type of boundary.

Constructors

 Inclusive The value at the boundary should be included in the bound. Exclusive The value at the boundary should be excluded in the bound.
Instances
 Source # Instance detailsDefined in Data.Range.Data Methods Source # Instance detailsDefined in Data.Range.Data MethodsshowList :: [BoundType] -> ShowS #

data Range a Source #

The Range Data structure; it is capable of representing any type of range. This is the primary data structure in this library. Everything should be possible to convert back into this datatype. All ranges in this structure are inclusively bound.

Constructors

 SingletonRange a Represents a single element as a range. SingletonRange a is equivalent to SpanRange (Bound a Inclusive) (Bound a Inclusive). SpanRange (Bound a) (Bound a) Represents a bounded span of elements. The first argument is expected to be less than or equal to the second argument. LowerBoundRange (Bound a) Represents a range with a finite lower bound and an infinite upper bound. UpperBoundRange (Bound a) Represents a range with an infinite lower bound and a finite upper bound. InfiniteRange Represents an infinite range over all values.
Instances
 Source # Instance detailsDefined in Data.Range.Data Methodsfmap :: (a -> b) -> Range a -> Range b #(<\$) :: a -> Range b -> Range a # Eq a => Eq (Range a) Source # Instance detailsDefined in Data.Range.Data Methods(==) :: Range a -> Range a -> Bool #(/=) :: Range a -> Range a -> Bool # Show a => Show (Range a) Source # Instance detailsDefined in Data.Range.Data MethodsshowsPrec :: Int -> Range a -> ShowS #show :: Range a -> String #showList :: [Range a] -> ShowS # Ord a => RangeAlgebra [Range a] Source # Multiple ranges represented by a list of disjoint ranges. Note that input ranges are allowed to overlap, but the output ranges are guaranteed to be disjoint. Instance detailsDefined in Data.Range.Algebra Methods