# [Om] Tuple and list : any distinction?

Michael Kohlhase m.kohlhase at jacobs-university.de
Thu Feb 18 18:09:34 CET 2010

```Dear Joe,

there are at least two possible answers to this question:

Mathematical:

generally spoken, tuples and lists are isomorphic as data raw
structures, but support conceptually different operations. Tuples are
usually thought of as having fixed length and operations are between
tuples of same length. Operations are mostly from linear algebra. In the
ecc CD we have dependent tuples that are mostly used for defining
functions.

Lists are thought of as of variable length, and the operations are
mostly constructing lists from the empty list by prepending, appending
lists, mapping functions over lists,.... Moreover, lists typically only
have members of the same "type".

So, even though everything you do with tuples,  the mathematical,
operational  intuitions are quite different.

Formally:

The levels of formality in the descirption of ecc and list1/2 are vastly
different. ECC (Extended Calculus of Construction) is a logical system,
where tupling has a very well-defined role. list1/2 is a (intendedly)
vague description of a vocabulary of lists without going into too much
detail, so that it can be universally used.

hope this helps,

Michael

On 17.02.10 14:51, Joe Collins wrote:
> The OpenMath ecc CD defines Tuple and the list1 CD defines list.
>
> Is there any essential distinction between Tuple and list?
> If so, what?
>
> Some of the definitions in list1, list2 suggest (to me) that the order of the
> list elements are arbitrary. Is this actually the case?
>
> Joe
>

--
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```

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