I play with Tuple :
> (1) -> a:INT:=3
> (2) -> b:INT:=7
> (3) -> (b,a):=(a,b)
> (4) -> a
> (5) -> b
I compare tuple to mupad/maple sequence :
With mupad/maple we can do :
aa := (11,22) // named sequence
fct := (a,b,c) -> a+b+c
fct (aa,100) // and get 133
fct (100, aa) // and get 133
So sequence are spanned in functions and list.
a+b$a=0..9$b=0..9
is read as (a+b$a=0..9)$b=0..9
becomes (0+b,1+b,2+b...9+b)$b=0..9 // a sequence
and finishs by 0+0,...,9+0,0+1,...,9+9
It isn't a good idea because user makes error in use of functions.
A sequence is ONE identificator but can have several terms : see fct bellow.
So I avoid sequences because I can't read fct (aa,100) as a function
with 3 parameters. It's too special !
Axiom doesn't span Tuple and keeps the parenthesis, it's all right...
I notice we play with Tuple, CartesianProduct and record.
I let record as a computer data structure.
Isn't possible to merge Tuple and CartesianProduct into one domain
with standard operators and take the better of these two domains.
1/ Create it by TT := (a,b)
2/ Acces to the field by TT.1 or TT.2
3/ Maybe change a field by TT.1 := ...
4/ Have a type for each field as cartesianProduct.
1/ makeprod in (cartesian)Product isn't a standard function.
and can only be use with 2 arguments, not 3 or any.
2/ TT.1 isn't allowed for Tuple,
select must be use and begins at 0, but index of lists begins at 1.
selectfirst and selectsecond isn't the classical function elt.
4/ Tuple aren't strong typed :
tuple any isn't a cartesianProduct(Integer,String)
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