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SICP - Lists, Accumulate and Flatmap, part 3

Published: September 15, 2018
Last Updated: December 5, 2020

In the third post of this series on lists in Scheme and SICP we are going to take a look at the flatmap procedure. In chapter 2, flatmap is made use of in a number of examples and in some of the exercises, so it’s worth taking a little bit of time to understand how it works and what it does. We’ll also take a quick look at it’s counterpart in the C# language, SelectMany, which is provided through the LINQ framework.

Flatmap, and in C#, SelectMany, both perform the same operation. What they do is flatten a sequence of sequences, or a list of lists. This means that you pass in a list of lists, and out comes one list containing all of the items. They flatten the list of lists by one level in effect.

This is easily seen in the following Scheme code, which uses the provided procedures from the SICP text.

The first call to flatmap in the code uses the identity procedure which is applied to each sequence provided. Then those sequences passed in are flattened into one sequence or list. This is done by flatmap by making use of the accumulate procdure. If you look at the code for flatmap, you’ll see it’s simply a call to accumulate with append passed in as the operation. It applies the supplied procedure to the sequence before calling accumulate.

The next call to flatmap, which is commented out, shows that an error is produced when flatmap is called with simply a list as its argument. Flatmap expects a list of lists, and breaks down when a simple list is passed.

The next example shows calling flatmap with just a list, however, this doesn’t result in an error. This example shows that the procedure is applied to the provided sequence before being flattened. In this example, we turn each item in the sequence into a list, which allows flatmap to procede to flatten the list of lists at this point. Granted, this example isn’t that useful in the real world, however, it shows the input that flatmap is expecting.

The final example is taken from SICP, and shows a way to generate a sequence of unique pairs using flatmap. Coming from a more imperative programming style this code to generate pairs would typically be written as a nested loop of some sort.

C#, and most other languages, provide a method such as flatmap. C# has this functionality through LINQ, and is a method called SelectMany.

The code below shows how SelectMany is used to flatten the sequences of books on each bookcase into one sequence of books. This is the same functionality that is provided by flatmap in SICP.

© Copyright 2021, Tyler Rhodes