feat(joinir): Phase 197 Pattern4 multi-carrier exit fix & AST-based update

Phase 197-B: Multi-Carrier Exit Mechanism
- Fixed reconnect_boundary() to use remapper for per-carrier exit values
- ExitMeta now uses carrier_param_ids (Jump arguments) instead of
  carrier_exit_ids (k_exit parameters)
- Root cause: k_exit parameters aren't defined when JoinIR functions
  merge into host MIR

Phase 197-C: AST-Based Update Expression
- LoopUpdateAnalyzer extracts update patterns from loop body AST
- Pattern4 lowerer uses UpdateExpr for semantically correct RHS
- sum = sum + i → uses i_next (current iteration value)
- count = count + 1 → uses const_1

Files modified:
- src/mir/builder/control_flow/joinir/merge/mod.rs
- src/mir/join_ir/lowering/loop_with_continue_minimal.rs
- src/mir/join_ir/lowering/loop_update_analyzer.rs (new)

Test results:
- loop_continue_multi_carrier.hako: 25, 5 ✅
- loop_continue_pattern4.hako: 25 ✅

Pattern 1–4 now unified with:
- Structure-based detection (LoopFeatures + classify)
- Carrier/Exit metadata (CarrierInfo + ExitMeta)
- Boundary connection (JoinInlineBoundary + LoopExitBinding)
- AST-based update expressions (LoopUpdateAnalyzer)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

src/mir/builder/control_flow/joinir/patterns/pattern4_with_continue.rs

@@ -99,6 +99,7 @@ impl MirBuilder {
         debug: bool,
     ) -> Result<Option<ValueId>, String> {
         use crate::mir::join_ir::lowering::carrier_info::{CarrierInfo, CarrierVar};
+        use crate::mir::join_ir::lowering::loop_update_analyzer::LoopUpdateAnalyzer;
         use crate::mir::join_ir::lowering::loop_with_continue_minimal::lower_loop_with_continue_minimal;
         use crate::mir::join_ir_vm_bridge::convert_join_module_to_mir_with_meta;
         use crate::mir::BasicBlockId;
@@ -143,6 +144,14 @@ impl MirBuilder {
             carrier_info.carriers.iter().map(|c| &c.name).collect::<Vec<_>>()
         );
 
+        // Phase 197: Analyze carrier update expressions from loop body
+        let carrier_updates = LoopUpdateAnalyzer::analyze_carrier_updates(_body, &carrier_info.carriers);
+
+        eprintln!("[pattern4] Analyzed {} carrier update expressions", carrier_updates.len());
+        for (carrier_name, update_expr) in &carrier_updates {
+            eprintln!("[pattern4]   {} → {:?}", carrier_name, update_expr);
+        }
+
         // Phase 195: Use unified trace
         trace::trace().varmap("pattern4_start", &self.variable_map);
 
@@ -162,8 +171,8 @@ impl MirBuilder {
             variable_definitions: BTreeMap::new(),
         };
 
-        // Call Pattern 4 lowerer
-        let (join_module, exit_meta) = match lower_loop_with_continue_minimal(scope) {
+        // Call Pattern 4 lowerer (Phase 197: pass carrier_updates for semantic correctness)
+        let (join_module, exit_meta) = match lower_loop_with_continue_minimal(scope, &carrier_info, &carrier_updates) {
             Some(result) => result,
             None => {
                 // Phase 195: Use unified trace
@@ -238,8 +247,17 @@ impl MirBuilder {
 
         // Merge JoinIR blocks into current function
         // Phase 196: Use dynamically generated exit_bindings and host_inputs
+        // Build join_inputs dynamically to match host_inputs length:
+        // [ValueId(0), ValueId(1), ValueId(2), ...] for i + N carriers
+        let mut join_inputs = vec![ValueId(0)];  // ValueId(0) = i_init in JoinIR
+        for idx in 0..carrier_info.carriers.len() {
+            join_inputs.push(ValueId((idx + 1) as u32));  // ValueId(1..N) = carrier inits
+        }
+
+        eprintln!("[pattern4] join_inputs: {:?}", join_inputs.iter().map(|v| v.0).collect::<Vec<_>>());
+
         let boundary = crate::mir::join_ir::lowering::inline_boundary::JoinInlineBoundary::new_with_exit_bindings(
-            vec![ValueId(0), ValueId(1)],      // JoinIR's main() parameters (i_init, sum_init)
+            join_inputs,                       // JoinIR's main() parameters (dynamic)
             host_inputs,                       // Host's loop variables (dynamic)
             exit_bindings,
         );