[R] Functional programming?

[Roger Koenker]

I have a (remarkably ugly!!) code snippet  (below) that, given
two simple functions, f and g,  generates
a list of new functions h_{k+1} =  h_k * g, k= 1, …, K.  Surely, there are vastly
better ways to do this.  I don’t particularly care about the returned list,
I’d be happy to have the final  h_K version of the function,
but I keep losing my way and running into the dreaded:

Error in h[[1]] : object of type 'closure' is not subsettable
or
Error: evaluation nested too deeply: infinite recursion / options(expressions=)?

Mainly I’d like to get rid of the horrible, horrible paste/parse/eval evils.  Admittedly
the f,g look a bit strange, so you may have to suspend disbelief to imagine that there is
something more sensible lurking beneath this minimal (toy)  example.

    f <- function(u) function(x) u * x^2
    g <- function(u) function(x) u * log(x)
    set.seed(3)
    a <- runif(5)
    h <- list()
    hit <- list()
    h[[1]] <- f(a[1])
    hit[[1]] <- f(a[1])
    for(i in 2:5){
	ht <- paste("function(x) h[[", i-1, "]](x) * g(", a[i], ")(x)")
	h[[i]] <- eval(parse(text = ht))
	hit[[i]] <- function(x) {force(i); return(h[[i]] (x))}
	}
    x <- 1:99/10
    plot(x, h[[1]](x), type = "l")
    for(i in 2:5)
	lines(x, h[[i]](x), col = i)

Thanks,
Roger