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

     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)

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.

class ChangeDistiller: View Source

    130class ChangeDistiller:
    131    """
    132    The implementation of the Change Distiller algorithm described by Beat Fluri and Martin Pinzger in
    133    their paper https://ieeexplore.ieee.org/document/4339230, which in turn is based on the algorithm by
    134    Chawathe et al. described in http://ilpubs.stanford.edu:8090/115/1/1995-46.pdf.
    135    """
    136
    137    def __init__(self, f: float = 0.6, t: float = 0.6) -> None:
    138        self.f = f
    139        self.t = t
    140        self._sql_generator = Dialect().generator()
    141
    142    def diff(
    143        self,
    144        source: exp.Expression,
    145        target: exp.Expression,
    146        matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
    147    ) -> t.List[Edit]:
    148        matchings = matchings or []
    149        pre_matched_nodes = {id(s): id(t) for s, t in matchings}
    150        if len({n for pair in pre_matched_nodes.items() for n in pair}) != 2 * len(matchings):
    151            raise ValueError("Each node can be referenced at most once in the list of matchings")
    152
    153        self._source = source
    154        self._target = target
    155        self._source_index = {id(n): n for n, *_ in self._source.bfs()}
    156        self._target_index = {id(n): n for n, *_ in self._target.bfs()}
    157        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
    158        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
    159        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
    160
    161        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
    162        return self._generate_edit_script(matching_set)
    163
    164    def _generate_edit_script(self, matching_set: t.Set[t.Tuple[int, int]]) -> t.List[Edit]:
    165        edit_script: t.List[Edit] = []
    166        for removed_node_id in self._unmatched_source_nodes:
    167            edit_script.append(Remove(self._source_index[removed_node_id]))
    168        for inserted_node_id in self._unmatched_target_nodes:
    169            edit_script.append(Insert(self._target_index[inserted_node_id]))
    170        for kept_source_node_id, kept_target_node_id in matching_set:
    171            source_node = self._source_index[kept_source_node_id]
    172            target_node = self._target_index[kept_target_node_id]
    173            if not isinstance(source_node, LEAF_EXPRESSION_TYPES) or source_node == target_node:
    174                edit_script.extend(
    175                    self._generate_move_edits(source_node, target_node, matching_set)
    176                )
    177                edit_script.append(Keep(source_node, target_node))
    178            else:
    179                edit_script.append(Update(source_node, target_node))
    180
    181        return edit_script
    182
    183    def _generate_move_edits(
    184        self, source: exp.Expression, target: exp.Expression, matching_set: t.Set[t.Tuple[int, int]]
    185    ) -> t.List[Move]:
    186        source_args = [id(e) for e in _expression_only_args(source)]
    187        target_args = [id(e) for e in _expression_only_args(target)]
    188
    189        args_lcs = set(_lcs(source_args, target_args, lambda l, r: (l, r) in matching_set))
    190
    191        move_edits = []
    192        for a in source_args:
    193            if a not in args_lcs and a not in self._unmatched_source_nodes:
    194                move_edits.append(Move(self._source_index[a]))
    195
    196        return move_edits
    197
    198    def _compute_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    199        leaves_matching_set = self._compute_leaf_matching_set()
    200        matching_set = leaves_matching_set.copy()
    201
    202        ordered_unmatched_source_nodes = {
    203            id(n): None for n, *_ in self._source.bfs() if id(n) in self._unmatched_source_nodes
    204        }
    205        ordered_unmatched_target_nodes = {
    206            id(n): None for n, *_ in self._target.bfs() if id(n) in self._unmatched_target_nodes
    207        }
    208
    209        for source_node_id in ordered_unmatched_source_nodes:
    210            for target_node_id in ordered_unmatched_target_nodes:
    211                source_node = self._source_index[source_node_id]
    212                target_node = self._target_index[target_node_id]
    213                if _is_same_type(source_node, target_node):
    214                    source_leaf_ids = {id(l) for l in _get_leaves(source_node)}
    215                    target_leaf_ids = {id(l) for l in _get_leaves(target_node)}
    216
    217                    max_leaves_num = max(len(source_leaf_ids), len(target_leaf_ids))
    218                    if max_leaves_num:
    219                        common_leaves_num = sum(
    220                            1 if s in source_leaf_ids and t in target_leaf_ids else 0
    221                            for s, t in leaves_matching_set
    222                        )
    223                        leaf_similarity_score = common_leaves_num / max_leaves_num
    224                    else:
    225                        leaf_similarity_score = 0.0
    226
    227                    adjusted_t = (
    228                        self.t if min(len(source_leaf_ids), len(target_leaf_ids)) > 4 else 0.4
    229                    )
    230
    231                    if leaf_similarity_score >= 0.8 or (
    232                        leaf_similarity_score >= adjusted_t
    233                        and self._dice_coefficient(source_node, target_node) >= self.f
    234                    ):
    235                        matching_set.add((source_node_id, target_node_id))
    236                        self._unmatched_source_nodes.remove(source_node_id)
    237                        self._unmatched_target_nodes.remove(target_node_id)
    238                        ordered_unmatched_target_nodes.pop(target_node_id, None)
    239                        break
    240
    241        return matching_set
    242
    243    def _compute_leaf_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    244        candidate_matchings: t.List[t.Tuple[float, int, exp.Expression, exp.Expression]] = []
    245        source_leaves = list(_get_leaves(self._source))
    246        target_leaves = list(_get_leaves(self._target))
    247        for source_leaf in source_leaves:
    248            for target_leaf in target_leaves:
    249                if _is_same_type(source_leaf, target_leaf):
    250                    similarity_score = self._dice_coefficient(source_leaf, target_leaf)
    251                    if similarity_score >= self.f:
    252                        heappush(
    253                            candidate_matchings,
    254                            (
    255                                -similarity_score,
    256                                len(candidate_matchings),
    257                                source_leaf,
    258                                target_leaf,
    259                            ),
    260                        )
    261
    262        # Pick best matchings based on the highest score
    263        matching_set = set()
    264        while candidate_matchings:
    265            _, _, source_leaf, target_leaf = heappop(candidate_matchings)
    266            if (
    267                id(source_leaf) in self._unmatched_source_nodes
    268                and id(target_leaf) in self._unmatched_target_nodes
    269            ):
    270                matching_set.add((id(source_leaf), id(target_leaf)))
    271                self._unmatched_source_nodes.remove(id(source_leaf))
    272                self._unmatched_target_nodes.remove(id(target_leaf))
    273
    274        return matching_set
    275
    276    def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float:
    277        source_histo = self._bigram_histo(source)
    278        target_histo = self._bigram_histo(target)
    279
    280        total_grams = sum(source_histo.values()) + sum(target_histo.values())
    281        if not total_grams:
    282            return 1.0 if source == target else 0.0
    283
    284        overlap_len = 0
    285        overlapping_grams = set(source_histo) & set(target_histo)
    286        for g in overlapping_grams:
    287            overlap_len += min(source_histo[g], target_histo[g])
    288
    289        return 2 * overlap_len / total_grams
    290
    291    def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]:
    292        if id(expression) in self._bigram_histo_cache:
    293            return self._bigram_histo_cache[id(expression)]
    294
    295        expression_str = self._sql_generator.generate(expression)
    296        count = max(0, len(expression_str) - 1)
    297        bigram_histo: t.DefaultDict[str, int] = defaultdict(int)
    298        for i in range(count):
    299            bigram_histo[expression_str[i : i + 2]] += 1
    300
    301        self._bigram_histo_cache[id(expression)] = bigram_histo
    302        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

    137    def __init__(self, f: float = 0.6, t: float = 0.6) -> None:
    138        self.f = f
    139        self.t = t
    140        self._sql_generator = Dialect().generator()

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

    142    def diff(
    143        self,
    144        source: exp.Expression,
    145        target: exp.Expression,
    146        matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
    147    ) -> t.List[Edit]:
    148        matchings = matchings or []
    149        pre_matched_nodes = {id(s): id(t) for s, t in matchings}
    150        if len({n for pair in pre_matched_nodes.items() for n in pair}) != 2 * len(matchings):
    151            raise ValueError("Each node can be referenced at most once in the list of matchings")
    152
    153        self._source = source
    154        self._target = target
    155        self._source_index = {id(n): n for n, *_ in self._source.bfs()}
    156        self._target_index = {id(n): n for n, *_ in self._target.bfs()}
    157        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
    158        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
    159        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
    160
    161        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
    162        return self._generate_edit_script(matching_set)