CS 135 Tutorials Fall 2007

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CS 135 Tutorial 4: Scintacks and Some Antics (Syntax and Semantics) (October 3-5, 2007)

This week we will be looking at the mathematical structure and meaning of a Scheme program. The material here comes primarily from Lecture Module 4 in the class notes. It's quite fortunate (and unusual) that we are working in a programming language in which we can rigorously define the meaning of every program with relatively few rules. The only unfortuanate side effect is that we'll have to endure a week without the fun stories and problem descriptions that we've all grown accustomed to in these tutorials.

Give a full syntactic/semantic analysis of each of the following Scheme programs. That is, go through (one by one) each of the substitution steps to completely evaluate each expression to a value. If an error occurs, making evaluation impossible, pinpoint the exact location and nature of the error (syntax, semantics, or other).

1. (and (symbol? 'hello)
        (= (- 5 1) (* 2 3))
        (/ "a string" "another string"))

2. (define a (+ 2 3))
   (define (foo2 x)
     (cond [(or (> x 1)
   	     (< x -1))
   	 (sqr x)]
   	[(zero? x) 1]))
   (foo2 a)
   (foo2 (/ a a))

3. (define (foo3 5)
     (+ 1 5))
   (/ (foo3 5)
      0)

4. (define-struct name (first middle last))
   (define (foo4 nme)
     (name-middle (+ nme 1)))
   (name-last (make-name "James" "A" "Garfield"))

5. (define (foo5 x)
     (cond [(= 1 x) 2]
   	[else
   	  (* 2
   	     (foo5 (sub1 x)))]))
   (foo5 3)
   (foo5 -2)