BE-494: HashQL: Loop-breaker selection for recursive inlining

[indietyp]

🌟 What is the purpose of this PR?

This PR implements a three-color depth-first search algorithm for directed graphs and integrates it with a loop-breaker selection system for the MIR inliner. The three-color DFS enables cycle detection and postorder traversal, while the loop-breaker system allows the inliner to handle mutually recursive functions by strategically selecting which functions to avoid inlining within strongly connected components (SCCs).

🔗 Related links

• Related to MIR optimization and inlining strategies for recursive function groups

🔍 What does this change?

• Adds a new three-color depth-first search implementation in libs/@local/hashql/core/src/graph/algorithms/color/mod.rs with support for cycle detection and visitor callbacks
• Implements a loop-breaker selection algorithm in libs/@local/hashql/mir/src/pass/transform/inline/loop_breaker.rs that uses scoring heuristics to choose which functions in recursive SCCs should not be inlined
• Extends the inline pass to process SCCs with loop-breaker awareness, allowing inlining of non-breaker functions while avoiding infinite recursion
• Adds comprehensive test coverage for both the three-color DFS algorithm and loop-breaker selection
• Updates the call graph analysis to support querying callers of a function
• Adds iterator support for SCC members with both immutable and mutable access
• Changes unary NOT operator representation from ! to ~ in MIR output formatting
• Extends inline configuration with InlineLoopBreakerConfig for tuning breaker selection heuristics

Pre-Merge Checklist 🚀

🚢 Has this modified a publishable library?

This PR:

• does not modify any publishable blocks or libraries, or modifications do not need publishing

📜 Does this require a change to the docs?

The changes in this PR:

• are internal and do not require a docs change

🕸️ Does this require a change to the Turbo Graph?

The changes in this PR:

• do not affect the execution graph

🛡 What tests cover this?

• Comprehensive unit tests for three-color DFS including cycle detection, postorder traversal, edge filtering, and state accumulation
• Loop-breaker selection tests covering mutual recursion, cost-based selection, multi-cycle SCCs, and ordering verification
• Integration tests showing the complete inlining behavior with loop breakers
• Existing MIR transformation tests updated to reflect the new unary operator formatting

❓ How to test this?

1. Run the test suite to verify all three-color DFS and loop-breaker functionality
2. Test with mutually recursive MIR functions to confirm proper breaker selection and inlining behavior
3. Verify that the inliner no longer gets stuck in infinite loops when processing recursive function groups

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[indietyp]

Warning

This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
Learn more

• BE-494: HashQL: Loop-breaker selection for recursive inlining #8600 👈 (View in Graphite)
• BE-482: HashQL: Remove logical not from MIR and fix postgres boolean lowering #8595
• BE-474: HashQL: Take into account terminator target eligibility in execution backend placement #8587
• BE-455: HashQL: Introduce evaluation orchestrator #8586
• BE-306: HashQL: PostgreSQL translation #8526
• BE-457: HashQL: MIR execution pipeline extensions for postgres compilation #8525
• BE-456: HashQL: Entity type model enrichment and graph store query extensions #8524
• BE-429: HashQL: Add island dependency graph with data requirement resolution #8501
• BE-428: HashQL: Simplify traversal tracking to path recording #8498
• BE-434: HashQL: Refactor entity storage path resolution with centralized schema mapping #8496
• BE-427: Add hashql-macros crate with procedural macros for ID types and symbols #8495
• main

This stack of pull requests is managed by Graphite. Learn more about stacking.

[codecov]

Codecov Report

❌ Patch coverage is 85.96491% with 32 lines in your changes missing coverage. Please review.
✅ Project coverage is 64.64%. Comparing base (d6dbdd5) to head (5012bc6).

Files with missing lines	Patch %	Lines
...cal/hashql/core/src/graph/algorithms/tarjan/mod.rs	0.00%	22 Missing ⚠️
...ocal/hashql/core/src/graph/algorithms/color/mod.rs	93.24%	5 Missing ⚠️
...al/hashql/core/src/graph/algorithms/color/tests.rs	96.21%	4 Missing and 1 partial ⚠️

Additional details and impacted files

@@                                     Coverage Diff                                      @@
##           bm/be-482-hashql-remove-logical-not-from-unary-operators    #8600      +/-   ##
============================================================================================
+ Coverage                                                     56.59%   64.64%   +8.04%     
============================================================================================
  Files                                                          1029      891     -138     
  Lines                                                        103401    76997   -26404     
  Branches                                                       4358     4035     -323     
============================================================================================
- Hits                                                          58522    49774    -8748     
+ Misses                                                        44239    26676   -17563     
+ Partials                                                        640      547      -93     

Flag	Coverage Δ
apps.hash-ai-worker-ts	1.40% <ø> (ø)
apps.hash-api	0.00% <ø> (ø)
blockprotocol.type-system	?
local.hash-graph-sdk	9.63% <ø> (ø)
local.hash-isomorphic-utils	0.00% <ø> (ø)
rust.hash-graph-api	2.52% <ø> (ø)
rust.hash-graph-authorization	?
rust.hash-graph-postgres-store	?
rust.hash-graph-store	?
rust.hash-graph-types	?
rust.hashql-compiletest	28.31% <ø> (ø)

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[codspeed-hq]

Merging this PR will not alter performance

✅ 80 untouched benchmarks

---

_{Comparing bm/be-494-hashql-scc-loop-breaker-inlining (5012bc6) with bm/be-482-hashql-remove-logical-not-from-unary-operators (d6dbdd5)}

[vercel]

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[github-actions]

Benchmark results

@rust/hash-graph-benches – Integrations

policy_resolution_large

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 2002	$$25.7 \mathrm{ms} \pm 191 \mathrm{μs}\left({\color{gray}1.40 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$3.39 \mathrm{ms} \pm 15.4 \mathrm{μs}\left({\color{gray}-1.778 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 1001	$$12.1 \mathrm{ms} \pm 81.7 \mathrm{μs}\left({\color{gray}0.225 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: high, policies: 3314	$$42.3 \mathrm{ms} \pm 289 \mathrm{μs}\left({\color{gray}0.114 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: low, policies: 1	$$14.3 \mathrm{ms} \pm 120 \mathrm{μs}\left({\color{gray}0.578 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: medium, policies: 1526	$$23.4 \mathrm{ms} \pm 163 \mathrm{μs}\left({\color{gray}-0.262 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 2078	$$26.1 \mathrm{ms} \pm 165 \mathrm{μs}\left({\color{gray}-0.291 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$3.67 \mathrm{ms} \pm 18.9 \mathrm{μs}\left({\color{gray}-2.063 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 1033	$$13.1 \mathrm{ms} \pm 88.6 \mathrm{μs}\left({\color{gray}-0.481 \mathrm{\%}}\right) $$	Flame Graph

policy_resolution_medium

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 102	$$3.70 \mathrm{ms} \pm 21.7 \mathrm{μs}\left({\color{gray}-0.877 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$2.97 \mathrm{ms} \pm 13.7 \mathrm{μs}\left({\color{gray}-0.996 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 51	$$3.30 \mathrm{ms} \pm 15.6 \mathrm{μs}\left({\color{gray}-1.399 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: high, policies: 269	$$5.10 \mathrm{ms} \pm 30.7 \mathrm{μs}\left({\color{gray}-0.357 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: low, policies: 1	$$3.55 \mathrm{ms} \pm 15.5 \mathrm{μs}\left({\color{gray}-1.258 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: medium, policies: 107	$$4.08 \mathrm{ms} \pm 17.7 \mathrm{μs}\left({\color{gray}-1.072 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 133	$$4.40 \mathrm{ms} \pm 31.7 \mathrm{μs}\left({\color{gray}0.206 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$3.40 \mathrm{ms} \pm 16.1 \mathrm{μs}\left({\color{gray}-1.493 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 63	$$3.99 \mathrm{ms} \pm 21.3 \mathrm{μs}\left({\color{gray}-0.687 \mathrm{\%}}\right) $$	Flame Graph

policy_resolution_none

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 2	$$2.73 \mathrm{ms} \pm 11.9 \mathrm{μs}\left({\color{gray}-1.522 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$2.68 \mathrm{ms} \pm 15.2 \mathrm{μs}\left({\color{gray}-1.216 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 1	$$2.80 \mathrm{ms} \pm 13.5 \mathrm{μs}\left({\color{gray}-1.570 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 8	$$3.02 \mathrm{ms} \pm 12.7 \mathrm{μs}\left({\color{gray}-1.518 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$2.85 \mathrm{ms} \pm 14.4 \mathrm{μs}\left({\color{gray}-1.195 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 3	$$3.11 \mathrm{ms} \pm 13.4 \mathrm{μs}\left({\color{gray}-3.100 \mathrm{\%}}\right) $$	Flame Graph

policy_resolution_small

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 52	$$3.06 \mathrm{ms} \pm 14.3 \mathrm{μs}\left({\color{gray}0.026 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$2.75 \mathrm{ms} \pm 12.0 \mathrm{μs}\left({\color{gray}-2.195 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 25	$$2.94 \mathrm{ms} \pm 13.7 \mathrm{μs}\left({\color{gray}-0.882 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: high, policies: 94	$$3.48 \mathrm{ms} \pm 18.8 \mathrm{μs}\left({\color{gray}-0.505 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: low, policies: 1	$$3.09 \mathrm{ms} \pm 18.3 \mathrm{μs}\left({\color{gray}0.049 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: medium, policies: 26	$$3.27 \mathrm{ms} \pm 14.9 \mathrm{μs}\left({\color{gray}-0.753 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 66	$$3.40 \mathrm{ms} \pm 16.8 \mathrm{μs}\left({\color{gray}-0.043 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$3.05 \mathrm{ms} \pm 14.5 \mathrm{μs}\left({\color{gray}-0.982 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 29	$$3.33 \mathrm{ms} \pm 16.2 \mathrm{μs}\left({\color{gray}-1.203 \mathrm{\%}}\right) $$	Flame Graph

read_scaling_complete

Function	Value	Mean	Flame graphs
entity_by_id;one_depth	1 entities	$$44.6 \mathrm{ms} \pm 203 \mathrm{μs}\left({\color{gray}-0.319 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	10 entities	$$80.6 \mathrm{ms} \pm 322 \mathrm{μs}\left({\color{gray}-4.243 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	25 entities	$$48.9 \mathrm{ms} \pm 232 \mathrm{μs}\left({\color{gray}-4.743 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	5 entities	$$50.3 \mathrm{ms} \pm 260 \mathrm{μs}\left({\color{gray}-1.056 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	50 entities	$$60.2 \mathrm{ms} \pm 274 \mathrm{μs}\left({\color{gray}-3.548 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	1 entities	$$45.5 \mathrm{ms} \pm 208 \mathrm{μs}\left({\color{gray}-1.551 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	10 entities	$$399 \mathrm{ms} \pm 902 \mathrm{μs}\left({\color{gray}-4.129 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	25 entities	$$99.5 \mathrm{ms} \pm 419 \mathrm{μs}\left({\color{gray}-1.397 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	5 entities	$$82.6 \mathrm{ms} \pm 330 \mathrm{μs}\left({\color{gray}-0.973 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	50 entities	$$284 \mathrm{ms} \pm 707 \mathrm{μs}\left({\color{lightgreen}-10.615 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	1 entities	$$19.4 \mathrm{ms} \pm 85.2 \mathrm{μs}\left({\color{gray}-3.204 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	10 entities	$$20.0 \mathrm{ms} \pm 109 \mathrm{μs}\left({\color{gray}-3.537 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	25 entities	$$19.9 \mathrm{ms} \pm 118 \mathrm{μs}\left({\color{gray}-3.018 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	5 entities	$$20.0 \mathrm{ms} \pm 99.7 \mathrm{μs}\left({\color{gray}-1.416 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	50 entities	$$24.3 \mathrm{ms} \pm 156 \mathrm{μs}\left({\color{gray}-1.633 \mathrm{\%}}\right) $$	Flame Graph

read_scaling_linkless

Function	Value	Mean	Flame graphs
entity_by_id	1 entities	$$19.2 \mathrm{ms} \pm 131 \mathrm{μs}\left({\color{gray}-1.289 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	10 entities	$$19.3 \mathrm{ms} \pm 105 \mathrm{μs}\left({\color{gray}-0.936 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	100 entities	$$19.2 \mathrm{ms} \pm 81.1 \mathrm{μs}\left({\color{gray}-0.231 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	1000 entities	$$19.7 \mathrm{ms} \pm 163 \mathrm{μs}\left({\color{gray}0.337 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	10000 entities	$$25.8 \mathrm{ms} \pm 207 \mathrm{μs}\left({\color{gray}1.73 \mathrm{\%}}\right) $$	Flame Graph

representative_read_entity

Function	Value	Mean	Flame graphs
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/block/v/1	$$32.4 \mathrm{ms} \pm 267 \mathrm{μs}\left({\color{gray}-3.096 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/book/v/1	$$34.8 \mathrm{ms} \pm 255 \mathrm{μs}\left({\color{gray}3.63 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/building/v/1	$$35.4 \mathrm{ms} \pm 248 \mathrm{μs}\left({\color{red}9.32 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/organization/v/1	$$34.4 \mathrm{ms} \pm 198 \mathrm{μs}\left({\color{gray}2.47 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/page/v/2	$$35.1 \mathrm{ms} \pm 275 \mathrm{μs}\left({\color{gray}3.67 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/person/v/1	$$33.9 \mathrm{ms} \pm 286 \mathrm{μs}\left({\color{gray}-0.029 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/playlist/v/1	$$34.3 \mathrm{ms} \pm 240 \mathrm{μs}\left({\color{gray}2.38 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/song/v/1	$$33.7 \mathrm{ms} \pm 240 \mathrm{μs}\left({\color{gray}0.788 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/uk-address/v/1	$$33.6 \mathrm{ms} \pm 250 \mathrm{μs}\left({\color{gray}1.01 \mathrm{\%}}\right) $$	Flame Graph

representative_read_entity_type

Function	Value	Mean	Flame graphs
get_entity_type_by_id	Account ID: bf5a9ef5-dc3b-43cf-a291-6210c0321eba	$$8.30 \mathrm{ms} \pm 42.0 \mathrm{μs}\left({\color{gray}0.111 \mathrm{\%}}\right) $$	Flame Graph

representative_read_multiple_entities

Function	Value	Mean	Flame graphs
entity_by_property	traversal_paths=0	0	$$89.2 \mathrm{ms} \pm 363 \mathrm{μs}\left({\color{gray}-1.470 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=255	1,resolve_depths=inherit:1;values:255;properties:255;links:127;link_dests:126;type:true	$$140 \mathrm{ms} \pm 534 \mathrm{μs}\left({\color{gray}-0.452 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:0;link_dests:0;type:false	$$96.7 \mathrm{ms} \pm 478 \mathrm{μs}\left({\color{gray}0.100 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:1;link_dests:0;type:true	$$104 \mathrm{ms} \pm 364 \mathrm{μs}\left({\color{gray}-0.283 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:2;links:1;link_dests:0;type:true	$$113 \mathrm{ms} \pm 561 \mathrm{μs}\left({\color{gray}-0.568 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:2;properties:2;links:1;link_dests:0;type:true	$$119 \mathrm{ms} \pm 502 \mathrm{μs}\left({\color{gray}-1.262 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=0	0	$$98.6 \mathrm{ms} \pm 376 \mathrm{μs}\left({\color{gray}-0.921 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=255	1,resolve_depths=inherit:1;values:255;properties:255;links:127;link_dests:126;type:true	$$127 \mathrm{ms} \pm 462 \mathrm{μs}\left({\color{gray}-0.287 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:0;link_dests:0;type:false	$$106 \mathrm{ms} \pm 443 \mathrm{μs}\left({\color{gray}-0.118 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:1;link_dests:0;type:true	$$114 \mathrm{ms} \pm 399 \mathrm{μs}\left({\color{gray}-0.405 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:2;links:1;link_dests:0;type:true	$$117 \mathrm{ms} \pm 393 \mathrm{μs}\left({\color{gray}-0.906 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:2;properties:2;links:1;link_dests:0;type:true	$$117 \mathrm{ms} \pm 475 \mathrm{μs}\left({\color{gray}-0.155 \mathrm{\%}}\right) $$

scenarios

Function	Value	Mean	Flame graphs
full_test	query-limited	$$140 \mathrm{ms} \pm 424 \mathrm{μs}\left({\color{gray}3.99 \mathrm{\%}}\right) $$	Flame Graph
full_test	query-unlimited	$$150 \mathrm{ms} \pm 511 \mathrm{μs}\left({\color{gray}2.69 \mathrm{\%}}\right) $$	Flame Graph
linked_queries	query-limited	$$107 \mathrm{ms} \pm 419 \mathrm{μs}\left({\color{gray}-0.245 \mathrm{\%}}\right) $$	Flame Graph
linked_queries	query-unlimited	$$591 \mathrm{ms} \pm 3.32 \mathrm{ms}\left({\color{gray}1.82 \mathrm{\%}}\right) $$	Flame Graph