Functional Programming: map

September 9, 2020

One of the famous functional programming concepts is higher-order functions, which are functions that either take functions as input or return functions as output. map is one of the most popular higher-order functions, and also one of the most useful. You can find it in popular languages like Python and JavaScript. R also has many variants of map.

This tutorial will explain map in general and give an overview of available implementations in R. For a more detailed look, I recommend reading the R for Data Science chapter on iteration.

map (Image source: http://keitheis.github.io/reactive-programming-in-python/)

What is `map`?

To put it shortly, map takes a function and a collection (e.g. list) as input, calls the function on each element of the collection, then returns as output a new collection of the results of such calls.

Let’s say that I have:

a function increment that simply takes a number and adds 1 to it
a colelction of numbers from 1 to 5

Calling map with the function increment and the number list will give back a new list of numbers from 2 to 6.

Why is it useful?

Anyone familiar with basic programming concepts should think of for loops when they want to iterate over a collection. But for loops contain too much code boilerplate and also requires initializing new variables like the “i” that gets incremented with each iteration and an empty collection that will take the new results. So, map is more concise and elegant than for loops.

Side note: this constrast is basically the difference between declarative programming and imperative programming, where the former says what the programmer wants to do and the latter explains to the computer more low-level steps on how to do it.

How to implement it in R?

Using map-like functions while using R in a statistics/data science setting is almost always about iterating with some function over columns of a data frame. The base R option for iterating (with a function) over columns of a data frame is the function sapply().

For example, one quick way to identify the column types without having to print a lot of extra output, like str() or summary(), is by doing something like this:

sapply(iris, class)

# Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species
#    "numeric"    "numeric"    "numeric"    "numeric"     "factor"

So, I applied the function class() on each column of the data frame iris and got a simple output of the class (data type) of every column. The same thing can be done with mean() or any other function that expects a vector (remember that iterating one each column means iterating on individual vectors).

sapply(iris, mean)

# Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species
#     5.843333     3.057333     3.758000     1.199333           NA

Notice that the parentheses are not written because I am not calling the function – I am passing it as an argument.

Another direct equivalent for this purpose is purrr::map(). It behaves almost the same, except the following:

map() returns a list instead of the behavior of sapply() which tries to “simplify” the output into a vector.
The package purrr has a set of map_* functions that enforce certain output types: map_dbl() ensures the output is a double (numeric) vector, map_df() ensures the output is a data frame, and so on.

iris_means <- map(iris, mean)
class(iris_means)

# [1] "list"

iris_means

# $Sepal.Length
# [1] 5.843333
#
# $Sepal.Width
# [1] 3.057333
#
# $Petal.Length
# [1] 3.758
#
# $Petal.Width
# [1] 1.199333
#
# $Species
# [1] NA

iris_means_dbl <- map_dbl(iris, mean)
class(iris_means_dbl)

# [1] "numeric"

iris_means_dbl

# Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species
#     5.843333     3.057333     3.758000     1.199333           NA

Anonymous functions

Sometimes the function you want to map over columns is not already defined with a name. In this case, you have to write your own function. But instead of defining a function in your script and using it only once in your iteration code, you could actually write an anonymous function as the function argument to sapply() or map(). If you are familiar with writing your own functions, it is the same except that you do not assign that function to a variable.

See this example:

sapply(iris,
       function(var) { is.numeric(var) | is.character(var) })

# Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species
#         TRUE         TRUE         TRUE         TRUE        FALSE

I wrote a function that returns TRUE if the variable is a numeric or character vector. That function has no name (i.e. anonymous) and will only be used in the sapply() call.

Now purrr has special syntax for writing anonymous functions. While the previously described syntax is perfectly valid for map(), the special syntax provided by purrr is more concise if you would prefer learning and using it.

map_lgl(iris,
        ~ is.numeric(.x) | is.character(.x))

# Sepal.Length  Sepal.Width Petal.Length  Petal.Width      Species
#         TRUE         TRUE         TRUE         TRUE        FALSE

The anonymous function syntax here starts with a tilde followed by your own function body, using “.x” as the argument.

Bonus: `map` in Python and JavaScript

Python:

list(map(lambda x: x + 1, [1, 2, 3, 4, 5]))

# [2, 3, 4, 5, 6]

JavaScript:

[1, 2, 3, 4, 5].map((x) => x + 1);

// [2, 3, 4, 5, 6]

I personally like JavaScript’s arrow function syntax for writing anonymous functions.

So, this was map! The concept behind it is relatively simple but really elegant, and it should save you a lot of time and code duplication if you get to use it often. Also, since it is a popular concept and already implemented in major languages, you can easily transfer your knowledge between languages.

Tags: