6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology Slide lll14 Sharing, Equivalence and Identity These ideas of mutation and testing of equality raise some How can we tell if two things are equivalent? Interesting For example, if we mutate an object, do Well, what do you mean by""? still have the same object when we are done? The answer is yes 1. The same object: test with eq provided we maintain the same pointer to the object. For 2. Objects that "look"the same: test with equal? cample, if we have some list structure with a pointer to its equa1?(1st12)(1⊥st12))=> (eq?(1st12)(1ist12))=> beginning, and we then mutate the contents of some of the cells If we change an object, is it the same object? in the structure, so long as we keep hold of the pointer to the Yes, if we retain the same pointer to the object beginning of the structure, we consider it to be the same. Its value has changed, but the object's identity is maintained 6 001 SICP his tells us how to keep track of a particular object. A related Sharing, Equivalence and Identity Slide 11.1.15 question is deciding when two objects share a common part How can we tell if two things are equivalent? Well, what do you mean by"equivalent? The answer is that if we mutate one object, and see the same hange occur in the other object, then we can deduce that these (eq?ab)一> 2. Objects that look"the same: test with equal? objects share parts. Because of our notion of equality as eqa1?(1st12)(1ist12))=> pointing to the same object, this means that changing that = shared object through one name will be reflected when seen If we change an object, is it the same object? through the second name If we mutate one, see if the other also changes Sharing, Equivalence and Identity Slide 11.1.16 How can we tell if So what we see is that introducing mutation into our language Well, what do y"equivalent"? has caused us to change how we think about equality, how we 1. The same st with eq? think about the finest level of detail in our representations. That (eq?ab)一># 2. Objects that look"the test with equal has raised interesting issues about identity, equivale equa1?(1ist12)(1st12))= equality and sharing of structure eq?(1s12)(1ist12))=> f an object, is it the same object? Yes, if we retain the same pointer to the object How tell if parts of an object is shared with another? If we mutate one, see if the other also changes Slide 1l.1.17 Your Turn To see if you are catching on to this, here are two definitions for list structure, with the names x and y. What is the value of x=(2) x一山 X after each sequence of evaluations? When you are ready, (set-car! x y) move on to the next slide to check your answers (set-cdr! y (cdr x)6.001 Structure and Interpretation of Computer Programs. Copyright © 2004 by Massachusetts Institute of Technology. Slide 11.1.14 These ideas of mutation and testing of equality raise some interesting issues. For example, if we mutate an object, do we still have the same object when we are done? The answer is yes, provided we maintain the same pointer to the object. For example, if we have some list structure with a pointer to its beginning, and we then mutate the contents of some of the cells in the structure, so long as we keep hold of the pointer to the beginning of the structure, we consider it to be the same. Its value has changed, but the object's identity is maintained. Slide 11.1.15 This tells us how to keep track of a particular object. A related question is deciding when two objects share a common part. The answer is that if we mutate one object, and see the same change occur in the other object, then we can deduce that these objects share parts. Because of our notion of equality as pointing to the same object, this means that changing that shared object through one name will be reflected when seen through the second name. Slide 11.1.16 So what we see is that introducing mutation into our language has caused us to change how we think about equality, how we think about the finest level of detail in our representations. That has raised interesting issues about identity, equivalence, equality and sharing of structure. Slide 11.1.17 To see if you are catching on to this, here are two definitions for list structure, with the names x and y. What is the value of x after each sequence of evaluations? When you are ready, move on to the next slide to check your answers