Really just add the identities defining a pointfree funcoid to the identities of an upper semilattice with least element.
I will list the exact list of identities defining a pointfree funcoid on a poset with least element:
(Here is a single relational symbol.)
This can be even generalized for upper semilattices with no requirement to have the least element, if we allow the least element constant symbol to be a partial function.
Note that for the general case of a pointfree funcoid between two upper semilattices, we have a partial algebraic structure because the operations are different for each of the two upper semilattices.
I am curious what are applications of this curious fact.