Safe Haskell | Safe |
---|---|

Language | Haskell98 |

Internally the range library converts your ranges into an internal
efficient representation of multiple ranges. When you do multiple unions and
intersections in a row converting to and from that data structure becomes
extra work that is not required. To amortize those costs away the `RangeExpr`

algebra exists. You can specify a tree of operations in advance and then
evaluate them all at once. This is not only useful for efficiency but for
parsing too. Build up `RangeExpr`

's whenever you wish to perform multiple
operations in a row, and evaluate it in one step to be as efficient as possible.

**Note:** This module is based on F-Algebras to do much of the heavy conceptual
lifting. If you have never seen F-Algebras before then I highly recommend reading
through this introductory content
from the School of Haskell.

## Examples

A simple example of using this module would look like this:

`>>>`

(A.eval . A.invert $ A.const [SingletonRange 5]) :: [Range Integer] [LowerBoundRange 6,UpperBoundRange 4] (0.01 secs, 597,656 bytes)`import qualified Data.Range.Algebra as A`

You can also use this module to evaluate range predicates.

## Synopsis

# Documentation

## Operations

invert :: RangeExpr a -> RangeExpr a Source #

Returns an expression that represents the inverse of the input expression.

union :: RangeExpr a -> RangeExpr a -> RangeExpr a Source #

Returns an expression that represents the set union of the input expressions.

intersection :: RangeExpr a -> RangeExpr a -> RangeExpr a Source #

Returns an expression that represents the set intersection of the input expressions.

difference :: RangeExpr a -> RangeExpr a -> RangeExpr a Source #

Returns an expression that represents the set difference of the input expressions.

## Evaluation

type Algebra f a = f a -> a Source #

This is an F-Algebra. You don't need to know what this is in order to be able to use this module, but, if you are interested you can read more on School of Haskell.

class RangeAlgebra a where Source #

Represents the fact that there exists an algebra for the given representation of a range, so that a range expression of the same type can be evaluated, yielding that representation.

eval :: Algebra RangeExpr a Source #

This function is used to convert your built expressions into ranges.

## Instances

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. |

RangeAlgebra (a -> Bool) Source # | Multiple ranges represented by a predicate function, indicating membership of a point in one of the ranges. |