Shouldn't the law be more like: ƒ(ƒ(x)) ≡ ƒ(x)

[seanparsons]

The law doesn't quite seem right to me, surely it should be:
a mappend b mappend b == a mappend b
Potentially as well as:
a mappend a == a

[prophile]

The latter (the current version of the law) is the usual definition of idempotence for a binary operation, as opposed to the usual unary operation definition given in the title of this issue.

The former law, as you state it, is a logical consequence of the latter law (and, potentially, the monoid associativity law depending on how mappend associates).

[seanparsons]

Works for me, I need to remember that monoid append is a binary operation like that, rather than thinking of it as the function "mappend a".