The last part, the latex part, should by done now ("should" be explained later). I have chosen the boxproof plugin. The result seems a bit prettier than the native logicproof plugin. And (and this is a big and) I have had trouble writing too nested proofs using logicproof. Anyway, paste BoxProver into the textbox below and click parse (omit the head as explained in the html section)
If you for what ever reason want to have this parser running on your own page, you can grab the boxproofs.js file from the Git Repo. Then obtain latex code as thusvar bproofs = new BoxProofs(); //returns a string of latex code var lcode = bproofs.createBoxLatex(null,code_input);
For the "should" part. Should you find any errors that will parse in BoxProver but not in this here application, please report by commenting below.