Help understanding Scheme's syntax, procedures and calls

[Fran]

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 a<b

(define (internal-range2 a b)
(-(this b) (this a)b))

Solution 3 using existing functions and dealing with a>b 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

 

[Peter Otten]

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.

 

[Eddie Corns]

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)))))

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

 

[Peter Hickman]

Unfortunately it looks more like 'broken scheme'.

(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?

 

[Grant Edwards]

Is this someone's homework by any chance?

According to the OP, it's part of a final exam.

 

[Peter Hickman]

According to the OP, it's part of a final exam.

So they are completely shot then?

 

[Michele Simionato]

(e-mail address removed) (Fran) wrote in message <Scheme question>

The right place where to ask this question is comp.lang.scheme.
They are pretty gentle with newbies, so don't worry

Michele Simionato

 

[Fran]

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.


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

 

[Fran]

Unfortunately it looks more like 'broken scheme'.


That looks fine, however:


Has 6 (s and 7 )s. I expect that the seconds line should read
(if (> b a)


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

 

[Fran]

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

 

[Eddie Corns]

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)

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

 

[Peter Hickman]

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'

 

[Fran]

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