"application: not a procedure" while computing binomial

Question

I am defining a function binomial(n k) (aka Pascal's triangle) but am getting an error:

    application: not a procedure;
    expected a procedure that can be applied to arguments
    given: 1
    arguments...:
    2

I don't understand the error because I thought this defined my function:

    (define (binomial n k)
      (cond  ((or (= n 0) (= n k)) 1)
          (else (+ (binomial(n) (- k 1))(binomial(- n 1) (- k 1)))))) 

Answer 1

In Scheme (and Lisps in general), parentheses are placed before a procedure application and after the final argument to the procedure. You've done this correctly in, e.g.,

(= n 0)
(= n k)
(- k 1)
(binomial(- n 1) (- k 1))

However, you've got an error in one of your arguments to one of your calls to binomial:

(define (binomial n k)
  (cond  ((or (= n 0) (= n k)) 1)
      (else (+ (binomial(n) (- k 1))(binomial(- n 1) (- k 1)))))) 
                        ***

Based on the syntax described above (n) is an application where n should evaluate to a procedure, and that procedure will be called with no arguments. Of course, n here actually evaluates to an integer, which is not a procedure, and can't be called (hence “application: not a procedure”). You probably want to remove the parentheses around n:

(binomial n (- k 1))

It's also worth pointing out that Dr. Racket should have highlighted the same portion of code that I did above. When I load your code and evaluate (binomial 2 1), I get the following results in which (n) is highlighted: