Program Extraction from Proofs

In classical mathematics, a Platonistic view of the mathematical universe is adopted according which mathematical entities including infinite sets are assumed to exist in some ‘ideal world’, like finite entities exist in the real world. Consequently, any mathematical statement is either true or false. Therefore, the Law of Excluded Middle, ∀x . P (x) ∨ ¬P (x), is classically valid, since for any object x either P (x) is true, or else P (x) is false in which case ¬P (x) is true.

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