This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In particular, we investigate the use of planning to construct elementary proofs in abstract algebra, which provides a rigorous and axiomatic framework for studying algebraic structures such as groups, rings, fields, and modules. We implement basic implications, equalities, and rules in both deterministic and non-deterministic domains to model commutative rings and deduce elementary results about them. The success of this initial implementation suggests that the well-established techniques seen in automated planning are applicable to the relatively newer field of automated theorem proving. Likewise, automated theorem proving provides a new, challenging domain for automated planning.

Deep learning had been used in program analysis for the prediction of hidden software defects using software defect datasets, security vulnerabilities using generative adversarial networks as well as identifying syntax errors by learning a trained neural machine translation on program codes. However, all these approaches either require defect datasets or bug-free source codes that are executable for training the deep learning model. Our neural network model is neither trained with any defect datasets nor bug-free programming source codes, instead it is trained using structural semantic details of Abstract Syntax Tree (AST) where each node represents a construct appearing in the source code. This model is implemented to fix one of the most common semantic errors, such as undeclared variable errors as well as infer their type information before program compilation. By this approach, the model has achieved in correctly locating and identifying 81% of the programs on prutor dataset of 1059 programs with only undeclared variable errors and also inferring their types correctly in 80% of the programs.