On Fri, 24 Apr 2020 18:50:11 -0700, Mario Carneiro <[email protected]> wrote:
> I like the idea of using ++ for concatenation, particularly in ascii
> notation, since I don't want to try to reproduce a frown symbol in ascii. I
> think the most common symbol for this is adjacency though.

I also have (mild) prefererence for "++" to represent concatenation.
In particular, I'd prefer "++" as the ASCII representation, with a Unicode 
display
of ⧺ (U+29FA) and \doubleplus in LaTeX (package unicode-math).
This is somewhat common in Computer Science; Haskell uses "++"
for concatenation, and many other programming languages use "+" for 
concatenation
(but they can use types to figure out what overloaded operation was meant).
I think ++ would make the ASCII display a little simpler, and many people think 
of
"add" and "concatenate" as related... so having intentionally similar symbols
has some mild advantages.

Frown looks a little like intersection, even though there's no relationship,
and that could be considered a negative for it.
That said, frown has significant use, it's not terribly ambiguous,
and it just works, so I'm not unhappy with it.

Bottom line: I have a minor preference for ++, but it's not a big deal to me.

I agree that "no displayed symbol, just adjacency" is common. However,
generally in Metamath we try to be very explicit, so I think we shouldn't have
"no displayed symbol" in Metamath (at least in set.mm) for concatenation.

Notation is hard. There's a brief related discussion here:
https://math.stackexchange.com/questions/298648/is-there-a-common-symbol-for-concatenating-two-finite-sequences
I don't like the other options discussed there (the other symbols already
have other conflicting meanings), so I think frown and doubleplus are the 
contenders.

--- David A. Wheeler

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