Functions and Arguments

Most of the functions you have written so far probably follow a familiar pattern: you pass in a value, the function does some work, and you get back another value. Before reading further, try to hold that picture in mind, because this article introduces a function that works differently. A type function is a building block that programmers and library implementers can use, and the key questions for understanding it are simple: what goes into a type function, what comes out, and when the work happens.

An ordinary function works with values. You pass in a number, a string, or a list, and you receive another value back. A type function changes the kind of thing that flows through the function. Instead of working with values, it works with types. The idea is that the type itself becomes the material that a function manipulates.

Think of the difference as a change in what sits on the conveyor belt. In an ordinary function, the items entering are data, such as a particular number or string. In a type function, the items entering are descriptions of kinds of things. The function's machinery is the same general idea of taking an input and producing an output, but the input and output are about the structure or properties of types rather than about any particular piece of runtime data.

A helpful way to understand a type function is to follow a type through it step by step. Imagine giving a type function a type as its argument. The function is evaluated at compile-time and produces a result. Because the input is a type, the work concerns the structure or properties of that type, not any particular runtime data. The diagram below traces this path from the type going in, through the function, to the result coming out.

The three questions from the opening, what goes in, what comes out, and when the work happens, are all answered by this path. The input is a type. The work is evaluated during compilation. The output is a result that is already settled by the time the program starts doing its ordinary work.

The definition names two possibilities separated by the word or. A type function may accept a type and return something else, or it may accept something and return a type. The source describes both shapes as belonging to one concept, so treat them as two variations of the same idea rather than two unrelated tools. The comparison below places the two shapes side by side so you can see where the input and output sit in each.

Timing is what separates a type function from the ordinary functions most learners know. A type function is evaluated while the program is being compiled, not while it is running. The work of deciding the type happens before the program executes, so the result is already settled by the time the program starts doing its ordinary work. The timeline below shows where the type function's evaluation sits relative to the start of program execution.

Because type functions look like the functions learners already know, several wrong assumptions are easy to make. The items below name the most common ones and correct them using the timing and shape ideas covered above.

Type functions extend the familiar idea of a function from values to types. The standard library provides a variety of ready-made type functions, so you do not need to invent them yourself. Their purpose is to help programmers and library implementers write code that takes advantage of the language, the standard library, and code in general. A dependable type function gives you a reliable way to ask a question about types or to produce a type, and you can build on that answer in your own code.