[Axiom-math] About mutable and functions.

[Francois Maltey]

I like this discuss about mutable variables.

You know I also teach caml. I notice that the 2 manners "mutable data" 
and "not-mutable" data must be separate. 
If not, everybody make a lot of errors.

Functional languages, mathematics and not-mutable datas are very close.

What do you think about this concrete matrix example ?

A := matrix [[1,2],[3,4]]
fct A == .... A.(1,1) := 10 .... and the result is a number or others.

Mathematics say that both 3*A matrices bellow are equal :
The variable A is the same and we don't see any assin command.

3*A 
fct A
3*A     --- ve verify the matrix.

We don't understand why A changes.
First we think about the result of fct, not about the manner we get it.

Is it possible to have an automatic copy of the variables in a function ?

On the other hand, if we want to code a matrix sequence we write :
M := matrix [[...]]
fct A == ...A.(1,1):=A.... A -- this A is the result, the new matrix.
M := fct M 
M := fct M -- to iterate.

The time for copying data-structure isn't so long that we must think 
everytime about it. Axiom is designed for mathematics.

Axiom Guru's find obvious to code
fct M == A:=copy M ... ....     in the first case.
fct A == A.(1,1) := 12 .... A   in the second case.
and it's a little faster.

But that forces to teach what are mutable/not-mutable data 
in the first courses of axiom. 
This isn't the aim of axiom which is a mathematical language.

fct A == ... ....               axiom copy the matrix.
fct A == A.(1,1) := 12 .... A   the outer M := explains the matrix change.

Maple use a silly evalm matrix command. 
And I never get difficult with mupad which copy data structure by default.

And what do you think about lists ?
My first thought for mathematics thinks that lists aren't mutable.
But list becomes mutable with L.3 := 33. This assign command is too easy.

A setelt! (L, 3, 33) doesn't hide the same difficult.

Francois.