Design a context-aware string interpolation engine that can: 1) Parse interpolation syntax like "" templates 2) Resolve variables from multiple contexts with fallback mechanisms 3) Handle function calls and expressions within interpolation 4) Implement lazy evaluation for performance 5) Provide sandboxing for security 6) Support type coercion and formatting directives 7) Maintain context scope rules with inheritance 8) Handle circular dependencies. Include formal specification, parsing strategy, resolution algorithm, and examples of complex nested interpolations.