Ferreira, GildaVasconcelos, Vasco T2020-03-022020-03-0220191367-0751http://hdl.handle.net/10400.2/9415We show that the number-theoretic functions de nable in the atomic polymorphic system (Fat) are exactly the extended polynomials. Two proofs of the above result are presented: one reducing the functions' de n- ability problem in Fat to de nability in the simply typed lambda-calculus and other directly adapting Helmut Schwichtenberg's strategy for de nability in the simply typed lambda-calculus to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda-calculus, is emphasized.engPredicative polymorphismRepresentable functionsLambda-calculusNormalizationBeta-equalityExtended polynomialsjournal article10.1093/jigpal/jzy0761368-9894