 
Summary: HumanReadable MachineVeriable Proofs for
Teaching Constructive Logic
Andreas Abel 1? , BorYuh Evan Chang 2 , and Frank Pfenning 2
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 rstorder in
tuitionistic logic is presented, which has been an eective 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 eÆcient algorithm is given.
1 Introduction
Teaching formal reasoning usually starts at the foundations that logic lays for
it. Since the seminal work of Gentzen [Gen35] his natural deduction calculus
has proven an adequate formalization of human reasoning at the logical level. To
teach the formal discipline of logic to students, a computer seems to be an ideal
tool to check proofs done by students.
