Lumiera
The new emerging NLE for GNU/Linux

Within the support library, in the namespace lib::diff, there is a collection of loosely coupled tools known as »the diff framework«. It revolves around generic representation and handling of structural differences. Beyond some rather general assumptions, to avoid stipulating the usage of specific data elements or containers, the framework is kept generic, cast in terms of elements, sequences and strategies for access, indexing and traversal.

motivation

Diff handling is multi purpose within Lumiera: Diff representation is seen as a meta language and abstraction mechanism; it enables tight collaboration without the need to tie and tangle the involved implementation data structures. Used this way, diff representation reduces coupling and helps to cut down overall complexity — so to justify the considerable amount of complexity seen within the diff framework implementation.

Definitions

element

the atomic unit treated in diff detection, representation and application.
Elements are considered to be

  • lightweight copyable values

  • equality comparable

  • bearing distinct identity

  • unique as far as concerned

sequence

data is delivered in the form of a sequence, which might or might not be ordered, but in any case will be traversed once only.

diff

the changes necessary to transform an input sequence (“old sequence”) into a desired target sequence (“new sequence”)

diff language

differences are spelled out in linearised form: as a sequence of constant-size diff actions, called »diff verbs«

diff verb

a single element within a diff. Diff verbs are conceived as operations, which, when applied consuming the input sequence, will produce the target sequence of the diff.

diff application

the process of consuming a diff (sequence of diff verbs), with the goal to produce some effect at the target of diff application. Typically we want to apply a diff to a data sequence, to mutate it into a new shape, conforming with the shape of the diff’s “target sequence”

tree mutator

a customisable intermediary, allowing to apply a diff sequence against an opaque data structure. For the purpose of diff application, the TreeMutator serves as target object, while in fact it is itself attached by a binding to the actual target data structure, which remains a hidden implementation detail. This allows to manipulate the target data structure without knowing its concrete representation.

diff generator

a facility producing a diff, which is a sequence of diff verbs. Typically, a diff generator works lazily, demand driven.

diff detector

special kind of diff generator, which takes two data sequences as input: an “old sequence” and a “new sequence”. The diff detector traverses and compares these sequences to produce a diff, which describes the steps necessary to transform the “old” shape into the “new” shape of the data.

List Diff Algorithm

While in general this is a well studied subject, in Lumiera we’ll confine ourselves to a very specific flavour of diff handling: we rely on elementary atomic units with well established object identity. And in addition, within the scope of one coherent diff handling task, we require those elements to be unique. The purpose of this design decision is to segregate the notorious matching problem and treat diff handling in isolation.

Effectively this means that, for any given element, there can be at most one matching counterpart in the other sequence, and the presence of such can be detected by using an index. In fact, we retrieve an index for every sequence involved into the diff detection task; this is our trade-off for simplicity in the diff detection algorithm.
[traditionally, diff detection schemes, especially those geared at text diff detection, engage into great lengths of producing an “optimal” diff, which effectively means to build specifically tuned pattern or decision tables, from which the final diff can then be pulled or interpreted. We acknowledge that in our case building a lookup table index with additional annotations can be as bad as O(n2) and worse; we might be able to do better, but likely for the price of turning the algorithm into some kind of mental challenge.]
In case this turns out as a performance problem, we might consider integrating the index maintenance into the data structure to be diffed, which shifts the additional impact of indexing onto the data population phase.
[in the general tree diff case this is far from trivial, since we need an self-contained element index for every node, and we need the ability to take a snapshot of the “old” state before mutating a node into “new” shape]

Element classification

By using the indices of the old and the new sequence, we are able to classify each element:

  • elements only present in the new sequence are treated as inserts

  • elements only present in the old sequence are treated as deletes

  • elements present in both sequences form the permutation

Processing pattern

We consume both the old and the new sequence synchronously, while emitting the diff sequence.

The diff describes a sequence of operations, which, when applied, consume a sequence congruent to the old sequence, while emitting a sequence congruent to the new sequence. We use the following list diff language here:

verb ins(elm)

insert the given argument element elm at the current processing position into the target sequence. This operation allows to inject new data

verb del(elm)

delete the next element elm at current position. For sake of verification, the element to be deleted is also included as argument (redundancy).

verb pick(elm)

accepts the next element at current position into the resulting altered sequence. The element is given redundantly as argument.

verb find(elm)

effect a re-ordering of the target list contents. This verb requires to search for the (next respective single occurrence of the) given element in the remainder of the datastructure, to bring it forward and insert it as the next element.

verb skip(elm)

processing hint, emitted at the position where an element previously fetched by some find verb happened to sit in the old order. This allows an optimising implementation to “fetch” a copy and just drop or skip the original, thereby avoiding to shift other elements.

Since inserts and deletes can be detected and emitted right at the processing frontier, for the remaining theoretical discussion, we consider the insert / delete part filtered away conceptually, and concentrate on generating the permutation part.

Handling sequence permutation

Permutation handling turns out to be the turning point and tricky part of diff generation; the handling of new and missing members can be built on top, once we manage to describe a permutation diff. If we thus consider — in theory — the inserts and deletes to be filtered away, what remains is a permutation of index numbers to cause the re-ordering. We may describe this re-ordering by the index numbers in the new sequence, given in the order of the old sequence. For such a re-ordering permutation, the theoretically optimal result can be achieved by Cycle Sort in linear time.
[ assuming random access by index is possible, Cycle Sort walks the sequence once. Whenever encountering an element out-of order, i.e. new postion != current position, we leap to the indicated new position, which necessarily will be out-of-order too, so we can leap from there to the next indicated position, until we jump back to the original position eventually. Such a closed cycle can then just be rotated into proper position. Each permutation can be decomposed into a finite number of closed cycles, which means, after rotating all cycles out of order, the permutation will be sorted completely.]
Starting from such “cycle rotations”, we possibly could work out a minimal set of moving operations.

But there is a twist: Our design avoids using index numbers, since we aim at stream processing of diffs. We do not want to communicate index numbers to the consumer of the diff; rather we want to communicate reference elements with our diff verbs. Thus we prefer the most simplistic processing mechanism, which happens to be some variation of Insertion Sort.
[to support this choice, Insertion Sort — in spite of being O(n2) — turns out to be the best choice at sorting small data sets for reasons of cache locality; even typical Quicksort implementations switch to insertion sorting of small subsets for performance reasons]
This is the purpose of our find verb: to extract some element known to be out of order, and insert it at the current position.

Implementation and Complexity

Based on these choices, we’re able to consume two permutations of the same sequence simultaneously, while emitting find and pick verbs to describe the re-ordering. Consider the two sequences split into an already-processed part, and a part still-to-be-processed.

Invariant

Matters are arranged such, that, in the to-be-processed part, each element appearing at the front of the “new” sequence can be consumed right away.

Now, to arrive at that invariant, we use indices to determine

  • if the element at head of the old sequence is not present in the new sequence, which means it has to be deleted

  • while an element appearing at head of the new sequence but not present in the old sequence needs to be inserted

  • and especially an element known to be present in both sequences, appearing at the head of the new sequence but non-matching at the old sequence prompts us to fetch the right element from further down in the sequence and insert it a current position

after that, the invariant is (re)established and we can consume the element and move the processing point forward.

For generating the diff description, we need index tables of the “old” and the “new” sequence, which causes a O(n log n) complexity and storage in the order of the sequence length. Application of the diff is quadratic, due to the find-and-insert passes.
[In the theoretical treatment of diff problems it is common to introduce a distance metric to describe how far apart the two sequences are in terms of atomic changes. This helps to make the quadratic (or worse) complexity of such algorithms look better: if we know the sequences are close, the nested sub-scans will be shorter than the whole sequence (with n·d < n2).
However, since our goal is to support permutations and we have to deal with arbitrary sequences, such an argument looks somewhat pointless. Let’s face it, structural diff computation is expensive; the only way to keep matters under control is to keep the local sequences short, which prompts us to exploit structural knowledge instead of comparing the entire data as flat sequence]

Tree structure differences

The handling of list differences can be used as prototype to build a description of structural changes in hierarchical data: traverse the structure and account for each element and each change. Such a description of changes won’t be optimal though. What appears as a insertion or deletion locally, might indeed be just the result of rearranging subtrees as a whole. The tree diff problem in this general form is known to be a rather tough challenge. But our goals are different here. Lumiera relies on a »External Tree Description« for symbolic representation of hierarchically structured elements, without actually implementing them. The purpose of this “external” description is to largely remove the need for a central data model to work against. A symbolic diff message allows to propagate data and structure changes, without even using the same data representation at both sides of the collaboration.

Generic Node Record

For this to work, we need some very generic meta representation. This can be a textual representation (e.g. JSON) — but within the application it seems more appropriate to use an abstracted and unspecific typed data representation, akin to “JSON with typed language data”. It can be considered symbolic, insofar it isn’t the data, it refers to it. To make such an approach work, we need the following parts:

  • a generic node, which has an identity and some payload data. This GenNode is treated as elementary value.

  • a record made from a collection of generic nodes, to take on the abstracted role of an object. Such a Record<GenNode> is a sequence of nodes, partitioned in two scopes: the (named) attributes and the children.

  • together these elements form an essentially recursive structure: The record is comprised of nodes and the nodes might, besides elementary values, also carry records.

  • and finally we need an identification scheme, allowing to produce named and unnamed yet unique identities, also including opaque type information.

Type information is deliberately kept opaque, to prevent switch-on-type. We always presume synced (similar) data structures on both ends of the collaboration, where the partners share common knowledge about types and structure. Changes are indicated and propagated, not probed.

Nested list differences

Exploiting the fact that Record<GenNode> is essentially a sequence, we’re able to build the description of structure changes as an extension layer on top of our linearised diff language format. We introduce a bracketing construct to open and close sub scopes. Within each scope, the verbs of our list diff language are deployed, just now with a GenNode as payload. This yields the following tree diff language

verb ins(GenNode)

prompts to insert the given argument element at the current processing position into the target sequence. This operation allows to inject new data

verb del(ID)

requires to delete the next element at current position.
[The payload of this and all the following verbs is a GenNode, but only the ID part matters. This allows to send a special ref element over the wire instead of having to send a full subtree, for obvious performance reasons.]
For sake of verification, the ID of the argument payload is required to match the ID of the element about to be discarded.

verb pick(ID)

just accepts the next element at current position into the resulting altered sequence. Again, the ID of the argument has to match the ID of the element to be picked, for sake of verification.

verb find(ID)

change the order of the target scope contents: this verb requires to search ahead for the (next respective single occurrence of the) given element further down into the remainder of the current record scope (but not into nested child scopes). The designated element is to be retrieved and inserted as the next element at current position.

verb skip(ID)

this is a mere processing hint, emitted at the position where an element previously extracted by a find(ID) verb happened to sit within the old order.

verb after(ID)

shortcut to pick existing elements up to the designated point.
As a special notation, after(Ref::ATTRIBUTES) allows to fast forward to the first child element, while after(Ref::END) means to accept all of the existing data contents as-is (possibly to append further elements beyond that point).

verb mut(ID)

bracketing construct to open a nested sub scope. The element designated by the ID of the argument needs to be a record (“nested child object”). Moreover, this element must have been mentioned with the preceding diff verbs at that level, which means that the element as such must already be present in the altered target structure. The mut(ID) verb then opens the designated nested record for diff handling, and all subsequent diff verbs are to be interpreted relative to this scope, until the corresponding emu(ID) verb is encountered.

verb emu(ID)

closing bracketing construct and counterpart to mut(ID). This verb must be given precisely at the end of the nested scope.
[it is not allowed to “return” from the middle of a scope, for sake of sanity. The diff messages transport a certain degree of redundancy to detect when the data structure at target does no longer conform to the assumptions made at the generation side.]
At this point, this child scope is left and the parent scope with all existing diff state is popped from an internal stack.

representation of objects

While we are talking about structured data, in fact what are about to handle are objects, understood in the standard flavour of object orientation, where an object is the instance of a type and offers a contract. Incidentally, this is not the original, “pure” meaning of object orientation, but the one that became prolific in brining our daily practice closer to the inherent structuring of modern human organisation. And in dealing with this kind of object, we sometimes get into conflict with the essentially open and permissive nature of structured data. So we need to establish a mapping rule, which translates into additional conventions about how to spell out matters in the diff language.

We choose to leave this largely on the level of stylistic rules, thus stressing the language nature of the diff. Even when this bears the danger to produce an exception very late, when it comes to applying the diff to a target data structure. The intention behind this whole diff approach is to transform tight coupling with strict rules into a loose collaboration based on a common understanding. So generally we’ll assume the diff is just right, and if not, we’ll get what we deserve.
[This gives rise to a tricky discussion about loss of strictness and the costs incurred by that happening. We should not treat this topic in isolation, but rather consider that loose coupling was chosen to avoid far more serious problems caused by tight coupling, and especially the poisoning and dire consequences of a global fixed common data model, when used in a large, not homogeneous system. But when a system indeed is not homogeneous, we better try to make each part open-closed, open for change but closed against extension. This is especially true in the case of the UI.]

object representation protocol

A diff is created to tell some partner about our data, and the »protocol to describe an object« is as follows

  • the ID is the object’s identity and is once given, right at start, and never changed

  • we spell out any metadata (esp. a type information) first, followed by all attributes, and then followed by contents of the object’s scope (children).

  • attributes are to be given in a way not in contradiction to the more stringent semantics of an object field or property

    • never attempt to re-order or delete such attributes, since their presence is fixed in the class definition

    • when a field is mandatory by its nature, it shall be required in construction, and the corresponding data is to be given with the ins verb causing the constructor call

    • on the other hand, the data for an optional field, when present, shall be spelled out by ins verb after construction, with the first population diff.

    • we do not support attribute map semantics (or extended “object properties” of any kind).
      If necessary, treat them as nested entity with map semantics