Open the Commutativity and Associativity Starter File. Complete the exploration to determine if beside, above, and overlay are associative.

1 Is beside associative? Make a prediction, then translate the two Circles of Evaluation into code. Test your code in Pyret.

Circle of Evaluation

(beside (beside aqua-star orange-dot) red-star)

(beside aqua-star (beside orange-dot red-star))

Code

2 Did both expressions produce identical images? Is the beside function associative or not?

3 Is above associative? Make a prediction, then draw a second Circle of Evaluation that changes the grouping without changing the order. Translate into code and test in Pyret.

Circle of Evaluation

(above yellow-rect (above purple-square orange-dot))

Code

4 Did both expressions produce identical images? Is the above function associative or not?

5 Is overlay associative? Draw two Circles of Evaluation that will help you decide if overlay is commutative. Translate into code and test in Pyret.

Circle of Evaluation

Code

6 Did both expressions produce identical images? Is the overlay function associative or not?

★ Make a prediction: is blend-images associative? Why or why not?

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