6.001 Structure and Interpretation of Computer Programs. Copyright o 2004 by Massachusetts Institute of Technology Slide 15.2.4 We are just walking through a tree Let's look at this in more detail. First, let's look at the input to this evaluation process. Remember that our expression, which we typed in, is converted into list structure, as a tree of symbols and numbers. It looks like what is shown on the slide. and this is what gets handed to the evaluator as a representation of our example expression. So let's treat this as if this exact tree structure were passed in to eval Slide 15.2.5 We are just walking through a tree And what does eval do with this input? Check the code on the handout eva l grabs the list and tests its tag. That means it first checks to see if this whole thing is a number. Since it is not, it takes the first element of this list structure and checks to see if it is the special symbol plus x [→“ 如m are just walking through a tree Slide 15.2.6 H+ Having done that it dispatches on type to the right procedure to handle this kind of expression. Having determine that it is sum by checking the tag, it sends it off to eval-sum, and (mn-→[团 We apply the procedure to the expression sum? checks the tag Slide 15.2.7 We are just walking through a tree o now eval has reduced this to applying eval-sum to →z the tree structure shown notice what the body ofeval sum does It walks down the tree, grabbing out subexpressions, that is the first and second components of this sum. Eval-sum then converts this into adding, using the built-in primitive, whatever I get by evaluating the first subexpression and whatever I get by evaluating the second subexpression6.001 Structure and Interpretation of Computer Programs. Copyright © 2004 by Massachusetts Institute of Technology. Slide 15.2.4 Let's look at this in more detail. First, let's look at the input to this evaluation process. Remember that our expression, which we typed in, is converted into list structure, as a tree of symbols and numbers. It looks like what is shown on the slide, and this is what gets handed to the evaluator as a representation of our example expression. So let's treat this as if this exact tree structure were passed in to eval. Slide 15.2.5 And what does eval do with this input? Check the code on the handout. Eval grabs the list and tests its tag. That means it first checks to see if this whole thing is a number. Since it is not, it takes the first element of this list structure and checks to see if it is the special symbol plus*. Slide 15.2.6 Having done that it dispatches on type to the right procedure to handle this kind of expression. Having determine that it is a sum by checking the tag, it sends it off to eval-sum, and this is (for now at least) just a normal procedure application. We apply the procedure to the expression. Slide 15.2.7 So now eval has reduced this to applying eval-sum to the tree structure shown. Notice what the body of eval￾sum does. It walks down the tree, grabbing out the two subexpressions, that is the first and second components of this sum. Eval-sum then converts this into adding, using the built-in primitive, whatever I get by evaluating the first subexpression and whatever I get by evaluating the second subexpression