| Portability | Haskell 98 |
|---|---|
| Stability | stable |
| Maintainer | haskell@henning-thielemann.de |
Numeric.NonNegative.Class
Description
A type class for non-negative numbers.
Prominent instances are Numeric.NonNegative.Wrapper.T and peano numbers.
This class cannot do any checks,
but it let you show to the user what arguments your function expects.
Thus you must define class instances with care.
In fact many standard functions (take, '(!!)', ...)
should have this type class constraint.
- class (Ord a, Monoid a) => C a where
- splitDefault :: (Ord b, Num b) => (a -> b) -> (b -> a) -> a -> a -> (a, (Bool, a))
- (-|) :: C a => a -> a -> a
- zero :: C a => a
- add :: C a => a -> a -> a
- sum :: C a => [a] -> a
- maximum :: C a => [a] -> a
- switchDifferenceNegative :: C a => a -> a -> (a -> b) -> (a -> b) -> b
- switchDifferenceOrdering :: C a => a -> a -> b -> (a -> b) -> (a -> b) -> b
Documentation
class (Ord a, Monoid a) => C a whereSource
Instances of this class must ensure non-negative values.
We cannot enforce this by types, but the type class constraint NonNegative.C
avoids accidental usage of types which allow for negative numbers.
The Monoid superclass contributes a zero and an addition.
Methods
split :: a -> a -> (a, (Bool, a))Source
split x y == (m,(b,d)) means that
b == (x<=y),
m == min x y,
d == max x y - min x y, that is d == abs(x-y).
We have chosen this function as base function, since it provides comparison and subtraction in one go, which is important for replacing common structures like
if x<=y then f(x-y) else g(y-x)
that lead to a memory leak for peano numbers.
We have choosen the simple check x<=y
instead of a full-blown compare,
since we want Zero <= undefined for peano numbers.
Because of undefined values split is in general
not commutative in the sense
let (m0,(b0,d0)) = split x y
(m1,(b1,d1)) = split y x
in m0==m1 && d0==d1
The result values are in the order
in which they are generated for Peano numbers.
We have chosen the nested pair instead of a triple
in order to prevent a memory leak
that occurs if you only use b and d and ignore m.
This is demonstrated by test cases
Chunky.splitSpaceLeak3 and Chunky.splitSpaceLeak4.
splitDefault :: (Ord b, Num b) => (a -> b) -> (b -> a) -> a -> a -> (a, (Bool, a))Source
(-|) :: C a => a -> a -> aSource
x -| y == max 0 (x-y)
The default implementation is not efficient,
because it compares the values and then subtracts, again, if safe.
max 0 (x-y) is more elegant and efficient
but not possible in the general case,
since x-y may already yield a negative number.
maximum :: C a => [a] -> aSource
Left biased maximum of a list of numbers that can also be empty. It holds
maximum [] == zero
switchDifferenceNegative :: C a => a -> a -> (a -> b) -> (a -> b) -> bSource
In switchDifferenceNegative x y branchXminusY branchYminusX
the function branchXminusY is applied to x-y
if this difference is non-negative,
otherwise branchYminusX is applied to y-x.
switchDifferenceOrdering :: C a => a -> a -> b -> (a -> b) -> (a -> b) -> bSource
In switchDifferenceOrdering x y branchZero branchXminusY branchYminusX