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We show some applications of the formulas-as-polynomials correspondence: 1) amethod for (dis)proving formula isomorphism and equivalence based on showing(in)equality; 2) a constructive analogue of the arithmetical hierarchy, basedon the exp-log normal form. The results are valid intuitionistically, as wellas classically.

Applications of the analogy between formulas and exponential polynomials to equivalence and normal forms