Pijul represents files internally as a graph, but how does it actually work?

This article began its life when I sat down and tried in earnest to understand how Pijul's graph model works in practice. Personally, I find that abstract concepts are much easier to understand when there exists something concrete that I can mentally hook it up to. A concrete hanger for the abstract clothing. To pursue this, I wrote small examples, recorded them with `pijul record`, produced graphs with `pijul debug` and tried to make sense of them. For this article I have tried my best to make the graphs more legible without modifying the structure produced by Pijul. It is meant to help the reader (and myself) develop an intuition of how Pijul works under the hood, how files and directories are represented in the graph and how edits modify the graph. In the end, we will see how merge conflicts are naturally modeled in the graph. The graph model is Pijul's tool for dealing with conflicts and it allows for recording how conflicts are resolved and those resolutions can be safely reverted.

## Change files A _change file_ records specific changes made to the file graph. The key take-away here is that a change file is *not* a patch or diff in the sense that git or other diff tools might produce. A change file in Pijul contains contains the precise changes to an existing collection-of-files-as-a-graph (call it "repo-graph" for short). See [Change files](/pijul-change-files.html) for an in-depth look at the structure of change files For example: a change file never contains deleted text (like deleted lines that might appear in a unified diff). A change file may refer to content introduced by other changes and indicate parts that should be marked deleted in the repo-graph. The actual text that is deleted is not part of the contents of a change file. Conversely, a given change file in isolation only contains text/content that is being added to the existing repo-graph. Change files also record a list of dependencies as a list of hashes of the change files that need to be applied before a given change file can be applied.

## Adding files The only thing we can really do with an empty repository is to begin adding files to it. To do that, we create a file, add some contents to it, run `pijul add `, then `pijul record -m `. Our first file graph

File addition: add main.c

The root change (also known as AAAAAAAAAAAAA) is a synthetic node not introduced by any changes, all the other nodes are introduced by changes. The first little surprise here is that we've only recorded one change, but two were created. The Pijul log command confirms this: $ pijul log Change YS4YZQKSU3ZUXKGRK65W52EKET2UIF4V6SOZMVOEFTMXFOXJEBHQC Author: ************ <****@*****> Date: Wed, 18 Oct 2023 04:17:49 +0000 add main.c Change WLNTADNCUR2X6BU4AFUIVAPTX77CORJ3T4OEXW63XPZ4ACCJ7H2AC Author: Date: Wed, 18 Oct 2023 04:17:49 +0000 The author-less change looks like this: $ pijul change WLNTA message = '' timestamp = '2023-10-18T04:17:49.400906844Z' authors = [] # Hunks 1. Root add up 1.0, new 0:0 The `C1` change is introduced by Pijul to "anchor" other changes. In Pijul it's possible to join histories from different repositories and, as I understand it, the separate, explicit root addition is what makes that possible. The C2 change is the actual file addition: 1. File addition: "main.c" in "" "UTF-8" up 2.1, new 0:30 + #include + + int + main(int argc, char *argv[]) + { + printf("hello world\n"); + }

## Edits & Replacements By far the most common operations after adding files is editing them. Pijul has two flavours of file edits: edits and replacements. The difference between the two is essentially that an edit only introduces new lines where replacements additionally remove lines. ### Simple edits The edit is rendered like this with `pijul change`: 1. Edit in "main.c":2 2.31 "UTF-8" up 2.51, new 0:41, down 2.51 + + void saymsg(char *msg) { printf(msg); } So all we've done is add two lines. The internal graph representation in Pijul ends up looking like this.

Sample edit adding new lines

From the `C2` change, Pijul has split the node `C2 [32;115[` into two nodes: `C2 [32;51[` and `C2 [51;115[`, and `C3` introduces a new node whose contents go between them. The range notation on a node label refers to a slice of bytes from the contents section of a given change. The green arrows indicate file content nodes and the order between them, and the red back arrows indicate the immediate predecessor. To render a file from this file graph, Pijul would attempt to do a total topological ordering of the content nodes, traverse them, grab the bytes from respective change files and concatenate them together to produce the final file. In our example, the content nodes are now `C2 [32;51]`, `C2 [51;115[`, and `C3 [0;41[`, and Pijul orders them by the outgoing green arrows:

If you look closely you'll note that the there's one edge labeled `C3` instead of `[C3]`. This means the edge exists only to provide a total ordering on the nodes. The current contents of our file is literally the concatenation of the byte sequences indicated by the three nodes. ### Replacements Next we'll try replacing some of the existing file content with new content. The change itself is quite simple. Now our file graph looks like this.

Replacement in a file

1. Replacement in "main.c":8 2.31 "UTF-8" B:BD 2.87 -> 2.87:113/2 up 2.87, new 0:26, down 2.113 - printf("hello world\n"); + saymsg("hello world\n"); Like `C3`, a new change is added with new contents, but there are some new things to observe: - As with `C3`, the nodes of `C2` have again been split. The `C2 [51;115[` node has been split into three nodes with the ranges [51;87[, [87;113[, and [113;115[. - The middle node of range [87;113[ is the text that we have removed, and it is indicated in the graph by dashed edges introduced by `C4`. - The node with deleted content retains edges to other content nodes. Pijul considers a node "dead" if all its incoming (ie green) edges are marked deleted. It is still allowed for a dead node to have live edges to other nodes. - There are new dotted edges between nodes `C2 [51;87[` and `C2 [113;115[`. These are pseudo-edges added by Pijul and are not explicitly introduced by any change. These edges exist to make it faster for Pijul to compute the live nodes without having to traverse all the dead nodes. In general, Pijul "deletes" text by splitting a node into three: a node to hold the deleted contents, and two nodes for the remaining (alive) contents before and after. Pseudo-edges are added to make file rendering faster by allowing it to skip dead nodes. The total number of nodes that make up the contents of our file is now five and are ordered as follows:

## Adding another file Files exist as independent subgraphs that only share a common root in the repository structure, so if we add another file to the repository it will not depend on any of the changes that introduced or modified our first file, it will only depend on the first change that introduced the root.

One of the powers of the graph representation begins to come to light: If we decided that we wanted to undo the change called `C4` (the last change on main.c) we could undo it without needing to consider the `C5` change. Our last change (adding readme.txt) does not in any way depend on `C4`, so clearly we should be able to modify the part of the file graph that represents main.c without touching the part that represents readme.txt. If, in our last change, we had also edited main.c, then we could have ended up depending on `C4` and undoing it would be more cumbersome, but in the current file graph that is not the case.

## Conflicts Now that we understand better how files and directories We did not show how directories are represented in the graph, but suffice it to say it is similar to "File addition" nodes are represented internally in Pijul, we can begin to understand how conflicts are modeled. To illustrate, we will reset the file graph that we have evolved until now and as it can quickly become complicated and challenging to read. An order conflict, in which changes A and B modify the same lines independently and, when merged, result in a graph with live nodes that do not have an ordering between them.

The following code creates a new repository, adds an initial file, then creates two independent changes (using _channels_) that modify the same line. The conflict is introduced by applying the change from one channel onto the other. (In Git, this is similar to creating two commits in different branches, then merging the branches.) $ pijul init test --channel alice $ cd test $ cat < test.txt A B C EOF $ pijul add test.txt $ pijul fork bob $ pijul record --all --message "add test.txt" $ pijul channel switch bob $ sed -i -e 's/B/X/g' test.txt $ pijul record --all --message "bob wuz here" $ pijul channel switch alice $ sed -i -e 's/B/Y/g' test.txt $ pijul record --all --message "alice wuz here" $ pijul apply $(pijul log --channel bob --limit 1 --hash-only) Outputting repository ↖ There were conflicts: - Order conflict in "file.txt" starting on line 2 - Order conflict in "file.txt" starting on line 2 In the graphical illustration, the change called `C1` introduces our test.txt file and then we make changes to in it different channels where we modify the same line. Merging the changes into the same channel results in an _order conflict_. The nodes `A [1;3[` and `B [1;3[` do not have any forward arrows from one to the other to impose a total ordering. The live nodes in the file graph are now only partially ordered. In general, a _conflict_ in Pijul is concretely the situation where multiple changes make modifications to the underlying file graph that results in a graph where there is no total ordering among all the live nodes. If we focus on just the nodes that make up the contents of our file, the graph looks like this:

Both changes delete the text represented by `C1 [4;6[` and replace them with their own text, but there is no relation between the new nodes. When Pijul outputs the file, the conflict (more specifically, an _order conflict_) is identified. Pijul then produces the file with conflict markers and prints a message informing about the conflict and its location. $ cat test.txt A >>>>>>> 1 [5FA3JXMK alice wuz here] Y ======= 1 [NXYTYEG7 bob wuz here] X <<<<<<< 1 C In the Pijul repo-graph model, there are different kinds of conflicts and they are enumerated. * An _order conflict_ is when there is not one unique ordering among all the text nodes that make up a file's contents * A _zombie conflict_ is when one change deletes text that is modified by another change. Zombie conflicts also occur with files, where one change edits a file and another deletes it * There are also _name conflicts_ stemming from renaming files or introducing files in different changes with the same name * There are even _cyclic conficts_ which, at the time of writing, I am not confident enough to attempt to explain All these kinds of conflicts are modeled in the repo-graph and allows Pijul to "remember" conflicts. To resolve a conflict, we need to add another change. Conflict resolution is a specific type of change, where nodes and edges are added to the graph to re-instate a total ordering on the live content nodes. We will apply this simplest resolution and remove the conflict markers in our file to indicate we want those lines in that order. Recording this change in Pijul produces a new change type: # Dependencies [2] 5FA3JXMKJAW4CZ5SDKQNE4X7ZGGS4SU27IDQGC4WEJ3DPBBCPXUAC # alice wuz here [3] NXYTYEG7LFI2COMCN3JZXR7GXKHHH5Y3IUNWRZZJ6KSKCZMMIL3QC # bob wuz here [4]+NDZBWWPUTO3QMOZ4UMZZGETAZQPGPJZJDY74FR7VICYUKO3RF3LAC # add test.txt # Hunks 1. Solving an order conflict in "test.txt":3 4.1 "UTF-8" up 2.3, new 0:0, down 3.1 The change file itself has no contents! The one hunk it contains only contains information about the graph. Specifically, a node `R [0;0[` is added to the graph with forward edges going from `A [1;3[` to `B [1;3[`. Now our live nodes have a total ordering among them again.

The astute reader will have noticed that at no point were nodes or edges removed from the graph. This is a feature of Pijul, it is an _append-only_ system. There does not appear to be a safe way to remove nodes or edges without potentially causing problems later on. The benefit here (which is hopefully clear now) is that we an undo the conflict resolution and apply some other resolution, because Pijul has all the information required to do that.