Hi, I made Deep Grammar. I also wrote a blog post about it https://www.linkedin.com/pulse/deep-grammar-checking-using-l...
TensorFlow has a tutorial that gets you most of the way[2].
Edit: playing a bit I don't think it is doing this. I think it's using Word2Vec style vectors to build similar sentences, and calculating the probability of each and maybe the edit-cost to change.
[1] http://arxiv.org/abs/1412.7449
[2] https://www.tensorflow.org/versions/master/tutorials/seq2seq...