Because internal definitions look sequential but are actually simultaneous, some people prefer to avoid them entirely, and use the special form letrec instead. Letrec looks like let, so it is not surprising that the variables it binds are bound simultaneously and have the same scope as each other. The sample procedure f above can be written without internal definitions, but with exactly the same meaning, as

are a variation on let in which the expressions that provide the initial values for the variables are evaluated in an environment that includes all the letrec bindings. This permits recursion in the bindings, such as the mutual recursion of even? and odd? in the example above, or the evaluation of 10 factorial with

a. Implement letrec as a derived expression, by transforming a letrec expression into a let expression as shown in the text above or in exercise 4.18. That is, the letrec variables should be created with a let and then be assigned their values with set!.

b. Louis Reasoner is confused by all this fuss about internal definitions. The way he sees it, if you don't like to use define inside a procedure, you can just use let. Illustrate what is loose about his reasoning by drawing an environment diagram that shows the environment in which the is evaluated during evaluation of the expression (f 5), with f defined as in this exercise. Draw an environment diagram for the same evaluation, but with let in place of letrec in the definition of f.

exercise 4.18

Consider an alternative strategy for scanning out definitions that translates the example in the text to

Here a and b are meant to represent new variable names, created by the interpreter, that do not appear in the user's program. Consider the solve procedure from section 3.5.4.

Will this procedure work if internal definitions are scanned out as shown in this exercise? What if they are scanned out as shown in the text? Explain