| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Numeric.Data.Fraction
Synopsis
- data Fraction a where
- pattern (:%:) :: a -> a -> Fraction a
- pattern (:%!) :: (HasCallStack, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Fraction a
- mkFraction :: (MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Either String (Fraction a)
- mkFractionTH :: (Lift a, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Code Q (Fraction a)
- (%%) :: (Lift a, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Code Q (Fraction a)
- unsafeFraction :: (HasCallStack, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Fraction a
- (%!) :: (HasCallStack, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Fraction a
- numerator :: Fraction a -> a
- denominator :: Fraction a -> a
- reduce :: (MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => Fraction a -> Fraction a
- _MkFraction :: (MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => ReversedPrism' (Fraction a) (a, a)
- rmatching :: (Is (ReversedOptic k) An_AffineTraversal, ReversibleOptic k) => Optic k NoIx b a t s -> s -> Either t a
Type
data Fraction a where Source #
Type for representing fractions. Designed to be similar to Ratio with
the primary difference that it does not require the following invariants
for its instances (e.g. Eq) to be sensible:
n / dis maximally reduced.d > 0.
This has a number of consequences.
Fraction's
Eqis based on an equivalence class, in contrast toRatio, which compares the numerator and denominator directly:- Fractions are reduced first, e.g.,
2 :%: 4 === 1 :%: 2. - Negative denominators are considered:
1 :%: 1 === -1 :%: -1.
- Fractions are reduced first, e.g.,
The denominator is given more consideration:
Showxxfirst. This is to make debugging easier.
Fraction IntegerField, and Fraction
NaturalSemiring.
Examples
>>>2 %! 6 == 1 %! 3True
>>>1 %! 1 == -1 %! -1True
>>>1 %! 7 >= 1 %! -2True
>>>-1 %! 7 >= 1 %! -2True
>>>import Data.Text.Display (display)>>>display $ 2 %! 6"1 / 3"
Since: 0.1
Bundled Patterns
| pattern (:%:) :: a -> a -> Fraction a infixr 5 | Unidirectional pattern synonym for Since: 0.1 |
| pattern (:%!) :: (HasCallStack, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Fraction a infixr 5 | Bidirectional pattern synonym for WARNING: Partial Since: 0.1 |
Instances
Creation
mkFraction :: (MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Either String (Fraction a) Source #
mkFractionTH :: (Lift a, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Code Q (Fraction a) Source #
Template haskell for creating a Fraction at compile-time.
Examples
>>>$$(mkFractionTH 7 2)UnsafeFraction 7 2
Since: 0.1
(%%) :: (Lift a, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Code Q (Fraction a) infixl 7 Source #
unsafeFraction :: (HasCallStack, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Fraction a Source #
Throws an error when given a denominator of 0.
WARNING: Partial
Examples
>>>unsafeFraction 7 2UnsafeFraction 7 2
Since: 0.1
(%!) :: (HasCallStack, MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => a -> a -> Fraction a infixl 7 Source #
Elimination
denominator :: Fraction a -> a Source #
Since: 0.1
Functions
reduce :: (MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => Fraction a -> Fraction a Source #
Reduces a fraction:
- Removes common factors.
- Factors out negative denominators.
reduce (0 :%: _) --> 0 :%: 1.
Examples
>>>reduce (7 %! 2)UnsafeFraction 7 2
>>>reduce (18 %! 10)UnsafeFraction 9 5
>>>reduce (-5 %! -5)UnsafeFraction 1 1
Since: 0.1
Optics
We provide a ReversedPrism' _MkFraction that allows for total
elimination and partial construction, along with LabelOptic instances for
"numerator" and "denominator".
Examples
>>>:set -XOverloadedLabels>>>import Optics.Core (set, view)>>>let x = 2 %! 7>>>view #numerator x2
>>>set #numerator 5 xUnsafeFraction 5 7
>>>view #denominator x7
_MkFraction :: (MEuclidean a, Normed a, Ord a, Semiring a, UpperBoundless a) => ReversedPrism' (Fraction a) (a, a) Source #
ReversedPrism' that enables total elimination and partial construction.
Examples
>>>import Optics.Core (view)>>>f = $$(2 %% 8)>>>view _MkFraction f(1,4)
>>>rmatching _MkFraction (0, 4)Right (UnsafeFraction 0 1)
>>>rmatching _MkFraction (1, 0)Left (1,0)
Since: 0.1
rmatching :: (Is (ReversedOptic k) An_AffineTraversal, ReversibleOptic k) => Optic k NoIx b a t s -> s -> Either t a Source #
Reversed matching. Useful with smart-constructor optics.
Since: 0.1