Computer Science Fundamentals (CS153 2003S)
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Back to Recursion with Numbers. On to Preconditions and Postconditions.
Held: Monday, 3 February 2003
Summary:
Today we consider how to bind names to values using Scheme's let
expressions.
Related Pages:
Assignments:
Notes:
(length (car '('(a)))
equal to 2?Overview:
let
.let*
.let
.closesttozero
(define closesttozero (lambda (lst) (cond ; If there's only one element in the list, it's closest to zero ((null? (cdr lst)) (car lst)) ; If the current element is closer to zero than the closest ; remaining thing, use that ((< (abs (car lst)) (abs (closesttozero (cdr lst)))) (car lst)) ; Otherwise, use the thing in the remainder closest to zero (else (closesttozero (cdr lst))))))
closesttozero
, we
can make one by naming the result and using it twice. One
possibility is to use a helper procedure
(define closesttozero (lambda (lst) (cond ((null? (cdr lst)) (car lst)) (closertozero (car lst) (closesttozero (cdr lst)))))) (define closertozero (lambda (guess1 guess2) (if (< (abs guess1) (abs guess2)) guess1 guess2)))
(define closesttozero (lambda (lst) (cond ((null? (cdr lst)) (car lst)) "Compute (closesttozero (cdr lst)) and call it guess" (if (< (abs (car lst)) (abs guess)) (car lst) guess))))
let
let
.
let
has the form
(let ((name_{1} exp_{1}) (name_{2} exp_{2}) ... (name_{n} exp_{n})) body)
let
has the meaning:
let
in a simple expression:
(define values (list 1 4 2 4 1 5 9)) (let ((largest (max values)) (smallest (min values))) (/ (+ largest smallest) 2))
let
within a procedure.
Here's a new version of closesttozero
that uses
let
.
(define closesttozero (lambda (lst) ; If there's only one element in the list, it's closest to zero (if (null? (cdr lst)) (car lst) ; Otherwise, find the remaining element closest to zero and ; call it guess (let ((guess (closesttozero (cdr lst)))) ; Choose the closer to zero of the first element and guess (if (< (abs (car lst)) (abs guess)) (car lst) guess)))))
let*
let*
rather than let
.
let*
has the form
(let* ((name_{1} exp_{1}) (name_{2} exp_{2}) ... (name_{n} exp_{n})) body)
let*
has the meaning:
;;; Procedure: ;;; exactaverage ;;; Parameters: ;;; num1, an exact number ;;; num2, an exact number ;;; Purpose: ;;; Average the two numbers. ;;; Produces: ;;; average, an exact number ;;; Preconditions: ;;; num1 is an exact number [Verified] ;;; num2 is an exact number [Verified] ;;; Postconditions: ;;; Guess. (define exactaverage (lambda (num1 num2) (let ((verify? (lambda (val) (and (number? val) (exact? val))))) (cond ((not (verify? num1)) (error "exactaverage" "first parameter is a nonnumber")) ((not (verify? num2)) (error "exactaverage" "second parameter is a nonnumber")) (else (/ (+ num1 num2) 2))))))
let
Thursday, 16 January 2003 [Samuel A. Rebelsky]
Sunday, 2 February 2003 [Samuel A. Rebelsky]
Back to Recursion with Numbers. On to Preconditions and Postconditions.
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Misc:
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[Scheme Reference]
[Scheme Report]
[CS153 2002S (Walker)]
[CS151 2003S (Rebelsky)]
[CS152 2000F (Rebelsky)]
[SamR]
Disclaimer:
I usually create these pages on the fly
, which means that I rarely
proofread them and they may contain bad grammar and incorrect details.
It also means that I tend to update them regularly (see the history for
more details). Feel free to contact me with any suggestions for changes.
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The source to the document was last modified on Sun Feb 2 23:23:39 2003.
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.
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