Co-dfns versus BQN's implementation

The BQN self-hosted compiler is directly inspired by the Co-dfns project, a compiler for a subset of Dyalog APL. I'm very grateful to Aaron for showing that array-oriented compilation is even possible! In addition to the obvious difference of target language, BQN differs from Co-dfns both in goals and methods.

The shared goals of BQN and Co-dfns are to implement a compiler for an array language with whole-array operations. This provides the theoretical benefit of a short critical path, which in practice means that both compilers can make good use of a GPU or a CPU's vector instructions simply by providing an appropriate runtime (however, only Co-dfns has such a runtime—an ArrayFire program on the GPU and Dyalog APL on the CPU). The two implementations also share a preference for working "close to the metal" by passing around arrays of numbers rather than creating abstract types to work with data. Objects are right out. These choices lead to a compact source code implementation, and may have some benefits in terms of how easy it is to write and understand the compiler.

Compilation strategy

Co-dfns development has primarily been focused on the core compiler, and not parsing, code generation, or the runtime. The associated Ph.D. thesis and famous 17 lines figure refer to this section, which transforms the abstract syntax tree (AST) of a program to a lower-level form, and resolves lexical scoping by linking variables to their definitions. While all of Co-dfns is written in APL, other sections aren't necessarily designed to be data-parallel and don't have the same performance guarantees. For example, the parser uses a parsing expression grammar (PEG), a sequential algorithm. In contrast, BQN is entirely written in a data-parallel style. It does not maintain the same clean separation between compiler sections: token formation and literal evaluation is separated into its own function, but parsing, AST manipulation, and code generation overlap.

The core Co-dfns compiler is based on manipulating the syntax tree, which is mostly stored as parent and sibling vectors—that is, lists of indices of other nodes in the tree. BQN is less methodical, but generally treats the source tokens as a simple list. This list is reordered in various ways, allowing operations that behave like tree traversals to be performed with scans under the right ordering. This strategy allows BQN to be much stricter in the kinds of operations it uses. Co-dfns regularly uses (repeat until convergence) for iteration and creates nested arrays with (Key, like Group), but BQN has only a single instance of iteration to resolve quotes and comments, plus one complex but parallelizable scan for numeric literal processing, and only uses Group to extract identifiers and strings. This means that most primitives, if we count simple reductions and scans as single primitives, are executed a fixed number of times during execution, making complexity analysis even easier than in Co-dfns.

Backends and optimization

Co-dfns was designed from the beginning to build GPU programs, and outputs code in ArrayFire (a C++ framework), which is then compiled. GPU programming is quite limiting, and as a result Co-dfns has strict limitations in functionality that are slowly being removed. It now has partial support for nested arrays and array ranks higher than 4. BQN is designed with performance in mind, but implementation effort focused on functionality first, so that arbitrary array structures as well as trains and lexical closures have been supported from the beginning. Rather than target a specific language, it outputs object code to be interpreted by a virtual machine. Another goal for BQN was to not only write the compiler in BQN but to use BQN for the runtime as much as possible. The BQN-based runtime uses a small number of basic array operations provided by the VM. The extra abstraction causes this runtime to be very slow, but this can be fixed by overwriting functions from the runtime with natively-implemented ones.

Neither BQN nor Co-dfns significantly optimize their output at the time of writing (it could be said that Co-dfns relies on the ArrayFire backend to optimize). BQN does have one optimization, which is to compute variable lifetimes in functions so that the last access to a variable can clear it. Further optimizations often require finding properties such as reachability in a graph of expressions that probably can't be done efficiently in a strict array style. For this and other reasons it would probably be best to structure compiler optimization as a set of additional modules that can be provided during a given compilation.

Error reporting

Co-dfns doesn't check for compilation errors, while BQN has complete error checking and good error messages, and includes source positions in compiler errors as well as in the compiled code for use in runtime errors. Position tracking and error checking add up to a little more than 20% overhead for the compiler, both in runtime and lines of code. And improving the way errors are reported once found has no cost for working programs, because reporting code only needs to be run if there's a compiler error. This leaves room for potentially very sophisticated error analysis to attempt to track down the root cause of a compilation error, but I haven't yet done any work along these lines.


Aaron advocates the almost complete separation of code from comments (thesis) in addition to his very terse style as a general programming methodology. I find that this practice makes it hard to connect the documentation to the code, and is very slow in providing a summary or reminder of functionality that a comment might. One comment on each line makes a better balance of compactness and faster accessibility in my opinion. However, I do plan to write long-form material providing the necessary context and explanations required to understand the compiler.