Docs: add Indexing subsection, README grammar, rebuild PDF for website

Made-with: Cursor

Author: Leo Louvar

README.md

@@ -39,7 +39,7 @@ Elixir orchestrates and restarts failed workers; Zig runs hot-path code; Python
 
 ### How it works
 
-Zixir has its **own grammar** (`let`, expressions, `engine.op(args)`, `python "module" "function" (args)`, literals, binary ops, 25+ built-in functions). Source is **parsed** in Elixir into a Zixir AST, then either:
+Zixir has its **own grammar** (`let`, expressions, array/map indexing `arr[i]` and `map["key"]`, `engine.op(args)`, `python "module" "function" (args)`, literals, binary ops, 25+ built-in functions). Source is **parsed** in Elixir into a Zixir AST, then either:
 
 - **Interpreted** — `Zixir.eval(source)` evaluates the AST in Elixir; `engine.*` calls run in Zig NIFs, `python` calls go to Python via a port.
 - **Compiled** — `Zixir.Compiler.compile(source)` type-checks, optimizes, and **emits Zig**; the Zig is compiled to a native binary or run JIT.

docs/Zixir Language complete guide.md

@@ -563,6 +563,27 @@ let all_values = values(user)  # ["Alice Johnson", 28, "alice@example.com"]
 let size = length(user)        # 3
 ```
 
+### Indexing (arrays and maps)
+
+Zixir uses **bracket notation** for both array and map access:
+
+| Target | Syntax | Index/key | Result |
+|--------|--------|-----------|--------|
+| **Array** | `arr[i]` | Integer, zero-based | Element at position `i`; error if out of bounds |
+| **Map** | `map["key"]` | Any value (often string) | Value for key, or `nil` if key missing |
+
+**Array indexing:** Zero-based and bounds-checked. Use a variable (or expression) on the left: `let arr = [1, 2, 3]` then `arr[0]`. Last element: `arr[length(arr) - 1]`.
+
+**Map indexing:** `user["name"]` returns the value or `nil` if the key is missing. Nested: `company["address"]["city"]`.
+
+```zixir
+let arr = [10, 20, 30]
+arr[0]           # 10
+let m = {"a": 1, "b": 2}
+m["a"]           # 1
+m["missing"]     # nil
+```
+
 ### Type Conversions
 
 Zixir provides built-in functions for type conversion: