Based on the Gröbner basis method, we present algorithms for a complete solution to the following problems in the implicitization of a set of rational parametric equations. (1) Find a basis of the implicit prime ideal determined by a set of rational parametric equations. (2) Decide whether the parameters of a set of rational parametric equations are independent. (3) If the parameters of a set o...

In the 1980s, John Reynolds postulated that a parametrically polymorphic function is an ad-hoc polymorphic function satisfying a uniformity principle. This allowed him to prove that his set-theoretic semantics has a relational lifting which satisfies the Identity Extension Lemma and the Abstraction Theorem. However, his definition (and subsequent variants) have only been given for specific mode...