One Approach to Efficient Structural Subtyping

An interesting challenge with [[Structural type system|structural subtyping]] is that of efficient implementation. In particular, without care, it may be impossible to determine a static offset for each field in a structure at runtime, meaning every field access will require a dictionary lookup. In this post, I’ll review the problem and outline one alternative approach.

The Problem

To properly understand the problem faced implementing a structural type system, we must consider things at a low level. In languages like C or Java, it is possible to determine a static offset for all fields at runtime. Consider this simple C example:

typedef struct { int day; int month; int year; } date; int getYear(date *ptr) { return ptr->year }

The C compiler will automatically determine a fixed layout for the struct named date (which may or may not including padding). For simplicity, let’s assume there’s no padding and an int corresponds to a [[Two’s complement|two’s-complement]] 32 bit integer. Then, the layout will look something like this:

Here, the offsets are measured in bytes and, thus, we know that the year field starts at an offset of 8 bytes. This means that, in function getYear() above, the compiler can implement the field access directly by loading the int stored in memory at an offset of 8 bytes from ptr .

In the presence of structural subtyping, things are a little more complicated. Consider a similar example in a psuedo-version of C which supports structural subtyping:

typedef struct { int day; int month; int year; } date; typedef struct { int year; } hasYear; int getYear(hasYear *ptr) { return ptr->year }

This is very similar to the original version, except that getYear() has been refined to accept a pointer to any structure which has a field year . For example, it will accept a pointer to an instance of date , as well as a pointer to an instance of hasYear .

The problem is that the compiler is now unable to determine a static offset for the field year within function getYear() . This is because field year is at offset 8 in a date instance, and at offset 0 in a hasYear instance — and, indeed, it could be at any offset (depending on the available structural subtypes of hasYear ). Therefore, the compiler is forced to resort to an altnerative strategy, such as using a dictionary lookup (i.e. where the struct is actually implemented as a dictionary keyed on field name).

One Solution

There are many different approaches to generating efficient code for languages with structural type systems, and I’m going to present just one here which I haven’t seen considered before. In fact, it’s really rather simple — we’re going to distinguish between exact subtypes and variable subtypes (note: in type system terminology, this corresponds to the difference between depth and width subtyping). An exact subtype must have exactly the same number of fields with the same names, whilst a variable subtype may have more fields than required. And, we’ll provide a distinct notation, ... , to distinguish them. For example:

typedef struct { int day; int month; int year; } date; typedef struct { int year; } hasYearExact; typedef struct { ...; int year; ... } hasYearVariable; int getYear(hasYearExact *ptr) { return ptr->year } int getYear(hasYearVariable *ptr) { return ptr->year }

In this example, an instance of date is not a subtype of hasYearExact because it does not have exactly the same number of fields with the same names. In contrast, an instance of date is a subtype of hasYearVariable , because this uses the ... notation to indicate that subtypes are may have more fields.

So, what’s the advantage here? Well, essentially, the point is that with exact types you can always determine a static offset of fields, whilst with variable types you cannot. This means that, in cases where performance is important, you can elect to use an exact type instead of a variable type to ensure that field accesses compile down to direct memory accesses. This isn’t rocket science, but it does give an interesting and alternative approach to the problem!