Errors

When we write Scheme programs, we must follow a few carefully designed rules, which are a compromise between a computer's capabilities and human behavior. Fortunately, forming Scheme definitions and expressions is intuitive. Expressions are either ATOMIC, that is, numbers and variables; or they are COMPOUND expressions, in which case they start with ``('', followed by an operation, some more expressions, and terminated by ``)''. Each expression in a compound expression should be preceded by at least one space; line breaks are permissible, and sometimes increase readability.

Definitions have the following schematic shape:

(define (f x ... y)
  an-expression) 

Syntax Errors: Not all parenthesized expressions are Scheme expressions. For example, (10) is a parenthesized expression, but Scheme does not accept it as a legal Scheme expression because numbers are not supposed to be included in parentheses. Similarly, a sentence like (10 + 20) is also ill formed; Scheme's rules demand that the operator is mentioned first. Finally, the following two definitions are not well formed:

(define (P x)
  (+ (x) 10))

(define (Q x) 
  x 10) 

When we click DrScheme's Execute button, the programming environment first determines whether the definitions are formed according to Scheme's rules. If some part of the program in the Definitions window is ill formed, DrScheme signals a SYNTAX ERROR with an appropriate error message and highlights the offending part. Otherwise it permits the user to evaluate expressions in the Interactions window.

Exercise 2.4.1

Evaluate the following sentences in DrScheme, one at a time:

(+ (10) 20)
(10 + 20) 
(+ +) 

Exercise 2.4.2

Enter the following sentences, one by one, into DrScheme's Definitions window and click Execute:

(define (f 1)
  (+ x 10))

(define (g x) 
  + x 10)

(define h(x) 
  (+ x 10)) 

Run-time Errors: The evaluation of Scheme expressions proceeds according to the intuitive laws of algebra and arithmetic. When we encounter new operations, we will extend these laws, first intuitively and then, in section , rigorously. For now, it is more important to understand that not all legal Scheme expressions have a result. One obvious example is (/ 1 0). Similarly, if we define

(define (f n)
  (+ (/ n 3) 2)) 

When the evaluation of a legal Scheme expression demands a division by zero or similarly nonsensical arithmetic operations, or when a program is applied to the wrong number of inputs, DrScheme stops the evaluation and signals a RUN-TIME ERROR. Typically it prints an explanation in the Interactions window and highlights the faulty expression. The highlighted expression triggered the error signal.

Exercise 2.4.3

Evaluate the following grammatically legal Scheme expressions in DrScheme's Interactions window:

(+ 5 (/ 1 0))

(sin 10 20)

(somef 10) 

Exercise 2.4.4

Enter the following grammatically legal Scheme program into the Definitions window and click the Execute button:

(define (somef x)
  (sin x x)) 

(somef 10 20)

(somef 10) 

Logical Errors: A good programming environment assists the programmer in finding syntax and runtime errors. The exercises in this section illustrate how DrScheme catches syntax and run-time errors. A programmer, however, can also make LOGICAL ERRORS. A logical mistake does not trigger any error messages; instead, the program computes incorrect results. Consider the wage program from the preceding section. If the programmer had accidentally defined it as

(define (wage h)
  (+ 12 h))