dplyr equivalent of sql row_number() over (partition by group order by value)

Question

Initial situation

I have a data set of the following form:

library(dplyr)

dat <- tribble(
  ~name, ~iq,
  "ben",  100,
  "alex",  98,
  "mia",  110,
  "paco", 124,
  "mia",  112,
  "mia",  120,
  "paco", 112,
  "ben",   90,
  "alex", 107
)

I'd like to create a new column which ranks, grouped by name, the values iq in descending order. In SQL one could write

select
  name,
  iq,
  row_number() over (partition by name order by iq desc) as rank
from
  dat;

which would produce the following expected output (already ordered for simplicity):

#>   name     iq  rank
#>   <chr> <dbl> <int>
#> 1 alex    107     1
#> 2 alex     98     2
#> 3 ben     100     1
#> 4 ben      90     2
#> 5 mia     120     1
#> 6 mia     112     2
#> 7 mia     110     3
#> 8 paco    124     1
#> 9 paco    112     2

Questions

With my data, one can achieve the desired result with:

dat %>%
  group_by(name) %>%
  mutate(rank = with_order(order_by = iq,
                           fun      = row_number, 
                           x        = desc(iq)
                           )
         ) %>% 
  arrange(name, rank)

#> # A tibble: 9 x 3
#> # Groups:   name [4]
#>   name     iq  rank
#>   <chr> <dbl> <int>
#> 1 alex    107     1
#> 2 alex     98     2
#> 3 ben     100     1
#> 4 ben      90     2
#> 5 mia     120     1
#> 6 mia     112     2
#> 7 mia     110     3
#> 8 paco    124     1
#> 9 paco    112     2

However, I don't understand why the code works. When reading the documentation of dplyr::with_order(), it says the arguments are

• order_by = the vector to order by
• fun = window function
• x, ... = arguments to f

Given the description in the documentation and the working code, I have two questions I cannot answer:

1. What is the purpose of the argument x? Why not just specify the vector to order by and the window function (like in sql)? What is meant by f?
2. Why don't I have to write order_by = desc(iq)? To get the result I expect I have to write x = desc(iq) and set order_by = iq. This seems to contradict the documentation, which states that order_by = the vector to order by.