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R - assign element names to column names inside a list of lists of dataframes in tidyverse

I have a list of lists of dataframes, each having one column, like this:

list(list(A = data.frame(X = 1:5),
          B = data.frame(Y = 6:10),
          C = data.frame(Z = 11:15)),
     list(A = data.frame(X = 16:20),
          B = data.frame(Y = 21:25),
          C = data.frame(Z = 26:30)),
     list(A = data.frame(X = 31:35),
          B = data.frame(Y = 36:40),
          C = data.frame(Z = 41:45))) -> dflist

I need to make it so that the column names X, Y and Z inside of each dataframe are changed to A, B and C. An important thing to add is that the names A, B and C are not known beforehand, but must be extracted from the list element names. I have a simple script that can accomplish this:

for(i in 1:3){
    for(j in 1:3){
        colnames(dflist[[i]][[j]]) <- names(dflist[[i]])[[j]]
    }
}

However, I need to do this in tidyverse style. I have found similar questions on here, however, they only deal with lists of dataframes and not with lists of lists of dataframes and I can't find a way to make it work.

Using combination of map and imap -

library(dplyr)
library(purrr)

map(dflist, function(x) 
  imap(x, function(data, name) 
    data %>% rename_with(function(y) name)))

#[[1]]
#[[1]]$A
#  A
#1 1
#2 2
#3 3
#4 4
#5 5

#[[1]]$B
#   B
#1  6
#2  7
#3  8
#4  9
#5 10

#[[1]]$C
#   C
#1 11
#2 12
#3 13
#4 14
#5 15
#...
#...

Also possible without purrr, using lapply and mapply (the latter with SIMPLIFY=FALSE ). If dflist is your list of lists:

lapply(dflist, function(x){
  mapply(function(y,z){
    `colnames<-`(y, z)
  }, y=x, z=names(x), SIMPLIFY=F)
})

#or on one line:
lapply(dflist, function(x) mapply(function(y,z) `colnames<-`(y, z), y=x, z=names(x), SIMPLIFY=F))

A solution with purrr:walk :

library(tidyverse)

walk(1:length(dflist), 
     function(x) 
       walk(names(dflist[[x]]), ~ {names(dflist[[x]][[.x]]) <<- .x}))

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