I am aware of at least two distinct uses of the equals sign in the R-programming language:
(1) as a deprecated assignment operator, i.e. x = 3 instead of x <- 3.
(2) for passing values of arguments to functions, e.g. ggplot(df, aes(x = length, y = width))
Do either of these operators correspond to symmetric relations (in the sense of mathematics)?
The 'equals' operator == does (I think), which is why it corresponds most closely to the use of the equals sign in mathematics (which is always a symmetric relation).
But for example if one tried to run ggplot(df, aes(length = x, width = y) one would get an error, and one would also get an error trying to run 3 = x.
Thus, is it true that, unlike in mathematics, the equals sign in R is not a symmetric relation? Is that why <- is preferred by some for assignment, because it better conveys the lack of symmetry?
Bonus question: are there other programming languages where the equals sign does not correspond to a symmetric relation? PowerShell (I have never heard of it before) might be one.
The = operator is not symmetric in R. When it comes to assignment, = is basically a function that takes a symbol and a value and assigns that value to that symbol. When it comes to named parameters, it's really just part of the syntax of naming a parameter.
<- is preferred for assignment simply because it has an unambiguous meaning.