Grokking the Sequent Calculus (Functional Pearl)

The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The λμμ-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 λμμ-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 λμμ-calculus as a compiler intermediate language.