In programming language theory, parametricity is an abstract uniformity property enjoyed by parametrically polymorphic functions, which captures the intuition that all instances of a polymorphic function act the same way.
Notice that all the component functions twiceX act "the same way" because they are given by the same rule.
fn, i.e., the polymorphic Church numeral for n. In contrast, the collection of all ad hoc families would be too large to be a set.
Despite being a lazy programming language, Haskell does support certain primitive operations—such as the operator seq—that enable so-called "selective strictness", allowing the programmer to force the evaluation of certain expressions.
In their paper "Free theorems in the presence of seq",[3] Patricia Johann and Janis Voigtlaender showed that because of the presence of these operations, the general parametricity theorem does not hold for Haskell programs; thus, these transformations are unsound in general.