[r6rs-discuss] Comparison procedures' number of arguments

[Abdulaziz Ghuloum]

On Oct 21, 2008, at 11:04 AM, Ken Dickey wrote:

> No.  Actually, I'd like a holds-for-all which returns #f as the  
> base case.

You can push it down, but you can't escape making these
exceptions.

Nonrecursive definitions:

for-all p? [a_i, ...] = (and (p? a_i) ...)

holds-for-all p? []  = #f ;;; Exception to the and rule
holds-for-all p? [a_i, ...]  = (and (p? a_i) ...)

this holds-for-all is more complex than the plain for-all.


Recursive definitions:

for-all p? [] = #t
for-all p? [a : as] = (and (p? a) (for-all p? as))

holds-for-all p? [] = #f  ;;; Exception again
holds-for-all p? [a] = (p? a)
holds-for-all p? [a : as] = (and (p? a) (holds-for-all p? as))

this holds-for-all is also more complex than the plain for-all.

There's a reason why this holds-for-all does not appear as often
in math (even elementary high-school math) as the vanilla for-all.

Aziz,,,