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Creators/Authors contains: "Foner, Kenneth"

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  1. ; ; (, Proceedings of the ACM on Programming Languages)
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  2. ; (, Proceedings of the ACM on Programming Languages)
    It is a straightforward exercise to write a program to add two bijections---resulting in a bijection between two sum types, which runs the first bijection on elements from the left summand and the second bijection on the right. It is much less obvious how to subtract one bijection from another. This problem has been studied in the context of combinatorics, with several computational principles known for producing the difference of two bijections. We consider the problem from a computational and algebraic perspective, showing how to construct such bijections at a high level, avoiding pointwise reasoning or being forced to construct the forward and backward directions separately---without sacrificing performance. 
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