Implement a Safe Expression Evaluator

Problem Implement a small, safe evaluator for user-provided expressions — arithmetic and variable interpolation like {{ user.name }} — WITHOUT using the host language's eval or any mechanism that could run arbitrary code.

Requirements

• Evaluate expressions against a provided scope object, e.g. eval("{{a}} + {{b}}", {a:2, b:3}) → 5.
• Support variable references (including dotted paths), arithmetic operators, and precedence / parentheses.
• Never execute arbitrary code; reject or safely handle malformed input.

Areas to design

• The tokenizer → parser → evaluator pipeline (or a shunting-yard evaluator).
• The scope-resolution model and how dotted paths are looked up.
• Sandboxing: which operations and property accesses are forbidden (e.g. prototype access), and how errors surface.
• Edge cases: undefined variables, division by zero, unbalanced braces/parens, type mismatches.