Questions?

  • Homework, otherwise

    Homework

  • Remember, homework 0 is due Wednesday night @ 10:00pm
  • Homework 1 available that evening

Truthiness

Help functions, etc, accumulator parameters.

let & letrec

let

It can let us avoid recomputing expressions

  (+ (f 50) (f 50) (f 50))

  ;; is equivalent to

  (let ((x (f 50)))
    (+ x x x))

  (let ((x e))
    b)
  ;; is equivalent to

  ((lambda (x) b) e)

> (let ((! (lambda (n)
      (if (zero? n) 
          1
          (* n (! (sub1 n)))))))
    (! 5))

ERROR: unbound identifier '!'
>

letrec

For our purposes, for constructing anonymous recursive or anonymous mutually recursive functions.

anonymous recursion

> (letrec 
    ((! (lambda (n)
          (if (zero? n) 
              1
             (* n (! (sub1 n)))))))
    (! 5))
120
>

anonymous mutual recursion

> (letrec 
    ((e? (lambda (n)
           (if (zero? n) 
               #t
        	   (o? (sub1 n)))))
     (o? (lambda (n)
           (if (zero? n) 
               #f
               (e? (sub1 n))))))
   (e? 5))
#f

We don’t need define to write recursive functions.

Pattern-matching and match

Why pattern matching

  • pay attention! you won’t get this anywhere else.
  • often unfriendly to use car and cdr; ugly to write, ugly to read
  • pattern matching gives us the same if-then-else structure of a cond expression, but uses the “shape” of an expression instead.
(define (fun x)
  (match x
    (`(,item1 ,item2 ,item3) `(,item1 ,item3))
    (`(,a . ,d) `(,d . ,a))
    (else x)))
  • it’s like Wheel of Fortune
  • pair? vs (,a . ,d)
  • comma for wildcards with superpowers
  • when patterns aren’t enough

A complicated example

(define (new-fun x)
  (match (fun x)
    (`(,a b ,c) (list c))
    (`(1 ,b 3) (* b b))
    (`,y #:when (symbol? y) (cons y y))
    (`,n #:when (number? n) (* 2 n))))

Try it out

> (new-fun '((b 2) 4))
???
> (new-fun '((2 3) . 1))
???
> (new-fun 'cat)
???
> (new-fun 12)
???

quasiquote and unquote

(list 'a 'thing 'that 'is 'built 'with 'all 'but (- 5 4) 'value)

Updated: