RFP - Part 9: Local Functions and Local Variables

A common thing to do in functional programming is to create, within a (outer) function, a local (inner) function that uses other variables in scope. Let me give you an example. The function countup_from1() uses a local helper function count() to accumulate results recursively. Its argument x is used directly inside count().

countup_from1 = function(x) { # x: integer
        count = function(from) { # from: integer
                if (from == x) x # can use x because count() is local
                else c(from, count(from+1))
        }
        count(1)
}
countup_from1(10)

##  [1]  1  2  3  4  5  6  7  8  9 10

Another common thing to do is to make local variables to store the results of expensive computations. Before I give you an example, let’s first define some helper functions.

# Check if a vector is empty. Returns TRUE if it is, FALSE otherwise.
is_empty = function(xs) { # xs: a vector of any type
        length(xs) == 0
}

# Get the first element of a vector, raising an exception if the vector is empty.
hd = function(xs) { # xs: a vector of any type
        if (is_empty(xs)) stop("Vector is empty.")
        else xs[1]
}

# Get the tail of a vector without its first element, raising an exception if the vector is empty.
tl = function(xs) { # xs: a vector of any type
        if (is_empty(xs)) stop("Vector is empty.")
        else xs[-1]
}

Using these helpers, we can write a function that returns the max value of an integer vector. Without using local variables to store intermediate results, bad_max() gets very expensive even for small-lengthed input vectors.

bad_max = function(xs) { # xs: integer vector
        if (is_empty(xs)) 0
        else if (is_empty(tl(xs))) hd(xs)
        else if (hd(xs) > bad_max(tl(xs))) hd(xs) # recursive call to bad_max()
        else bad_max(tl(xs)) # recursive call to bad_max(), these two recursive
                             # calls hugely slow down the computation.
}
bad_max(1:10)

## [1] 10

bad_max(1:20)

## [1] 20

# bad_max(1:30) # this will take "forever"!

We can re-write the function by using a local variable to store the intermediate result of the expensive recursive step.

good_max = function(xs) {
        if (is_empty(xs)) 0
        else if (is_empty(tl(xs))) hd(xs)
        else {
                tl_ans = good_max(tl(xs)) # use local variable to store expensive computation
                hd_xs  = hd(xs) 
                if (hd_xs > tl_ans) hd_xs
                else tl_ans
        }
}
good_max(1:30)

## [1] 30

good_max(1:100)

## [1] 100

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