Weakening & strengthening discard functions forms a monoid: we should test this.

[barrucadu]

weakenDiscard and strengthenDiscard each form a commutative monoid. In fact, they correspond to the monoid operation which picks the least (or greatest) element, according to some ordering. Each has a unit:

• For weakenDiscard it's the strongest: const (Just DiscardResultAndTrace)
• For strengthenDiscard it's the weakest: const Nothing

I think the properties we want to check are:

-- ordering (for appropriately-defined min/max functions):
\d1 d2 a -> weakenDiscard     d1 d2 a = min (d1 a) (d2 a)
\d1 d2 a -> strengthenDiscard d1 d2 a = max (d1 a) (d2 a)

-- commutativity
\d1 d2 a -> weakenDiscard     d1 d2 a == weakenDiscard     d2 d1 a
\d1 d2 a -> strengthenDiscard d1 d2 a == strengthenDiscard d2 d1 a

-- identity
\d a -> weakenDiscard     (const (Just DiscardResultAndTrace)) d a == d a
\d a -> strengthenDiscard (const Nothing)                      d a == d a

These could also serve as nice documentation, if presented well. Perhaps we should even add newtype'd monoids!

newtype Weaken     { getWeakDiscarder   :: Either Failure a -> Maybe Discard }
newtype Strengthen { getStrongDiscarder :: Either Failure a -> Maybe Discard }

instance Semigroup Weaken     where ...
instance Monoid    Weaken     where ...
instance Semigroup Strengthen where ...
instance Monoid    Strengthen where ...

weakenDiscard     d1 d2 = getWeakDiscarder   (Weaken     d1 <> Weaken     d2)
strengthenDiscard d1 d2 = getStrongDiscarder (Strengthen d1 <> Strengthen d2)