Скачать или смотреть Gentzen's Sequent Calculus: Logic, Proofs, and Programming

The source provides an overview of Gerhard Gentzen's sequent calculus, a logical system developed in the 1930s to create perfectly clear and transparent arguments. The explanation details the central component, the sequent, which represents a fundamental logical building block stating that if the assumptions on the left are true, then something on the right must follow. A crucial element of Gentzen’s work is the Cut Elimination Theorem, also known as the Hauptsatz, which guarantees that any proof can be simplified into a direct, "cut-free" argument with no unnecessary detours. This concept, leading to the sub-formula property, has profound implications for modern computer science, as the text ultimately connects Gentzen's pursuit of perfect proofs to the development of clean, efficient computer programs through the Curry-Howard isomorphism.