In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof.
The notion of analytic proof was introduced by Gerhard Gentzen for the sequent calculus; there the analytic proofs are those that are cut-free. His natural deduction calculus also supports a notion of analytic proof, as was shown by Dag Prawitz; the definition is slightly more complex — we say the analytic proofs are the normal forms, which are related to the notion of normal form in term rewriting.
Reference:
http://en.wikipedia.org/wiki/Structural_proof_theory
