Infix operators

[tkf]

As briefly discussed in #8 (comment), it'd be nice to have some infix operator for Mul and Add.

FYI here is the list of infix operators with plus and time precedence (from https://github.com/JuliaLang/julia/blob/master/src/julia-parser.scm):

(define prec-plus (append! '($) (add-dots '(+ - |\|| ⊕ ⊖ ⊞ ⊟ |++| ∪ ∨ ⊔ ± ∓ ∔ ∸ ≏ ⊎ ⊻ ⊽ ⋎ ⋓ ⧺ ⧻ ⨈ ⨢ ⨣ ⨤ ⨥ ⨦ ⨧ ⨨ ⨩ ⨪ ⨫ ⨬ ⨭ ⨮ ⨹ ⨺ ⩁ ⩂ ⩅ ⩊ ⩌ ⩏ ⩐ ⩒ ⩔ ⩖ ⩗ ⩛ ⩝ ⩡ ⩢ ⩣))))

(define prec-times (add-dots '(* / ÷ % & ⋅ ∘ × |\\| ∩ ∧ ⊗ ⊘ ⊙ ⊚ ⊛ ⊠ ⊡ ⊓ ∗ ∙ ∤ ⅋ ≀ ⊼ ⋄ ⋆ ⋇ ⋉ ⋊ ⋋ ⋌ ⋏ ⋒ ⟑ ⦸ ⦼ ⦾ ⦿ ⧶ ⧷ ⨇ ⨰ ⨱ ⨲ ⨳ ⨴ ⨵ ⨶ ⨷ ⨸ ⨻ ⨼ ⨽ ⩀ ⩃ ⩄ ⩋ ⩍ ⩎ ⩑ ⩓ ⩕ ⩘ ⩚ ⩜ ⩞ ⩟ ⩠ ⫛ ⊍ ▷ ⨝ ⟕ ⟖ ⟗)))

We can also add suffixes and combining characters JuliaLang/julia#22089

Some ideas:

• *″ +″: Declare some common suffix to represent lazy version (e.g., double-prime ″). It would be handy if we need more operators in the future (e.g, -″).

• *ₗ +ₗ: Same idea but with a subscript l (or maybe superscript).

• *̂ +̂: Same idea but with combining character. It may be hard to recognize in some fonts.

• ⋆: good for lazy multiplication, as it looks like * but sufficiently different to distinguish?

• ⊕: good for lazy sum as it already has semantics of element wise sum (direct sum)? But this does not apply to Mul.

I think common suffix (like ₗ and ″) is a good choice as it provides a uniform style and it is extensible.

[tkf]

Here is a snippet to show * and + with the combining characters

for c in '\u0300':'\u036f'
    print("*", c, " ", "+", c, " ")
end
println()

Output:

*̀ +̀ *́ +́ *̂ +̂ *̃ +̃ *̄ +̄ *̅ +̅ *̆ +̆ *̇ +̇ *̈ +̈ *̉ +̉ *̊ +̊ *̋ +̋ *̌ +̌ *̍ +̍ *̎ +̎ *̏ +̏ *̐ +̐ *̑ +̑ *̒ +̒ *̓ +̓ *̔ +̔ *̕ +̕ *̖ +̖ *̗ +̗ *̘ +̘ *̙ +̙ *̚ +̚ *̛ +̛ *̜ +̜ *̝ +̝ *̞ +̞ *̟ +̟ *̠ +̠ *̡ +̡ *̢ +̢ *̣ +̣ *̤ +̤ *̥ +̥ *̦ +̦ *̧ +̧ *̨ +̨ *̩ +̩ *̪ +̪ *̫ +̫ *̬ +̬ *̭ +̭ *̮ +̮ *̯ +̯ *̰ +̰ *̱ +̱ *̲ +̲ *̳ +̳ *̴ +̴ *̵ +̵ *̶ +̶ *̷ +̷ *̸ +̸ *̹ +̹ *̺ +̺ *̻ +̻ *̼ +̼ *̽ +̽ *̾ +̾ *̿ +̿ *̀ +̀ *́ +́ *͂ +͂ *̓ +̓ *̈́ +̈́ *ͅ +ͅ *͆ +͆ *͇ +͇ *͈ +͈ *͉ +͉ *͊ +͊ *͋ +͋ *͌ +͌ *͍ +͍ *͎ +͎ *͏ +͏ *͐ +͐ *͑ +͑ *͒ +͒ *͓ +͓ *͔ +͔ *͕ +͕ *͖ +͖ *͗ +͗ *͘ +͘ *͙ +͙ *͚ +͚ *͛ +͛ *͜ +͜ *͝ +͝ *͞ +͞ *͟ +͟ *͠ +͠ *͡ +͡ *͢ +͢ *ͣ +ͣ *ͤ +ͤ *ͥ +ͥ *ͦ +ͦ *ͧ +ͧ *ͨ +ͨ *ͩ +ͩ *ͪ +ͪ *ͫ +ͫ *ͬ +ͬ *ͭ +ͭ *ͮ +ͮ *ͯ +ͯ

Here is how it looks in my terminal (using UbuntuMono font in urxvt):

[tkf]

Here is how it is rendered in Emacs with DejaVu Sans Mono:

It looks like combining characters going below the symbol (e.g., *̰ +̰) are easier to recognize in general.

[dlfivefifty]

Unfortunately the subscript l does not show up for me (in either Juno or REPL), so I think that's out, unless there's an easy fix.

I just added ⋆ to mean rmaterialize(Mul(...)): that is, to force the materialize to go right-to-left. Though this syntax has not been tagged, so we can easily change that to, say, ⨴. I think at the moment I like ⋆ best, but let me think a bit more.

[tkf]

Sadly, ⨴ cannot be rendered in my environment (in browser, terminal and editor).

⋆ sounds good to me too, but I'd like to have a lazy addition API as well. How about ⊕?

[dlfivefifty]

I don't know about ⊕: it means direct sum and I think of it more of a a "block-diagonal" operation, and based on the definition you might expect (A ⊕ B) * (C ⊕ D) == (A*B) ⊕ (C*D), though I suppose if the group operation is + then its a different story.

Do we envision other lazy operations? If so, a sub/superscript may be the best. If only subscript l rendered for me!

[tkf]

Ah, I get what you are saying about ⊕. Yes, ⊕ would be confusing.

Do we envision other lazy operations?

Point-wise subtraction could be useful to have.

If only subscript l rendered for me!

How about the superscript?: *ˡ

[tkf]

Do we envision other lazy operations?

I think an important question here is if we want to have a lazy Hadamard/elementwise product because then we need two flavors of *. But I can't imagine the situation you'd need it.

[dlfivefifty]

I think an important question here is if we want to have a lazy Hadamard/elem

Remember we always have the explicit broadcasted(*, A, B) and BroadcastArray(*, A, B) so the unicode are only needed for often used cases. I don't think lazy Hadamard is important enough to warrant a special syntax.

[tkf]

I just wanted to point out the naming system that just append a suffix is going to break if we want infix operator for the two flavors of multiplication. But I agree that's very unlikely.

[dlfivefifty]

I think @~ has superseded this.