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# Semantic Diff for SQL

by Iaroslav Zeigerman

## Motivation

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

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

Consider the following diff generated by Git:

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

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

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

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

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

## The Search for a Solution

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

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

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

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

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

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

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

### Naïve Brute-Force

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

### Myers Algorithm

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

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

## Change Distiller

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

The algorithm consists of two high-level steps:

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

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

### Building the Matching Set

#### Matching Leaves

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

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

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

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

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

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

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

    from collections import defaultdict

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

The dice coefficient formula looks like following:

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

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

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

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

        return 2 * overlap_len / total_grams

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

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

The two nodes are matched if two conditions are met:

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

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

    from heapq import heappush, heappop

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

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

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

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

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

#### Matching Inner Nodes

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

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

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

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

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

There are two additional heuristics associated with this matching criteria:

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

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

    leaves_matching_set = matching_set.copy()

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

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

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

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

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

### Generating the Edit Script

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

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

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

The latter two cases are pretty straightforward to implement:

    edit_script = []

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

Traversing the matching set requires a little more thought:

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

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

Now with this knowledge, the implementation becomes straightforward:

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

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

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

        return move_edits

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

### Output

The implemented algorithm produces the output that resembles the following:

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

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

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

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

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

### Optimizations

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

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

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

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

## Alternative Solutions

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

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

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

## Conclusion

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

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

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

## References

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

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

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

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

View Source

      1"""
      2.. include:: ../posts/sql_diff.md
      3
      4----
      5"""
      6
      7from __future__ import annotations
      8
      9import typing as t
     10from collections import defaultdict
     11from dataclasses import dataclass
     12from heapq import heappop, heappush
     13
     14from sqlglot import Dialect, expressions as exp
     15from sqlglot.helper import ensure_list
     16
     17
     18@dataclass(frozen=True)
     19class Insert:
     20    """Indicates that a new node has been inserted"""
     21
     22    expression: exp.Expression
     23
     24
     25@dataclass(frozen=True)
     26class Remove:
     27    """Indicates that an existing node has been removed"""
     28
     29    expression: exp.Expression
     30
     31
     32@dataclass(frozen=True)
     33class Move:
     34    """Indicates that an existing node's position within the tree has changed"""
     35
     36    expression: exp.Expression
     37
     38
     39@dataclass(frozen=True)
     40class Update:
     41    """Indicates that an existing node has been updated"""
     42
     43    source: exp.Expression
     44    target: exp.Expression
     45
     46
     47@dataclass(frozen=True)
     48class Keep:
     49    """Indicates that an existing node hasn't been changed"""
     50
     51    source: exp.Expression
     52    target: exp.Expression
     53
     54
     55if t.TYPE_CHECKING:
     56    from sqlglot._typing import T
     57
     58    Edit = t.Union[Insert, Remove, Move, Update, Keep]
     59
     60
     61def diff(
     62    source: exp.Expression,
     63    target: exp.Expression,
     64    matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
     65    **kwargs: t.Any,
     66) -> t.List[Edit]:
     67    """
     68    Returns the list of changes between the source and the target expressions.
     69
     70    Examples:
     71        >>> diff(parse_one("a + b"), parse_one("a + c"))
     72        [
     73            Remove(expression=(COLUMN this: (IDENTIFIER this: b, quoted: False))),
     74            Insert(expression=(COLUMN this: (IDENTIFIER this: c, quoted: False))),
     75            Keep(
     76                source=(ADD this: ...),
     77                target=(ADD this: ...)
     78            ),
     79            Keep(
     80                source=(COLUMN this: (IDENTIFIER this: a, quoted: False)),
     81                target=(COLUMN this: (IDENTIFIER this: a, quoted: False))
     82            ),
     83        ]
     84
     85    Args:
     86        source: the source expression.
     87        target: the target expression against which the diff should be calculated.
     88        matchings: the list of pre-matched node pairs which is used to help the algorithm's
     89            heuristics produce better results for subtrees that are known by a caller to be matching.
     90            Note: expression references in this list must refer to the same node objects that are
     91            referenced in source / target trees.
     92
     93    Returns:
     94        the list of Insert, Remove, Move, Update and Keep objects for each node in the source and the
     95        target expression trees. This list represents a sequence of steps needed to transform the source
     96        expression tree into the target one.
     97    """
     98    matchings = matchings or []
     99    matching_ids = {id(n) for pair in matchings for n in pair}
    100
    101    def compute_node_mappings(
    102        original: exp.Expression, copy: exp.Expression
    103    ) -> t.Dict[int, exp.Expression]:
    104        return {
    105            id(old_node): new_node
    106            for (old_node, _, _), (new_node, _, _) in zip(original.walk(), copy.walk())
    107            if id(old_node) in matching_ids
    108        }
    109
    110    source_copy = source.copy()
    111    target_copy = target.copy()
    112
    113    node_mappings = {
    114        **compute_node_mappings(source, source_copy),
    115        **compute_node_mappings(target, target_copy),
    116    }
    117    matchings_copy = [(node_mappings[id(s)], node_mappings[id(t)]) for s, t in matchings]
    118
    119    return ChangeDistiller(**kwargs).diff(source_copy, target_copy, matchings=matchings_copy)
    120
    121
    122LEAF_EXPRESSION_TYPES = (
    123    exp.Boolean,
    124    exp.DataType,
    125    exp.Identifier,
    126    exp.Literal,
    127)
    128
    129
    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, 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                                -_parent_similarity_score(source_leaf, target_leaf),
    257                                len(candidate_matchings),
    258                                source_leaf,
    259                                target_leaf,
    260                            ),
    261                        )
    262
    263        # Pick best matchings based on the highest score
    264        matching_set = set()
    265        while candidate_matchings:
    266            _, _, _, source_leaf, target_leaf = heappop(candidate_matchings)
    267            if (
    268                id(source_leaf) in self._unmatched_source_nodes
    269                and id(target_leaf) in self._unmatched_target_nodes
    270            ):
    271                matching_set.add((id(source_leaf), id(target_leaf)))
    272                self._unmatched_source_nodes.remove(id(source_leaf))
    273                self._unmatched_target_nodes.remove(id(target_leaf))
    274
    275        return matching_set
    276
    277    def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float:
    278        source_histo = self._bigram_histo(source)
    279        target_histo = self._bigram_histo(target)
    280
    281        total_grams = sum(source_histo.values()) + sum(target_histo.values())
    282        if not total_grams:
    283            return 1.0 if source == target else 0.0
    284
    285        overlap_len = 0
    286        overlapping_grams = set(source_histo) & set(target_histo)
    287        for g in overlapping_grams:
    288            overlap_len += min(source_histo[g], target_histo[g])
    289
    290        return 2 * overlap_len / total_grams
    291
    292    def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]:
    293        if id(expression) in self._bigram_histo_cache:
    294            return self._bigram_histo_cache[id(expression)]
    295
    296        expression_str = self._sql_generator.generate(expression)
    297        count = max(0, len(expression_str) - 1)
    298        bigram_histo: t.DefaultDict[str, int] = defaultdict(int)
    299        for i in range(count):
    300            bigram_histo[expression_str[i : i + 2]] += 1
    301
    302        self._bigram_histo_cache[id(expression)] = bigram_histo
    303        return bigram_histo
    304
    305
    306def _get_leaves(expression: exp.Expression) -> t.Iterator[exp.Expression]:
    307    has_child_exprs = False
    308
    309    for _, node in expression.iter_expressions():
    310        has_child_exprs = True
    311        yield from _get_leaves(node)
    312
    313    if not has_child_exprs:
    314        yield expression
    315
    316
    317def _is_same_type(source: exp.Expression, target: exp.Expression) -> bool:
    318    if type(source) is type(target) and (
    319        not isinstance(source, exp.Identifier) or type(source.parent) is type(target.parent)
    320    ):
    321        if isinstance(source, exp.Join):
    322            return source.args.get("side") == target.args.get("side")
    323
    324        if isinstance(source, exp.Anonymous):
    325            return source.this == target.this
    326
    327        return True
    328
    329    return False
    330
    331
    332def _parent_similarity_score(
    333    source: t.Optional[exp.Expression], target: t.Optional[exp.Expression]
    334) -> int:
    335    if source is None or target is None or type(source) is not type(target):
    336        return 0
    337
    338    return 1 + _parent_similarity_score(source.parent, target.parent)
    339
    340
    341def _expression_only_args(expression: exp.Expression) -> t.List[exp.Expression]:
    342    args: t.List[t.Union[exp.Expression, t.List]] = []
    343    if expression:
    344        for a in expression.args.values():
    345            args.extend(ensure_list(a))
    346    return [a for a in args if isinstance(a, exp.Expression)]
    347
    348
    349def _lcs(
    350    seq_a: t.Sequence[T], seq_b: t.Sequence[T], equal: t.Callable[[T, T], bool]
    351) -> t.Sequence[t.Optional[T]]:
    352    """Calculates the longest common subsequence"""
    353
    354    len_a = len(seq_a)
    355    len_b = len(seq_b)
    356    lcs_result = [[None] * (len_b + 1) for i in range(len_a + 1)]
    357
    358    for i in range(len_a + 1):
    359        for j in range(len_b + 1):
    360            if i == 0 or j == 0:
    361                lcs_result[i][j] = []  # type: ignore
    362            elif equal(seq_a[i - 1], seq_b[j - 1]):
    363                lcs_result[i][j] = lcs_result[i - 1][j - 1] + [seq_a[i - 1]]  # type: ignore
    364            else:
    365                lcs_result[i][j] = (
    366                    lcs_result[i - 1][j]
    367                    if len(lcs_result[i - 1][j]) > len(lcs_result[i][j - 1])  # type: ignore
    368                    else lcs_result[i][j - 1]
    369                )
    370
    371    return lcs_result[len_a][len_b]  # type: ignore

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

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

Indicates that a new node has been inserted

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

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

Indicates that an existing node has been removed

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

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

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

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

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

Indicates that an existing node has been updated

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

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

Indicates that an existing node hasn't been changed

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

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

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

###### Examples:

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

###### Arguments:

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

###### Returns:

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

LEAF_EXPRESSION_TYPES = (<class 'sqlglot.expressions.Boolean'>, <class 'sqlglot.expressions.DataType'>, <class 'sqlglot.expressions.Identifier'>, <class 'sqlglot.expressions.Literal'>)
class ChangeDistiller: View Source

    131class ChangeDistiller:
    132    """
    133    The implementation of the Change Distiller algorithm described by Beat Fluri and Martin Pinzger in
    134    their paper https://ieeexplore.ieee.org/document/4339230, which in turn is based on the algorithm by
    135    Chawathe et al. described in http://ilpubs.stanford.edu:8090/115/1/1995-46.pdf.
    136    """
    137
    138    def __init__(self, f: float = 0.6, t: float = 0.6) -> None:
    139        self.f = f
    140        self.t = t
    141        self._sql_generator = Dialect().generator()
    142
    143    def diff(
    144        self,
    145        source: exp.Expression,
    146        target: exp.Expression,
    147        matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None,
    148    ) -> t.List[Edit]:
    149        matchings = matchings or []
    150        pre_matched_nodes = {id(s): id(t) for s, t in matchings}
    151        if len({n for pair in pre_matched_nodes.items() for n in pair}) != 2 * len(matchings):
    152            raise ValueError("Each node can be referenced at most once in the list of matchings")
    153
    154        self._source = source
    155        self._target = target
    156        self._source_index = {id(n): n for n, *_ in self._source.bfs()}
    157        self._target_index = {id(n): n for n, *_ in self._target.bfs()}
    158        self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes)
    159        self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values())
    160        self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {}
    161
    162        matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()}
    163        return self._generate_edit_script(matching_set)
    164
    165    def _generate_edit_script(self, matching_set: t.Set[t.Tuple[int, int]]) -> t.List[Edit]:
    166        edit_script: t.List[Edit] = []
    167        for removed_node_id in self._unmatched_source_nodes:
    168            edit_script.append(Remove(self._source_index[removed_node_id]))
    169        for inserted_node_id in self._unmatched_target_nodes:
    170            edit_script.append(Insert(self._target_index[inserted_node_id]))
    171        for kept_source_node_id, kept_target_node_id in matching_set:
    172            source_node = self._source_index[kept_source_node_id]
    173            target_node = self._target_index[kept_target_node_id]
    174            if not isinstance(source_node, LEAF_EXPRESSION_TYPES) or source_node == target_node:
    175                edit_script.extend(
    176                    self._generate_move_edits(source_node, target_node, matching_set)
    177                )
    178                edit_script.append(Keep(source_node, target_node))
    179            else:
    180                edit_script.append(Update(source_node, target_node))
    181
    182        return edit_script
    183
    184    def _generate_move_edits(
    185        self, source: exp.Expression, target: exp.Expression, matching_set: t.Set[t.Tuple[int, int]]
    186    ) -> t.List[Move]:
    187        source_args = [id(e) for e in _expression_only_args(source)]
    188        target_args = [id(e) for e in _expression_only_args(target)]
    189
    190        args_lcs = set(_lcs(source_args, target_args, lambda l, r: (l, r) in matching_set))
    191
    192        move_edits = []
    193        for a in source_args:
    194            if a not in args_lcs and a not in self._unmatched_source_nodes:
    195                move_edits.append(Move(self._source_index[a]))
    196
    197        return move_edits
    198
    199    def _compute_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    200        leaves_matching_set = self._compute_leaf_matching_set()
    201        matching_set = leaves_matching_set.copy()
    202
    203        ordered_unmatched_source_nodes = {
    204            id(n): None for n, *_ in self._source.bfs() if id(n) in self._unmatched_source_nodes
    205        }
    206        ordered_unmatched_target_nodes = {
    207            id(n): None for n, *_ in self._target.bfs() if id(n) in self._unmatched_target_nodes
    208        }
    209
    210        for source_node_id in ordered_unmatched_source_nodes:
    211            for target_node_id in ordered_unmatched_target_nodes:
    212                source_node = self._source_index[source_node_id]
    213                target_node = self._target_index[target_node_id]
    214                if _is_same_type(source_node, target_node):
    215                    source_leaf_ids = {id(l) for l in _get_leaves(source_node)}
    216                    target_leaf_ids = {id(l) for l in _get_leaves(target_node)}
    217
    218                    max_leaves_num = max(len(source_leaf_ids), len(target_leaf_ids))
    219                    if max_leaves_num:
    220                        common_leaves_num = sum(
    221                            1 if s in source_leaf_ids and t in target_leaf_ids else 0
    222                            for s, t in leaves_matching_set
    223                        )
    224                        leaf_similarity_score = common_leaves_num / max_leaves_num
    225                    else:
    226                        leaf_similarity_score = 0.0
    227
    228                    adjusted_t = (
    229                        self.t if min(len(source_leaf_ids), len(target_leaf_ids)) > 4 else 0.4
    230                    )
    231
    232                    if leaf_similarity_score >= 0.8 or (
    233                        leaf_similarity_score >= adjusted_t
    234                        and self._dice_coefficient(source_node, target_node) >= self.f
    235                    ):
    236                        matching_set.add((source_node_id, target_node_id))
    237                        self._unmatched_source_nodes.remove(source_node_id)
    238                        self._unmatched_target_nodes.remove(target_node_id)
    239                        ordered_unmatched_target_nodes.pop(target_node_id, None)
    240                        break
    241
    242        return matching_set
    243
    244    def _compute_leaf_matching_set(self) -> t.Set[t.Tuple[int, int]]:
    245        candidate_matchings: t.List[t.Tuple[float, int, int, exp.Expression, exp.Expression]] = []
    246        source_leaves = list(_get_leaves(self._source))
    247        target_leaves = list(_get_leaves(self._target))
    248        for source_leaf in source_leaves:
    249            for target_leaf in target_leaves:
    250                if _is_same_type(source_leaf, target_leaf):
    251                    similarity_score = self._dice_coefficient(source_leaf, target_leaf)
    252                    if similarity_score >= self.f:
    253                        heappush(
    254                            candidate_matchings,
    255                            (
    256                                -similarity_score,
    257                                -_parent_similarity_score(source_leaf, target_leaf),
    258                                len(candidate_matchings),
    259                                source_leaf,
    260                                target_leaf,
    261                            ),
    262                        )
    263
    264        # Pick best matchings based on the highest score
    265        matching_set = set()
    266        while candidate_matchings:
    267            _, _, _, source_leaf, target_leaf = heappop(candidate_matchings)
    268            if (
    269                id(source_leaf) in self._unmatched_source_nodes
    270                and id(target_leaf) in self._unmatched_target_nodes
    271            ):
    272                matching_set.add((id(source_leaf), id(target_leaf)))
    273                self._unmatched_source_nodes.remove(id(source_leaf))
    274                self._unmatched_target_nodes.remove(id(target_leaf))
    275
    276        return matching_set
    277
    278    def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float:
    279        source_histo = self._bigram_histo(source)
    280        target_histo = self._bigram_histo(target)
    281
    282        total_grams = sum(source_histo.values()) + sum(target_histo.values())
    283        if not total_grams:
    284            return 1.0 if source == target else 0.0
    285
    286        overlap_len = 0
    287        overlapping_grams = set(source_histo) & set(target_histo)
    288        for g in overlapping_grams:
    289            overlap_len += min(source_histo[g], target_histo[g])
    290
    291        return 2 * overlap_len / total_grams
    292
    293    def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]:
    294        if id(expression) in self._bigram_histo_cache:
    295            return self._bigram_histo_cache[id(expression)]
    296
    297        expression_str = self._sql_generator.generate(expression)
    298        count = max(0, len(expression_str) - 1)
    299        bigram_histo: t.DefaultDict[str, int] = defaultdict(int)
    300        for i in range(count):
    301            bigram_histo[expression_str[i : i + 2]] += 1
    302
    303        self._bigram_histo_cache[id(expression)] = bigram_histo
    304        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

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

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

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