numeric-prelude-0.1.3.4: An experimental alternative hierarchy of numeric type classes

Number.NonNegativeChunky

Description

A lazy number type, which is a generalization of lazy Peano numbers. Comparisons can be made lazy and thus computations are possible which are impossible with strict number types, e.g. you can compute `let y = min (1+y) 2 in y`. You can even work with infinite values. However, depending on the granularity, the memory consumption is higher than that for strict number types. This number type is of interest for the merge operation of event lists, which allows for co-recursive merges.

Synopsis

# Documentation

data T a Source

A chunky non-negative number is a list of non-negative numbers. It represents the sum of the list elements. It is possible to represent a finite number with infinitely many chunks by using an infinite number of zeros.

Note the following problems:

Addition is commutative only for finite representations. E.g. `let y = min (1+y) 2 in y` is defined, `let y = min (y+1) 2 in y` is not.

The type is equivalent to `Numeric.NonNegative.Chunky`.

Instances

 C a => Eq (T a) (C a, Eq a, Show a, C a) => Fractional (T a) (C a, Eq a, Show a, C a) => Num (T a) C a => Ord (T a) Show a => Show (T a) (C a, Arbitrary a) => Arbitrary (T a) C a => Monoid (T a) C a => C (T a) (C a, C a) => C (T a) C a => C (T a) (Ord a, C a, C a) => C (T a) (C a, C a, C a) => C (T a) C a => C (T a) C a => C (T a) (C a, C a) => C (T a) (C a, C a) => C (T a) (C a, C a) => C (T a)

fromChunks :: C a => [a] -> T aSource

toChunks :: C a => T a -> [a]Source

fromNumber :: C a => a -> T aSource

toNumber :: C a => T a -> aSource

fromChunky98 :: (C a, C a) => T a -> T aSource

toChunky98 :: (C a, C a) => T a -> T aSource

minMaxDiff :: C a => T a -> T a -> (T a, T a, Bool)Source

In `minMaxDiff x y == (z,r,b)` `z` represents `min x y`, `r` represents `max x y - min x y`, and `xy == b` or `x>y ==> not b`, for `x==y` the value of b is arbitrary.

normalize :: C a => T a -> T aSource

Remove zero chunks.

isNull :: C a => T a -> BoolSource

isPositive :: C a => T a -> BoolSource