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>

src/parsers/smt2/smt2parser.cpp

@@ -21,6 +21,7 @@ Revision History:
 #include "ast/bv_decl_plugin.h"
 #include "ast/arith_decl_plugin.h"
 #include "ast/seq_decl_plugin.h"
+#include "ast/array_decl_plugin.h"
 #include "ast/ast_pp.h"
 #include "ast/well_sorted.h"
 #include "ast/rewriter/rewriter.h"
@@ -2140,10 +2141,7 @@ namespace smt2 {
             SASSERT(num_decls <= m_num_bindings);
             m_num_bindings -= num_decls;
             if (fr->m_kind == choice_k) {
-                // create expression (choice new_q)
-                // add to expr_stack().push_back(choice_expr);
-                // 
-                throw default_exception("parsing of choice expressions is NYI");
+                expr_stack().push_back(array_util(m()).mk_choice(new_q));
             }
             else 
                 expr_stack().push_back(new_q);