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Sequent Calculus and Notation – Par Part 1


This post is the first in a series on Logic. These ideas are very useful in understanding many important papers on programming language theory, especially papers on type theory and the lambda calculus.

A brilliant logician named Gerhard Gentzen (unfortunately a Nazi, though some argue it was apathetically, or even under duress) developed the following notation for reasoning in 1934, which will be important to understand for the rest of the post. Since inference rules are descriptions of valid steps in a derivation tree, we often fill their top sequents with "metavariables," which are like wildcards that match anything. Then that simply-typed lambda calculus gives proof terms to this "implicational fragment" of propositional intuitionistic logic.

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