monad laws

All monads should follow (and in practice, all built-ins do), with respect to the above three operations,

• left identity return a >>= k = k a
  • k will be a function that acceps a and gives m a, so instead of wrapping a to bind it to k, we should be able to apply.
• right identity m >>= return = m
  • returning an "empty" monad should just give the monad instance itself
• associativity (m a >>= f) >>= g = m a >>= (\x -> f x >>= g)
  • On the LHS;
    • f is of type a -> m b, so the first term is m b
    • g is of type b -> m c, result is m c
  • On the RHS:
    • \x -> f x immediately takes type a and gives m b
    • bound to g to give m c
    • in this sense, the bracket part is a lambda wrapper on simply f >>= g that allows it to be a function that fits the bind typesig.

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