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Interface type sets

April 20, 2023

With what we’ve learned so far about interfaces, we can now draw some general conclusions about the precise definitions of an interfce’s type set. The spec summarizes nicely.

General interfaces

… Together with method specifications, these elements enable the precise definition of an interface’s type set as follows:

  • The type set of the empty interface is the set of all non-interface types.
  • The type set of a non-empty interface is the intersection of the type sets of its interface elements.
  • The type set of a method specification is the set of all non-interface types whose method sets include that method.
  • The type set of a non-interface type term is the set consisting of just that type.
  • The type set of a term of the form ~T is the set of all types whose underlying type is T.
  • The type set of a union of terms t1|t2|…|tn is the union of the type sets of the terms.

The first point in this list deserves some additional discussion, because it may not be obvious at first, but interfaces match only non-interface types. This isn’t necissarily obvious, because code like the following works:

	var x error = errors.New("foo") // `x` is of interface type `error`
	var y any = x                   // `y` is of interface type `any`

The variable y, which is of interface type any, appears to match x, which is of an interface type (error). However, what it’s actually matching isn’t the interface type, but the underlying type returned by errors.New, which is of type *errors.errorString, as we can see from the source code.

Quotes from The Go Programming Language Specification Version of December 15, 2022

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Type parameter restrictions

We’ll get to a full discussion of type parameters later on, but knowing at least what they look like is useful for the next section. So here’s an example, used in the definition of a generic function: func min[T ~int|~float64](x, y T) T { In this example, min[T ~int|~float64] represents the type parameter. With that in mind… General interfaces … The type T in a term of the form T or ~T cannot be a type parameter, and the type sets of all non-interface terms must be pairwise disjoint (the pairwise intersection of the type sets must be empty).

General interfaces

Today we’re venturing into generics territory. General interfaces In their most general form, an interface element may also be an arbitrary type term T, or a term of the form ~T specifying the underlying type T, or a union of terms t1|t<sub<>2|…|tn. We haven’t actually learned about type terms yet–they’re coming in a few weeks. But for now, the TL;DR is that they let us specify a type by its name, rather than by its method(s).

Unions of type sets

General interfaces … Union elements denote unions of type sets: // The Float interface represents all floating-point types // (including any named types whose underlying types are // either float32 or float64). type Float interface { ~float32 | ~float64 } Here we see our first example of a union of type sets. The example shows an interface of all types with an underlying float type. The equivalent for integer types is a bit longer, due to the large number of distinct integer types in Go, but would look like: