On Mon, Jan 16, 2023 at 07:14:49PM +0300, Jean Louis wrote:
> * Yuri Khan <yuri.v.khan@gmail.com> [2023-01-16 19:01]:
> > On Mon, 16 Jan 2023 at 22:50, Jean Louis <bugs@gnu.support> wrote:
> > 
> > > There are no elements in this context.
> > >
> > > (+) ➜ 0
> > 
> > There is a list of elements, and the length of that list is zero.
> > 
> > > Multiplication of zero elements is also zero:
> > > (* 0 0) ➜ 0
> > > but Lisp:
> > > (*) ➜ 1
> > 
> > You are conflating elements of zero value with a zero count of elements.
> > 
> > You are not willing to understand. I suspect you also will not believe
> > me if I tell you all my dogs have green hair.
> 
> I am very willing to understand. This should not be place of laughing
> me out because I keep asking questions.

Again: the behaviour of Lisp's + and * is modeled after maths
conventions. Assuming you've read both Wikipedia references I
linked to you might understand why those conventions "make sense"
(no they are not theorems or some such, just conventions, you
notice that proofs and formulae are usually simpler).

The mathematical things modeled by Lisp's + and * are the
summation Σ and the product Π. In maths, the empty sum
evaluates to 0, the empty product to 1 [1] [2] (for the
last one: otherwise this would be at odds that a number
raised to the zeroth power also yields 1).

So why would Lisp, modeling numbers (roughly) after maths,
deviate from math conventions?

If you do functional programming, this corresponds nicely
to anamorphisms [3]: you have a start value and a two-place
funtion and calculate the next "start" value by combininb
the old one with the next in the list.

For sums, your start value would be zero. For products?
Nah :)

Cheers

[1] "If the summation has no summands, then the evaluated sum is
     zero, because zero is the identity for addition. This is
     known as the empty sum."
    https://en.wikipedia.org/wiki/Sigma_notation#Special_cases

[2] "[...] an empty product whose value is 1 -- regardless of the
     expression for the factors."
    https://en.wikipedia.org/wiki/Capital-pi_notation#Capital_pi_notation

[3] Google called them "reduce" in their "map-reduce" framework,
    but they try to put their scent on everything. They didn't
    invent them. Oh, that's the way you can define aggregates
    in your beloved PostgreSQL, too.
    https://en.wikipedia.org/wiki/Anamorphism
-- 
t