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Free theorems are a popular tool in reasoning about parametrically polymorphic code. They are also of instructive use in teaching. Their derivation, though, can be tedious, as it involves unfolding a lot of definitions, then hoping to be able to simplify the resulting logical formula to something nice and short. Even in a mechanised generator it is not easy to get the right heuristics in place to achieve good outcomes. Dinaturality is a categorical abstraction that captures many instances of<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1908.07776v1">arXiv:1908.07776v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/znjtga5pw5hgtn5tgtsq7spg3a">fatcat:znjtga5pw5hgtn5tgtsq7spg3a</a> </span>
more »... e theorems. Arguably, its origins are more conceptually involved to explain, though, and generating useful statements from it also has its pitfalls. We present a simple approach for obtaining dinaturality-related free theorems from the standard formulation of relational parametricity in a rather direct way. It is conceptually appealing and easy to control and implement, as the provided Haskell code shows.
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