# Semantic Diff for SQL

## 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:

**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.**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:

- The node labels match (in our case labels are just node types).
- 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

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

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

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

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

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

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

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.

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.

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)