Summary: Human-Readable Machine-Verifiable Proofs for
Teaching Constructive Logic
, Bor-Yuh Evan Chang2
, and Frank Pfenning2
Dept. of Computer Science, Ludwig Maximilian University, Munich, Germany
Dept. of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA
Abstract. A linear syntax for natural deduction proofs in first-order in-
tuitionistic logic is presented, which has been an effective tool for teach-
ing logic. The proof checking algorithm is also given, which is the core of
the tutorial proof checker Tutch. This syntax is then extended to proofs
on the assertion level which resemble single inferences one would make
in a rigorous proof. The resulting language has only four constructs.
Checking of these proofs is decidable, and an efficient algorithm is given.
Teaching formal reasoning usually starts at the foundations that logic lays for