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Author SHA1 Message Date
davedets
69cd7e0c4c
Fixes necessary to compile z3 included in clang-tidy via FetchContents. (#9768)
The page
https://github.com/Z3Prover/z3/blob/master/README-CMake.md#adding-z3-as-a-dependency-to-a-cmake-project
advises using the CMake FetchContent feature to include z3 as source
into other CMake project. I'm trying to do this to use Z3 within a
ClangTidy checker. This is one of a series of PR's aimed at getting Z3
to compile cleanly when included this way.

This initial PR fixes all the errors, allowing the compilation to
succeed. Subsequent diffs will address warnings.

I tested only the CMake compilation, on a Mac.

*Missing Z3_THROWs*

Update z3++.h to use Z3_THROW in a couple of places. Clang compiles with
exceptions disabled so we get messages like:

```
/Users/daviddetlefs/llvm-project/build_dbg/_deps/z3-src/src/api/c++/z3++.h:4928:17: error: cannot use 'throw' with exceptions disabled4928 |                 throw exception("rcf_num objects from different contexts");
```

NOTE TO REVIEWERS: I'm not complete clear on the usage conventions for
Z3_THROW. With exception disabled, it seems like the throwing function
will just continue. If there's somethign else that should be done, like
setting some error state, please let me know.

*CMake component name collision*

There was an error at the CMake level, a name collision (on "opt").
Apparently CMake components are named using a flat namespace, so it's
easy to see how this could occur. It seems to me that the right global
way to fix this would be to encourage people to use some form of
"qualified name" convention in naming their component. The fix I chose
was a local version of this, changing the Z3 component name to z3_opt.
(It didn't seem feasible to make the change in clang.)

NOTE TO REVIEWERS: If you think this is OK, please let me know if

a) You'd like me to also change the name of the opt directory, to keep
thecomponent-name == directory-name invariant, and

b) You'd like me to make this z3_ change more globally, to future-proof
(somewhat) against similar component name collisions.
2026-06-08 19:44:01 -07:00
Copilot
49014fe302
Fix right-side can_add indexing in sls_seq_plugin edit-distance repair (#9773)
`seq_plugin::edit_distance_with_updates` used the left-string DP index
when checking whether the right string could accept an insertion from
the `d[i][j - 1]` transition. This miscomputed updateable edit distance
and could suppress valid repair proposals when `i != j`.

- **Bug fix**
- Change the right-side insertion guard in
`src/ast/sls/sls_seq_plugin.cpp` from `b.can_add(i - 1)` to `b.can_add(j
- 1)`.
- This aligns the mutability check with the DP transition being
evaluated and with the existing update-generation logic below it.

- **Regression coverage**
- Add a focused test in `src/test/sls_seq_plugin.cpp` for an asymmetric
variable/value layout on the right-hand side.
- The test asserts that the repair logic admits the right-side add at `j
- 1`, which is the case that the previous index mixup could reject.

- **Reference**
  - The updated condition now matches the intended transition semantics:

```cpp
if (d[i][j - 1] < u[i][j] && b.can_add(j - 1)) {
    m_string_updates.reset();
    u[i][j] = d[i][j - 1];
}
```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-06-08 19:36:14 -07:00
Lev Nachmanson
aa872bd289
spacer: enable model completion in arith qe_project (#9776)
Variables to be projected may not be assigned in the model (e.g.
grounded auxiliary variables that are don't-cares). Enable model
completion in the arith `qe_project` so their evaluation yields concrete
numerals, matching the behavior of the native MBP arith projector.

Two call sites in `arith_project_util`
(`src/muz/spacer/spacer_qe_project.cpp`) now install a
`model::scoped_model_completion` before evaluating projected variables
against the model.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
2026-06-08 19:35:49 -07:00
Lev Nachmanson
2ed4e90c75
Fix Java UnsatisfiedLinkError on macOS (#7640) (#9027)
On macOS, libz3java.dylib was built without an rpath to find libz3.dylib
in the same directory. When Java loaded the JNI library, the dynamic
linker could not resolve the libz3 dependency, causing
UnsatisfiedLinkError.

Three fixes:
- mk_util.py: add -Wl,-rpath,@loader_path to the macOS JNI link command
- CMakeLists.txt: set MACOSX_RPATH, BUILD_RPATH, INSTALL_RPATH for
z3java target; remove duplicate headerpad block
- update_api.py: improve Native.java error message to show the root
cause from both load attempts instead of only the fallback error

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
2026-06-08 19:35:04 -07:00
Nikolaj Bjorner
1f5132c396 refactor solver to include settable stats 2026-06-07 14:17:38 -07:00
Copilot
d5779a6993
sls_seq_plugin: remove hard aborts in is_sat for str.len and seq.last_indexof (#9736)
`src/ast/sls/sls_seq_plugin.cpp::is_sat()` had two unconditional abort
paths (`VERIFY(false)` and `NOT_IMPLEMENTED_YET()`) reachable from valid
string formulas under SLS. This changes those paths to graceful
repair/fail behavior so SLS can continue search instead of terminating
the process.

- **Length coherence fallback no longer aborts**
- Replaced the terminal `VERIFY(false)` in the `str.len` coherence block
with a normal `return false` repair failure path.
- Effect: failed local repair is propagated to the outer SLS loop
instead of crashing.

- **Implemented `seq.last_indexof` coherence handling**
  - Replaced `NOT_IMPLEMENTED_YET()` with concrete coherence logic:
    - read current `x`, `y`, and `e`,
    - compute `actual = sx.last_indexof(sy)`,
    - update `e` when `e != actual`,
    - otherwise continue.
- Effect: formulas containing `seq.last_indexof` are handled in SLS
coherence checks instead of aborting.

- **No new hard-abort behavior introduced**
- In the new `last_index` block, non-numeral `e` is handled by graceful
`return false` (repair failure), not assertion abort.

```cpp
if (seq.str.is_last_index(e, x, y) && seq.is_string(x->get_sort())) {
    auto sx = strval0(x), sy = strval0(y);
    rational val_e;
    if (!a.is_numeral(ctx.get_value(e), val_e))
        return false;
    rational actual(sx.last_indexof(sy));
    if (val_e == actual) continue;
    update(e, actual);
    return false;
}
```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-06-06 13:26:01 -07:00
Julien Stephan
cf58fa027d
python: make Statistics doctests robust to optional ":time" counter (#9729)
The doctests for Statistics.__len__ and Statistics.__getitem__ in
src/api/python/z3/z3.py asserted a fixed counter count (len(st) == 7).
This is fragile because the ":time" entry is only added to statistics
when the elapsed wall-clock time of check() is non-zero (see
collect_timer_stats in src/solver/check_sat_result.h). On fast native
builds, ":time" rounds to 0 and is omitted; under slow environments
(e.g. riscv64 under qemu emulation), it becomes non-zero and is
included, changing len(st).

Fix this by checking the presence of statistics rather than an exact
count.

Signed-off-by: Julien Stephan <jstephan@baylibre.com>
2026-06-06 13:24:19 -07:00
Copilot
2f280a7baf
sls_seq_plugin: fix breakcontinue in add_substr_edit_updates (#9735)
`add_substr_edit_updates` uses a `HashSet` to deduplicate substrings of
`val_other`, but on a duplicate hit it `break`s the inner loop instead
of skipping just that entry. This causes all longer substrings from the
same starting position to be silently dropped as repair candidates.

## Change

- **`src/ast/sls/sls_seq_plugin.cpp`** — replace `break` with `continue`
in the inner substring-enumeration loop.

```cpp
// Before — exits the inner loop on first duplicate, missing e.g. "ab" in "aab"
if (set.contains(sub))
    break;

// After — skips only the duplicate, continues with longer substrings at same offset
if (set.contains(sub))
    continue;
```

For `val_other = "aab"`, the old code never proposed `"ab"` (i=1, j=2)
as a repair candidate because the duplicate `"a"` (i=1, j=1) terminated
the inner loop prematurely.

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-06-06 13:23:44 -07:00
Copilot
e561387900
Handle choice_k in SMT pretty-printer switch to remove macOS -Wswitch warning (#9734)
`src/ast/ast_smt_pp.cpp` emitted a compiler warning on macOS because
`quantifier_kind::choice_k` was not handled in
`smt_printer::visit_quantifier`. This change makes the switch exhaustive
and preserves printer behavior for existing quantifier kinds.

- **Problem**
- `visit_quantifier` handled `forall_k`, `exists_k`, and `lambda_k`, but
omitted `choice_k`, triggering `-Wswitch`.

- **Change**
- Added an explicit `choice_k` branch in the quantifier-kind switch in
`/tmp/workspace/Z3Prover/z3/src/ast/ast_smt_pp.cpp`.
- The branch prints `choice` in SMT output, consistent with how other
quantifier headers are emitted.

- **Code snippet**
  ```cpp
  switch (q->get_kind()) {
  case forall_k: m_out << "forall "; break;
  case exists_k: m_out << "exists "; break;
  case lambda_k: m_out << "lambda "; break;
  case choice_k: m_out << "choice "; break;
  }
  ```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-06-06 11:37:56 -07:00
Can Cebeci
5ebf5a0d9f
Fix quoting in low-level pretty printer (#9716)
Co-authored-by: Can Cebeci <t-cancebeci@microsoft.com>
2026-06-04 15:48:27 -07:00
Hari Govind V K
98ce7f5d05
Cleanup thanks to Copilot (#9709) 2026-06-04 10:46:33 -07:00
Can Cebeci
b2401b87db
Remove redundant min_gen_match search (#9696)
While working on https://github.com/Z3Prover/z3/pull/9405, I noticed
that euf_mam.cpp code was slightly out of sync with mam.cpp and did some
redundant work.

Co-authored-by: Can Cebeci <t-cancebeci@microsoft.com>
2026-06-03 13:36:51 -07:00
Can Cebeci
14746d7fb6
Update used_enodes properly (#9695)
https://github.com/Z3Prover/z3/pull/9405 made the trace report
used_enodes incorrectly, since the previous code relied on
update_max_generation to maintain the relevant data structure. This
should fix it.

Co-authored-by: Can Cebeci <t-cancebeci@microsoft.com>
2026-06-03 13:36:37 -07:00
Copilot
d64ce41b2e
Remove unused defined_names artifacts and simplify fingerprint_set::contains (#9702)
Cleans up dead code left by the "remove side definitions" refactoring
(a0a3047).

- **`smt_model_checker.cpp`** — Remove `defined_names dn(m)` variable
that was declared but never used
- **`smt_model_checker.h`** — Drop the now-unnecessary `#include
"ast/normal_forms/defined_names.h"`
- **`fingerprints.cpp`** — Collapse redundant tail in
`fingerprint_set::contains`:
  ```cpp
  // Before
  if (m_set.contains(d))
      return true;
  return false;

  // After
  return m_set.contains(d);
  ```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-06-03 08:16:46 -07:00
Clément Pit-Claudel
1d706e875c
Handle SIGXCPU like a regular timeout (#9697)
Z3's -T measures wall clock time, whereas `ulimit -t` measures CPU time.
Currently, an expired ulimit timeout crashes Z3 without printing
statistics; this patch makes it react cleanly (just as if it has
encountered a regular timeout) to SIGXCPU, the signal that ulimit sends
before sending SIGKILL.
2026-06-03 07:26:38 -07:00
Hari Govind V K
922f49e187
Fix MBP QEL soundness bug in datatype accessor elimination (#9571) (#9692)
Two fixes for mbp_dt_tg::apply() when encountering an accessor whose
argument has a different constructor in the model:

1. Don't call rm_accessor (which would assert a contradictory
recognizer, making the formula false). This prevents the original bug
where QEL returned 'false' for satisfiable formulas.

2. Branch on the model-assigned constructor for the accessor's argument.

The correct output should include the literal introduced in (2).
However, this fix does not produce it. Spacer is sound with this
over-approximation, as long as the counter example does not depend on
value of mismatched accessors (e.g. (tl nil)).

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
2026-06-03 07:23:21 -07:00
Nikolaj Bjorner
a0a3047e36 remove side definitions 2026-06-02 21:43:55 -07:00
Nikolaj Bjorner
77f8b33794 re-enable unit tests 2026-06-02 10:39:41 -07:00
Nikolaj Bjorner
2dbe233f6a fix condition that skipped mbqi
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-06-02 10:38:52 -07:00
Nikolaj Bjorner
eaf7562a1d disable test in tptp, move to native lambdas 2026-06-02 10:38:51 -07:00
Nikolaj Bjorner
3e0a350411
Comment out ho_curried_application and ho_choice_expression tests
Comment out two test functions for debugging purposes.
2026-06-02 08:47:43 -07:00
Nikolaj Bjorner
78a7b4d3a6
Update model_core.h 2026-06-01 19:47:40 -07:00
Nikolaj Bjorner
358378a6f0 remove tptp from all
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-06-01 19:36:18 -07:00
Nikolaj Bjorner
94b981024e set up udoc relation to use datalog engine 2026-06-01 19:06:25 -07:00
Nikolaj Bjorner
c4366e57f8
Update udoc_relation.cpp 2026-06-01 17:22:06 -07:00
Copilot
947af23fc4
[code-simplifier] Align choice axiom naming in theory_array_full (#9660)
This simplifies the recent `choice` axiom path in the SMT array solver
for consistency with the SAT-side implementation. The change is purely
structural: align local naming with the quantifier body it represents,
inline a single-use literal, and remove stray whitespace in the array
decl header.

- **Choice axiom cleanup**
- Rename the local implication term in
`theory_array_full::instantiate_choice_axiom` from `ax` to `body`
- Match the naming already used in
`sat/smt/array_axioms.cpp::assert_choice_axiom`

- **Single-use literal inlining**
- Replace the temporary `literal l = mk_literal(q); assert_axiom(l);`
with a direct call
  - Reduce noise without changing behavior

- **Header whitespace cleanup**
  - Remove trailing whitespace in `src/ast/array_decl_plugin.h`

```c++
expr_ref body(m.mk_implies(px, pc), m);
expr_ref q(m.mk_forall(1, &x_sort, &x_name, body), m);
ctx.get_rewriter()(q);
assert_axiom(mk_literal(q));
```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-06-01 16:03:42 -07:00
Can Cebeci
8ddd435835
Fix misleading generation number in trace (#9687)
Current implementation prints 0 when the cached generation is used
2026-06-01 16:00:59 -07:00
Nikolaj Bjorner
d025b34606 prepare for enodes over lambdas 2026-06-01 13:00:35 -07:00
Nikolaj Bjorner
705569df24 add include directive 2026-06-01 11:39:18 -07:00
Nikolaj Bjorner
ebdf031c8f ensure engine is datalog for dl_table and dl_util tests 2026-05-31 15:32:23 -07:00
Nikolaj Bjorner
24e5a6ae3f ensure base class has propagation
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-05-30 22:21:15 -07:00
Nikolaj Bjorner
a595e98707 fix regression: m_tmp_diseq has 0 arguments, you have to access the expression
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-05-30 18:57:21 -07:00
Nikolaj Bjorner
dbe986fdf7 move closure conversion to solver internalization
- only the internalizer performs closure conversion
- theory_array treats propagation of lambdas similar to stores
- ho_matcher treats top-level flex patterns as first-order
- pattern-inference fix to handle quantifiers (lambdas) in patterns that are computed
2026-05-30 18:41:37 -07:00
Nikolaj Bjorner
2cc4422018 use expr based access to enodes to allow for storing first-class lambas 2026-05-30 15:13:08 -07:00
Nikolaj Bjorner
30df8e7ece build warnings 2026-05-29 10:17:46 -07:00
Nikolaj Bjorner
48bcee8e62 add lambda-t case in addition to p-lambda case 2026-05-29 01:18:34 -07:00
Copilot
b74e35f4fb
Fix mpz_manager leak in algebraic root comparison (#9654)
A `root-obj`-driven unsat case was exiting with a leaked `mpz_manager`
allocation even though solver output was correct. The leak came from
temporary rational bounds created during algebraic-number comparison and
not released before shutdown.

- **Root cause**
- `algebraic_numbers::compare_core()` materialized interval bounds as
raw `mpq` temporaries.
- Those temporaries could allocate backing `mpz` storage, but their
lifetime was not tied to the manager, so the allocator retained leaked
cells at process exit.

- **Change**
- Replace the raw `mpq` temporaries with `scoped_mpq` in
`/src/math/polynomial/algebraic_numbers.cpp`.
- This keeps the comparison logic unchanged while making temporary bound
conversion use RAII-managed cleanup.

- **Effect**
- `root-obj` comparisons no longer leave `mpz_manager` allocations
behind.
- Solver behavior is unchanged; the fix is limited to temporary numeral
lifetime management.

```c++
- mpq l_a, u_a, l_b, u_b;
+ scoped_mpq l_a(qm()), u_a(qm()), l_b(qm()), u_b(qm());
```

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-05-28 09:06:05 -07:00
Nikolaj Bjorner
0b56db7f07 fix #9657 2026-05-28 09:01:48 -07:00
Nikolaj Bjorner
b34a7b4319 use trail stack from context for ho-matcher 2026-05-28 07:57:07 -07:00
Nikolaj Bjorner
9d09a050e8 use max-top-generation
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-05-27 14:37:37 -07:00
Nikolaj Bjorner
17c6e0729b control recursion depth for check function 2026-05-27 14:29:53 -07:00
Nikolaj Bjorner
5fe4d88d43 recognize ubv_to_int as part of BV logic 2026-05-27 13:08:54 -07:00
Copilot
51da9db615
Add SMT-LIB choice support via array OP_CHOICE and instantiate choice axioms in array solvers (#9649)
This change wires SMT-LIB Hilbert choice parsing to a concrete
array-theory operator and ensures both array backends enforce the
expected semantic axiom. Previously, `(choice ((x T)) phi)` parsed as
NYI and had no solver-side instantiation path.

- **Parser: lower `choice_k` into array `OP_CHOICE`**
- `pop_quant_frame(choice_k)` now builds `(choice p)` instead of
throwing.
- Added parser include/use of array utilities to construct the term
directly from the generated lambda predicate.

- **Array decl plugin: add `OP_CHOICE` typing + surface syntax**
  - Added declaration support for `choice` with signature:
- `(Array T Bool) -> T` (encoded as `('a -> Bool) -> 'a` in HO view).
- Added recognizer/util helpers (`is_choice`, `mk_choice`) and exposed
`"choice"` in op names.

- **SMT array theory (`theory_array_full`): instantiate choice axiom**
  - Added instantiation for each encountered `choice(p)`:
    - `forall x . p(x) => p(choice(p))`
  - Integrated into internalization/relevancy paths and statistics.

- **SAT/SMT array backend (`sat/smt/array_*`): instantiate choice
axiom**
- Added new axiom record kind for choice, internalization hook,
assertion routine, and diagnostics/stat tracking.
  - Uses the same quantified implication schema as above.

- **Regression coverage**
- Extended SMT2 parser regression with an HO `choice` example to ensure
parser/eval pipeline accepts and processes choice terms.

Example of the now-supported input:

```smt2
(set-logic HO_ALL)
(declare-sort U 0)
(declare-fun P () (-> U Bool))
(assert (exists ((x U)) (P x)))
(assert (= witness (choice ((x U)) (P x))))
```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-05-27 10:05:06 -07:00
yhx-12243
690cdd3f25
fix(make-ts-wrapper): correct out buffer size for WASM (#9644) 2026-05-27 10:03:39 -07:00
Copilot
1564e00215
smt2parser: realign pop_app_frame non-expr_head else block indentation (#9646)
This updates a formatting regression introduced in the `pop_app_frame`
non-`expr_head` path, where block indentation made control flow harder
to read. The patch is whitespace-only and keeps parser behavior
unchanged.

- **What changed**
- Reindented the `else` body in
`src/parsers/smt2/smt2parser.cpp::pop_app_frame` so nested `if/else`
structure is visually unambiguous.
- Removed trailing spaces on the `m_ctx.mk_app(symbol("select"), ...)`
lines in the same block.

- **Scope**
  - No control-flow, data-flow, or API changes.
  - No changes outside `pop_app_frame`.

```cpp
// Before
else {
local l;
if (m_env.find(fr->m_f, l)) {
    ...
}
else {
    ...
}
}

// After
else {
    local l;
    if (m_env.find(fr->m_f, l)) {
        ...
    }
    else {
        ...
    }
}
```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-05-27 09:35:54 -07:00
Nikolaj Bjorner
1aa2158bf4 fix comment
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-05-27 09:02:39 -07:00
Nikolaj Bjorner
5d23edd473 adding choice
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-05-27 08:59:19 -07:00
ValentinPromies
f124cacf1e
fix edge case in algebraic number comparison (#9498)
So far, `algebraic_numbers compare_core ` handles an edge case
incorrectly:
- If the two compared numbers (`a`, `b`) are different,
- the intervals still overlap after refinements, and
- both a and b are a root of the second polynomial (`cell_b->m_p`), e.g.
they are the first and second root

then the method would return `sign_zero` (i.e. "equal"). This behavior
can be replicated with the provided test case (before the fix). This
requires `algebraic.factor=false`, though i first encountered it during
solver runs on QF_NRA instances with the default
`algebraic.factor=true`, which apparently means that the polynomials for
anums are still not always factored.

The fix is to compare the interval bounds of b to a and vice versa. Then
the Sturm-Tarski check is only run if `a` and `b` both lie in the
intersection of the intervals, because only then is it guaranteed to be
correct.
2026-05-27 05:01:47 -07:00
Copilot
316d249b3f
SMT2 front-end: accept HO_ALL and normalize curried expression-head applications (#9636)
The SMT2 front-end rejected valid higher-order inputs using `HO_ALL` and
failed on curried applications where the function position is itself an
expression (e.g., `((transfer top) 0)`).
This update adds `HO_ALL` support and makes curried parsing consistently
lower to implicit `select` chains.

- **Logic recognition**
  - Treat `HO_ALL` as an `ALL`-class logic in SMT logic classification.
- This unblocks `(set-logic HO_ALL)` in the standard SMT2 command path.

- **Curried application parsing**
- Extend application-frame handling to support parenthesized expression
heads, not only symbol heads.
- When the head is an expression, parse application arguments normally
and construct nested implicit selects:
    - `(f a b)` → `(select (select f a) b)`
- Preserve existing behavior for symbol-based applications, qualified
identifiers, and lambda-led forms.

- **Regression coverage**
- Add a focused parser/eval regression using the reported higher-order
case to lock in behavior.

```smt2
(set-logic HO_ALL)
(declare-fun transfer () (-> (-> Int Bool) (-> Int Bool)))
(assert (forall ((P (-> Int Bool))) (=> (P 0) ((transfer P) 0))))
(declare-fun top () (-> Int Bool))
(assert (forall ((x Int)) (top x)))
(assert (not ((transfer top) 0)))
(check-sat)
```

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
2026-05-26 18:39:38 -07:00
Arie
73151f1960
nla_grobner: add mod_residue pattern to propagate_quotients (#9597)
Adds a new lemma pattern to nla_grobner::propagate_quotients that
derives a modular-residue constraint from polynomial divisibility,
filling a gap between quotient1-5 (model-value-driven case splits) and
the polynomials Grobner actually produces on Skolem-encoded mod
arithmetic.

Pattern
-------

For a polynomial p with all-integer free variables and a linear monomial
c_v * v (single integer var), the pattern computes M = gcd(|c_i/c_v|)
over the other monomials and K = c0/c_v for the constant term. When both
are integers, dividing p by c_v gives

    v + M*Q + K = 0   with Q an integer

so v ≡ -K (mod M). The pattern emits the sound disjunctive lemma

    (v < 0)  ∨  (v ≥ M)  ∨  (v = target)

where target = (-K) mod M ∈ [0, M-1]. This encodes "v ∈ target + M·Z" in
a form the LP / SAT layer can refute against current bounds.

Motivation
----------

QF_UFNIA verification benchmarks over fixed-prime modular arithmetic
(e.g. zk applications using the BabyBear prime 2013265921) regularly
produce basis polynomials of the form

    -p*v_div + p*(v_a * v_b) - v_mod = 0

where v_mod is the result of (mod (* v_a v_b) p). The polynomial sits in
the Grobner basis but none of quotient1-5 fires: they all require
specific model-value alignments (r_value == 0, |v_value| > |r_value|,
etc.) that don't hold when all variables in scope are similarly sized
integers in [0, p). The proof spins on interval-tightening lemmas
without ever extracting the modular conclusion.

The author of propagate_quotients flagged this gap with the comment
\"other division lemmas are possible\" preceding the fall-through \"no
lemmas found\" CTRACE. This patch supplies one.

Soundness
---------

The lemma is sound regardless of v's LP bounds — the bound-negation
disjuncts (v < 0) and (v ≥ M) make the disjunction unconditionally true
under the polynomial identity, with v = target as the canonical residue
in [0, M-1]. M is derived from the polynomial's coefficient gcd, not
from any LP-side bound.

Validated under smt.arith.validate=true on the mod-factor-propagation
reproducers (PR #9235 follow-up), zk verifier benchmarks, and a broader
QF_UFNIA sample — 50+ files total, zero validate_conflict() assertion
violations.

Performance
-----------

A model-value gate (skip emission when v's current value already
satisfies one of the disjuncts) prevents the pattern from
short-circuiting the propagate_quotients || propagate_gcd_test ||
propagate_eqs || propagate_factorization || propagate_linear_equations
chain with redundant emissions. Without the gate, a single (v, M,
target) triple can re-emit each Grobner round and starve the downstream
propagators — observed in regression testing as thousands of identical
emissions on a small benchmark, turning a sub-second closure into a
timeout.

On six small mod-factor-propagation reproducers, the patch closes four
cases that previously timed out at 30 s (~1 s typical under the
Grobner-ramped config: smt.arith.nl.gr_q=50,
smt.arith.nl.grobner_eqs_growth=50,
smt.arith.nl.grobner_exp_delay=false, smt.arith.nl.grobner_frequency=1).
The two remaining timeouts in that set are attributable to different
gaps (Boolean-disjunction propagation, and the multi-bounded-mod-result
polynomial shape that needs Grobner over Z/pZ), not to mod_residue
itself.

Diagnostics
-----------

TRACE under the existing 'grobner' tag emits one line per lemma
emission, recording v, M, c_v, c0, and target.

---------

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2026-05-26 18:12:38 -07:00