# sqlglot.diff API documentation

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# Semantic Diff for SQL

by Iaroslav Zeigerman

## Motivation

Software is constantly changing and evolving, and identifying what has changed and reviewing those changes is an integral part of the development process. SQL code is no exception to this.

Text-based diff tools such as `git diff`, when applied to a code base, have certain limitations. First, they can only detect insertions and deletions, not movements or updates of individual pieces of code. Second, such tools can only detect changes between lines of text, which is too coarse for something as granular and detailed as source code. Additionally, the outcome of such a diff is dependent on the underlying code formatting, and yields different results if the formatting should change.

Consider the following diff generated by Git:

Semantically the query hasn’t changed. The two arguments `b` and `c` have been swapped (moved), posing no impact on the output of the query. Yet Git replaced the whole affected expression alongside a bulk of unrelated elements.

The alternative to text-based diffing is to compare Abstract Syntax Trees (AST) instead. The main advantage of ASTs are that they are a direct product of code parsing, which represents the underlying code structure at any desired level of granularity. Comparing ASTs may yield extremely precise diffs; changes such as code movements and updates can also be detected. Even more importantly, this approach facilitates additional use cases beyond eyeballing two versions of source code side by side.

The use cases I had in mind for SQL when I decided to embark on this journey of semantic diffing were the following:

- Query similarity score. Identifying which parts the two queries have in common to automatically suggest opportunities for consolidation, creation of intermediate/staging tables, and so on.
- Differentiating between cosmetic / structural changes and functional ones. For example when a nested query is refactored into a common table expression (CTE), this kind of change doesn’t have any functional impact on either a query or its outcome.
- Automatic suggestions about the need to retroactively backfill data. This is especially important for pipelines that populate very large tables for which restatement is a runtime-intensive procedure. The ability to discern between simple code movements and actual modifications can help assess the impact of a change and make suggestions accordingly.

The implementation discussed in this post is now a part of the SQLGlot library. You can find a complete source code in the diff.py module. The choice of SQLglot was an obvious one due to its simple but powerful API, lack of external dependencies and, more importantly, extensive list of supported SQL dialects.

## The Search for a Solution

When it comes to any diffing tool (not just a semantic one), the primary challenge is to match as many elements of compared entities as possible. Once such a set of matching elements is available, deriving a sequence of changes becomes an easy task.

If our elements have unique identifiers associated with them (for example, an element’s ID in DOM), the matching problem is trivial. However, the SQL syntax trees that we are comparing have neither unique keys nor object identifiers that can be used for the purposes of matching. So, how do we suppose to find pairs of nodes that are related?

To better illustrate the problem, consider comparing the following SQL expressions: `SELECT a + b + c, d, e` and `SELECT a - b + c, e, f`. Matching individual nodes from respective syntax trees can be visualized as follows:

Figure 1: Example of node matching for two SQL expression trees.

By looking at the figure of node matching for two SQL expression trees above, we conclude that the following changes should be captured by our solution:

- Inserted nodes: `Sub` and `f`. These are the nodes from the target AST which do not have a matching node in the source AST.
- Removed nodes: `Add` and `d`. These are the nodes from the source AST which do not have a counterpart in the target AST.
- Remaining nodes must be identified as unchanged.

It should be clear at this point that if we manage to match nodes in the source tree with their counterparts in the target tree, then computing the diff becomes a trivial matter.

### Naïve Brute-Force

The naïve solution would be to try all different permutations of node pair combinations, and see which set of pairs performs the best based on some type of heuristics. The runtime cost of such a solution quickly reaches the escape velocity; if both trees had only 10 nodes each, the number of such sets would approximately be 10! ^ 2 = 3.6M ^ 2 ~= 13 * 10^12. This is a very bad case of factorial complexity (to be precise, it’s actually much worse - O(n! ^ 2) - but I couldn’t come up with a name for it), so there is little need to explore this approach any further.

### Myers Algorithm

After the naïve approach was proven to be infeasible, the next question I asked myself was “how does git diff work?”. This question led me to discover the Myers diff algorithm [1]. This algorithm has been designed to compare sequences of strings. At its core, it’s looking for the shortest path on a graph of possible edits that transform the first sequence into the second one, while heavily rewarding those paths that lead to longest subsequences of unchanged elements. There’s a lot of material out there describing this algorithm in greater detail. I found James Coglan’s series of blog posts to be the most comprehensive.

Therefore, I had this “brilliant” (actually not) idea to transform trees into sequences by traversing them in topological order, and then applying the Myers algorithm on resulting sequences while using a custom heuristics when checking the equality of two nodes. Unsurprisingly, comparing sequences of strings is quite different from comparing hierarchical tree structures, and by flattening trees into sequences, we lose a lot of relevant context. This resulted in a terrible performance of this algorithm on ASTs. It often matched completely unrelated nodes, even when the two trees were mostly the same, and produced extremely inaccurate lists of changes overall. After playing around with it a little and tweaking my equality heuristics to improve accuracy, I ultimately scrapped the whole implementation and went back to the drawing board.

## Change Distiller

The algorithm I settled on at the end was Change Distiller, created by Fluri et al. [2], which in turn is an improvement over the core idea described by Chawathe et al. [3].

The algorithm consists of two high-level steps:

1. Finding appropriate matchings between pairs of nodes that are part of compared ASTs. Identifying what is meant by “appropriate” matching is also a part of this step.
2. Generating the so-called “edit script” from the matching set built in the 1st step. The edit script is a sequence of edit operations (for example, insert, remove, update, etc.) on individual tree nodes, such that when applied as transformations on the source AST, it eventually becomes the target AST. In general, the shorter the sequence, the better. The length of the edit script can be used to compare the performance of different algorithms, though this is not the only metric that matters.

The rest of this section is dedicated to the Python implementation of the steps above using the AST implementation provided by the SQLGlot library.

### Building the Matching Set

#### Matching Leaves

We begin composing the matching set by matching the leaf nodes. Leaf nodes are the nodes that do not have any children nodes (such as literals, identifiers, etc.). In order to match them, we gather all the leaf nodes from the source tree and generate a cartesian product with all the leaves from the target tree, while comparing pairs created this way and assigning them a similarity score. During this stage, we also exclude pairs that don’t pass basic matching criteria. Then, we pick pairs that scored the highest while making sure that each node is matched no more than once.

Using the example provided at the beginning of the post, the process of building an initial set of candidate matchings can be seen on Figure 2.

Figure 2: Building a set of candidate matchings between leaf nodes. The third item in each triplet represents a similarity score between two nodes.

First, let’s analyze the similarity score. Then, we’ll discuss matching criteria.

The similarity score proposed by Fluri et al. [2] is a dice coefficient applied to bigrams of respective node values. A bigram is a sequence of two adjacent elements from a string computed in a sliding window fashion:

    def bigram(string):
        count = max(0, len(string) - 1)
        return [string[i : i + 2] for i in range(count)]

For reasons that will become clear shortly, we actually need to compute bigram histograms rather than just sequences:

    from collections import defaultdict

    def bigram_histo(string):
        count = max(0, len(string) - 1)
        bigram_histo = defaultdict(int)
        for i in range(count):
            bigram_histo[string[i : i + 2]] += 1
        return bigram_histo

The dice coefficient formula looks like following:

Where X is a bigram of the source node and Y is a bigram of the second one. What this essentially does is count the number of bigram elements the two nodes have in common, multiply it by 2, and then divide by the total number of elements in both bigrams. This is where bigram histograms come in handy:

    def dice_coefficient(source, target):
        source_histo = bigram_histo(source.sql())
        target_histo = bigram_histo(target.sql())

        total_grams = (
            sum(source_histo.values()) + sum(target_histo.values())
        )
        if not total_grams:
            return 1.0 if source == target else 0.0

        overlap_len = 0
        overlapping_grams = set(source_histo) & set(target_histo)
        for g in overlapping_grams:
            overlap_len += min(source_histo[g], target_histo[g])

        return 2 * overlap_len / total_grams

To compute a bigram given a tree node, we first transform the node into its canonical SQL representation,so that the `Literal(123)` node becomes just “123” and the `Identifier(“a”)` node becomes just “a”. We also handle a scenario when strings are too short to derive bigrams. In this case, we fallback to checking the two nodes for equality.

Now when we know how to compute the similarity score, we can take care of the matching criteria for leaf nodes. In the original paper [2], the matching criteria is formalized as follows:

The two nodes are matched if two conditions are met:

1. The node labels match (in our case labels are just node types).
2. The similarity score for node values is greater than or equal to some threshold “f”. The authors of the paper recommend setting the value of “f” to 0.6.

With building blocks in place, we can now build a matching set for leaf nodes. First, we generate a list of candidates for matching:

    from heapq import heappush, heappop

    candidate_matchings = []
    source_leaves = _get_leaves(self._source)
    target_leaves = _get_leaves(self._target)
    for source_leaf in source_leaves:
        for target_leaf in target_leaves:
            if _is_same_type(source_leaf, target_leaf):
                similarity_score = dice_coefficient(
                    source_leaf, target_leaf
                )
                if similarity_score >= 0.6:
                    heappush(
                        candidate_matchings,
                        (
                            -similarity_score,
                            len(candidate_matchings),
                            source_leaf,
                            target_leaf,
                        ),
                    )

In the implementation above, we push each matching pair onto the heap to automatically maintain the correct order based on the assigned similarity score.

Finally, we build the initial matching set by picking leaf pairs with the highest score:

    matching_set = set()
    while candidate_matchings:
        _, _, source_leaf, target_leaf = heappop(candidate_matchings)
        if (
            source_leaf in unmatched_source_nodes
            and target_leaf in unmatched_target_nodes
        ):
            matching_set.add((source_leaf, target_leaf))
            unmatched_source_nodes.remove(source_leaf)
            unmatched_target_nodes.remove(target_leaf)

To finalize the matching set, we should now proceed with matching inner nodes.

#### Matching Inner Nodes

Matching inner nodes is quite similar to matching leaf nodes, with the following two distinctions:

- Rather than ranking a set of possible candidates, we pick the first node pair that passes the matching criteria.
- The matching criteria itself has been extended to account for the number of leaf nodes the pair of inner nodes have in common.

Figure 3: Matching inner nodes based on their type as well as how many of their leaf nodes have been previously matched.

Let’s start with the matching criteria. The criteria is formalized as follows:

Alongside already familiar similarity score and node type criteria, there is a new one in the middle: the ratio of leaf nodes that the two nodes have in common must exceed some threshold “t”. The recommended value for “t” is also 0.6. Counting the number of common leaf nodes is pretty straightforward, since we already have the complete matching set for leaves. All we need to do is count how many matching pairs do leaf nodes from the two compared inner nodes form.

There are two additional heuristics associated with this matching criteria:

- Inner node similarity weighting: if the similarity score between the node values doesn’t pass the threshold “f” but the ratio of common leaf nodes (“t”) is greater than or equal to 0.8, then the matching is considered successful.
- The threshold “t” is reduced to 0.4 for inner nodes with the number of leaf nodes equal to 4 or less, in order to decrease the false negative rate for small subtrees.

We now only have to iterate through the remaining unmatched nodes and form matching pairs based on the outlined criteria:

    leaves_matching_set = matching_set.copy()

    for source_node in unmatched_source_nodes.copy():
        for target_node in unmatched_target_nodes:
            if _is_same_type(source_node, target_node):
                source_leaves = set(_get_leaves(source_node))
                target_leaves = set(_get_leaves(target_node))

                max_leaves_num = max(len(source_leaves), len(target_leaves))
                if max_leaves_num:
                    common_leaves_num = sum(
                        1 if s in source_leaves and t in target_leaves else 0
                        for s, t in leaves_matching_set
                    )
                    leaf_similarity_score = common_leaves_num / max_leaves_num
                else:
                    leaf_similarity_score = 0.0

                adjusted_t = (
                    0.6
                    if min(len(source_leaves), len(target_leaves)) > 4
                    else 0.4
                )

                if leaf_similarity_score >= 0.8 or (
                    leaf_similarity_score >= adjusted_t
                    and dice_coefficient(source_node, target_node) >= 0.6
                ):
                    matching_set.add((source_node, target_node))
                    unmatched_source_nodes.remove(source_node)
                    unmatched_target_nodes.remove(target_node)
                    break

After the matching set is formed, we can proceed with generation of the edit script, which will be the algorithm’s output.

### Generating the Edit Script

At this point, we should have the following 3 sets at our disposal:

- The set of matched node pairs.
- The set of remaining unmatched nodes from the source tree.
- The set of remaining unmatched nodes from the target tree.

We can derive 3 kinds of edits from the matching set: either the node’s value was updated (Update), the node was moved to a different position within the tree (Move), or the node remained unchanged (Keep). Note that the Move case is not mutually exclusive with the other two. The node could have been updated or could have remained the same while at the same time its position within its parent node or the parent node itself could have changed. All unmatched nodes from the source tree are the ones that were removed (Remove), while unmatched nodes from the target tree are the ones that were inserted (Insert).

The latter two cases are pretty straightforward to implement:

    edit_script = []

    for removed_node in unmatched_source_nodes:
        edit_script.append(Remove(removed_node))
    for inserted_node in unmatched_target_nodes:
        edit_script.append(Insert(inserted_node))

Traversing the matching set requires a little more thought:

    for source_node, target_node in matching_set:
        if (
            not isinstance(source_node, LEAF_EXPRESSION_TYPES)
            or source_node == target_node
        ):
            move_edits = generate_move_edits(
                source_node, target_node, matching_set
            )
            edit_script.extend(move_edits)
            edit_script.append(Keep(source_node, target_node))
        else:
            edit_script.append(Update(source_node, target_node))

If a matching pair represents a pair of leaf nodes, we check if they are the same to decide whether an update took place. For inner node pairs, we also need to compare the positions of their respective children to detect node movements. Chawathe et al. [3] suggest applying the longest common subsequence (LCS) algorithm which, no surprise here, was described by Myers himself [1]. There is a small catch, however: instead of checking the equality of two children nodes, we need to check whether the two nodes form a pair that is a part of our matching set.

Now with this knowledge, the implementation becomes straightforward:

    def generate_move_edits(source, target, matching_set):
        source_children = _get_child_nodes(source)
        target_children = _get_child_nodes(target)

        lcs = set(
            _longest_common_subsequence(
                source_children,
                target_children,
                lambda l, r: (l, r) in matching_set
            )
        )

        move_edits = []
        for node in source_children:
            if node not in lcs and node not in unmatched_source_nodes:
                move_edits.append(Move(node))

        return move_edits

I left out the implementation of the LCS algorithm itself here, but there are plenty of implementation choices out there that can be easily looked up.

### Output

The implemented algorithm produces the output that resembles the following:

    >>> from sqlglot import parse_one, diff
    >>> diff(parse_one("SELECT a + b + c, d, e"), parse_one("SELECT a - b + c, e, f"))

    Remove(Add)
    Remove(Column(d))
    Remove(Identifier(d))
    Insert(Sub)
    Insert(Column(f))
    Insert(Identifier(f))
    Keep(Select, Select)
    Keep(Add, Add)
    Keep(Column(a), Column(a))
    Keep(Identifier(a), Identifier(a))
    Keep(Column(b), Column(b))
    Keep(Identifier(b), Identifier(b))
    Keep(Column(c), Column(c))
    Keep(Identifier(c), Identifier(c))
    Keep(Column(e), Column(e))
    Keep(Identifier(e), Identifier(e))

Note that the output above is abbreviated. The string representation of actual AST nodes is significantly more verbose.

The implementation works especially well when coupled with the SQLGlot’s query optimizer which can be used to produce canonical representations of compared queries:

    >>> schema={"t": {"a": "INT", "b": "INT", "c": "INT", "d": "INT"}}
    >>> source = """
    ... SELECT 1 + 1 + a
    ... FROM t
    ... WHERE b = 1 OR (c = 2 AND d = 3)
    ... """
    >>> target = """
    ... SELECT 2 + a
    ... FROM t
    ... WHERE (b = 1 OR c = 2) AND (b = 1 OR d = 3)
    ... """
    >>> optimized_source = optimize(parse_one(source), schema=schema)
    >>> optimized_target = optimize(parse_one(target), schema=schema)
    >>> edit_script = diff(optimized_source, optimized_target)
    >>> sum(0 if isinstance(e, Keep) else 1 for e in edit_script)
    0

### Optimizations

The worst case runtime complexity of this algorithm is not exactly stellar: O(n^2 * log n^2). This is because of the leaf matching process, which involves ranking a cartesian product between all leaf nodes of compared trees. Unsurprisingly, the algorithm takes a considerable time to finish for bigger queries.

There are still a few basic things we can do in our implementation to help improve performance:

- Refer to individual node objects using their identifiers (Python’s id()) instead of direct references in sets. This helps avoid costly recursive hash calculations and equality checks.
- Cache bigram histograms to avoid computing them more than once for the same node.
- Compute the canonical SQL string representation for each tree once while caching string representations of all inner nodes. This prevents redundant tree traversals when bigrams are computed.

At the time of writing only the first two optimizations have been implemented, so there is an opportunity to contribute for anyone who’s interested.

## Alternative Solutions

This section is dedicated to solutions that I’ve investigated, but haven’t tried.

First, this section wouldn’t be complete without Tristan Hume’s blog post. Tristan’s solution has a lot in common with the Myers algorithm plus heuristics that is much more clever than what I came up with. The implementation relies on a combination of dynamic programming and A* search algorithm to explore the space of possible matchings and pick the best ones. It seemed to have worked well for Tistan’s specific use case, but after my negative experience with the Myers algorithm, I decided to try something different.

Another notable approach is the Gumtree algorithm by Falleri et al. [4]. I discovered this paper after I’d already implemented the algorithm that is the main focus of this post. In sections 5.2 and 5.3 of their paper, the authors compare the two algorithms side by side and claim that Gumtree is significantly better in terms of both runtime performance and accuracy when evaluated on 12 792 pairs of Java source files. This doesn’t surprise me, as the algorithm takes the height of subtrees into account. In my tests, I definitely saw scenarios in which this context would have helped. On top of that, the authors promise O(n^2) runtime complexity in the worst case which, given the Change Distiller's O(n^2 * log n^2), looks particularly tempting. I hope to try this algorithm out at some point, and there is a good chance you see me writing about it in my future posts.

## Conclusion

The Change Distiller algorithm yielded quite satisfactory results in most of my tests. The scenarios in which it fell short mostly concerned identical (or very similar) subtrees located in different parts of the AST. In those cases, node mismatches were frequent and, as a result, edit scripts were somewhat suboptimal.

Additionally, the runtime performance of the algorithm leaves a lot to be desired. On trees with 1000 leaf nodes each, the algorithm takes a little under 2 seconds to complete. My implementation still has room for improvement, but this should give you a rough idea of what to expect. It appears that the Gumtree algorithm [4] can help address both of these points. I hope to find bandwidth to work on it soon and then compare the two algorithms side-by-side to find out which one performs better on SQL specifically. In the meantime, Change Distiller definitely gets the job done, and I can now proceed with applying it to some of the use cases I mentioned at the beginning of this post.

I’m also curious to learn whether other folks in the industry faced a similar problem, and how they approached it. If you did something similar, I’m interested to hear about your experience.

## References

[1] Eugene W. Myers. An O(ND) Difference Algorithm and Its Variations. Algorithmica 1(2): 251-266 (1986)

[2] B. Fluri, M. Wursch, M. Pinzger, and H. Gall. Change Distilling: Tree differencing for fine-grained source code change extraction. IEEE Trans. Software Eng., 33(11):725–743, 2007.

[3] S.S. Chawathe, A. Rajaraman, H. Garcia-Molina, and J. Widom. Change Detection in Hierarchically Structured Information. Proc. ACM Sigmod Int’l Conf. Management of Data, pp. 493-504, June 1996

[4] Jean-Rémy Falleri, Floréal Morandat, Xavier Blanc, Matias Martinez, Martin Monperrus. Fine-grained and Accurate Source Code Differencing. Proceedings of the International Conference on Automated Software Engineering, 2014, Västeras, Sweden. pp.313-324, 10.1145/2642937.2642982. hal-01054552

View Source

      1"""
      2.. include:: ../posts/sql_diff.md
      3
      4----
      5"""
      6
      7from __future__ import annotations
      8
      9import typing as t
     10from collections import defaultdict
     11from dataclasses import dataclass
     12from heapq import heappop, heappush
     13
     14from sqlglot import Dialect, expressions as exp
     15from sqlglot.helper import ensure_list
     16
     17
     18@dataclass(frozen=True)
     19class Insert:
     20    """Indicates that a new node has been inserted"""
     21
     22    expression: exp.Expression
     23
     24
     25@dataclass(frozen=True)
     26class Remove:
     27    """Indicates that an existing node has been removed"""
     28
     29    expression: exp.Expression
     30
     31
     32@dataclass(frozen=True)
     33class Move:
     34    """Indicates that an existing node's position within the tree has changed"""
     35
     36    expression: exp.Expression
     37
     38
     39@dataclass(frozen=True)
     40class Update:
     41    """Indicates that an existing node has been updated"""
     42
     43    source: exp.Expression
     44    target: exp.Expression
     45
     46
     47@dataclass(frozen=True)
     48class Keep:
     49    """Indicates that an existing node hasn't been changed"""
     50
     51    source: exp.Expression
     52    target: exp.Expression
     53
     54
     55if t.TYPE_CHECKING:
     56    from sqlglot._typing import T
     57
     58    Edit = t.Union[Insert, Remove, Move, Update, Keep]
     59
     60
     61def diff(
     62    source: exp.Expression,
     63    target: exp.Expression,
     64    matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
     65    **kwargs: t.Any,
     66) -> t.List[Edit]:
     67    """
     68    Returns the list of changes between the source and the target expressions.
     69
     70    Examples:
     71        >>> diff(parse_one("a + b"), parse_one("a + c"))
     72        [
     73            Remove(expression=(COLUMN this: (IDENTIFIER this: b, quoted: False))),
     74            Insert(expression=(COLUMN this: (IDENTIFIER this: c, quoted: False))),
     75            Keep(
     76                source=(ADD this: ...),
     77                target=(ADD this: ...)
     78            ),
     79            Keep(
     80                source=(COLUMN this: (IDENTIFIER this: a, quoted: False)),
     81                target=(COLUMN this: (IDENTIFIER this: a, quoted: False))
     82            ),
     83        ]
     84
     85    Args:
     86        source: the source expression.
     87        target: the target expression against which the diff should be calculated.
     88        matchings: the list of pre-matched node pairs which is used to help the algorithm's
     89            heuristics produce better results for subtrees that are known by a caller to be matching.
     90            Note: expression references in this list must refer to the same node objects that are
     91            referenced in source / target trees.
     92
     93    Returns:
     94        the list of Insert, Remove, Move, Update and Keep objects for each node in the source and the
     95        target expression trees. This list represents a sequence of steps needed to transform the source
     96        expression tree into the target one.
     97    """
     98    matchings = matchings or []
     99    matching_ids = {id(n) for pair in matchings for n in pair}
    100
    101    def compute_node_mappings(
    102        original: exp.Expression, copy: exp.Expression
    103    ) -> t.Dict[int, exp.Expression]:
    104        return {
    105            id(old_node): new_node
    106            for old_node, new_node in zip(original.walk(), copy.walk())
    107            if id(old_node) in matching_ids
    108        }
    109
    110    source_copy = source.copy()
    111    target_copy = target.copy()
    112
    113    node_mappings = {
    114        **compute_node_mappings(source, source_copy),
    115        **compute_node_mappings(target, target_copy),
    116    }
    117    matchings_copy = [(node_mappings[id(s)], node_mappings[id(t)]) for s, t in matchings]
    118
    119    return ChangeDistiller(**kwargs).diff(source_copy, target_copy, matchings=matchings_copy)
    120
    121
    122# The expression types for which Update edits are allowed.
    123UPDATABLE_EXPRESSION_TYPES = (
    124    exp.Boolean,
    125    exp.DataType,
    126    exp.Literal,
    127    exp.Table,
    128    exp.Column,
    129    exp.Lambda,
    130)
    131
    132IGNORED_LEAF_EXPRESSION_TYPES = (exp.Identifier,)
    133
    134
    135class ChangeDistiller:
    136    """
    137    The implementation of the Change Distiller algorithm described by Beat Fluri and Martin Pinzger in
    138    their paper https://ieeexplore.ieee.org/document/4339230, which in turn is based on the algorithm by
    139    Chawathe et al. described in http://ilpubs.stanford.edu:8090/115/1/1995-46.pdf.
    140    """
    141
    142    def __init__(self, f: float = 0.6, t: float = 0.6) -> None:
    143        self.f = f
    144        self.t = t
    145        self._sql_generator = Dialect().generator()
    146
    147    def diff(
    148        self,
    149        source: exp.Expression,
    150        target: exp.Expression,
    151        matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
    152    ) -> t.List[Edit]:
    153        matchings = matchings or []
    154        pre_matched_nodes = {id(s): id(t) for s, t in matchings}
    155        if len({n for pair in pre_matched_nodes.items() for n in pair}) != 2 * len(matchings):
    156            raise ValueError("Each node can be referenced at most once in the list of matchings")
    157
    158        self._source = source
    159        self._target = target
    160        self._source_index = {
    161            id(n): n for n in self._source.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
    162        }
    163        self._target_index = {
    164            id(n): n for n in self._target.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
    165        }
    166        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
    167        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
    168        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
    169
    170        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
    171        return self._generate_edit_script(matching_set)
    172
    173    def _generate_edit_script(self, matching_set: t.Set[t.Tuple[int, int]]) -> t.List[Edit]:
    174        edit_script: t.List[Edit] = []
    175        for removed_node_id in self._unmatched_source_nodes:
    176            edit_script.append(Remove(self._source_index[removed_node_id]))
    177        for inserted_node_id in self._unmatched_target_nodes:
    178            edit_script.append(Insert(self._target_index[inserted_node_id]))
    179        for kept_source_node_id, kept_target_node_id in matching_set:
    180            source_node = self._source_index[kept_source_node_id]
    181            target_node = self._target_index[kept_target_node_id]
    182            if (
    183                not isinstance(source_node, UPDATABLE_EXPRESSION_TYPES)
    184                or source_node == target_node
    185            ):
    186                edit_script.extend(
    187                    self._generate_move_edits(source_node, target_node, matching_set)
    188                )
    189                edit_script.append(Keep(source_node, target_node))
    190            else:
    191                edit_script.append(Update(source_node, target_node))
    192
    193        return edit_script
    194
    195    def _generate_move_edits(
    196        self, source: exp.Expression, target: exp.Expression, matching_set: t.Set[t.Tuple[int, int]]
    197    ) -> t.List[Move]:
    198        source_args = [id(e) for e in _expression_only_args(source)]
    199        target_args = [id(e) for e in _expression_only_args(target)]
    200
    201        args_lcs = set(_lcs(source_args, target_args, lambda l, r: (l, r) in matching_set))
    202
    203        move_edits = []
    204        for a in source_args:
    205            if a not in args_lcs and a not in self._unmatched_source_nodes:
    206                move_edits.append(Move(self._source_index[a]))
    207
    208        return move_edits
    209
    210    def _compute_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    211        leaves_matching_set = self._compute_leaf_matching_set()
    212        matching_set = leaves_matching_set.copy()
    213
    214        ordered_unmatched_source_nodes = {
    215            id(n): None for n in self._source.bfs() if id(n) in self._unmatched_source_nodes
    216        }
    217        ordered_unmatched_target_nodes = {
    218            id(n): None for n in self._target.bfs() if id(n) in self._unmatched_target_nodes
    219        }
    220
    221        for source_node_id in ordered_unmatched_source_nodes:
    222            for target_node_id in ordered_unmatched_target_nodes:
    223                source_node = self._source_index[source_node_id]
    224                target_node = self._target_index[target_node_id]
    225                if _is_same_type(source_node, target_node):
    226                    source_leaf_ids = {id(l) for l in _get_leaves(source_node)}
    227                    target_leaf_ids = {id(l) for l in _get_leaves(target_node)}
    228
    229                    max_leaves_num = max(len(source_leaf_ids), len(target_leaf_ids))
    230                    if max_leaves_num:
    231                        common_leaves_num = sum(
    232                            1 if s in source_leaf_ids and t in target_leaf_ids else 0
    233                            for s, t in leaves_matching_set
    234                        )
    235                        leaf_similarity_score = common_leaves_num / max_leaves_num
    236                    else:
    237                        leaf_similarity_score = 0.0
    238
    239                    adjusted_t = (
    240                        self.t if min(len(source_leaf_ids), len(target_leaf_ids)) > 4 else 0.4
    241                    )
    242
    243                    if leaf_similarity_score >= 0.8 or (
    244                        leaf_similarity_score >= adjusted_t
    245                        and self._dice_coefficient(source_node, target_node) >= self.f
    246                    ):
    247                        matching_set.add((source_node_id, target_node_id))
    248                        self._unmatched_source_nodes.remove(source_node_id)
    249                        self._unmatched_target_nodes.remove(target_node_id)
    250                        ordered_unmatched_target_nodes.pop(target_node_id, None)
    251                        break
    252
    253        return matching_set
    254
    255    def _compute_leaf_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    256        candidate_matchings: t.List[t.Tuple[float, int, int, exp.Expression, exp.Expression]] = []
    257        source_leaves = list(_get_leaves(self._source))
    258        target_leaves = list(_get_leaves(self._target))
    259        for source_leaf in source_leaves:
    260            for target_leaf in target_leaves:
    261                if _is_same_type(source_leaf, target_leaf):
    262                    similarity_score = self._dice_coefficient(source_leaf, target_leaf)
    263                    if similarity_score >= self.f:
    264                        heappush(
    265                            candidate_matchings,
    266                            (
    267                                -similarity_score,
    268                                -_parent_similarity_score(source_leaf, target_leaf),
    269                                len(candidate_matchings),
    270                                source_leaf,
    271                                target_leaf,
    272                            ),
    273                        )
    274
    275        # Pick best matchings based on the highest score
    276        matching_set = set()
    277        while candidate_matchings:
    278            _, _, _, source_leaf, target_leaf = heappop(candidate_matchings)
    279            if (
    280                id(source_leaf) in self._unmatched_source_nodes
    281                and id(target_leaf) in self._unmatched_target_nodes
    282            ):
    283                matching_set.add((id(source_leaf), id(target_leaf)))
    284                self._unmatched_source_nodes.remove(id(source_leaf))
    285                self._unmatched_target_nodes.remove(id(target_leaf))
    286
    287        return matching_set
    288
    289    def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float:
    290        source_histo = self._bigram_histo(source)
    291        target_histo = self._bigram_histo(target)
    292
    293        total_grams = sum(source_histo.values()) + sum(target_histo.values())
    294        if not total_grams:
    295            return 1.0 if source == target else 0.0
    296
    297        overlap_len = 0
    298        overlapping_grams = set(source_histo) & set(target_histo)
    299        for g in overlapping_grams:
    300            overlap_len += min(source_histo[g], target_histo[g])
    301
    302        return 2 * overlap_len / total_grams
    303
    304    def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]:
    305        if id(expression) in self._bigram_histo_cache:
    306            return self._bigram_histo_cache[id(expression)]
    307
    308        expression_str = self._sql_generator.generate(expression)
    309        count = max(0, len(expression_str) - 1)
    310        bigram_histo: t.DefaultDict[str, int] = defaultdict(int)
    311        for i in range(count):
    312            bigram_histo[expression_str[i : i + 2]] += 1
    313
    314        self._bigram_histo_cache[id(expression)] = bigram_histo
    315        return bigram_histo
    316
    317
    318def _get_leaves(expression: exp.Expression) -> t.Iterator[exp.Expression]:
    319    has_child_exprs = False
    320
    321    for node in expression.iter_expressions():
    322        if not isinstance(node, IGNORED_LEAF_EXPRESSION_TYPES):
    323            has_child_exprs = True
    324            yield from _get_leaves(node)
    325
    326    if not has_child_exprs:
    327        yield expression
    328
    329
    330def _is_same_type(source: exp.Expression, target: exp.Expression) -> bool:
    331    if type(source) is type(target):
    332        if isinstance(source, exp.Join):
    333            return source.args.get("side") == target.args.get("side")
    334
    335        if isinstance(source, exp.Anonymous):
    336            return source.this == target.this
    337
    338        return True
    339
    340    return False
    341
    342
    343def _parent_similarity_score(
    344    source: t.Optional[exp.Expression], target: t.Optional[exp.Expression]
    345) -> int:
    346    if source is None or target is None or type(source) is not type(target):
    347        return 0
    348
    349    return 1 + _parent_similarity_score(source.parent, target.parent)
    350
    351
    352def _expression_only_args(expression: exp.Expression) -> t.List[exp.Expression]:
    353    args: t.List[t.Union[exp.Expression, t.List]] = []
    354    if expression:
    355        for a in expression.args.values():
    356            args.extend(ensure_list(a))
    357    return [
    358        a
    359        for a in args
    360        if isinstance(a, exp.Expression) and not isinstance(a, IGNORED_LEAF_EXPRESSION_TYPES)
    361    ]
    362
    363
    364def _lcs(
    365    seq_a: t.Sequence[T], seq_b: t.Sequence[T], equal: t.Callable[[T, T], bool]
    366) -> t.Sequence[t.Optional[T]]:
    367    """Calculates the longest common subsequence"""
    368
    369    len_a = len(seq_a)
    370    len_b = len(seq_b)
    371    lcs_result = [[None] * (len_b + 1) for i in range(len_a + 1)]
    372
    373    for i in range(len_a + 1):
    374        for j in range(len_b + 1):
    375            if i == 0 or j == 0:
    376                lcs_result[i][j] = []  # type: ignore
    377            elif equal(seq_a[i - 1], seq_b[j - 1]):
    378                lcs_result[i][j] = lcs_result[i - 1][j - 1] + [seq_a[i - 1]]  # type: ignore
    379            else:
    380                lcs_result[i][j] = (
    381                    lcs_result[i - 1][j]
    382                    if len(lcs_result[i - 1][j]) > len(lcs_result[i][j - 1])  # type: ignore
    383                    else lcs_result[i][j - 1]
    384                )
    385
    386    return lcs_result[len_a][len_b]  # type: ignore

@dataclass(frozen=True)
class Insert: View Source

    19@dataclass(frozen=True)
    20class Insert:
    21    """Indicates that a new node has been inserted"""
    22
    23    expression: exp.Expression

Indicates that a new node has been inserted

Insert(expression: sqlglot.expressions.Expression)
expression: sqlglot.expressions.Expression
@dataclass(frozen=True)
class Remove: View Source

    26@dataclass(frozen=True)
    27class Remove:
    28    """Indicates that an existing node has been removed"""
    29
    30    expression: exp.Expression

Indicates that an existing node has been removed

Remove(expression: sqlglot.expressions.Expression)
expression: sqlglot.expressions.Expression
@dataclass(frozen=True)
class Move: View Source

    33@dataclass(frozen=True)
    34class Move:
    35    """Indicates that an existing node's position within the tree has changed"""
    36
    37    expression: exp.Expression

Indicates that an existing node's position within the tree has changed

Move(expression: sqlglot.expressions.Expression)
expression: sqlglot.expressions.Expression
@dataclass(frozen=True)
class Update: View Source

    40@dataclass(frozen=True)
    41class Update:
    42    """Indicates that an existing node has been updated"""
    43
    44    source: exp.Expression
    45    target: exp.Expression

Indicates that an existing node has been updated

Update( source: sqlglot.expressions.Expression, target: sqlglot.expressions.Expression)
source: sqlglot.expressions.Expression
target: sqlglot.expressions.Expression
@dataclass(frozen=True)
class Keep: View Source

    48@dataclass(frozen=True)
    49class Keep:
    50    """Indicates that an existing node hasn't been changed"""
    51
    52    source: exp.Expression
    53    target: exp.Expression

Indicates that an existing node hasn't been changed

Keep( source: sqlglot.expressions.Expression, target: sqlglot.expressions.Expression)
source: sqlglot.expressions.Expression
target: sqlglot.expressions.Expression
def diff( source: sqlglot.expressions.Expression, target: sqlglot.expressions.Expression, matchings: Optional[List[Tuple[ sqlglot.expressions.Expression , sqlglot.expressions.Expression ]]] = None, **kwargs: Any) -> List[Union[ Insert , Remove , Move , Update , Keep ]]: View Source

     62def diff(
     63    source: exp.Expression,
     64    target: exp.Expression,
     65    matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
     66    **kwargs: t.Any,
     67) -> t.List[Edit]:
     68    """
     69    Returns the list of changes between the source and the target expressions.
     70
     71    Examples:
     72        >>> diff(parse_one("a + b"), parse_one("a + c"))
     73        [
     74            Remove(expression=(COLUMN this: (IDENTIFIER this: b, quoted: False))),
     75            Insert(expression=(COLUMN this: (IDENTIFIER this: c, quoted: False))),
     76            Keep(
     77                source=(ADD this: ...),
     78                target=(ADD this: ...)
     79            ),
     80            Keep(
     81                source=(COLUMN this: (IDENTIFIER this: a, quoted: False)),
     82                target=(COLUMN this: (IDENTIFIER this: a, quoted: False))
     83            ),
     84        ]
     85
     86    Args:
     87        source: the source expression.
     88        target: the target expression against which the diff should be calculated.
     89        matchings: the list of pre-matched node pairs which is used to help the algorithm's
     90            heuristics produce better results for subtrees that are known by a caller to be matching.
     91            Note: expression references in this list must refer to the same node objects that are
     92            referenced in source / target trees.
     93
     94    Returns:
     95        the list of Insert, Remove, Move, Update and Keep objects for each node in the source and the
     96        target expression trees. This list represents a sequence of steps needed to transform the source
     97        expression tree into the target one.
     98    """
     99    matchings = matchings or []
    100    matching_ids = {id(n) for pair in matchings for n in pair}
    101
    102    def compute_node_mappings(
    103        original: exp.Expression, copy: exp.Expression
    104    ) -> t.Dict[int, exp.Expression]:
    105        return {
    106            id(old_node): new_node
    107            for old_node, new_node in zip(original.walk(), copy.walk())
    108            if id(old_node) in matching_ids
    109        }
    110
    111    source_copy = source.copy()
    112    target_copy = target.copy()
    113
    114    node_mappings = {
    115        **compute_node_mappings(source, source_copy),
    116        **compute_node_mappings(target, target_copy),
    117    }
    118    matchings_copy = [(node_mappings[id(s)], node_mappings[id(t)]) for s, t in matchings]
    119
    120    return ChangeDistiller(**kwargs).diff(source_copy, target_copy, matchings=matchings_copy)

Returns the list of changes between the source and the target expressions.

###### Examples:

>     >>> diff(parse_one("a + b"), parse_one("a + c"))
>     [
>         Remove(expression=(COLUMN this: (IDENTIFIER this: b, quoted: False))),
>         Insert(expression=(COLUMN this: (IDENTIFIER this: c, quoted: False))),
>         Keep(
>             source=(ADD this: ...),
>             target=(ADD this: ...)
>         ),
>         Keep(
>             source=(COLUMN this: (IDENTIFIER this: a, quoted: False)),
>             target=(COLUMN this: (IDENTIFIER this: a, quoted: False))
>         ),
>     ]

###### Arguments:

- source: the source expression.
- target: the target expression against which the diff should be calculated.
- matchings: the list of pre-matched node pairs which is used to help the algorithm's heuristics produce better results for subtrees that are known by a caller to be matching. Note: expression references in this list must refer to the same node objects that are referenced in source / target trees.

###### Returns:

> the list of Insert, Remove, Move, Update and Keep objects for each node in the source and the target expression trees. This list represents a sequence of steps needed to transform the source expression tree into the target one.

UPDATABLE_EXPRESSION_TYPES = (<class 'sqlglot.expressions.Boolean'>, <class 'sqlglot.expressions.DataType'>, <class 'sqlglot.expressions.Literal'>, <class 'sqlglot.expressions.Table'>, <class 'sqlglot.expressions.Column'>, <class 'sqlglot.expressions.Lambda'>)
IGNORED_LEAF_EXPRESSION_TYPES = (<class 'sqlglot.expressions.Identifier'>,)
class ChangeDistiller: View Source

    136class ChangeDistiller:
    137    """
    138    The implementation of the Change Distiller algorithm described by Beat Fluri and Martin Pinzger in
    139    their paper https://ieeexplore.ieee.org/document/4339230, which in turn is based on the algorithm by
    140    Chawathe et al. described in http://ilpubs.stanford.edu:8090/115/1/1995-46.pdf.
    141    """
    142
    143    def __init__(self, f: float = 0.6, t: float = 0.6) -> None:
    144        self.f = f
    145        self.t = t
    146        self._sql_generator = Dialect().generator()
    147
    148    def diff(
    149        self,
    150        source: exp.Expression,
    151        target: exp.Expression,
    152        matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
    153    ) -> t.List[Edit]:
    154        matchings = matchings or []
    155        pre_matched_nodes = {id(s): id(t) for s, t in matchings}
    156        if len({n for pair in pre_matched_nodes.items() for n in pair}) != 2 * len(matchings):
    157            raise ValueError("Each node can be referenced at most once in the list of matchings")
    158
    159        self._source = source
    160        self._target = target
    161        self._source_index = {
    162            id(n): n for n in self._source.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
    163        }
    164        self._target_index = {
    165            id(n): n for n in self._target.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
    166        }
    167        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
    168        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
    169        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
    170
    171        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
    172        return self._generate_edit_script(matching_set)
    173
    174    def _generate_edit_script(self, matching_set: t.Set[t.Tuple[int, int]]) -> t.List[Edit]:
    175        edit_script: t.List[Edit] = []
    176        for removed_node_id in self._unmatched_source_nodes:
    177            edit_script.append(Remove(self._source_index[removed_node_id]))
    178        for inserted_node_id in self._unmatched_target_nodes:
    179            edit_script.append(Insert(self._target_index[inserted_node_id]))
    180        for kept_source_node_id, kept_target_node_id in matching_set:
    181            source_node = self._source_index[kept_source_node_id]
    182            target_node = self._target_index[kept_target_node_id]
    183            if (
    184                not isinstance(source_node, UPDATABLE_EXPRESSION_TYPES)
    185                or source_node == target_node
    186            ):
    187                edit_script.extend(
    188                    self._generate_move_edits(source_node, target_node, matching_set)
    189                )
    190                edit_script.append(Keep(source_node, target_node))
    191            else:
    192                edit_script.append(Update(source_node, target_node))
    193
    194        return edit_script
    195
    196    def _generate_move_edits(
    197        self, source: exp.Expression, target: exp.Expression, matching_set: t.Set[t.Tuple[int, int]]
    198    ) -> t.List[Move]:
    199        source_args = [id(e) for e in _expression_only_args(source)]
    200        target_args = [id(e) for e in _expression_only_args(target)]
    201
    202        args_lcs = set(_lcs(source_args, target_args, lambda l, r: (l, r) in matching_set))
    203
    204        move_edits = []
    205        for a in source_args:
    206            if a not in args_lcs and a not in self._unmatched_source_nodes:
    207                move_edits.append(Move(self._source_index[a]))
    208
    209        return move_edits
    210
    211    def _compute_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    212        leaves_matching_set = self._compute_leaf_matching_set()
    213        matching_set = leaves_matching_set.copy()
    214
    215        ordered_unmatched_source_nodes = {
    216            id(n): None for n in self._source.bfs() if id(n) in self._unmatched_source_nodes
    217        }
    218        ordered_unmatched_target_nodes = {
    219            id(n): None for n in self._target.bfs() if id(n) in self._unmatched_target_nodes
    220        }
    221
    222        for source_node_id in ordered_unmatched_source_nodes:
    223            for target_node_id in ordered_unmatched_target_nodes:
    224                source_node = self._source_index[source_node_id]
    225                target_node = self._target_index[target_node_id]
    226                if _is_same_type(source_node, target_node):
    227                    source_leaf_ids = {id(l) for l in _get_leaves(source_node)}
    228                    target_leaf_ids = {id(l) for l in _get_leaves(target_node)}
    229
    230                    max_leaves_num = max(len(source_leaf_ids), len(target_leaf_ids))
    231                    if max_leaves_num:
    232                        common_leaves_num = sum(
    233                            1 if s in source_leaf_ids and t in target_leaf_ids else 0
    234                            for s, t in leaves_matching_set
    235                        )
    236                        leaf_similarity_score = common_leaves_num / max_leaves_num
    237                    else:
    238                        leaf_similarity_score = 0.0
    239
    240                    adjusted_t = (
    241                        self.t if min(len(source_leaf_ids), len(target_leaf_ids)) > 4 else 0.4
    242                    )
    243
    244                    if leaf_similarity_score >= 0.8 or (
    245                        leaf_similarity_score >= adjusted_t
    246                        and self._dice_coefficient(source_node, target_node) >= self.f
    247                    ):
    248                        matching_set.add((source_node_id, target_node_id))
    249                        self._unmatched_source_nodes.remove(source_node_id)
    250                        self._unmatched_target_nodes.remove(target_node_id)
    251                        ordered_unmatched_target_nodes.pop(target_node_id, None)
    252                        break
    253
    254        return matching_set
    255
    256    def _compute_leaf_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    257        candidate_matchings: t.List[t.Tuple[float, int, int, exp.Expression, exp.Expression]] = []
    258        source_leaves = list(_get_leaves(self._source))
    259        target_leaves = list(_get_leaves(self._target))
    260        for source_leaf in source_leaves:
    261            for target_leaf in target_leaves:
    262                if _is_same_type(source_leaf, target_leaf):
    263                    similarity_score = self._dice_coefficient(source_leaf, target_leaf)
    264                    if similarity_score >= self.f:
    265                        heappush(
    266                            candidate_matchings,
    267                            (
    268                                -similarity_score,
    269                                -_parent_similarity_score(source_leaf, target_leaf),
    270                                len(candidate_matchings),
    271                                source_leaf,
    272                                target_leaf,
    273                            ),
    274                        )
    275
    276        # Pick best matchings based on the highest score
    277        matching_set = set()
    278        while candidate_matchings:
    279            _, _, _, source_leaf, target_leaf = heappop(candidate_matchings)
    280            if (
    281                id(source_leaf) in self._unmatched_source_nodes
    282                and id(target_leaf) in self._unmatched_target_nodes
    283            ):
    284                matching_set.add((id(source_leaf), id(target_leaf)))
    285                self._unmatched_source_nodes.remove(id(source_leaf))
    286                self._unmatched_target_nodes.remove(id(target_leaf))
    287
    288        return matching_set
    289
    290    def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float:
    291        source_histo = self._bigram_histo(source)
    292        target_histo = self._bigram_histo(target)
    293
    294        total_grams = sum(source_histo.values()) + sum(target_histo.values())
    295        if not total_grams:
    296            return 1.0 if source == target else 0.0
    297
    298        overlap_len = 0
    299        overlapping_grams = set(source_histo) & set(target_histo)
    300        for g in overlapping_grams:
    301            overlap_len += min(source_histo[g], target_histo[g])
    302
    303        return 2 * overlap_len / total_grams
    304
    305    def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]:
    306        if id(expression) in self._bigram_histo_cache:
    307            return self._bigram_histo_cache[id(expression)]
    308
    309        expression_str = self._sql_generator.generate(expression)
    310        count = max(0, len(expression_str) - 1)
    311        bigram_histo: t.DefaultDict[str, int] = defaultdict(int)
    312        for i in range(count):
    313            bigram_histo[expression_str[i : i + 2]] += 1
    314
    315        self._bigram_histo_cache[id(expression)] = bigram_histo
    316        return bigram_histo

The implementation of the Change Distiller algorithm described by Beat Fluri and Martin Pinzger in their paper https://ieeexplore.ieee.org/document/4339230, which in turn is based on the algorithm by Chawathe et al. described in http://ilpubs.stanford.edu:8090/115/1/1995-46.pdf.

ChangeDistiller(f: float = 0.6, t: float = 0.6) View Source

    143    def __init__(self, f: float = 0.6, t: float = 0.6) -> None:
    144        self.f = f
    145        self.t = t
    146        self._sql_generator = Dialect().generator()

f
t
def diff( self, source: sqlglot.expressions.Expression, target: sqlglot.expressions.Expression, matchings: Optional[List[Tuple[ sqlglot.expressions.Expression , sqlglot.expressions.Expression ]]] = None) -> List[Union[ Insert , Remove , Move , Update , Keep ]]: View Source

    148    def diff(
    149        self,
    150        source: exp.Expression,
    151        target: exp.Expression,
    152        matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
    153    ) -> t.List[Edit]:
    154        matchings = matchings or []
    155        pre_matched_nodes = {id(s): id(t) for s, t in matchings}
    156        if len({n for pair in pre_matched_nodes.items() for n in pair}) != 2 * len(matchings):
    157            raise ValueError("Each node can be referenced at most once in the list of matchings")
    158
    159        self._source = source
    160        self._target = target
    161        self._source_index = {
    162            id(n): n for n in self._source.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
    163        }
    164        self._target_index = {
    165            id(n): n for n in self._target.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
    166        }
    167        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
    168        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
    169        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
    170
    171        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
    172        return self._generate_edit_script(matching_set)