Debugging lazy functional programs poses serious challenges. In support of the stop, examine, and resume debugging style of imperative languages, some debugging tools abandon lazy evaluation. Other debuggers preserve laziness but present it in a way that may confuse programmers because the focus of evaluation jumps around in a seemingly random manner. In this paper, we introduce a supplemental tool, the algebraic program stepper. An algebraic stepper shows computation as a mathematical calculation. Algebraic stepping could be particularly useful for novice programmers or programmers new to lazy programming. Mathematically speaking, an algebraic stepper renders computation as the standard rewriting sequence of a lazy lambda-calculus. Our novel lazy semantics introduces lazy evaluation as a form of parallel program rewriting. It represents a compromise between Launchburys store-based semantics and a simple, axiomatic description of lazy computation as sharing-via-parameters. Finally, we prove that the steppers run-time machinery correctly reconstructs the standard rewriting sequence.
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