 
Summary: Introduction to Parigot's –¯Calculus
Andreas Abel
March 30, 2001
Abstract
The firstorder fragment of Parigot's –¯Calculus is formalization of
the implicational fragment of classical logic. The proof term syntax, proof
reductions and normal forms are gently introduced in this article.
1 Proof Terms and Proof Rules
In his seminal 1992 paper Parigot [Par92] introduced the –¯calculus. We will
restrict on the firstorder fragment, which assigns proof terms to classical natural
deductions in propositional logic. Consider the !fragment plus the rule for
absurdity elimination together with a rule how to obtain absurdity:
x
A \Delta \Delta \Delta
B
! I x
A ! B
A ! B A
! E
B
