[Haskell-beginners] Re: Why is there no notion of a one-tuple (e.g., a '([])' as opposed to a '[]') in Haskell?

On Wed, 24 Sep 2008 21:27:37 -0400, ajb@spamcop.net wrote:

G'day all.

Quoting "Benjamin L.Russell" :

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Haskell doesn't have a notion of a one-element tuple.

Why not?

As noted by others, there's no syntactic space for them.

Perhaps more crucially, it's hard to see where such a thing would be useful. The 2-tuple (i.e. pair) is a categorical product, and can be used to carry around two things where you would normally only have space for one. The 0-tuple (i.e. void) is a categorical terminal object, and can be used to fill in space in a parametric data structure where no annotation is actually needed.

One reason why they're provided in the Prelude is so that standard functions can do operations on them. It's hard to see where a standard function would use a generic 1-tuple.

Generally speaking, if you need a type-checked 1-tuple, you almost certainly don't want a generic one.

So, basically generic one-element tuples don't exist because they're not needed, and there is no elegant way to represent them syntactically. That makes sense. Nevertheless, I can't help feeling that Haskell could perhaps been made even more elegant if some alternative tuple notation not conflicting with parentheses had been used; e.g., '{}' (braces) (please forgive me if braces are already used for some other purpose of which I am not aware). Then, for example, we could have the following: {} (a unit, or void), {{}} (a one-tuple), {{{}}} (a one-tuple consisting of a one-tuple), {{{{}}}} (a one-tuple consisting of a one-tuple consisting of a one-tuple), ... We could then come up with an n-depth-ordering on tuples, as opposed to an ordering on n-tuples. While perhaps not immediately useful, this ordering would have an interesting structure, and perhaps lead to some kind of mathematics of n-depth-orderings, which could be even more interesting, and which could be expressed in Haskell. -- Benjamin L. Russell