feat(joinir): Phase 213 AST-based if-sum lowerer for Pattern 3

Implement dual-mode architecture for Pattern 3 (Loop with If-Else PHI):

- Add is_simple_if_sum_pattern() detection helper
  - Detects 1 CounterLike + 1-2 AccumulationLike carrier patterns
  - Unit tests for various carrier compositions

- Add dual-mode dispatch in Pattern3 lowerer
  - ctx.is_if_sum_pattern() branches to AST-based vs legacy PoC
  - Legacy mode preserved for backward compatibility

- Create loop_with_if_phi_if_sum.rs (~420 lines)
  - AST extraction: loop condition, if condition, updates
  - JoinIR generation: main, loop_step, k_exit structure
  - Helper functions: extract_loop_condition, extract_if_condition, etc.

- Extend PatternPipelineContext for Pattern 3
  - is_if_sum_pattern() detection using LoopUpdateSummary
  - extract_if_statement() helper for body analysis

Note: E2E RC=2 not yet achieved due to pre-existing Pattern 3
pipeline issue (loop back branch targets wrong block). This
affects both if-sum and legacy modes. Fix planned for Phase 214.

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

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

docs/development/current/main/phase213-if-sum-implementation.md

@@ -0,0 +1,98 @@
+# Phase 213: Pattern 3 If-Sum AST-based Lowerer
+
+## Overview
+
+Phase 213 implements an AST-based JoinIR lowerer for "simple if-sum" patterns in Pattern 3 (Loop with If-Else PHI).
+
+## Design Decision: Approach B
+
+**Dual-mode architecture**:
+1. **if-sum mode**: AST-based lowering for simple patterns (e.g., `phase212_if_sum_min.hako`)
+2. **legacy mode**: Hardcoded PoC lowering for existing tests (e.g., `loop_if_phi.hako`)
+
+This approach:
+- Minimizes risk by keeping legacy code path intact
+- Only generalizes for detected if-sum patterns
+- Enables incremental migration
+
+## Implementation
+
+### Files Modified/Created
+
+1. **`loop_update_summary.rs`**
+   - Added `is_simple_if_sum_pattern()` method
+   - Detects: 1 CounterLike + 1-2 AccumulationLike carriers
+
+2. **`pattern_pipeline.rs`**
+   - Added `is_if_sum_pattern()` to PatternPipelineContext
+   - Added `extract_if_statement()` helper
+
+3. **`pattern3_with_if_phi.rs`**
+   - Dual-mode dispatch: `ctx.is_if_sum_pattern()` → branch
+   - `lower_pattern3_if_sum()`: calls AST-based lowerer
+   - `lower_pattern3_legacy()`: existing hardcoded logic
+
+4. **`loop_with_if_phi_if_sum.rs`** (NEW)
+   - AST-based if-sum lowerer (~420 lines)
+   - Extracts from AST:
+     - Loop condition (`i < len`)
+     - If condition (`i > 0`)
+     - Then update (`sum = sum + 1`)
+     - Counter update (`i = i + 1`)
+   - Generates JoinIR with dynamic values
+
+### Pattern Detection
+
+```rust
+pub fn is_simple_if_sum_pattern(&self) -> bool {
+    if self.counter_count() != 1 { return false; }
+    if self.accumulation_count() < 1 { return false; }
+    if self.accumulation_count() > 2 { return false; }
+    true
+}
+```
+
+### AST Extraction
+
+The lowerer extracts pattern components from AST:
+- `extract_loop_condition()`: `i < 3` → (var="i", op=Lt, limit=3)
+- `extract_if_condition()`: `i > 0` → (var="i", op=Gt, value=0)
+- `extract_then_update()`: `sum = sum + 1` → (var="sum", addend=1)
+- `extract_counter_update()`: `i = i + 1` → (var="i", step=1)
+
+## Testing Results
+
+### AST Extraction: Working ✅
+```
+[joinir/pattern3/if-sum] Loop condition: i Lt 3
+[joinir/pattern3/if-sum] If condition: i Gt 0
+[joinir/pattern3/if-sum] Then update: sum += 1
+[joinir/pattern3/if-sum] Counter update: i += 1
+```
+
+### Known Issue: Pattern 3 Pipeline
+
+**Both if-sum mode and legacy mode return RC=0 instead of expected values.**
+
+This is a pre-existing issue in the JoinIR → MIR conversion pipeline (Phase 33-21/177):
+- Loop back branch targets `bb5` instead of loop header `bb4`
+- PHI nodes not properly updated on loop back
+
+**This issue is NOT specific to Phase 213** - the legacy `loop_if_phi.hako` has the same problem.
+
+## Future Work
+
+1. **Phase 214+**: Fix Pattern 3 JoinIR → MIR pipeline
+   - Investigate loop back branch target
+   - Ensure PHI updates are correctly wired
+
+2. **Phase 213-B** (optional): Support variable limits
+   - Currently only integer literals supported
+   - `i < len` where `len` is a variable → Phase 214+
+
+## File Locations
+
+- Lowerer: `src/mir/join_ir/lowering/loop_with_if_phi_if_sum.rs`
+- Dispatcher: `src/mir/builder/control_flow/joinir/patterns/pattern3_with_if_phi.rs`
+- Pattern detection: `src/mir/join_ir/lowering/loop_update_summary.rs`
+- Pipeline context: `src/mir/builder/control_flow/joinir/patterns/pattern_pipeline.rs`