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arXiv · 2406.14719

Grokking the Sequent Calculus (Functional Pearl)

David Binder·Marco Tzschentke·Marius Müller·Klaus Ostermann
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Abstract

The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler intermediate languages due to its first-class representation of evaluation contexts. Unfortunately, only experts of the sequent calculus can appreciate its beauty. To remedy this, we present the first introduction to the {\lambda}{\mu}{\mu}-calculus which is not directed at type theorists or logicians but at compiler hackers and programming-language enthusiasts. We do this by writing a compiler from a small but interesting surface language to the {\lambda}{\mu}{\mu}-calculus as a compiler intermediate language.

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David Binder, Marco Tzschentke, Marius Müller, Klaus Ostermann. 2024-06-20. Grokking the Sequent Calculus (Functional Pearl). https://doi.org/10.1145/3674639

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