Exercise 195: Argue why the following sentences are now legal definitions

Exercise 195: Argue why the following sentences are now legal definitions:

1. (define (f x) (x 10))
2. (define (f x) (x f))
3. (define (f x y) (x 'a y 'b))

Explain your reasoning.

1)  (define (f x) (x 10))

We are now allowed to:

1. include the names of functions and primitive operations in the definition. 
2. use variables and function parameters in the first position in a definition

In this case the parameter x is a function that will have the value 10 applied to it.  As we can include functions in a function definition this is legal.

2) (define (f x) (x f))

In this case, both x and f are functions. This function will call the function x passing in the value of itself (ie f). As we can include functions in function definitions, this is now legal.

3) (define (f x y) (x 'a y 'b))

In this case f and x are functions, and y is a value (that could potentially be a function!). The function x will be called, with the values 'a, y and 'b being passed into it. At this point y could either be a value, or a function and provided that the function x is expected the actual item in, this code is legal.