Posted on August 21, 2019 by Troels Henriksen

Futhark 0.12.1 has just escaped (full changelog). It contains a handful of minor changes and fixes, and two major ones. The largest change is to the internal representation and is (hopefully) not user-visible. Simply put, we rewrote the internal representation of kernel parallelism to closely resemble the one we presented in our PPoPP’19 paper. The intent is to make it easier to cleanly express sophisticated mapping of application parallelism to GPU parallelism. I’d usually write in detail about this change, but I feel it’s rather dwarfed by an addition to the source language that has me much more excited. So…

Futhark was originally an extremely austere language - fully monomorphic, barely any pattern matching, and fully first order (although with some syntactical sugar that tried to imitate second-order functions). This was because our main compilation target (GPUs) is such a hostile environment, and we did not want to support any features that we could not compile efficiently. Over time, the restrictions were lessened:

We added a higher-order module system around late 2016.

Records came about in early 2017, and gained their current form with the 0.2 release.

Higher-order functions and parametric polymorphism were added in 0.4.

Apart from recursion, there was one feature common to functional languages that we were still missing: sum types (sometimes called algebraic data types, although that’s a slightly broader term). This meant that FP classics such as option and either types could not be expressed in Futhark, and other kinds of enumerations had to be encoded using integers. Most if not all functional languages implement sum types via pointer structures, which is a no-go for us. As of Futhark 0.12.1, this omission has been rectified! (But do read on for the fine print.) I should note that most of the implementation work, particularly the type system details, was done by Robert.

Futhark is structurally typed in both its records and module system. Structural typing means that names are just abbreviations, and that only the actual contents of types matter. Structural sum types are fairly rare because they tend to be unwieldy when recursive (although this has not deterred OCaml). However, Futhark’s sum types do not support recursion, so we chose to keep full structural typing. As an example, a sum type with two constructors can be written #foo i32 | #bar bool in Futhark. It need not be given a name, although it is in most cases a good idea:

type bool_or_int = #foo i32 | #bar bool

Constructors are # -prefixed to disambiguate variable names from nullary constructors when pattern matching with match :

type my_bool = #true | #false -- Nullary constructors. ... match x : my_bool case #true -> ... -- Matches specific constructor case true -> ... -- Matches anything, and binds -- the variable 'true'.

There are some limitations due to the structural typing. Most notably, constructors must be fully applied to all their arguments whenever they appear. Also, because constructors no longer uniquely identify a type, type annotations are sometimes necessary to disambiguate:

type my_bool = #true | #false type another_bool = #true | #false | #maybe let x = #true -- Error: ambiguous type. let y : another_bool = #true -- OK!

Structural sum types allow convenient use of ad-hoc types, much like tuples or records in other languages. It remains to be seen whether this design is ultimately a good idea, though.

For reasons of simplicity, we did not wish to add sum types to our core language, so the Futhark compiler front-end flattens sum types to tuples. As a starting point, the constructor is turned into an 8-bit integer ( i8 ), and the payload types are just concatenated. For example, the type #foo i32 | #bar bool will be represented as (i8, i32, bool) . A value #foo 2 of this type is turned into (0, 2, false) . The values for the unused payload (the bool in this case) is given an arbitrary value (I’ll return to this, because it has some unsolved problems). Pattern-matching is turned into chains of if-then-else expressions.

This simple representation has some inefficiencies. In the example above, it is wasteful to store both the i32 and bool , because we know only one of them will ever have a meaningful value. Hence, the Futhark compiler performs a kind of deduplication, where payload values of the same type share the same tuple slot in the flattened representation. For example, the type #foo i32 | #bar i32 will be represented as (i8, i32) . Currently, this only works if the primitive types match exactly (but we do flatten out nested records and sum types first), but eventually we’d like to handle more complex cases. A bool (8 bits) easily fits within an i32 (32 bits), and our core language do support the bit-casts that we would need to pack it. For that matter, it would be nice if we could pack four bools to an i32 , or two i32 s to an f64 . However, this is a fiddly optimisation that sounds easy to get wrong, so I’d rather wait until we have some more test programs that make aggressive use of sum types.

Even the current simple scheme gives good results. I wrote a ray tracer partly to try out this new feature, where I use the following sum type:

type vec3 = {x: f32, y: f32, z: f32} type material = #lambertian {albedo: vec3} | #metal {albedo: vec3, fuzz: f32} | #dielectric {ref_idx: f32}

Even our current simple deduplication managed to reduce the overall run-time of the ray tracer by a factor of two. This is of course a best-case scenario, since all the primitives involved are ultimately of type f32 .

Apart from the lack of deduplication across types, which is an optimisation problem, there is also a correctness problem in the current implementation. Consider the usual parametric option type:

type opt 'a = #some a | #none

A value #some [1,2,3] is represented as (0, [1,2,3]) . But what about #none (where we know the result must have type opt []i32 )? We need to come up with an arbitrary value of type []i32 . Currently the compiler will just use an empty array, giving (1, []) . Now consider constructing an array of these option values:

[#some [1,2,3], #none]

This is desugared to:

[(0, [1,2,3]), (1, [])]

But this is not a valid Futhark array! For this array to be valid it should be describable as [n](i8, [m]i32) for some n and m , but while n=2 , a proper m cannot exist, as it would need to be both 3 and 0. Specifically, attempting to construct this array would fail at run-time. This is a problem, and it will crop up in a number of other cases, like map , where the Futhark compiler tries to predict the sizes of array elements using slicing techniques.

Fortunately, this issue is (hopefully) rare in practice, and only crops up in the specific case where we have an array of sum types with more than 1 constructor, where the payload of some constructor is itself an array. For the moment, we merely document the issue and hope people can code their way around it. In the future, size types will be used to assign the correct size to the “arbitrary” arrays.