Structures Definable in Polymorphism

Encodings in polymorphism with finite product types are considered. These encodings aregiven in terms of I-algebras. They have the property that the ground terms are precisely theclosed normal terms of the encoded types. The proof of a well-known result is transplantedto the setting and it is shown why weak recursion is admissible. The paper also shows how tocarry out the dual encodingS using the existential quantifier.