@technocrat is correct.
Composing usually means that output of one function is exactly the input of the second function. This also means that input of first function should be the input to only first function. Your hunch about currying is correct, but in R we usually do it with partial as you did in your example. However, if I understood you correctly, you want to have multiple functions with possibly multiple regexes going over the same text file. You can achieve this with partial by creating multiple functions that all take only one argument, so one implementation can be something like the following:
library(magrittr)
regexes <- list("[^0-9]+", "[^a-z]+")
reg_fun <- purrr::map(regexes, ~purrr::partial(stringr::str_split, pattern = .x, simplify = TRUE)) %>%
purrr::reduce(purrr::compose)
string <- "some string that is not that useful in this example, but demonstrates the approach"
reg_fun(string)
#> [,1] [,2]
#> [1,] "" ""
#> [2,] "" ""
#> [3,] "" ""
#> [4,] "" ""
#> [5,] "" ""
#> [6,] "" ""
#> [7,] "" ""
#> [8,] "" ""
#> [9,] "" ""
#> [10,] "" ""
#> [11,] "" ""
#> [12,] "" ""
#> [13,] "" ""
#> [14,] "" ""
Created on 2019-01-11 by the reprex package (v0.2.1)