CMP.12:5.2 - Preserve a function’s binding when its call site changes

Extend the evaluator with immutable lexical bindings, function values and function application. Evaluate:

let x = 2 in
  let f = (lambda y: x + y) in
    let x = 100 in f(3)

Creating f saves its body, parameter y and the environment in which x is 2. Calling f extends that saved environment with y=3, so the body returns 5. Looking up free x in the caller’s environment would return 103 and implement a different binding rule.

The closure makes a rule available as a value without discarding its needed surroundings. A procedure can return it, receive it as an argument or construct a new closure that composes it with another rule. Each later application follows the saved bindings and the new arguments.

Changed feature: now permit assignment to the original captured x before calling f. If the language specifies capture of that variable’s location, assigning it 7 makes f(3) return 10. Keeping a copied value 2 would instead return 5. Represent the environment as names mapped to locations and obtain current values from the store; a later shadowing declaration must allocate a different binding. Revise the capture and lookup rules without changing the arithmetic rule.