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Update Associativity Section in Expressions.Rmd #1781

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3 changes: 2 additions & 1 deletion Expressions.Rmd
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Expand Up @@ -473,7 +473,8 @@ Note the appearance of the parentheses in the AST as a call to the `(` function.

### Associativity

The second source of ambiguity is introduced by repeated usage of the same infix function. For example, is `1 + 2 + 3` equivalent to `(1 + 2) + 3` or to `1 + (2 + 3)`? This normally doesn't matter because `x + (y + z) == (x + y) + z`, i.e. addition is associative, but is needed because some S3 classes define `+` in a non-associative way. For example, ggplot2 overloads `+` to build up a complex plot from simple pieces; this is non-associative because earlier layers are drawn underneath later layers (i.e. `geom_point()` + `geom_smooth()` does not yield the same plot as `geom_smooth()` + `geom_point()`).
The second source of ambiguity is introduced by repeated usage of the same infix function. For example, is `1 + 2 + 3` equivalent to `(1 + 2) + 3` or to `1 + (2 + 3)`? This normally doesn't matter because `x + (y + z) == (x + y) + z`, i.e. addition is associative, but is needed because some S3 classes define `+` in a non-associative way. For example, ggplot2 overloads `+` to build up a complex plot from simple pieces. This is non-associative because the plot must be initialized before a layer is added to it: `(ggplot(mtcars, aes(x = disp, y = mpg)) + geom_point()) + geom_smooth()` will work, while `ggplot(mtcars, aes(x = disp, y = mpg)) + (geom_point() + geom_smooth())` will not.
Furthermore, this is also non-commutative because later layers are drawn on top of earlier layers (i.e. `geom_point()` + `geom_smooth()` does not yield the same plot as `geom_smooth()` + `geom_point()`).

In R, most operators are __left-associative__, i.e. the operations on the left are evaluated first:

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