What is the "core" tidyverse packages?

Here is a reprex of running library(tidyverse) as well as the sessionInfo. As you can see, the core packages are attached.

library(tidyverse)
sessionInfo()
#> R version 3.4.2 (2017-09-28)
#> Platform: x86_64-apple-darwin15.6.0 (64-bit)
#> Running under: macOS Sierra 10.12.6
#> 
#> Matrix products: default
#> BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
#> LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
#> 
#> locale:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] forcats_0.2.0      stringr_1.2.0      dplyr_0.7.4.9000  
#> [4] purrr_0.2.4        readr_1.1.1.9000   tidyr_0.7.2       
#> [7] tibble_1.3.4       ggplot2_2.2.1.9000 tidyverse_1.2.1   
#> 
#> loaded via a namespace (and not attached):
#>  [1] Rcpp_0.12.14          cellranger_1.1.0      compiler_3.4.2       
#>  [4] plyr_1.8.4            bindr_0.1             tools_3.4.2          
#>  [7] digest_0.6.12         lubridate_1.7.1       jsonlite_1.5         
#> [10] evaluate_0.10.1       nlme_3.1-131          gtable_0.2.0         
#> [13] lattice_0.20-35       pkgconfig_2.0.1       rlang_0.1.4.9000     
#> [16] psych_1.7.8           cli_1.0.0             yaml_2.1.16          
#> [19] parallel_3.4.2        haven_1.1.0           bindrcpp_0.2         
#> [22] xml2_1.1.9000         httr_1.3.1            knitr_1.17.20        
#> [25] hms_0.4.0             rprojroot_1.2         grid_3.4.2           
#> [28] tidyselect_0.2.3      glue_1.2.0.9000       R6_2.2.2             
#> [31] readxl_1.0.0          foreign_0.8-69        rmarkdown_1.8        
#> [34] modelr_0.1.1          reshape2_1.4.3        magrittr_1.5         
#> [37] backports_1.1.2       scales_0.5.0.9000     htmltools_0.3.6      
#> [40] rvest_0.3.2.9000      assertthat_0.2.0.9000 mnormt_1.5-5         
#> [43] colorspace_1.3-2      stringi_1.1.6         lazyeval_0.2.1.9000  
#> [46] munsell_0.4.3         broom_0.4.3           crayon_1.3.4

Created on 2017-12-15 by the reprex package (v0.1.1.9000).

The non-core members of the tidyverse are installed by

install.packages("tidyverse")

but are not attached. Though the "membership" has changed, you can read here for what makes tidyverse packages part of a coherent system.

Packages, such as cli (since you mentioned it), tidyselect, and crayon are part of what's called r-lib. While the tidyverse consists of highly-opinionated tools for data science; r-lib contains mostly-unopinionated infrastructure tools. Their specific uses differ, but, for the most part, r-lib packages are not something the average R user will need. They're more for development, testing, and are utilized by the tidyverse packages (e.g. tidyselect provides backend of functions like dplyr::select() or dplyr::pull() as well as several tidyr verbs) and other activities more akin to programming with R.

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