The link you provided points to the AllegroGraph API documentation. The documentation says:
The protocol described here is compatible (is a super-set of) with the Sesame 2.0 HTTP protocol and the W3C SPARQL protocol (SPARQL endpoint).
I think you may want to develop a small library that sits between AllegroGraph and the client applications and 'speaks' this protocol, which appears to be a combination of "normal" REST and SPARQL. A client application can then pass the arguments to your library, which translates them to arguments in a SPARQL query or normal REST request.
For these operations, you may be able to use one of the tools mentioned in this answer, or use an SPARQL API like Jena ARQ and a general REST API like JAX-RS, or similar functions in programming language of your project.
Depending on your project, you can integrate these functions (SPARQL and REST calls) with the client application. You could of course provide the services again as a web service (using e.g. CXF or Axis), but if you control the client application(s) this may be too much for your project.