Pass in function as input and return function

Question

I want to write an R function that takes a mathematical function in x and returns a new function in x as an output. For example:

The input should be passed in as a mathematical function (or relation) in x:

g <- x^2 + 9*x + log(x)

And the resulting output should be:

function(x) (exp(g))

i.e. I want to return the symbolic exponential expression of the original function in x i.e. exp(x^2 + 9*x + log(x)) in this illustrative example

So ideally it would return the function object:

function(x) (exp(x^2 + 9*x + log(x)))

I tried as follows:

test <- function(g){
h <- function(x){exp(g)}
return(h)
}
m <- test(x^2 + 9*x + log(x))
m(10)

So m(10) should return:

exp(10^2 + 9*10 + log(10))

which is exp(192.3026) in this case.

Could anyone show how to do this please?

Answer 1

You could use package functional:

library(functional)
fun <- Compose(function(x) x^2 + 9*x + log(x), exp)
fun(1)
#[1] 22026.47

Answer 2

Here is one approach:

test <- function(e) {
    ee <- substitute(e)
    eee <- substitute(exp(X), list(X=ee))
    f <- function(x) {}
    body(f) <- eee
    environment(f) <- parent.frame()
    f
}

## Check that it works
m <- test(x^2 + 9*x + log(x))
m
# function (x) 
# exp(x^2 + 9 * x + log(x))
m(1)
# [1] 22026.47
m(1) == exp(10)
# [1] TRUE

Answer 3

edit - for functionality in question

f <- function(...) {
  l <- eval(substitute(alist(x = x, ...)))
  l[[2]] <- substitute(exp(X), list(X = l[[2]]))
  as.function(`names<-`(l, l[sapply(l, is.symbol)]))
}

g <- f(x^2 + 2*x + 5)
# function (x = x) 
#   exp(x^2 + 2 * x + 5)

g(1)
# [1] 2980.958

---

Here is another way for a general case:

f <- function(...) {
  l <- eval(substitute(alist(...)))
  as.function(`names<-`(l, l[sapply(l, is.symbol)]))
}

g <- f(x, x^2 + 9*x + log(x))

# function (x = x) 
#   x^2 + 9 * x + log(x)

g(10)
# [1] 192.3026

This version will also work for any number of variables, just define them followed by the function:

g <- f(x, y, z, x + 2 * y + z ** 3)

# function (x = x, y = y, z = z) 
#   x + 2 * y + z^3

g(1, 2, 0)
# [1] 5

---

There may be a better way to add ... to functions, but here is how you can do that

f <- function(..., use_dots = FALSE) {
  l <- eval(substitute(alist(...)))
  if (use_dots)
    l <- c(head(l, -1), list('...' = as.symbol('...')), tail(l, 1))
  as.function(`names<-`(l, l[sapply(l, is.symbol)]))
}

So now you don't have to name all the variables/arguments

g <- f(x, y, plot(x, y, ...), use_dots = TRUE)
g(1:5, 1:5, main = 'main title', pch = 16, col = 3, cex = 3, xpd = NA)