The Howdy Glossary

Polymorphic recursion is a technique that employs parametric polymorphism in recursive function definitions, enabling functions to operate without specifying types. This method leads to more flexible and generic code capable of handling different input types without the need for distinct recursive functions for each type. It is often utilized in programming languages like Haskell or Scala that support higher-kinded types and generics. While it allows for defining functions with general type signatures, it can also introduce performance considerations that require careful handling.

The concept of polymorphic recursion is rooted in the development of functional programming languages and parametric polymorphism. It isn't attributed to a single creator but has evolved through contributions from researchers and developers within the functional programming community. By allowing recursive function definitions to be more abstract, this technique facilitates writing more generalized algorithms, enhancing code flexibility and reusability across various data types.

Polymorphic recursion differs from ad hoc polymorphism—which necessitates multiple functions with the same name for different types—and monomorphic recursion, which involves type-specific implementations. Its ability to leverage parametric polymorphism means a single function can adapt to different input types seamlessly, promoting efficient code reuse and abstraction. Despite its advantages in creating versatile algorithms with reduced code duplication and enhanced maintainability, programmers must consider potential runtime performance impacts when employing this technique in languages supporting higher-kinded types and generics like Haskell or Scala.