Building program optimizers with rewriting strategies
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We use strategies to specify how a wide range of exercises can be solved incrementally, such as bringing a logic proposition to disjunctive normal form, reducing a matrix, or calculating with fractions. With such a strategy, we can automatically generate worked-out solutions, track the progress of a student by inspecting submitted intermediate answers, and report back suggestions in case the student deviates from the strategy. Because we can calculate all kinds of feedback automatically from a strategy specification, it becomes less labor-intensive and less ad-hoc to specify new exercise domains and exercises within that domain. A strategy describes valid sequences of transformation rules that solve the exercise at hand, which turns tracking intermediate steps into a parsing problem. This is a promising view at the problem because it allows us to take advantage of many years of experience in parsing sentences of context-free languages, and transfer this knowledge and technology to the domain of stepwise solving exercises. In this paper we work out the similarities between parsing and solving exercises incrementally, and we discuss the implementation of a recognizer for strategies. We present a full implementation of such a recognizer, and discuss a number of design choices we have made. In particular, we discuss the use of a fixed point combinator to deal with repetition, and labels to mark positions in the strategy.