6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology Slide 152.8 We are just walking through a tree That leads to this form Notice what we have done we have amn→→[一 reduced evaluation of one expression into some simple primitive operations on evaluation of other subexpressions. And 日-团 what has that done? It has literally just walked down the tree structure that represents this expression, pulling out the right ((eval 24)(eval-4-4B-4u pieces It has used the tag to tell us who to send the expression to, and then it has simply grabbed cars and cdrs of the list structure and handed them off to new evaluations now at this stage, evaluating the first subexpression(eval 24) asy. We see from our code that it will use type checking to tm determine this is a number and simply return that expression And thats nice! This is just pointing to the number 2 4 so the number 24 gets returned What about the other piece? Slide 15.2,9 Well this just looks like the kind of expression we started with We are just walking through a tree We are evaluating some list structure that happens to represent →团 a sum. It's got a tag at the front to say it is one of these plus* expressions, so we can do exactly the same thing The evaluation of this expression will unwrap into an eval +(ea124)(evA1 sum of the same list structure. and that will reduce to a primitive application of t to whatever I get by evaluating the subexpressions, and that I get by walking down the tree, grabbing the right pieces, applying eval and getting back the We are just walking through a tree Slide 15.2.10 And now we see that we have unwrapped this abstraction down to some primitive operations, primitive application of addition E ra to some simple expressions, in this case just numbers And of ourse this will finally reduce to the answer we exl unwrapped it into successive evaluations until it reduces to a se of applications of primitive built-in procedures to primitive +(eva15)(eva16)) values6.001 Structure and Interpretation of Computer Programs. Copyright © 2004 by Massachusetts Institute of Technology. Slide 15.2.8 That leads to this form. Notice what we have done: we have reduced evaluation of one expression into some simple primitive operations on evaluation of other subexpressions. And what has that done? It has literally just walked down the tree structure that represents this expression, pulling out the right pieces. It has used the tag to tell us who to send the expression to, and then it has simply grabbed cars and cdrs of the list structure, and handed them off to new evaluations. Now at this stage, evaluating the first subexpression (eval 24) is easy. We see from our code that it will use type checking to determine this is a number and simply return that expression. And that’s nice! This is just pointing to the number 24 so the number 24 gets returned. What about the other piece? Slide 15.2.9 Well this just looks like the kind of expression we started with. We are evaluating some list structure that happens to represent a sum. It's got a tag at the front to say it is one of these plus* expressions, so we can do exactly the same thing. The evaluation of this expression will unwrap into an eval￾sum of the same list structure, and that will reduce to a primitive application of + to whatever I get by evaluating the subexpressions, and that I get by walking down the tree, grabbing the right pieces, applying eval and getting back the numbers. Slide 15.2.10 And now we see that we have unwrapped this abstraction down to some primitive operations, primitive application of addition to some simple expressions, in this case just numbers. And of course this will finally reduce to the answer we expect. However, a key thing to note is how this simple evaluator has taken in a tree structure representing an expression and has unwrapped it into successive evaluations until it reduces to a set of applications of primitive built-in procedures to primitive values