Dr. David J. Pearce

Understanding Effective Unions in Whiley

The concept of effective union types in Whiley exposes some interesting features worth considering.  In particular, they result in a separation between the readable and writeable view of a type.  But, we’re getting ahead of ourselves!  Let’s start with what exactly effective unions are…

Effective Unions

An effective union is a union type which has some commonality which can be exploited.  Here’s a simple example to illustrate:

type Rectangle is { int x, int y, int width, int height }
type Circle is { int x, int y, int radius }

// A shape is either a rectangle or a circle
type Shape is Rectangle | Circle

// Move the center point by a given translation
function translate(Shape s, int dx, int dy) -> (Shape r):
    s.x = s.x + dx
    s.y = s.y + dy
    return s

This little function is responsible for moving the position of a given Shape. Since both Rectangle and Circle have the fields x and y, we can access them when given just a Shape. We say that the effective union type of Shape is { int x, int y, ... }, where ... represents zero or more unknown fields.

Effective union types have some analogies in other programming languages. For example, in the C programming language, they are similar to the notion of a Common Initial Sequence (see e.g. here and here). In Java, effective union types perhaps share some connection with type bounds as, for example, the type T where T extends Shape can be regarded as containing everything common to a Shape.

Readability vs Writeability

An interesting question is what we can do with an effective union.  In particular, what types we can read from it and write to it.  Let’s consider another, slightly more interesting example:

type Message is Request | Response
type Request is { int meth, URL data }
type Response is { int code, byte[] data }

Type Message is an effective union which "looks" like { URL|(byte[]) data, ... }. Given a variable m of type Message, reading the field m.data returns a value of type URL|(byte[]). That makes sense. So, can we write to the field m.data? In this case, no we can’t.

Reading from the field of an effective union returns the union of types for that field. But, for writing, we can only write values common to all instances of that field in the union. To motivate this, let’s refine our example a little:

type Message is Request | Response
type Request is { int meth, null|URL data }
type Response is { int code, null|(byte[]) data }

Again, suppose we have a variable m of type Message. Since null is supported by both instances of the data field, we can safely write m.data = null. But, we cannot assign a URL to m.data as we don’t know whether m represents a Request or a Response (and if we allowed the assignment regardless, we might end up with a mangled value).


Effective union types are an interesting feature of Whiley which leads to a distinction between the “readable” view of a type, and the “writeable” view. At this point in time, it’s fair to say that it is unclear how useful this will turn out to be. But, it’s definitely something I’m going to continue exploring …