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# Help understanding Scheme's syntax, procedures and calls

 P: n/a I'm trying to understand a functional language code fragment so I can explain its syntax and workings to my non English-speaking background neighbour, who is doing her finals. What in heaven's name is this code fragment intending? (In English prose if possible). It looks like a fragment from a language called "scheme" (define (this n) (if (=n 0) 0 (= n (this (- n 1))))) (define (f1 a b) (if >b a) 0 (+ b (f1 a (+ b 1))))) (define (that n) (f1 n1) a) Describe the processing that occurs during the evaluation of the expression (this 4) b) Explain why the expression (=(this n)(that n) always evaluates to true when n is a positive integer. c) Write a fragment of code in the above language that adds up all the integers within a given range, not including the two numbers specified. For example, if the specified range was 4 à 9 then code should add 5à 8. Suggested answers: a) This 4 call started As n-1=3 a recursive This 3 call is started As n-1=2 a This 2 call starts As n-1=1 a This 1 call starts As n-1=0 a This 0 call is started and is returned as n=0 This 1 call is resolved by adding 1+0 This 2 call is resolved by adding 2+1 This 3 call is resolved by adding 3+3 Finally 10 is returned when This 4 call is resolved by adding 4 + 6. I no more grasp the pattern of the suggested answer than the question, and am much less in a position to explain it to anyone. b) Both the This and the That functions have the same output, and furthermore both functions result in infinite recursion if n<0. When n is a positive integer, the This function calculates (n+…(3+(2+(1+(0)))) and the that function calculates (1+(2+(3+…(n=(0)))). Both will always result in the same answer. The list (=a b) only evaluates to true when a=b, as a does equal b the list always evaluates to true for n>0. Perhaps this answer will make more sense when I understand the code fragment. c) Solution 1 (without existing functions) (define (internal-range a b) (if(>=(+ a 1)b) 0 (+(= a 1)(internal-range(+ a 1)b)))) Solution 2 using existing functions. And assuming ab case (define (internal-range3 a b) (if (< a b) (-(this b) (this a)b) (-(this a) (this b)a))) What is the role of the "0" character in solution 1 and the initial fragment? What is the syntax rule being followed by the parentheses? They note that the code was tested by "Dr Scheme" at www.plt-scheme.org Thanks Jul 18 '05 #1
12 Replies

 P: n/a Fran wrote: I'm trying to understand a functional language code fragment so I can explain its syntax and workings to my non English-speaking background neighbour, who is doing her finals. What in heaven's name is this code fragment intending? (In English prose if possible). It looks like a fragment from a language called "scheme" (define (this n) (if (=n 0) 0 (= n (this (- n 1))))) (define (f1 a b) (if >b a) 0 (+ b (f1 a (+ b 1))))) (define (that n) (f1 n1) [silly disclaimer] I don't know Scheme but I'd suppose the above to be equivalent to the following python (you seem to have some problems counting the brackets :-) def this(n): if n == 0: return 0 else: return n + this(n-1) def f1(a, b): if b > a: return 0 else: return b + f1(a, b+1) def that(n): return f1(n, 1) # try it out print this(4) print 'experimental "proof"' ALL_POSITIVE_INTEGERS = range(1, 10) for i in ALL_POSITIVE_INTEGERS: print "%s:" % i, this(i), that(i) Otherwise I'd suggest that you download Scheme and just try it out. Perhaps they even have a debugger so you can step through the instructions one at a time... Peter PS: More help would certainly lead to disqualification. Jul 18 '05 #2

 P: n/a fr********@mail.com (Fran) writes: I'm trying to understand a functional language code fragment so I canexplain its syntax and workings to my non English-speaking backgroundneighbour, who is doing her finals. What in heaven's name is this code fragment intending? (In Englishprose if possible). It looks like a fragment from a language called "scheme" (define (this n) (if (=n 0) 0 (= n (this (- n 1))))) As given this is almost certainly wrong. The first problem is possibly just a transcription error in that (=n 0) should probably be (= n 0). The second one is the that the last line doesn't make sense. It looks like someone is confused about how if statements work. Since this looks suspiciously like homework I'm only giving a hint. If statements work like (if expr1 (expr to return if exp1 is true) (expr to return if exp1 is false)) Since each arm is an expression to evaluate it means you evaluate '=' as a function in the last line hence it returns a boolean, which is going to cause you grief after a short while. (define (f1 a b) (if >b a) 0 (+ b (f1 a (+ b 1))))) This is wrong syntactically (hint: the first expression for the if statement) The questions wouldn't make sense until you fixed the functions. There is a comp.lang.scheme incidentally. Eddie Jul 18 '05 #3

 P: n/a Unfortunately it looks more like 'broken scheme'. Fran wrote: (define (this n) (if (=n 0) 0 (= n (this (- n 1))))) That looks fine, however: (define (f1 a b) (if >b a) 0 (+ b (f1 a (+ b 1))))) Has 6 (s and 7 )s. I expect that the seconds line should read (if (> b a) (define (that n) (f1 n1) Again there is an imbalance in the ( and ), I think the second line should read (f1 n 1)), note the space between then 'n' and the '1'. Is this someone's homework by any chance? Jul 18 '05 #4

 P: n/a On 2004-08-12, Peter Hickman wrote: Is this someone's homework by any chance? According to the OP, it's part of a final exam. -- Grant Edwards grante Yow! Yow! Those people at look exactly like Donnie visi.com and Marie Osmond!! Jul 18 '05 #5

 P: n/a Grant Edwards wrote: On 2004-08-12, Peter Hickman wrote:Is this someone's homework by any chance? According to the OP, it's part of a final exam. So they are completely shot then? Jul 18 '05 #6

 P: n/a fr********@mail.com (Fran) wrote in message news:<95**************************@posting.google. com>... The right place where to ask this question is comp.lang.scheme. They are pretty gentle with newbies, so don't worry ;) Michele Simionato Jul 18 '05 #7

 P: n/a ed***@holyrood.ed.ac.uk (Eddie Corns) wrote in message news:... fr********@mail.com (Fran) writes:I'm trying to understand a functional language code fragment so I canexplain its syntax and workings to my non English-speaking backgroundneighbour, who is doing her finals.What in heaven's name is this code fragment intending? (In Englishprose if possible).It looks like a fragment from a language called "scheme"(define (this n) (if (=n 0) 0 (= n (this (- n 1))))) As given this is almost certainly wrong. The first problem is possibly just a transcription error in that (=n 0) should probably be (= n 0). The second one is the that the last line doesn't make sense. It looks like someone is confused about how if statements work. Since this looks suspiciously like homework I'm only giving a hint. If statements work like (if expr1 (expr to return if exp1 is true) (expr to return if exp1 is false)) Since each arm is an expression to evaluate it means you evaluate '=' as a function in the last line hence it returns a boolean, which is going to cause you grief after a short while.(define (f1 a b) (if >b a) 0 (+ b (f1 a (+ b 1))))) This is wrong syntactically (hint: the first expression for the if statement) The questions wouldn't make sense until you fixed the functions. There is a comp.lang.scheme incidentally. Eddie Thanks for the help. It's not homework but from an old exam paper, but the girl's English isn't absolutely fluent and I'm looking for a simple way to explain the expressions and functions. FRAN Jul 18 '05 #8

 P: n/a Peter Hickman wrote in message news:<41***********************@news.easynet.co.uk >... Unfortunately it looks more like 'broken scheme'. Fran wrote: (define (this n) (if (=n 0) 0 (= n (this (- n 1))))) That looks fine, however: (define (f1 a b) (if >b a) 0 (+ b (f1 a (+ b 1))))) Has 6 (s and 7 )s. I expect that the seconds line should read (if (> b a) (define (that n) (f1 n1) Again there is an imbalance in the ( and ), I think the second line should read (f1 n 1)), note the space between then 'n' and the '1'. Is this someone's homework by any chance? Thanks for the help. It's not homework but from an old exam paper, but the girl's English isn't absolutely fluent and I'm looking for a simple way to explain the expressions and functions. FRAN Jul 18 '05 #9

 P: n/a Grant Edwards wrote in message news:<41***********************@newsreader.visi.co m>... On 2004-08-12, Peter Hickman wrote: Is this someone's homework by any chance? According to the OP, it's part of a final exam. It's not a final exam (that won't come until October-November) but from an old exam paper. The girl's English isn't absolutely fluent and I'm looking for a simple way to explain the expressions and functions. FRAN Jul 18 '05 #10

 P: n/a fr********@mail.com (Fran) writes: I'm trying to understand a functional language code fragment so I canexplain its syntax and workings to my non English-speaking backgroundneighbour, who is doing her finals. What in heaven's name is this code fragment intending? (In Englishprose if possible). It looks like a fragment from a language called "scheme" (define (this n) (if (=n 0) 0 (= n (this (- n 1)))))(define (f1 a b) (if >b a) 0 (+ b (f1 a (+ b 1)))))(define (that n)(f1 n1) For the record these three functions should have been written. (define (this n) (if (= n 0) 0 (+ n (this (- n 1))))) (define (f1 a b) (if (> b a) 0 (+ b (f1 a (+ b 1))))) (define (that n) (f1 n 1)) Which would have been obvious if I'd bothered to read the detailed stuff later instead of assuming. Peter's translation is correct. It's basically testing reasoning about recursive functions. You need to know that, unlike Python, every expression returns a value and every '(...)' is an expression to be evaluated. So the 'if' statement returns the result of whichever of the arms it takes, which in turn becomes the result of the function. Eddie Jul 18 '05 #11

 P: n/a > Thanks for the help. It's not homework but from an old exam paper, but the girl's English isn't absolutely fluent and I'm looking for a simple way to explain the expressions and functions. If there are points to be won for brevity then the answer is 'two functions (one with a helper) to compute factorials' Jul 18 '05 #12

 P: n/a Peter Hickman wrote in message news:<41**********************@news.easynet.co.uk> ... Thanks for the help. It's not homework but from an old exam paper, but the girl's English isn't absolutely fluent and I'm looking for a simple way to explain the expressions and functions. If there are points to be won for brevity then the answer is 'two functions (one with a helper) to compute factorials' Thanks greatly ... Admirably concise. FRAN Jul 18 '05 #13

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