🔧 Fix peek expression terminator issues and add ternary operator support

- Fix LLVM IR terminator missing in peek expression entry blocks
- Add proper jump instructions between peek blocks
- Implement ternary operator (? :) as syntactic sugar for peek
- Update Python LLVM externcall handling for improved compatibility
- Add comprehensive test cases for peek and ternary expressions
- Update language guide with ternary operator documentation

ChatGPTが頑張って修正してくれたにゃ！🐱

Co-Authored-By: ChatGPT <noreply@openai.com>

docs/guides/language-guide.md

@@ -15,6 +15,39 @@ Common Constructs
 - Null-coalesce: `x ?? y` → `peek x { null => y, else => x }`
 - Safe access: `a?.b` → `peek a { null => null, else => a.b }`
 
+Minimal Examples
+- Ternary
+  ```nyash
+  static box Main {
+    main(args) {
+      local a = 3
+      local b = 5
+      // Nested ternary is supported
+      local v = (a < b) ? ((b < 0) ? 40 : 50) : 60
+      return v
+    }
+  }
+  ```
+- Peek as expression block (last expression is the value)
+  ```nyash
+  static box Main {
+    main(args) {
+      local d = "1"
+      // Each arm can be a block; the last expression becomes the value
+      local dv = peek d {
+        "0" => { print("found zero") 0 }
+        "1" => { print("found one") 1 }
+        else => { print("other") 0 }
+      }
+      return dv
+    }
+  }
+  ```
+
+must_use Notes
+- Peek arms are expressions. When using a block arm `{ ... }`, the last expression is the resulting value; statements without a final expression yield no usable value.
+- Ternary is an expression; ensure both branches are type-compatible at MIR level (e.g., both yield integer or both yield string handle in current phase).
+
 When you need the implementation details
 - Tokenizer: src/tokenizer.rs
 - Parser: src/parser/expressions.rs, src/parser/statements.rs

docs/reference/architecture/parser_mvp_stage2.md

@@ -0,0 +1,59 @@
+# Parser MVP Stage-2 Design (Phase 15)
+
+Scope
+- Expand Stage-1 (const/binop/return) to cover the minimal everyday surface:
+  - local bindings: `local x = expr`
+  - if/else: `if cond { ... } else { ... }`
+  - loop: `loop(cond) { ... }` and `loop cond { ... }`
+  - call: `f(a, b)` (free function)
+  - method: `obj.method(a, b)`
+  - constructor: `new BoxType(args)`
+  - implicit receiver `me` in box methods
+  - String methods: `substring`, `length`, `lastIndexOf`
+
+Grammar Sketch (incremental)
+- Expression
+  - precedence keeps Phase 12.7: ternary inside pipe; ternary lowers to if/branch
+  - postfix: method call, field access
+  - primary: literals, identifiers, parenthesized
+- Statement
+  - `local ident = expr` (no rebind in Stage-2)
+  - expression statement (for side effects)
+  - return
+
+AST Nodes (delta)
+- Add nodes for Local, If, Loop, Call, MethodCall, New, Identifier, Return.
+- Keep Peek and Ternary in the AST; lower to MIR via the same builder hooks.
+
+Lowering to MIR JSON v0
+- Local → assign to fresh value id, store into vmap
+- If/Ternary → compare + branch blocks; PHI for join values when used as expression
+- Loop → cond block → body block → back-edge; loop-carried values explicitly phied
+- Call → `call { func: "name", args: [...] }`
+- Method → `boxcall { box: vid, method: "name", args: [...] }`
+- New → `newbox { type: "BoxType", args: [...] }`
+- String ops
+  - `length()` → i64 length on string handle (VM: Python len; LLVM: handle→ptr at call sites only)
+  - `substring(a,b)` → `nyash.string.substring_hh` equivalent
+  - `lastIndexOf(x)` → returns i64 index or -1
+
+Type Meta (emitted with JSON where needed)
+- Compare: when both sides are string → `cmp_kind: "string"`
+- BinOp `+`: if `dst_type = { kind: "handle", box_type: "StringBox" }`, force concat_hh
+- Known APIs: annotate `dst_type` for Console.println (i64), dirname/join/read as `StringBox(handle)`
+
+Policy & Invariants
+- Resolver-only: do not wire PHIs in-lowering; snapshots + `finalize_phis` bind incomings
+- Strings: inter-block are handle(i64) only; i8* materialized at call sites
+- PHI placeholders: created at block heads from JSON-declared phi
+
+Acceptance
+- Parity on:
+  - `apps/tests/min_str_cat_loop/main.nyash`
+  - `apps/tests/esc_dirname_smoke.nyash`
+  - Stage-2 new smokes (ternary nested, peek return)
+- `tools/parity.sh --lhs pyvm --rhs llvmlite --show-diff <app>` → green
+
+Notes
+- Keep Stage-2 additive and test-driven; avoid broad refactors.
+- Future: numeric methods, map/array minimal, and using/namespace gate.