Flattening ASTs and other compiler data structures (2023)
51 comments
·January 10, 2025dmagyari
"Instead of allocating Expr objects willy-nilly on the heap, we’ll pack them into a single, contiguous array." Zig compiler pipeline (AST, Zir, Air, Sema) does exactly this on all layers. Not only contiguous, but instead of array-of-structs it is struct-of-arrays, so walking the tree is even more cache friendly. For AST see: https://github.com/ziglang/zig/blob/master/lib/std/zig/Ast.z...
gritzko
I work on a C dialect where everything is flattened. JSON and other trees in particular. Binary heaps are flat, merge sort and iterator heaps are absolutely great, can build LSM databases with that. Stacks, circular buffers, hash maps, etc, all flat. Templated output (PHP like) is done by a flat data structure.
https://github.com/gritzko/librdx/blob/master/abc/B.md
Apart from locality and lifetimes, these flat data structures improve composability. When every data structure is a flat buffer, you can mmap them or zip them or send them by the network, all by the same routine. They are uniform like bricks, in a sense.
rurban
I worked in a language where all datastructures were "flattened", could be trivially serialized to disk, and read in again. Called print and read. The language was called lisp. All flat, just parens.
Some of my compilers export the AST as lisp trees. Much smaller and more readable than json, and it can be executed. Uniform like bricks
vanderZwan
> All flat, just parens.
So not flat then. Prefix is not postfix. Forth, and most concatenative languages, are much closer to actually bein, flat.
Lisp is trivial to flatten, but that's not the same thing.
agumonkey
Makes me wonder if people in APL/J/K community have not been influenced or influencing this kind of technique. IIRC Aaron Hsu does tree processing through arrays (but i'm not skilled enough to analyze his code)
gsf_emergency
Do you have a link to such an example of Aaron's code? Thank you in advance!
082349872349872
https://scholarworks.iu.edu/dspace/items/3ab772c9-92c9-4f59-...
Iverson's 1962 book also mentions tree representations, see pp45-62: https://archive.org/details/aprogramminglanguage1962/page/n6...
agumonkey
Can't remember where exactly but he did demo his code in talks/conferences with links.
torginus
I guess Rust's contribution to high performance programming is that its borrow checker is so loathsome that it pushes people into using ideas like ECS or arenas just to not have to bother with it.
kazinator
> Instead of allocating Expr objects willy-nilly on the heap, we’ll pack them into a single, contiguous array.
This happens naturally if you bump-allocate them in a garbage-collected run-time, particularly under a copying collector. Free lists also tend to co-locate because they are produced during sweep phases of GC which run through heaps in order of address.
Don't make me bring out the L word for the billionth time.
> A flat array of Exprs can make it fun and easy to implement hash consing
OK, it's not a case of L-ignorance, just willful neglect.
samps
FWIW I did acknowledge this in the article:
> A sufficiently smart memory allocator might achieve the same thing, especially if you allocate the whole AST up front and never add to it
> Again, a really fast malloc might be hard to compete with—but you basically can’t beat bump allocation on sheer simplicity.
layer8
And if you don’t need more than 32 GB of heap space, the JVM also gives you the ability to reduce reference sizes to 32 bits, with compressed references. (Due to alignment requirements, the lower 3 bits of a pointer are zero and hence do not need to be stored, which effectively gives you a 35-bit address space.) Of course, the presence of object headers counteracts this to a certain extent.
Agraillo
About 10 years ago working with AST trees I (re)invented a flat structure representing trees in a flat array. It reminds me of what is described here but not exactly. In my case I needed only two indices per node: total sub-region length of all the children and sub-children and parent index (so no need to have indices of all children). Total sub-length basically can be interpreted as the index of the next sibling. With such a structure it's easy/cheap to execute FindFirstChild/FindNextSibling.
Later the theory behind such structures was revealed as "Nested set model" [1]. The article seems to not mention the internal representation, but I think that the implementation should use something like my solution, so fixed number of references per node
cardanome
Amazing article, very good advice to keep your data structures flat.
Adding to that, it also makes editing the AST vastly more efficient.
I have discovered that principle on my own when I worked on an editor that directly operated on the AST instead of text. I found manipulating the tree-style AST so painful, constantly traversing the tree and all. Once I made it flat, my life was a hell lot easier. You can just directly index any part of AST in linear time.
userbinator
Rediscovering techniques that were somewhat well-known in the 70s and 80s.
Taniwha
heh - I built compilers this back in the 70s because the machine I was working on didn't really do pointers as a 1st class data structure (B6700 algol), it's not really surprising finding someone doing something similar in another language that makes pointers difficult to deal with
torginus
Yup, and chances are if you're using a good C++ stl implementation, most containers already use packed storage internally. It doesn't even have a heap data structure, it uses an std::vector, with a set of helper functions.
emptysea
Rust-analyzer uses a similar technique for parsing https://github.com/rust-lang/rust-analyzer/blob/master/crate... which then gets fed into https://github.com/rust-analyzer/rowan (lossless syntax tree)
bradrn
There is a longer overview of it here: https://github.com/rust-lang/rust-analyzer/blob/master/docs/...
Tarean
Twee (an equational theorem prover in Haskell used by quickspec) has an interesting take on this. Terms are slices of arrays, but you get a normal interface including pattern matching via synonyms. It can also be nice to use phantom types of your references (array offsets), so if you project them into flat view types you can do so type safely
Requires the language to have something equivalent to pattern synonyms to be as invisible as twee, though.
In twee a TermList is a slice of a bytearray (two ints for offset/length plus a pointer).
And a term is an int for the function symbol and an unpacked TermList for the arguments.
The pattern match synonyms load a flat representation from the array into a view type, and the allocation of the view type cancels out with the pattern matching so everything remains allocation free.
https://hackage.haskell.org/package/twee-lib-2.4.2/docs/Twee...
Tarean
Forgot to mention: In the twee style, the int for the function id contains metadata (is it a unification variable or constant name? how many args does it take?). That way f1(f3(f5(), f7())) would be serialised as something like [1,3,5,7], without even references to other offsets
ww520
This is a fantastic idea. AST works well in an array based allocation block since it has no need for freeing individual nodes. It’s an add-only allocation.
JonChesterfield
What about transforming the AST after it is built, or deriving a new tree which partly aliases the original in persistent structure fashion?
ndesaulniers
Cool! Carbon is doing exactly this. I had asked leads if there was a paper on this approach, but they didn't have anything for me. I'll send them this post!
wrsh07
Chandler discusses it in this video though! https://youtu.be/ZI198eFghJk
You get some traversals for free with this layout (preorder, reverse post order). Can search for subtrees with string searching algorithms or more complex things with regex.
ndesaulniers
Ah, forgot if they had talked about that pattern externally yet. Thanks for the link.
benatkin
Zig uses a MultiArrayList which sounds similar https://mitchellh.com/zig/parser
pfdietz
One advantage to this is the ease with which it handles ephemeral annotations.
Suppose you want to attach additional information to some of the nodes of the AST. Different algorithms on the AST will attach different information; you don't necessarily need them all at the same time or know ahead of time what you'll need.
With nodes, you have to have some sort of node/value hash table, or hang a key/value map off each node. But with this flattened representation, each datum gets its own flat array as well, which can be independently allocated and deallocated.
One other thing I noticed about this flat representation is that it throws static typing into a cocked hat! All you have to refer to other nodes is indices. All different kinds of nodes are stored in the same array.
I thought a reddit comment on this article had an interesting point:
https://www.reddit.com/r/rust/comments/1d3b356/my_new_favori...
[–]Timzhy0 3 points 7 months ago
Btw I think one can go a step further than the author, there is no need to keep two explicit ExprRef baked in a binary node (lhs, rhs). You can exploit locality, basically the AST, seen it the LISP way, is just an arbitrarily nestable list, where elements are atoms or other lists. Hence all you need to know is where each list ends (and if it's an atom you can assume it spans one node) and actually one bit to know if it is the last entry in the list is quite ergonomic as well (because then you can distinguish whether moving next slot in the AST means there is a sibling). Basically it's easier to keep it sync while constructing and takes up less memory per node. I pay 40 bits per node, stored interleaved for best cache locality (some unaligned accesses but I think it's still worthwhile), 8 bits for the tag, 32 for the data, if data is bigger, 32 is an index into some auxiliary segment (basically a ptr).