Documentation

Laws for instances of FactorialMonoid.

Includes the following laws:

null a == null (factors a)

factors a ==         (unfoldr              splitPrimePrefix  a)
factors a == reverse (unfoldr (fmap swap . splitPrimeSuffix) a)

reverse a == mconcat (reverse (factors a))

primePrefix a == maybe mempty fst (splitPrimePrefix a)
primeSuffix a == maybe mempty snd (splitPrimeSuffix a)

inits a == fmap mconcat (inits (factors a))
tails a == fmap mconcat (tails (factors a))

span p a == bimap mconcat mconcat (span p (factors a))

all (all (not . p) . factors) (split p a)

mconcat (intersperse p (split (== p) a)) == a

splitAt i a == bimap mconcat mconcat (splitAt i (factors a))

Note that the following superclass laws are not included:

• factorialLaws
• monoidNullLaws