2024/06/20 by David Binder, David A. Binder, Marco Tzschentke +2 · 2 voices · 1 citation
Computer Science · Dentistry · Mathematics · Medicine · #Calculus (dental) #Computability, Logic, AI Algorithms #Cut-elimination theorem #Dentistry #Discrete mathematics #Formal Methods in Verification #Geometry #Logic, programming, and type systems #Mathematical proof #Mathematics #Medicine #Natural deduction #Pearl #Philosophy #Proof calculus #Sequent #Sequent calculus
paper · pdf · open access · doi:10.1145/3674639
published in Proceedings of the ACM on Programming Languages 8(ICFP), 395-425 (Association for Computing Machinery)
openalex publication_date 2024/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26
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.