<div class="gmail_quote">---------- Forwarded message ---------- From: "Sean Kemplay" <<a href="mailto:sean.kemplay@gmail.com">sean.kemplay@gmail.com</a>> Date: Jul 31, 2012 2:32 PM Subject: Re: [racket] Tabulate from build-list To: "Matthias Felleisen" <<a href="mailto:matthias@ccs.neu.edu">matthias@ccs.neu.edu</a>> Thanks Matthias, (define (tabulate f n) (build-list (+ n 1) (lambda (x) (f (- n x))))) I am glad I went the other way as well - I learnt something implementing it - and a lot from the transformation to the one liner. Kind regards, Sean On Tue, Jul 31, 2012 at 1:43 PM, Matthias Felleisen <div class="elided-text"><<a href="mailto:matthias@ccs.neu.edu">matthias@ccs.neu.edu</a>> wrote: > > Some suggestions: > > 1. (+ (* -1 x) y) is (- y x) > 2. f is in scope of the entire definition; there is no need to pass it along. > 3. Once you fix 2, you see that g == (inverter n) == (lambda (x) (f (- n x)) > 4. So why not replace all occurrences of g with the lambda expression? > > Voilà, you have a one-line definition. Send it back when done. > > > On Jul 31, 2012, at 8:12 AM, Sean Kemplay wrote: > >> Ok, not sure if I went down the same route as Matthias was alluding to >> but here is my solution - >> >> (define (tabulate f n) >> (local >> ((define (inverter y f) (lambda (x) (f (+ (* x -1) y)))) >> (define g (inverter n f))) >> (build-list (+ n 1) g))) >> >> >> (check-expect (tabulate (lambda (x) x) 3) '(3 2 1 0)) >> >> I used a curried function to 'invert' each number in place before the >> function provided to build list is applied. >> >> Regards, >> Sean >> >> On Mon, Jul 30, 2012 at 10:32 PM, Matthias Felleisen >> <<a href="mailto:matthias@ccs.neu.edu">matthias@ccs.neu.edu</a>> wrote: >>> >>> Here is how I suggest our freshmen to find this function: >>> >>> ;; tabulate : (x -> y) Nat -> (listof y) ;; <------- MF: not fix of signature >>> ;; to tabulate f between n >>> ;; and 0 (inclusive) in a list >>> >>> (check-expect (tabulate (lambda (x) x) 3) '(3 2 1 0)) >>> >>> (define (tabulate.v0 f n) >>> (cond >>> [(= n 0) (list (f 0))] >>> [else >>> (cons (f n) >>> (tabulate f (sub1 n)))])) >>> >>> ;; Using build-list >>> ;; build-list : N (N -> X) -> (listof X) >>> ;; to construct (list (f 0) ... (f (- n 1))) >>> >>> (define (tabulate f n) >>> (local (;; Nat -> Y ;; <-------------- MF: you know you want build-list, design (!) the 'loop' function now >>> (define (g i) ... f n i ...)) ;; <---- this is the data that's available >>> (build-list (+ n 1) g))) >>> >>> Also see '2e'. >>> >>> >>> On Jul 30, 2012, at 4:10 PM, Sean Kemplay wrote: >>> >>>> Hello, >>>> >>>> I am looking at the exercise from htdp 1e on building the tabulate >>>> function from build-list. >>>> >>>> Would I be on the right track that I need to create a function to >>>> reverse the result of (build-list (+ n 1) f) to do this? >>>> >>>> the function this is to emulate - >>>> >>>> ;; tabulate : (x -> y) x -> (listof y) >>>> ;; to tabulate f between n >>>> ;; and 0 (inclusive) in a list >>>> (define (tabulate f n) >>>> (cond >>>> [(= n 0) (list (f 0))] >>>> [else >>>> (cons (f n) >>>> (tabulate f (sub1 n)))])) >>>> >>>> Using build-list >>>> ;; build-list : N (N -> X) -> (listof X) >>>> ;; to construct (list (f 0) ... (f (- n 1))) >>>> (define (build-list n f) ...) >>>> >>>> Regards, >>>> Sean >>>> ____________________ >>>> Racket Users list: >>>> <a href="http://lists.racket-lang.org/users" target="_blank">http://lists.racket-lang.org/users</a> >>> > </div></div>