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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:

Git diff output

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 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. 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:

Dice Coefficient

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:

Matching criteria for leaf nodes

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. 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:

Matching criteria for inner nodes

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


  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
162            for n, *_ in self._source.bfs()
163            if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
164        }
165        self._target_index = {
166            id(n): n
167            for n, *_ in self._target.bfs()
168            if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
169        }
170        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
171        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
172        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
173
174        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
175        return self._generate_edit_script(matching_set)
176
177    def _generate_edit_script(self, matching_set: t.Set[t.Tuple[int, int]]) -> t.List[Edit]:
178        edit_script: t.List[Edit] = []
179        for removed_node_id in self._unmatched_source_nodes:
180            edit_script.append(Remove(self._source_index[removed_node_id]))
181        for inserted_node_id in self._unmatched_target_nodes:
182            edit_script.append(Insert(self._target_index[inserted_node_id]))
183        for kept_source_node_id, kept_target_node_id in matching_set:
184            source_node = self._source_index[kept_source_node_id]
185            target_node = self._target_index[kept_target_node_id]
186            if (
187                not isinstance(source_node, UPDATABLE_EXPRESSION_TYPES)
188                or source_node == target_node
189            ):
190                edit_script.extend(
191                    self._generate_move_edits(source_node, target_node, matching_set)
192                )
193                edit_script.append(Keep(source_node, target_node))
194            else:
195                edit_script.append(Update(source_node, target_node))
196
197        return edit_script
198
199    def _generate_move_edits(
200        self, source: exp.Expression, target: exp.Expression, matching_set: t.Set[t.Tuple[int, int]]
201    ) -> t.List[Move]:
202        source_args = [id(e) for e in _expression_only_args(source)]
203        target_args = [id(e) for e in _expression_only_args(target)]
204
205        args_lcs = set(_lcs(source_args, target_args, lambda l, r: (l, r) in matching_set))
206
207        move_edits = []
208        for a in source_args:
209            if a not in args_lcs and a not in self._unmatched_source_nodes:
210                move_edits.append(Move(self._source_index[a]))
211
212        return move_edits
213
214    def _compute_matching_set(self) -> t.Set[t.Tuple[int, int]]:
215        leaves_matching_set = self._compute_leaf_matching_set()
216        matching_set = leaves_matching_set.copy()
217
218        ordered_unmatched_source_nodes = {
219            id(n): None for n, *_ in self._source.bfs() if id(n) in self._unmatched_source_nodes
220        }
221        ordered_unmatched_target_nodes = {
222            id(n): None for n, *_ in self._target.bfs() if id(n) in self._unmatched_target_nodes
223        }
224
225        for source_node_id in ordered_unmatched_source_nodes:
226            for target_node_id in ordered_unmatched_target_nodes:
227                source_node = self._source_index[source_node_id]
228                target_node = self._target_index[target_node_id]
229                if _is_same_type(source_node, target_node):
230                    source_leaf_ids = {id(l) for l in _get_leaves(source_node)}
231                    target_leaf_ids = {id(l) for l in _get_leaves(target_node)}
232
233                    max_leaves_num = max(len(source_leaf_ids), len(target_leaf_ids))
234                    if max_leaves_num:
235                        common_leaves_num = sum(
236                            1 if s in source_leaf_ids and t in target_leaf_ids else 0
237                            for s, t in leaves_matching_set
238                        )
239                        leaf_similarity_score = common_leaves_num / max_leaves_num
240                    else:
241                        leaf_similarity_score = 0.0
242
243                    adjusted_t = (
244                        self.t if min(len(source_leaf_ids), len(target_leaf_ids)) > 4 else 0.4
245                    )
246
247                    if leaf_similarity_score >= 0.8 or (
248                        leaf_similarity_score >= adjusted_t
249                        and self._dice_coefficient(source_node, target_node) >= self.f
250                    ):
251                        matching_set.add((source_node_id, target_node_id))
252                        self._unmatched_source_nodes.remove(source_node_id)
253                        self._unmatched_target_nodes.remove(target_node_id)
254                        ordered_unmatched_target_nodes.pop(target_node_id, None)
255                        break
256
257        return matching_set
258
259    def _compute_leaf_matching_set(self) -> t.Set[t.Tuple[int, int]]:
260        candidate_matchings: t.List[t.Tuple[float, int, int, exp.Expression, exp.Expression]] = []
261        source_leaves = list(_get_leaves(self._source))
262        target_leaves = list(_get_leaves(self._target))
263        for source_leaf in source_leaves:
264            for target_leaf in target_leaves:
265                if _is_same_type(source_leaf, target_leaf):
266                    similarity_score = self._dice_coefficient(source_leaf, target_leaf)
267                    if similarity_score >= self.f:
268                        heappush(
269                            candidate_matchings,
270                            (
271                                -similarity_score,
272                                -_parent_similarity_score(source_leaf, target_leaf),
273                                len(candidate_matchings),
274                                source_leaf,
275                                target_leaf,
276                            ),
277                        )
278
279        # Pick best matchings based on the highest score
280        matching_set = set()
281        while candidate_matchings:
282            _, _, _, source_leaf, target_leaf = heappop(candidate_matchings)
283            if (
284                id(source_leaf) in self._unmatched_source_nodes
285                and id(target_leaf) in self._unmatched_target_nodes
286            ):
287                matching_set.add((id(source_leaf), id(target_leaf)))
288                self._unmatched_source_nodes.remove(id(source_leaf))
289                self._unmatched_target_nodes.remove(id(target_leaf))
290
291        return matching_set
292
293    def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float:
294        source_histo = self._bigram_histo(source)
295        target_histo = self._bigram_histo(target)
296
297        total_grams = sum(source_histo.values()) + sum(target_histo.values())
298        if not total_grams:
299            return 1.0 if source == target else 0.0
300
301        overlap_len = 0
302        overlapping_grams = set(source_histo) & set(target_histo)
303        for g in overlapping_grams:
304            overlap_len += min(source_histo[g], target_histo[g])
305
306        return 2 * overlap_len / total_grams
307
308    def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]:
309        if id(expression) in self._bigram_histo_cache:
310            return self._bigram_histo_cache[id(expression)]
311
312        expression_str = self._sql_generator.generate(expression)
313        count = max(0, len(expression_str) - 1)
314        bigram_histo: t.DefaultDict[str, int] = defaultdict(int)
315        for i in range(count):
316            bigram_histo[expression_str[i : i + 2]] += 1
317
318        self._bigram_histo_cache[id(expression)] = bigram_histo
319        return bigram_histo
320
321
322def _get_leaves(expression: exp.Expression) -> t.Iterator[exp.Expression]:
323    has_child_exprs = False
324
325    for _, node in expression.iter_expressions():
326        if not isinstance(node, IGNORED_LEAF_EXPRESSION_TYPES):
327            has_child_exprs = True
328            yield from _get_leaves(node)
329
330    if not has_child_exprs:
331        yield expression
332
333
334def _is_same_type(source: exp.Expression, target: exp.Expression) -> bool:
335    if type(source) is type(target):
336        if isinstance(source, exp.Join):
337            return source.args.get("side") == target.args.get("side")
338
339        if isinstance(source, exp.Anonymous):
340            return source.this == target.this
341
342        return True
343
344    return False
345
346
347def _parent_similarity_score(
348    source: t.Optional[exp.Expression], target: t.Optional[exp.Expression]
349) -> int:
350    if source is None or target is None or type(source) is not type(target):
351        return 0
352
353    return 1 + _parent_similarity_score(source.parent, target.parent)
354
355
356def _expression_only_args(expression: exp.Expression) -> t.List[exp.Expression]:
357    args: t.List[t.Union[exp.Expression, t.List]] = []
358    if expression:
359        for a in expression.args.values():
360            args.extend(ensure_list(a))
361    return [
362        a
363        for a in args
364        if isinstance(a, exp.Expression) and not isinstance(a, IGNORED_LEAF_EXPRESSION_TYPES)
365    ]
366
367
368def _lcs(
369    seq_a: t.Sequence[T], seq_b: t.Sequence[T], equal: t.Callable[[T, T], bool]
370) -> t.Sequence[t.Optional[T]]:
371    """Calculates the longest common subsequence"""
372
373    len_a = len(seq_a)
374    len_b = len(seq_b)
375    lcs_result = [[None] * (len_b + 1) for i in range(len_a + 1)]
376
377    for i in range(len_a + 1):
378        for j in range(len_b + 1):
379            if i == 0 or j == 0:
380                lcs_result[i][j] = []  # type: ignore
381            elif equal(seq_a[i - 1], seq_b[j - 1]):
382                lcs_result[i][j] = lcs_result[i - 1][j - 1] + [seq_a[i - 1]]  # type: ignore
383            else:
384                lcs_result[i][j] = (
385                    lcs_result[i - 1][j]
386                    if len(lcs_result[i - 1][j]) > len(lcs_result[i][j - 1])  # type: ignore
387                    else lcs_result[i][j - 1]
388                )
389
390    return lcs_result[len_a][len_b]  # type: ignore
@dataclass(frozen=True)
class Insert:
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)
@dataclass(frozen=True)
class Remove:
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)
@dataclass(frozen=True)
class Move:
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)
@dataclass(frozen=True)
class Update:
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

@dataclass(frozen=True)
class Keep:
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

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]]:
 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.

IGNORED_LEAF_EXPRESSION_TYPES = (<class 'sqlglot.expressions.Identifier'>,)
class ChangeDistiller:
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
163            for n, *_ in self._source.bfs()
164            if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
165        }
166        self._target_index = {
167            id(n): n
168            for n, *_ in self._target.bfs()
169            if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
170        }
171        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
172        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
173        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
174
175        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
176        return self._generate_edit_script(matching_set)
177
178    def _generate_edit_script(self, matching_set: t.Set[t.Tuple[int, int]]) -> t.List[Edit]:
179        edit_script: t.List[Edit] = []
180        for removed_node_id in self._unmatched_source_nodes:
181            edit_script.append(Remove(self._source_index[removed_node_id]))
182        for inserted_node_id in self._unmatched_target_nodes:
183            edit_script.append(Insert(self._target_index[inserted_node_id]))
184        for kept_source_node_id, kept_target_node_id in matching_set:
185            source_node = self._source_index[kept_source_node_id]
186            target_node = self._target_index[kept_target_node_id]
187            if (
188                not isinstance(source_node, UPDATABLE_EXPRESSION_TYPES)
189                or source_node == target_node
190            ):
191                edit_script.extend(
192                    self._generate_move_edits(source_node, target_node, matching_set)
193                )
194                edit_script.append(Keep(source_node, target_node))
195            else:
196                edit_script.append(Update(source_node, target_node))
197
198        return edit_script
199
200    def _generate_move_edits(
201        self, source: exp.Expression, target: exp.Expression, matching_set: t.Set[t.Tuple[int, int]]
202    ) -> t.List[Move]:
203        source_args = [id(e) for e in _expression_only_args(source)]
204        target_args = [id(e) for e in _expression_only_args(target)]
205
206        args_lcs = set(_lcs(source_args, target_args, lambda l, r: (l, r) in matching_set))
207
208        move_edits = []
209        for a in source_args:
210            if a not in args_lcs and a not in self._unmatched_source_nodes:
211                move_edits.append(Move(self._source_index[a]))
212
213        return move_edits
214
215    def _compute_matching_set(self) -> t.Set[t.Tuple[int, int]]:
216        leaves_matching_set = self._compute_leaf_matching_set()
217        matching_set = leaves_matching_set.copy()
218
219        ordered_unmatched_source_nodes = {
220            id(n): None for n, *_ in self._source.bfs() if id(n) in self._unmatched_source_nodes
221        }
222        ordered_unmatched_target_nodes = {
223            id(n): None for n, *_ in self._target.bfs() if id(n) in self._unmatched_target_nodes
224        }
225
226        for source_node_id in ordered_unmatched_source_nodes:
227            for target_node_id in ordered_unmatched_target_nodes:
228                source_node = self._source_index[source_node_id]
229                target_node = self._target_index[target_node_id]
230                if _is_same_type(source_node, target_node):
231                    source_leaf_ids = {id(l) for l in _get_leaves(source_node)}
232                    target_leaf_ids = {id(l) for l in _get_leaves(target_node)}
233
234                    max_leaves_num = max(len(source_leaf_ids), len(target_leaf_ids))
235                    if max_leaves_num:
236                        common_leaves_num = sum(
237                            1 if s in source_leaf_ids and t in target_leaf_ids else 0
238                            for s, t in leaves_matching_set
239                        )
240                        leaf_similarity_score = common_leaves_num / max_leaves_num
241                    else:
242                        leaf_similarity_score = 0.0
243
244                    adjusted_t = (
245                        self.t if min(len(source_leaf_ids), len(target_leaf_ids)) > 4 else 0.4
246                    )
247
248                    if leaf_similarity_score >= 0.8 or (
249                        leaf_similarity_score >= adjusted_t
250                        and self._dice_coefficient(source_node, target_node) >= self.f
251                    ):
252                        matching_set.add((source_node_id, target_node_id))
253                        self._unmatched_source_nodes.remove(source_node_id)
254                        self._unmatched_target_nodes.remove(target_node_id)
255                        ordered_unmatched_target_nodes.pop(target_node_id, None)
256                        break
257
258        return matching_set
259
260    def _compute_leaf_matching_set(self) -> t.Set[t.Tuple[int, int]]:
261        candidate_matchings: t.List[t.Tuple[float, int, int, exp.Expression, exp.Expression]] = []
262        source_leaves = list(_get_leaves(self._source))
263        target_leaves = list(_get_leaves(self._target))
264        for source_leaf in source_leaves:
265            for target_leaf in target_leaves:
266                if _is_same_type(source_leaf, target_leaf):
267                    similarity_score = self._dice_coefficient(source_leaf, target_leaf)
268                    if similarity_score >= self.f:
269                        heappush(
270                            candidate_matchings,
271                            (
272                                -similarity_score,
273                                -_parent_similarity_score(source_leaf, target_leaf),
274                                len(candidate_matchings),
275                                source_leaf,
276                                target_leaf,
277                            ),
278                        )
279
280        # Pick best matchings based on the highest score
281        matching_set = set()
282        while candidate_matchings:
283            _, _, _, source_leaf, target_leaf = heappop(candidate_matchings)
284            if (
285                id(source_leaf) in self._unmatched_source_nodes
286                and id(target_leaf) in self._unmatched_target_nodes
287            ):
288                matching_set.add((id(source_leaf), id(target_leaf)))
289                self._unmatched_source_nodes.remove(id(source_leaf))
290                self._unmatched_target_nodes.remove(id(target_leaf))
291
292        return matching_set
293
294    def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float:
295        source_histo = self._bigram_histo(source)
296        target_histo = self._bigram_histo(target)
297
298        total_grams = sum(source_histo.values()) + sum(target_histo.values())
299        if not total_grams:
300            return 1.0 if source == target else 0.0
301
302        overlap_len = 0
303        overlapping_grams = set(source_histo) & set(target_histo)
304        for g in overlapping_grams:
305            overlap_len += min(source_histo[g], target_histo[g])
306
307        return 2 * overlap_len / total_grams
308
309    def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]:
310        if id(expression) in self._bigram_histo_cache:
311            return self._bigram_histo_cache[id(expression)]
312
313        expression_str = self._sql_generator.generate(expression)
314        count = max(0, len(expression_str) - 1)
315        bigram_histo: t.DefaultDict[str, int] = defaultdict(int)
316        for i in range(count):
317            bigram_histo[expression_str[i : i + 2]] += 1
318
319        self._bigram_histo_cache[id(expression)] = bigram_histo
320        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)
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]]:
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
163            for n, *_ in self._source.bfs()
164            if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
165        }
166        self._target_index = {
167            id(n): n
168            for n, *_ in self._target.bfs()
169            if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES)
170        }
171        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
172        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
173        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
174
175        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
176        return self._generate_edit_script(matching_set)