Rewrite maps, tuples, lists as BDDs. Performance improvements. #14693

gldubc · 2025-08-04T16:38:04Z

Changing the representation of maps, tuples to instead use trees (binary decision diagrams).

As we use more and more the difference operator in the type system (e.g. to compute fun_from_inferred_clauses(args_clauses) for inferred function types from patterns), the "DNF" representation started running into pathological cases and hog out time during emptiness checks, and printing.

The BDD is now used for set operations and subtyping, and translated (using previous logic and simplications) to DNF for printing and type operations like map fetch.

The BDD representation is common to maps, tuples, lists and functions. Some functions are generic (called bdd_difference, bdd_intersection, ...).

We also changes some algorithms:

tuple_eliminate_negation was not generating disjoint tuples. It now does, which greatly improves performance and printing quality.
-tuple_empty? now uses the same logic, this improves performances.
pivot_overlapping_clauses algorithm was not generating disjoint tuples. It now does.
The computation of subtyping for functions and function application is too slow for large arrow intersections (>30). This adds a special case apply_disjoint, when the functions are disjoint and non-empty (as produced by fun_from_inferred_clauses, for instance), which is much faster.

- Updated the representation of non-empty lists and empty intersections/differences to use BDD structures. - Introduced new functions for BDD operations including list_get, list_get_pos, and list_all? for better handling of BDD paths. - Modified list normalization and difference functions to work with BDDs

…alize` and `fun_get`

lib/elixir/lib/module/types/descr.ex

sabiwara · 2025-09-02T04:48:04Z

Note: I haven't reviewed the code or investigated properly yet, but I tried the branch on a project and noticed:

that Ecto.Repo seems to take several minutes to verify
Inspect.Algebra.is_doc/1 takes ~10s to check

  defguard is_doc(doc)
           when is_list(doc) or is_binary(doc) or doc == :doc_line or
                  (is_tuple(doc) and elem(doc, 0) in @docs)

Removing one element from @docs moves it down to ~2s, adding one element makes it ~45s.
It seems to be trying to type the whole AST tree of the guard macro.

josevalim · 2025-09-02T08:19:29Z

I beleive the issue is the usage of comparison in the BDD. For example, maps only use comparisons up to 32 terms, because from them on, the linear time of each comparison becomes too high.

lib/elixir/lib/module/types/descr.ex

sabiwara

I noticed that to_quoted can now be very verbose for unions since it adds these and not - technically correct but not very useful - which I'm worried might harm readability:

union(
  open_map(a: number(), b: binary()),
  open_map(a: integer())
)

# 1.18
%{..., a: float() or integer()}

# this branch
%{..., a: float() or integer(), b: binary()} or
  (%{..., a: integer()} and not %{..., a: float() or integer(), b: binary()})

lib/elixir/lib/module/types/descr.ex

Co-authored-by: Jean Klingler <[email protected]>

gldubc · 2025-09-17T13:28:37Z

I noticed that to_quoted can now be very verbose for unions since it adds these and not - technically correct but not very useful - which I'm worried might harm readability:
union(
  open_map(a: number(), b: binary()),
  open_map(a: integer())
)

# 1.18
%{..., a: float() or integer()}

# this branch
%{..., a: float() or integer(), b: binary()} or
  (%{..., a: integer()} and not %{..., a: float() or integer(), b: binary()})

This is a drawback of the BDD representation. It is possible, I think, to get rid of those by using a more sophisticated normalization algorithm for printing (that I implemented in the past for a prototype, but not for this version).

there is now map_dnf_fetch_static to avoid calling map_bdd_get in a loop. also, renamed map_bdd_get to map_bdd_to_dnf (avoids confusion with get operation on maps)

michallepicki · 2025-09-26T11:36:17Z

After reporting #14790 I checked with this branch merged to main, and while Oban.Telemetry compilation terminates, our Phoenix projects compilation is extra slow at compiling and then verifying our router modules (I wasn't patient enough to wait for it to terminate on our projects). To reproduce:

mix phx.new thingy
cd thingy
mix phx.gen.html Users users name:string age:integer
mix phx.gen.html Users2 users2 name:string age:integer
# ... repeat a few times
mix phx.gen.html Users10 users10 name:string age:integer

and add this to the router under PageController, :home:

resources "/users", UserController
resources "/users2", User2Controller
resources "/users3", User3Controller
# ...
resources "/users10", User10Controller

Even with 3 resources it's extra slow. Both compilation and verifying takes a long time: when using sufficiently small number of routes and waiting long enough, after Compiling lib/thingy_web/router.ex (it's taking more than 10s), there will be another message about Verifying ThingyWeb.Router (it's taking more than 10s).

I am on Erlang 27.3.4.2

I hope this helps, I am sorry I was not able to narrow it down further 🙏🏻

sabiwara · 2025-09-27T04:44:10Z

Compiling lib/thingy_web/router.ex (it's taking more than 10s)

I can reproduce this. I seems it's stuck trying to type FooWeb.Router.call/2 which code AST is:

%{method: method, path_info: path_info, host: host} = conn = prepare(conn)
decoded = Enum.map(path_info, &URI.decode/1)

case __match_route__(decoded, method, host) do
  {metadata, prepare, pipeline, plug_opts} ->
    Phoenix.Router.__call__(conn, metadata, prepare, pipeline, plug_opts)

  :error ->
    :erlang.error(Phoenix.Router.NoRouteError.exception(conn: conn, router: FooWeb.Router))
end

I seems to spend a lot of time in map_line_empty?, here is a slow example taking more than half a second (need to make the fun public first: def pub_map_line_empty?(tag, fields, neg), do: map_line_empty?(tag, fields, neg):

 Module.Types.Descr.pub_map_line_empty?(
    :closed,
    %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.EpsilonController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{atom: {:union, %{api: [], require_authenticated_user: []}}}, %{bitmap: 2}},
           :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{create: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.OmegaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{new: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.OmegaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{index: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.OmegaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{create: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.PiController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{new: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.PiController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{index: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.PiController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{create: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.DeltaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{new: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.DeltaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{index: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.DeltaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{create: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.GammaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{new: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.GammaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{index: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.GammaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{create: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.AlphaModelController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{index: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.AlphaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{new: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.AlphaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{index: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.AlphaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{create: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.BetaController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list:
          {{%{
              atom: {:union, %{api: [], require_authenticated_user: []}}
            }, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{list_checked_out: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.UserSessionController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list: {{%{atom: {:union, %{browser: []}}}, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{new: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.UserSessionController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list: {{%{atom: {:union, %{browser: []}}}, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{delete: []}}}
    },
    closed: %{
      log: %{atom: {:union, %{debug: []}}},
      plug: %{atom: {:union, %{FooWeb.UserSessionController => []}}},
      conn: %{atom: {:union, %{nil: []}}},
      path_params: %{map: {{:closed, %{}}, :bdd_top, :bdd_bot}},
      route: %{bitmap: 1},
      pipe_through: %{
        list: {{%{atom: {:union, %{browser: []}}}, %{bitmap: 2}}, :bdd_top, :bdd_bot}
      },
      plug_opts: %{atom: {:union, %{create: []}}}
    }
  )

The key change is that map_line_empty was checking the whole tree no matter what, due to an or condition that should not be checked as the previous Enum.all? are enough to conclude. Also clarified the invariant that allows not to check the positives fields as a base case (still in map_line_empty?)

josevalim · 2025-09-28T17:04:49Z

💚 💙 💜 💛 ❤️

gldubc added 9 commits July 24, 2025 16:56

Fix list_get_pos bug

d3fc8b2

Add test

09a8599

Add test

5a65190

Functioning map BDDs

b03ed23

Rewrite of every type as bdd

d6f0217

Cleanup

415a3a2

Updated the handling of positive and negative functions in `fun_norm…

ec5906b

…alize` and `fun_get`

Remove commented-out test

f933a16

josevalim mentioned this pull request Aug 12, 2025

Compilation gets stuck on Oban.Telemetry for 1.19.0-rc-0 OTP 28 #14709

Closed

josevalim and others added 2 commits September 1, 2025 15:42

Move test to proper clause

654b2b5

Fixed a bug on disjoint?\2 due to incorrect special cases

67e8ab5

josevalim reviewed Sep 1, 2025

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gldubc added 2 commits September 1, 2025 19:00

Optimization suggested

bc49349

Optimize pop_elem function

92a5411

josevalim reviewed Sep 2, 2025

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josevalim added 2 commits September 2, 2025 18:48

Simplify element intersection

8118ab4

Remove empty list check on intersections/differences

1123a6f

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Use consistent naming

d4c670b

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josevalim and others added 5 commits September 17, 2025 15:15

Bump checker version as representation changed

3529577

Remove unused function

4a0c84b

Make map_empty? short-circuiting

8664e7f

Sort map_union to preserve invariant

fd486f7

Co-authored-by: Jean Klingler <[email protected]>

Update comment

7765fea

Co-authored-by: Jean Klingler <[email protected]>

gldubc added 9 commits September 17, 2025 15:42

Add test for map representation invariant

f541e71

Formatting

272c4f0

Fix test

c941281

Remove higher order implementation for tuple_normalize

95412fd

Improve map_fetch static, removing circularity

13dedd4

there is now map_dnf_fetch_static to avoid calling map_bdd_get in a loop. also, renamed map_bdd_get to map_bdd_to_dnf (avoids confusion with get operation on maps)

Unify renaming bdd_get to bdd_to_dnf

4666d36

Make fun_empty? short-circuiting

7b780c1

Naming fun_line_empty? for precision

8dfaa10

Remove high order list_empty? implem

8221515

This was referenced Sep 22, 2025

infinite loop when compiling oban telemetry #14785

Closed

Verification hangs with :telemetry specific case on main #14786

Closed

main branch: compilation stuck at Verifying Oban.Telemetry #14790

Closed

gldubc and others added 2 commits September 28, 2025 18:49

Use simpler algorithm for inferred clauses

c1c7249

josevalim merged commit 5a2a5ae into elixir-lang:main Sep 28, 2025
13 checks passed

josevalim deleted the lists-as-bdd branch September 28, 2025 17:05

josevalim restored the lists-as-bdd branch September 28, 2025 17:05

josevalim pushed a commit that referenced this pull request Sep 28, 2025

Rewrite maps, tuples, lists as BDDs and improve performance (#14693)

5b2f9c9

gldubc mentioned this pull request Sep 29, 2025

Using lazy BDD structure for functions #14799

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Rewrite maps, tuples, lists as BDDs. Performance improvements. #14693

Rewrite maps, tuples, lists as BDDs. Performance improvements. #14693

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Rewrite maps, tuples, lists as BDDs. Performance improvements. #14693

Rewrite maps, tuples, lists as BDDs. Performance improvements. #14693

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