Re: How to pass a fraction as a parameter for a Scheme function

[Aaron Hill]

On 2020-06-10 10:28 am, Paolo Prete wrote:
> ... I have been misled by the term "rational". In fact, in the italian
> language the term "rational" (---> razionale)  means an irreducible
> fraction of two coprime integers, while in the english language it 
> means a
> number that can be expressed as the quotient or fraction p/q of two
> integers.
> For example, "2/4" is not rational in italian, but it is rational in
> english. Then I did not even consider that predicate.
> I suggest the italian maintainer of the translation to keep note of 
> this
> ambiguity.

I would not be so hasty.

A rational value and a fraction are two related but distinct things.  A 
fraction is the thing that consists of a numerator and a denominator, 
whereas the rational value is the ratio between the two components of 
the fraction.  So to say "2/4 is rational in English" is potentially 
misleading.  Regardless of native tongue, 2/4 is specifically a fraction 
that simply has a rational value of 1:2.  2/4 is not the rational value, 
1:2 is.  2/4 may be reduced to 1/2 which shares the same ratio, so we 
would say we have two fractions but only one rational value.

Connecting the above to Scheme, fraction? and rational? are distinct 
type predicates.  A fraction? is simply a pair of numbers--the car 
holding the numerator, the cdr holding the denominator.  On the other 
hand, a rational? refers to one of the primitive numeric types.  Of most 
importance, a rational? will be reduced whereas a fraction? will 
preserve the original numerator and denominator.

Going back to the original question regarding fractions, my suggested 
use of rational? would *not* be useful if you need to preserve the 
original numerator and denominator.  Otherwise, things like 4/4 and 2/2 
would look identical to the function.  In fact, the function would 
simply see the integer 1 as input for #4/4.  If all that was needed was 
to specify a duration, then it might not matter since four quarters is 
the same as two halves.  However then, David's suggestion of using 
ly:duration? would make much more sense.


-- Aaron Hill