Numeric.Lens

Documentation

base :: Integral a => Int -> Prism' String a

A prism that shows and reads integers in base-2 through base-36

Note: This is an improper prism, since leading 0s are stripped when reading.

>>> "100" ^? base 16
Just 256

>>> 1767707668033969 ^. re (base 36)
"helloworld"

integral :: (Integral a, Integral b) => Prism Integer Integer a b

This Prism extracts can be used to model the fact that every Integral type is a subset of Integer.

Embedding through the Prism only succeeds if the Integer would pass through unmodified when re-extracted.

Predefined bases

binary :: Integral a => Prism' String a

binary = base 2

octal :: Integral a => Prism' String a

octal = base 8

decimal :: Integral a => Prism' String a

decimal = base 10

hex :: Integral a => Prism' String a

hex = base 16

Arithmetic lenses

adding :: Num a => a -> Iso' a a

adding n = iso (+n) (subtract n)

>>> [1..3]^..traverse.adding 1000
[1001,1002,1003]

subtracting :: Num a => a -> Iso' a a

 subtracting n = iso (subtract n) ((+n)
 subtracting n = from (adding n)

multiplying :: (Fractional a, Eq a) => a -> Iso' a a

multiplying n = iso (*n) (/n)

Note: This errors for n = 0

>>> 5 & multiplying 1000 +~ 3
5.003

>>> let fahrenheit = multiplying (9/5).adding 32 in 230^.from fahrenheit
110.0

dividing :: (Fractional a, Eq a) => a -> Iso' a a

 dividing n = iso (/n) (*n)
 dividing n = from (multiplying n)

Note: This errors for n = 0

exponentiating :: (Floating a, Eq a) => a -> Iso' a a

exponentiating n = iso (**n) (**recip n)

Note: This errors for n = 0

>>> au (_Wrapping Sum . from (exponentiating 2)) (foldMapOf each) (3,4) == 5
True

negated :: Num a => Iso' a a

negated = iso negate negate

>>> au (_Wrapping Sum . negated) (foldMapOf each) (3,4) == 7
True

>>> au (_Wrapping Sum) (foldMapOf (each.negated)) (3,4) == -7
True