Mapping between a generic Web API and an LDP Server

Hi everybody,
this is the first post I write on this list so I will introduce myself
first...

I am Miguel Ceriani, a PhD candidate in computer science at Sapienza,
University of Rome.
I am working on a platform to define linked data applications using a
dataflow language based on SPARQL.
I am new to the Hydra spec and I am still sudying it.

I have a problem that is not striclty in the scope of Hydra, but it seems
to me quite related.
I hope that I am not completely out of topic.

Let's say I want to build a server that have to comply with a given Web
API, that uses JSON, and I want to implement it backed on an LDP server.
I can define a suitable Linked Data model and then map it from/to JSON with
a JSON-LD profile.
Then I have to map  somehow the operations supported by the Web API with
operations on LDP (assuming that the operations offered by the Web API are
simple enough to be mapped directly to LDP operations).

The question is: is there a standard way to do this second mapping?
I can do it ad-hoc in different server-side languages, but ideally I would
use some RDF vocabulary, like Hydra.
As a fact Hydra seems very close to what I need, because it maps Web API
operations to their Linked Data meaning.
The main difference is that I would like to use this mapping to DEFINE the
behaviour of a Web API, while (if I understood its purpose correctly) Hydra
is used to DOCUMENT (to the client) the behaviour of a Web API.

In general, it seems to me that such mapping could be useful to integrate
existing Web APIs with linked data workflows.

What do you think about it?

Thanks,
Miguel