When such a compound identifier is used to name, e.g., a sort in the body of a generic specification, the translation determined by fitting arguments to parameters applies to the components ID+ of the compound identifier as well. Thus instantiations with different arguments generally give rise to different compound identifiers for what would otherwise be the same sort, which avoids unintended identifications when the instantiations are united.

E.g., a generic specification of sequences of arbitrary elements might use the simple identifier Elem for a sort in the parameter, and a compound identifier compound-id Seq Elem for the sort of sequences in the body. Fitting various argument sorts to Elem in different instantiations then results in distinct sorts of sequences.

In general, subsort embeddings between component sorts do not induce subsort embeddings between compound sorts. For instance, consider a specification with Nat declared as a subsort of Int. When putting together two extensions of it with sorts (compound-id List Nat), respectively (compound-id List Int), one does not get (compound-id List Nat) declared automatically as a subsort of (compound-id List Int)--this has to be specified explicitly, if required. However, instantiation behaves as expected here: if in a generic specification we have Elem declared as a subsort of (compound-id Seq Elem), where Elem is a parameter sort, then in the result of instantiation of Elem by Nat, one does get Nat automatically declared as a subsort of (compound-id Seq Nat).

Higher-order extensions of CASL are expected to provide a more semantic treatment of parametrized sorts, etc.