Functors in PHP Programming

For languages like PHP that don’t have default userland functor supportA type class that implements functor-compatible methods is an effective replacement for the functor concept. The fantasyland package helps with functor compliance checks. It’s a PHP port of a more complex JavaScript package of the same name. In addition to the required functor design, the fantasyland project also includes verification of laws that functors must satisfy.

Functors are type classes

To effectively create a working functor, we need to implement the functor rubric—defined by category theory from the previous section—as a type class. A type class is a composite data type, which supports operator overloading. With a type class, it is possible to, with each invocation of a class method, overwrite its internal state and create a new immutable entity. Overriding in functors is expressed in the signatures of functions meant to be methods of the type class. Also referred to as ad-hoc polymorphism, operator overloading minimizes the redundancy of writing multiple methods to operationalize a new state. It truncates the boilerplate quite effectively.

Formally, a T class with an x parameter is a type class if the value of x can be influenced by a set of operations (functions) that maintain its type constraints. Type classes are interfaces that influence behavior in Haskell, a language that promotes type usage.

The Calculator class shown below is a simple demonstration of these ideas.