# 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) 120 121 122# The expression types for which Update edits are allowed. 123UPDATABLE_EXPRESSION_TYPES = ( 124 exp.Boolean, 125 exp.DataType, 126 exp.Literal, 127 exp.Table, 128 exp.Column, 129 exp.Lambda, 130) 131 132IGNORED_LEAF_EXPRESSION_TYPES = (exp.Identifier,) 133 134 135class ChangeDistiller: 136 """ 137 The implementation of the Change Distiller algorithm described by Beat Fluri and Martin Pinzger in 138 their paper https://ieeexplore.ieee.org/document/4339230, which in turn is based on the algorithm by 139 Chawathe et al. described in http://ilpubs.stanford.edu:8090/115/1/1995-46.pdf. 140 """ 141 142 def __init__(self, f: float = 0.6, t: float = 0.6) -> None: 143 self.f = f 144 self.t = t 145 self._sql_generator = Dialect().generator() 146 147 def diff( 148 self, 149 source: exp.Expression, 150 target: exp.Expression, 151 matchings: t.List[t.Tuple[exp.Expression, exp.Expression]] | None = None, 152 ) -> t.List[Edit]: 153 matchings = matchings or [] 154 pre_matched_nodes = {id(s): id(t) for s, t in matchings} 155 if len({n for pair in pre_matched_nodes.items() for n in pair}) != 2 * len(matchings): 156 raise ValueError("Each node can be referenced at most once in the list of matchings") 157 158 self._source = source 159 self._target = target 160 self._source_index = { 161 id(n): n for n in self._source.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES) 162 } 163 self._target_index = { 164 id(n): n for n in self._target.bfs() if not isinstance(n, IGNORED_LEAF_EXPRESSION_TYPES) 165 } 166 self._unmatched_source_nodes = set(self._source_index) - set(pre_matched_nodes) 167 self._unmatched_target_nodes = set(self._target_index) - set(pre_matched_nodes.values()) 168 self._bigram_histo_cache: t.Dict[int, t.DefaultDict[str, int]] = {} 169 170 matching_set = self._compute_matching_set() | {(s, t) for s, t in pre_matched_nodes.items()} 171 return self._generate_edit_script(matching_set) 172 173 def _generate_edit_script(self, matching_set: t.Set[t.Tuple[int, int]]) -> t.List[Edit]: 174 edit_script: t.List[Edit] = [] 175 for removed_node_id in self._unmatched_source_nodes: 176 edit_script.append(Remove(self._source_index[removed_node_id])) 177 for inserted_node_id in self._unmatched_target_nodes: 178 edit_script.append(Insert(self._target_index[inserted_node_id])) 179 for kept_source_node_id, kept_target_node_id in matching_set: 180 source_node = self._source_index[kept_source_node_id] 181 target_node = self._target_index[kept_target_node_id] 182 if ( 183 not isinstance(source_node, UPDATABLE_EXPRESSION_TYPES) 184 or source_node == target_node 185 ): 186 edit_script.extend( 187 self._generate_move_edits(source_node, target_node, matching_set) 188 ) 189 edit_script.append(Keep(source_node, target_node)) 190 else: 191 edit_script.append(Update(source_node, target_node)) 192 193 return edit_script 194 195 def _generate_move_edits( 196 self, source: exp.Expression, target: exp.Expression, matching_set: t.Set[t.Tuple[int, int]] 197 ) -> t.List[Move]: 198 source_args = [id(e) for e in _expression_only_args(source)] 199 target_args = [id(e) for e in _expression_only_args(target)] 200 201 args_lcs = set(_lcs(source_args, target_args, lambda l, r: (l, r) in matching_set)) 202 203 move_edits = [] 204 for a in source_args: 205 if a not in args_lcs and a not in self._unmatched_source_nodes: 206 move_edits.append(Move(self._source_index[a])) 207 208 return move_edits 209 210 def _compute_matching_set(self) -> t.Set[t.Tuple[int, int]]: 211 leaves_matching_set = self._compute_leaf_matching_set() 212 matching_set = leaves_matching_set.copy() 213 214 ordered_unmatched_source_nodes = { 215 id(n): None for n in self._source.bfs() if id(n) in self._unmatched_source_nodes 216 } 217 ordered_unmatched_target_nodes = { 218 id(n): None for n in self._target.bfs() if id(n) in self._unmatched_target_nodes 219 } 220 221 for source_node_id in ordered_unmatched_source_nodes: 222 for target_node_id in ordered_unmatched_target_nodes: 223 source_node = self._source_index[source_node_id] 224 target_node = self._target_index[target_node_id] 225 if _is_same_type(source_node, target_node): 226 source_leaf_ids = {id(l) for l in _get_leaves(source_node)} 227 target_leaf_ids = {id(l) for l in _get_leaves(target_node)} 228 229 max_leaves_num = max(len(source_leaf_ids), len(target_leaf_ids)) 230 if max_leaves_num: 231 common_leaves_num = sum( 232 1 if s in source_leaf_ids and t in target_leaf_ids else 0 233 for s, t in leaves_matching_set 234 ) 235 leaf_similarity_score = common_leaves_num / max_leaves_num 236 else: 237 leaf_similarity_score = 0.0 238 239 adjusted_t = ( 240 self.t if min(len(source_leaf_ids), len(target_leaf_ids)) > 4 else 0.4 241 ) 242 243 if leaf_similarity_score >= 0.8 or ( 244 leaf_similarity_score >= adjusted_t 245 and self._dice_coefficient(source_node, target_node) >= self.f 246 ): 247 matching_set.add((source_node_id, target_node_id)) 248 self._unmatched_source_nodes.remove(source_node_id) 249 self._unmatched_target_nodes.remove(target_node_id) 250 ordered_unmatched_target_nodes.pop(target_node_id, None) 251 break 252 253 return matching_set 254 255 def _compute_leaf_matching_set(self) -> t.Set[t.Tuple[int, int]]: 256 candidate_matchings: t.List[t.Tuple[float, int, int, exp.Expression, exp.Expression]] = [] 257 source_leaves = list(_get_leaves(self._source)) 258 target_leaves = list(_get_leaves(self._target)) 259 for source_leaf in source_leaves: 260 for target_leaf in target_leaves: 261 if _is_same_type(source_leaf, target_leaf): 262 similarity_score = self._dice_coefficient(source_leaf, target_leaf) 263 if similarity_score >= self.f: 264 heappush( 265 candidate_matchings, 266 ( 267 -similarity_score, 268 -_parent_similarity_score(source_leaf, target_leaf), 269 len(candidate_matchings), 270 source_leaf, 271 target_leaf, 272 ), 273 ) 274 275 # Pick best matchings based on the highest score 276 matching_set = set() 277 while candidate_matchings: 278 _, _, _, source_leaf, target_leaf = heappop(candidate_matchings) 279 if ( 280 id(source_leaf) in self._unmatched_source_nodes 281 and id(target_leaf) in self._unmatched_target_nodes 282 ): 283 matching_set.add((id(source_leaf), id(target_leaf))) 284 self._unmatched_source_nodes.remove(id(source_leaf)) 285 self._unmatched_target_nodes.remove(id(target_leaf)) 286 287 return matching_set 288 289 def _dice_coefficient(self, source: exp.Expression, target: exp.Expression) -> float: 290 source_histo = self._bigram_histo(source) 291 target_histo = self._bigram_histo(target) 292 293 total_grams = sum(source_histo.values()) + sum(target_histo.values()) 294 if not total_grams: 295 return 1.0 if source == target else 0.0 296 297 overlap_len = 0 298 overlapping_grams = set(source_histo) & set(target_histo) 299 for g in overlapping_grams: 300 overlap_len += min(source_histo[g], target_histo[g]) 301 302 return 2 * overlap_len / total_grams 303 304 def _bigram_histo(self, expression: exp.Expression) -> t.DefaultDict[str, int]: 305 if id(expression) in self._bigram_histo_cache: 306 return self._bigram_histo_cache[id(expression)] 307 308 expression_str = self._sql_generator.generate(expression) 309 count = max(0, len(expression_str) - 1) 310 bigram_histo: t.DefaultDict[str, int] = defaultdict(int) 311 for i in range(count): 312 bigram_histo[expression_str[i : i + 2]] += 1 313 314 self._bigram_histo_cache[id(expression)] = bigram_histo 315 return bigram_histo 316 317 318def _get_leaves(expression: exp.Expression) -> t.Iterator[exp.Expression]: 319 has_child_exprs = False 320 321 for node in expression.iter_expressions(): 322 if not isinstance(node, IGNORED_LEAF_EXPRESSION_TYPES): 323 has_child_exprs = True 324 yield from _get_leaves(node) 325 326 if not has_child_exprs: 327 yield expression 328 329 330def _is_same_type(source: exp.Expression, target: exp.Expression) -> bool: 331 if type(source) is type(target): 332 if isinstance(source, exp.Join): 333 return source.args.get("side") == target.args.get("side") 334 335 if isinstance(source, exp.Anonymous): 336 return source.this == target.this 337 338 return True 339 340 return False 341 342 343def _parent_similarity_score( 344 source: t.Optional[exp.Expression], target: t.Optional[exp.Expression] 345) -> int: 346 if source is None or target is None or type(source) is not type(target): 347 return 0 348 349 return 1 + _parent_similarity_score(source.parent, target.parent) 350 351 352def _expression_only_args(expression: exp.Expression) -> t.List[exp.Expression]: 353 args: t.List[t.Union[exp.Expression, t.List]] = [] 354 if expression: 355 for a in expression.args.values(): 356 args.extend(ensure_list(a)) 357 return [ 358 a 359 for a in args 360 if isinstance(a, exp.Expression) and not isinstance(a, IGNORED_LEAF_EXPRESSION_TYPES) 361 ] 362 363 364def _lcs( 365 seq_a: t.Sequence[T], seq_b: t.Sequence[T], equal: t.Callable[[T, T], bool] 366) -> t.Sequence[t.Optional[T]]: 367 """Calculates the longest common subsequence""" 368 369 len_a = len(seq_a) 370 len_b = len(seq_b) 371 lcs_result = [[None] * (len_b + 1) for i in range(len_a + 1)] 372 373 for i in range(len_a + 1): 374 for j in range(len_b + 1): 375 if i == 0 or j == 0: 376 lcs_result[i][j] = [] # type: ignore 377 elif equal(seq_a[i - 1], seq_b[j - 1]): 378 lcs_result[i][j] = lcs_result[i - 1][j - 1] + [seq_a[i - 1]] # type: ignore 379 else: 380 lcs_result[i][j] = ( 381 lcs_result[i - 1][j] 382 if len(lcs_result[i - 1][j]) > len(lcs_result[i][j - 1]) # type: ignore 383 else lcs_result[i][j - 1] 384 ) 385 386 return lcs_result[len_a][len_b] # type: ignore

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.

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

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

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