SICP

Exercise 4.9.    Many languages support a variety of iteration constructs, such as  do ,  for ,  while , and  until . In Scheme, iterative processes can be expressed in terms of ordinary procedure calls, so special iteration constructs provide no essential gain in computational power. On the other hand, such constructs are often convenient. Design some iteration constructs, give examples of their use, and show how to implement them as derived expressions. SOLUTION The code and tests are  here . I have implemented the following expressions: do-while do-until for while The 'do-while' construct can be as follows: (do   (<one or more statements>)   while (condition) ) Use the while block construct to convert it as follows: (begin   <statements>   (while (condition)   <statements>   ) ) The 'do-until' construct can be as follows: (do   (<one or more statements>) ...

Exercise 4.8.    ``Named  let '' is a variant of  let  that has the form (let < var > < bindings > < body >) The < bindings > and < body > are just as in ordinary  let , except that < var > is bound within < body > to a procedure whose body is < body > and whose parameters are the variables in the < bindings >. Thus, one can repeatedly execute the < body > by invoking the procedure named < var >. For example, the iterative Fibonacci procedure (section  1.2.2 ) can be rewritten using named  let  as follows: (define (fib n)   (let fib-iter ((a 1)                  (b 0)                  (count n))     (if (= count...

Exercise 4.7.    Let*  is similar to  let , except that the bindings of the  let  variables are performed sequentially from left to right, and each binding is made in an environment in which all of the preceding bindings are visible. For example (let* ((x 3)        (y (+ x 2))        (z (+ x y 5)))   (* x z)) returns 39. Explain how a  let*  expression can be rewritten as a set of nested  let  expressions, and write a procedure  let*->nested-lets  that performs this transformation. If we have already implemented  let  (exercise  4.6 ) and we want to extend the evaluator to handle  let* , is it sufficient to add a clause to  eval  whose action is (eval (let*->nested-lets exp) env) or must we explicitly expand  let*  in terms of...

Exercise 4.6.    Let  expressions are derived expressions, because (let ((< var 1 > < exp 1 >)  ...  (< var n > < exp n >))   < body >) is equivalent to ((lambda (< var 1 >  ...  < var n >)    < body >)  < exp 1 >  .  .  .  < exp n >) Implement a syntactic transformation  let->combination  that reduces evaluating  let  expressions to evaluating combinations of the type shown above, and add the appropriate clause to  eval  to handle  let  expressions. SOLUTION The code and tests are here .

Exercise 4.5.    Scheme allows an additional syntax for  cond  clauses,  (< test > => < recipient >) . If < test > evaluates to a true value, then < recipient > is evaluated. Its value must be a procedure of one argument; this procedure is then invoked on the value of the < test >, and the result is returned as the value of the  cond  expression. For example (cond ((assoc 'b '((a 1) (b 2))) => cadr)       (else false)) returns 2. Modify the handling of  cond  so that it supports this extended syntax. SOLUTION The following example code shows how the extended syntax described in this problem can be represented using an 'if' structure: (cond ((< a b) exp1)     ((assoc 'b '((a 1) (b 2))) => single-argument-proc)     ((< m n) exp2)     (else exp3)) is equivalent to: (if (< a b) ...

Exercise 4.4.    Recall the definitions of the special forms  and  and  or  from chapter 1: and : The expressions are evaluated from left to right. If any expression evaluates to false, false is returned; any remaining expressions are not evaluated. If all the expressions evaluate to true values, the value of the last expression is returned. If there are no expressions then true is returned. or : The expressions are evaluated from left to right. If any expression evaluates to a true value, that value is returned; any remaining expressions are not evaluated. If all expressions evaluate to false, or if there are no expressions, then false is returned. Install  and  and  or  as new special forms for the evaluator by defining appropriate syntax procedures and evaluation procedures  eval-and  and  eval-or . Alternatively, show how to implement  and  and  or  as derived expressions. SOLUTION I h...

Exercise 4.3.    Rewrite  eval  so that the dispatch is done in data-directed style. Compare this with the data-directed differentiation procedure of exercise  2.73 . (You may use the  car  of a compound expression as the type of the expression, as is appropriate for the syntax implemented in this section.). SOLUTION The code and tests are here .  Note: The tests demonstrate that the data-directed dispatch happens correctly. Ignore the subsequent (environment related) errors for now. (These will be corrected in the upcoming exercises.)

Exercise 4.2.    Louis Reasoner plans to reorder the  cond  clauses in  eval  so that the clause for procedure applications appears before the clause for assignments. He argues that this will make the interpreter more efficient: Since programs usually contain more applications than assignments, definitions, and so on, his modified  eval  will usually check fewer clauses than the original  eval  before identifying the type of an expression. a. What is wrong with Louis's plan? (Hint: What will Louis's evaluator do with the expression  (define x 3) ?) b. Louis is upset that his plan didn't work. He is willing to go to any lengths to make his evaluator recognize procedure applications before it checks for most other kinds of expressions. Help him by changing the syntax of the evaluated language so that procedure applications start with  call . For example, instead of  (factorial 3)  we will now have to write  (c...

Exercise 4.1.    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. SOLUTION The code and tests are here .