Question

Notice that we cannot tell whether the metacircular evaluator evaluates operands from left to right or from right to left. Its evaluation order is inherited from the underlying Lisp: If the arguments to cons in list-of-values are evaluated from left to right, then list-of-values will evaluate operands from left to right; and if the arguments to cons are evaluated from right to left, then list-of-values will evaluate operands from right to left. Write a version of list-of-values that evaluates operands from left to right regardless of the order of evaluation in the underlying Lisp. Also write a version of list-of-values that evaluates operands from right to left.

Short answer

Implement `list-of-values-left-to-right` and `list-of-values-right-to-left` using recursive evaluation order control to dictate operand evaluation order explicitly.

Step-by-step solution

Understanding the Current Behavior

The current `list-of-values` function uses `cons` to combine evaluated operands, and the order (left-to-right or right-to-left) of operand evaluation depends on the underlying Lisp interpreter. We need to alter this inherent behavior.

Implementing Left-to-Right Evaluation

To ensure left-to-right evaluation irrespective of the Lisp interpreter behavior, evaluate each operand one by one starting from the leftmost and store the results. Use an iterative or recursive approach to build the resulting list in the required order. ```lisp (define (list-of-values-left-to-right exps) (if (null? exps) '() (let ((first-val (eval (car exps)))) (cons first-val (list-of-values-left-to-right (cdr exps)))))) ``` This function first evaluates the leftmost expression and then recursively processes the rest.

Implementing Right-to-Left Evaluation

For right-to-left evaluation, reverse the order of recursive evaluation or store evaluations temporarily and build the list in reverse at the end. ```lisp (define (list-of-values-right-to-left exps) (if (null? exps) '() (let ((rest-of-values (list-of-values-right-to-left (cdr exps))) (last-val (eval (car exps)))) (append rest-of-values (list last-val))))) ``` This function processes the rest of the list first, ensuring the right-to-left order.

Testing the Functions

To confirm that both versions of `list-of-values` work as intended, test them with a range of expressions. Pass expressions that print their evaluation to notice the order. Witness that in `list-of-values-left-to-right`, the leftmost expression evaluates first, whereas in `list-of-values-right-to-left`, the rightmost evaluates first.

Key concepts

Left-to-Right Evaluation

In programming, the order of evaluation can often influence the outcome of computations. This is particularly true when side effects are present. The left-to-right evaluation means starting from the first operand on the left and moving sequentially to the right until all operands have been evaluated. The left-to-right evaluation in a `list-of-values` function in Lisp can be achieved by using a recursive approach. The function processes the leftmost expression first, then moves onto the next one, eventually evaluating all expressions in the list sequentially:

• The first operand is taken, evaluated, and its value is stored.
• Subsequent operands are treated similarly until the entire list is processed.
• The results are combined in the original order of expressions.

This method ensures that the side effects of evaluating each expression happen in the order they appear. In Lisp, you can implement a left-to-right evaluation efficiently using recursive or iterative methods to collect the results.

Right-to-Left Evaluation

The right-to-left evaluation is the reverse approach. Here, the interpreter starts evaluating from the rightmost operand and moves to the left. This can be valuable when the order of operations needs to preserve certain dependencies that are better suited to right-to-left processing. To implement a right-to-left evaluation in Lisp, you can reverse the order in which the operands are processed or use temporary storage to handle evaluations:

• Begin with the rightmost expression, evaluate it, and hold the result.
• Progress through the list in reverse, storing or combining evaluated results.
• Finally, the results are appended or aggregated to reflect the desired reverse order.

This recursive approach allows the metacircular evaluator in Lisp to maintain the order of operations defined by the user. The rightmost operand gets priority, flipping the traditional sequence on its head while preventing unintentional side effects when consistent evaluation order is crucial.

Lisp Interpreter Behavior

The Lisp interpreter plays a critical role in determining how expressions are evaluated in terms of order. This behavior is fundamental since, in a typical scenario, the order of evaluation may not be explicitly defined and can vary based on underlying implementation. Lisp, famed for its flexibility and power, inherits evaluation behavior from its host interpreter. This means that:

• If the host evaluates expressions from left to right, the Lisp interpreter will do the same.
• If it evaluates from right to left, Lisp will follow that approach.
• Such behavior can be unpredictable if not explicitly specified or overridden.

To exert control over evaluation order, especially in metacircular evaluators—a kind of interpreter written in the language it interprets—Lisp programmers can manually construct the desired evaluation behavior, whether left-to-right or right-to-left. This deliberate manipulation allows for precise control over program execution and is vital for programs where evaluation order impacts outcomes, such as those involving complex dependencies or side effects.