Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 into proof theory by Gerhard Gentzen for the sequent calculus; 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.

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