 
Summary: HumanReadable MachineVerifiable Proofs for
Teaching Constructive Logic
Andreas Abel1
, BorYuh Evan Chang2
, and Frank Pfenning2
1
Dept. of Computer Science, Ludwig Maximilian University, Munich, Germany
abel@informatik.unimuenchen.de
2
Dept. of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA
bechang@andrew.cmu.edu, fp@cs.cmu.edu
Abstract. A linear syntax for natural deduction proofs in firstorder 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.
1 Introduction
Teaching formal reasoning usually starts at the foundations that logic lays for
