feat(joinir): Phase 188 StringAppend support in Pattern2/4

- Extended Pattern2/4 whitelist to accept StringLiteral updates
- CarrierUpdateEmitter now emits JoinIR for string append
- Selective Fail-Fast: accept safe patterns, reject complex

Changes:
- pattern2_with_break.rs: StringLiteral whitelist
- pattern4_with_continue.rs: StringLiteral whitelist
- carrier_update_emitter.rs: StringLiteral JoinIR emission

Tests:
- phase188_string_append_char.hako
- phase188_string_append_literal.hako
- 10/10 carrier_update_emitter tests PASS

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

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

src/mir/builder/control_flow/joinir/patterns/pattern2_with_break.rs

@@ -57,7 +57,8 @@ pub fn can_lower(_builder: &MirBuilder, ctx: &super::router::LoopPatternContext)
         return false;
     }
 
-    // Phase 178: Check for string/complex carrier updates
+    // Phase 178/188: Check for complex carrier updates
+    // Phase 188: StringAppendChar/StringAppendLiteral are now allowed
     // Create dummy carriers from body assignment targets for analysis
     let dummy_carriers: Vec<CarrierVar> = ctx.body.iter().filter_map(|node| {
         match node {
@@ -78,15 +79,27 @@ pub fn can_lower(_builder: &MirBuilder, ctx: &super::router::LoopPatternContext)
 
     let updates = LoopUpdateAnalyzer::analyze_carrier_updates(ctx.body, &dummy_carriers);
 
-    // Check if any update is string/complex
+    // Phase 188: Check if any update is complex (reject only UpdateRhs::Other)
+    // Allow: Const (numeric), Variable (numeric/string), StringLiteral
+    // Reject: Other (method calls, nested BinOp)
     for update in updates.values() {
         if let UpdateExpr::BinOp { rhs, .. } = update {
             match rhs {
-                UpdateRhs::StringLiteral(_) | UpdateRhs::Other => {
-                    eprintln!("[pattern2/can_lower] Phase 178: String/complex update detected, rejecting Pattern 2 (unsupported)");
+                UpdateRhs::Const(_) => {
+                    // Numeric: i = i + 1 (allowed)
+                }
+                UpdateRhs::Variable(_) => {
+                    // Phase 188: StringAppendChar: s = s + ch (allowed)
+                    // Or numeric: sum = sum + i (allowed)
+                }
+                UpdateRhs::StringLiteral(_) => {
+                    // Phase 188: StringAppendLiteral: s = s + "x" (allowed)
+                }
+                UpdateRhs::Other => {
+                    // Phase 188: Complex update (method call, nested BinOp) - reject
+                    eprintln!("[pattern2/can_lower] Phase 188: Complex update detected (UpdateRhs::Other), rejecting Pattern 2");
                     return false;
                 }
-                _ => {}
             }
         }
     }

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

@@ -70,7 +70,8 @@ pub fn can_lower(_builder: &MirBuilder, ctx: &super::router::LoopPatternContext)
         return false;
     }
 
-    // Phase 178: Check for string/complex carrier updates
+    // Phase 178/188: Check for complex carrier updates
+    // Phase 188: StringAppendChar/StringAppendLiteral are now allowed
     // Create dummy carriers from body assignment targets for analysis
     let dummy_carriers: Vec<CarrierVar> = ctx.body.iter().filter_map(|node| {
         match node {
@@ -91,15 +92,27 @@ pub fn can_lower(_builder: &MirBuilder, ctx: &super::router::LoopPatternContext)
 
     let updates = LoopUpdateAnalyzer::analyze_carrier_updates(ctx.body, &dummy_carriers);
 
-    // Check if any update is string/complex
+    // Phase 188: Check if any update is complex (reject only UpdateRhs::Other)
+    // Allow: Const (numeric), Variable (numeric/string), StringLiteral
+    // Reject: Other (method calls, nested BinOp)
     for update in updates.values() {
         if let UpdateExpr::BinOp { rhs, .. } = update {
             match rhs {
-                UpdateRhs::StringLiteral(_) | UpdateRhs::Other => {
-                    eprintln!("[pattern4/can_lower] Phase 178: String/complex update detected, rejecting Pattern 4 (unsupported)");
+                UpdateRhs::Const(_) => {
+                    // Numeric: i = i + 1 (allowed)
+                }
+                UpdateRhs::Variable(_) => {
+                    // Phase 188: StringAppendChar: s = s + ch (allowed)
+                    // Or numeric: sum = sum + i (allowed)
+                }
+                UpdateRhs::StringLiteral(_) => {
+                    // Phase 188: StringAppendLiteral: s = s + "x" (allowed)
+                }
+                UpdateRhs::Other => {
+                    // Phase 188: Complex update (method call, nested BinOp) - reject
+                    eprintln!("[pattern4/can_lower] Phase 188: Complex update detected (UpdateRhs::Other), rejecting Pattern 4");
                     return false;
                 }
-                _ => {}
             }
         }
     }