Install some constituent-based parser and use it (not just a web interface) to parse non-trivial examples of text involving several types of sentences. Critique the output structures for coverage, correctness, etc. You can do this exercise in English or in any other language you know.
Possible tools:
coreNLP (make sure to pay attention to annotator dependencies in building your pipeline)
NLTK: Work through this chapter and this howTo (for generating sentences). Add new rules to the toy grammars they provide and demonstrate/document how well they work.
Send an email discussing which tool and text documents you used, sample output, and your assessment of the parser's performance (i.e. coverage with respect to all possibilities the language's grammar provides).