Can anyone recommend me an open-source full OCaml parser?
Essentially, I would like to implement my own type-checker for OCaml. Ideally, the parser is written in OCaml. I would just use it to get the AST of the input program. (it is probably too much to ask for the initial typing environment pre-filled with standard library function signatures)
Use compiler-lib that is distributed with OCaml under QPL license. It has everything needed to create your own compiler (and even has some documentation). compiler-lib is essentially a compiler shipped as library.
Otherwise, you can use camlp4 to get the parsetree, but then you need to reimplement everything else from scratch. But at this case you're not restricted with QPL.