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Add SMT-LIB choice support via array OP_CHOICE and instantiate choice axioms in array solvers (#9649)

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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>
This commit is contained in:
Copilot 2026-05-27 10:05:06 -07:00 • committed by GitHub
parent 690cdd3f25
commit 51da9db615
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12 changed files with 124 additions and 17 deletions
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src/smt/theory_array.h
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@ -28,7 +28,7 @@ namespace smt {
unsigned m_num_axiom1, m_num_axiom2a, m_num_axiom2b, m_num_extensionality, m_num_eq_splits;
unsigned m_num_map_axiom, m_num_default_map_axiom;
unsigned m_num_select_const_axiom, m_num_default_store_axiom, m_num_default_const_axiom, m_num_default_as_array_axiom;
unsigned m_num_select_as_array_axiom, m_num_default_lambda_axiom;
unsigned m_num_select_as_array_axiom, m_num_default_lambda_axiom, m_num_choice_axiom;
void reset() { memset(this, 0, sizeof(theory_array_stats)); }
theory_array_stats() { reset(); }
};
@ -115,4 +115,3 @@ namespace smt {
};