Pex: white box test generation for .NET
TAP'08 Proceedings of the 2nd international conference on Tests and proofs
The Art of Computer Programming: Combinatorial Algorithms, Part 1
The Art of Computer Programming: Combinatorial Algorithms, Part 1
Synthesizing geometry constructions
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
Automated feedback generation for introductory programming assignments
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
A trace-based framework for analyzing and synthesizing educational progressions
Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
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Natural deduction, which is a method for establishing validity of propositional type arguments, helps develop important reasoning skills and is thus a key ingredient in a course on introductory logic. We present two core components, namely solution generation and practice problem generation, for enabling computer-aided education for this important subject domain. The key enabling technology is use of an offline-computed data-structure called Universal Proof Graph (UPG) that encodes all possible applications of inference rules over all small propositions abstracted using their bitvector-based truth-table representation. This allows an efficient forward search for solution generation. More interestingly, this allows generating fresh practice problems that have given solution characteristics by performing a backward search in UPG. We obtained around 300 natural deduction problems from various textbooks. Our solution generation procedure can solve many more problems than the traditional forward-chaining based procedure, while our problem generation procedure can efficiently generate several variants with desired characteristics.