Calculating threesomes, with blame

Coercions and threesomes both enable a language to combine static and dynamic types while avoiding cast-based space leaks. Coercion calculi elegantly specify space-efficient cast behavior, even when augmented with blame tracking, but implementing their semantics directly is difficult. Threesomes, on the other hand, have a straightforward recursive implementation, but endowing them with blame tracking is challenging. In this paper, we show that you can use that elegant spec to produce that straightforward implementation: we use the coercion calculus to derive threesomes with blame. In particular, we construct novel threesome calculi for blame tracking strategies that detect errors earlier, catch more errors, and reflect an intuitive conception of safe and unsafe casts based on traditional subtyping.