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"

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

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

binary = base 2

octal = base 8

decimal = base 10

hex = base 16

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

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

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

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

Note: This errors for n = 0

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 = iso negate negate

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

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