This question comes from a simple observation that really puzzles me.
Constructions (in CxG) are defined as form-function pairings. My focus here is not so much on the function of constructions but rather on their form. If we take the ditransitive construction (as in I sent her a letter), for instance, it is often described to have the form in (1). However, in the literature, you also often find the form of the ditransitive construction to be discussed as in (2), as the ‘double-object’ construction.
(1) NP V NP NP
(2) SUBJ V OBJ OBJ2
The problem for me is that in (2), the 'form' of the ditransitive construction is not described in terms of syntactic properties (such as ‘NP’), but in terms of functional properties (an object is a function, not a form). So my question is simple: why use the description in (2), a semantic/functional description, instead of the description in (1) to talk about the formal properties of the ditransitive construction? Is there a particular purpose for using one instead of the other? Or is it simply because (1) might fail to properly differentiate the ditransitive construction from other syntactic patterns? (e.g. They elected him president, also an pattern, yet supposedly instantiating a different (resultative?) construction) And in the latter case, is that not a problem for the theory?
These questions may have to do with the syntax/semantics interface, but should CxG therefore not address these questions more explicitely?