Lookup list of formulas in other list - r

Question

I am comparing two lists of formulas to see if some previously computed models can be reused. Right now I'm doing this like this:
set.seed(123)
# create some random formulas
l1 <- l2 <- list()
for (i in 1:10) {
l1[[i]] <- as.formula(paste("z ~", paste(sample(letters, 3), collapse = " + ")))
l2[[i]] <- as.formula(paste("z ~", paste(sample(letters, 3), collapse = " + ")))
}
# at least one appears in the other list
l1[[5]] <- l2[[7]]
# helper function to convert formulas to character strings
as.formulaCharacter <- function(x) paste(deparse(x))
# convert both lists to strings
s1 <- sapply(l1, as.formulaCharacter)
s2 <- sapply(l2, as.formulaCharacter)
# look up elements of one vector in the other
idx <- match(s1, s2, nomatch = 0L) # 7
s1[idx] # found matching elements
However, I noticed that some formulas are not retrieved although they are practically equivalent.
f1 <- z ~ b + c + b:c
f2 <- z ~ c + b + c:b
match(as.formulaCharacter(f1), as.formulaCharacter(f2)) # no match
I get why this result is different, the strings just aren't the same, but I'm struggling with how to extend this approach method to also work for formulas with reordered elements. I could use strsplit to first sort all formula components independently, but that sounds horribly inefficient to me.
Any ideas?

Answer 1

If the formulas are restricted to a sum of terms which contain colon separated variables then we can create a standardized string by extracting the term labels, exploding those with colons, sorting them, pasting the exploded terms back together, sorting this and turning that into a formula string.
stdize <- function(fo) {
s <- strsplit(attr(terms(f2), "term.labels"), ":")
terms <- sort(sapply(lapply(s, sort), paste, collapse = ":"))
format(reformulate(terms, all.vars(fo)[1]))
}
stdize(f1) == stdize(f2)
## [1] TRUE