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of an implication corresponds to a function that takes a term of type as input and produces a term of type as output. Similarly, a proof of a conjunction (a product type) corresponds to a pair containing a term of type and a term of type . This relationship is not merely superficial. The process of proof normalization, where redundant logical steps are eliminated to simplify a proof, corresponds directly to the process of program execution, i.e., beta-reduction, in typed lambda calculus. This isomorphism

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