Functional Programming and Intelligent Algorithms

Tutorial 3.2: I/O in Haskell

Week 3: The Perceptron

2 Tutorial 3.2: I/O in Haskell

2.1 Overview

Reading: Simon Thompson: Chapter 7

In this tutorial we shall use real data to test the perceptron algorithm. In order to do this, we need to be able to read files from disk in a Haskell program.

2.2 Problem 1: Your first compiled program

2.2.1 Step 1: an output function

Try the following two evaluations in ghci "Hello World!" 
putStr "Hello World!"

What is the difference between the two? Why is there a difference?

What are the types of the two expressions above? Do you know? Try it out using the :type command and see if it matches your expectation: :type "Hello World!" 
:type putStr "Hello World!"

The IO () type is an example of a monad, a concept which will take some time to get used to. For the time being, we will only be concerned with the IO monad and how to use it to control I/O. We will learn more about monads later.

IO is a type constructor, so it wraps another type. In the case above, we had IO (), with () as the inner type. This is the singleton type; i.e. the type () has only one possible value, namly (). What use can we have of singleton type?

The IO can be viewed as an action. Thus the type stores an action which can be subject to calculations and used to construct other actions. When the program runs, the action will eventually be performed.

Output actions, such as the one returned by putStr, will typically have type IO (). They are interesting because of the output they generate, not because of the data contained. An input function, in contrast, could have type (say) IO String where the type wraps the data (string) read from input.

2.2.2 Step 2: sequencing

A program, typically, is a sequence of actions (e.g. IO objects). The easiest way to construct a program is the syntactic sugar of the do notation.

Create a new Haskell module called Main for this exercise.
Add the following definition: hello :: IO () 
hello = do 
   n < getLine 
   putStr ( "Hello,␣" ++ n ++ "\n" )

Note that we use two functions above, getLine and putStr.

What type does putStr have? Use the :type command if you do not know.
What type does getLine have? Use the :type command if you do not know.

The IO () type is just an action, with no contents. The getLine function returns an action with contents, and the <- operator assigns this contents to n.

Load your Main module in GHCI and evaluate hello. When nothing happens and you don’t get a prompt, it is waiting for your input.
Type your name (or whatever), finish with Enter. What happens?

2.2.3 Step 3: compilation

The interpreter (ghci) is great to test individual functions, but at the end of the project you will probably want to produce a stand-alone program. This requires a compiler, namely ghc.

A standalone program is a module called Main with a function main :: IO a for some type a.

Add a main function to your Main module. main = hello
Save your module, and find a terminal window. Do not start GHCi. Compile your main module with the following command. ghc Main.hs
List the contents of the directory ls (The Windows equivalent to ls is dir.) Which new files have been created?
Run the resulting program on the command line, as follows: ./Main (On Windows you may need to run Main.exe instead of ./Main.) What happens?

It is possible to get GHC to make programs with names other than Main, but let’s cross that bridge when we need it.

2.3 Problem 2: Reading a data set

We want to test our machine learning algorithm on real data. University of California, Irvine hosts the machine learning repository which provides a large collection of real data for testing. We will use some breast cancer data from Wisconsin.

2.3.1 Step 1: What does the data look like?

Have a brief look at the details about the data set. What kind of information is available?
Download the data file.
Move the data file to the directory you use for this tutorial.
Open the data file in your text editor (the same as you use to write Haskell code).
Discuss: How is the data formatted? Where do you find the class label?
Discuss: Which data types are used in the data set?

Comma separated values (CSV) is a common format to store data. Each row is a record, and each item of the record is separated by commas. We need to figure out how to read such files in Haskell.

2.3.2 Step 2: Reading a text file

In the previous step we download a file with comma-separated values (CSV), which we want to use with our perceptron. Let’s explore how we can read the file in Haskell.

Make sure you have the data file in your current directory, and start GHCi.
Run the following in expression: readFile ""

What do you get?

2.3.3 Step 3: Installing a library

To parse the CSV file, we will use a library which is not installed by default. Hackage is a database of libraries for Haskell, and you are likely to consult it frequently for new libraries. We shall take a brief look at Hackage and the documentation found there.

Look up the Text.CSV library. The first page gives an overview.
Look at the list of modules. Once you have installed the library, these modules are accessible with the import statement in Haskell.

Which modules are available?

Click on the Text.CSV module. This gives the API documentation for this module. Which types and functions can you use? (Don’t spend too much time on this if you don’t see the answer. We will walk through together.)
Look at the header line of the web page, in the top left corner. This is the package name: csv. To install the package, you have to find a terminal window (do not start GHCi) and run the following command: cabal update 
cabal install csv

2.3.4 Step 4: Testing the CSV library

As yoe see in the API documentation, the CSV library has several functions to parse CSV data. Since we have already learnt how to read the file into a String, we will use the function parseCSVTest which parses a String.

Find a terminal window and start ghci.
Import the CSV module import Text.CSV
Lets define a String object with CSV data. let s = "1,2,3\n4,5,6"
The parseCSVTest function takes one argument, namely the CSV formatted string. Try this parseCSVTest s Look at the output. What data type is returned?
What is the return type of parseCSVTest? You can check the documentation or use GHCi with the following command. :type parseCSVTest

Discuss: Does this type make parseCSVTest suitable in a program?

2.3.5 Step 5: Parsing CSV from a string

The parseCSVTest is a test function which prints the data on the terminal. It does not actually return the data. To be able to use the data for further computation, we will use parseCSV.

What is the return type of parseCSV?
There are two ‘kinds’ of objects of the Either type. Try the following in GHCi: :type Left ’a’ 
:type Right 2
The Either type allows us to pack two constituent types (the left and the right type) into one. We can use an Either object without knowing which constituent type is used.
The return type of parseCSV is either a ‘Left’ which means it is a ParseError, or ‘Right’ which means it is a valid CSV object.

Doscuss: Why doesn’t parseCSV just return CSV? What is the ParseError for?

In production software you have to take care of ParseError to do error handling. However, there is a simple and crude fix to convert the Either object to a plain CSV object. We will make a function for this.

Create a new module called ANNData and add the following definition.

stripError :: Either a b > b 
stripError (Left _) = error ~Parsererror!~ 
stripError (Right csv) = csv

Discuss the following:

How is pattern matching applied to objects of the Either type?
What does a and b mean in the type declaration?
What does the error function do?
Test the stripError function in GHCi. Do for instance: stripError (Left "foobar") 
stripError (Right 3.14)
Discuss: What does the error function do?
The first argument to parseCSV is the name of a log file. We won’t use that for now, so let’s write a simple wrapper for parseCSV. Add the following to the ANNData module: parseCSVsimple :: String > CSV 
parseCSVsimple s = stripError (parseCSV ~/dev/null~ s)

Here, /dev/null is a special file discarding all data written thereto. (The special file does not exist on Windows, and Windows users may have to use a real file instead.)

Test parseCSVsimple in the GHCi, in same way as you tested parseCSVTest.

2.3.6 Step 6: Parsing a real CSV file

We have learnt to read a file into a string, and to parse a string for CSV data. Now, we will put these two operations together and make a function to read and parse a real data set from file.

Add the following type declaration to the ANNData module. getRawData’ :: String IO [[String]]

The input argument is the filename from which the data will be read. The output is a list of lists, where each constituent list is one row from the CSV file, and each string in the inner list is one value from the comma separated line.

We implement getRawData’ as follows: getRawData’ fn = do 
              s < readFile fn 
              return $ parseCSVsimple s

The return function wraps the given value in an IO action.

Discuss: What is the meaning of the <- operator?

Test the function getRawData’ on the Wisconsin Breast Cancer Data file. getRawData’ ""

What output do you see? Does it fit you expectation?

Remark 1 There is a slightly simpler way to do this. You can make a wrapper similar to parseCSVsimple, using parseCSVFromFile instead of parseCSV. Try it out for yourself if you have time.

2.3.7 Step 7: A little problem with real CSV data

It is possible that the data from parseCSVsimple includes an empty row, [""].

Write a function dropEmpty which takes a list of lists, as returned by getRawData’, and drops any list containing just the empty string, and keeping all others.

Add both type declaration and definition to the ANNData module.

Define the following function getRawData :: String IO [[String]] 
getRawData fn = do 
                d < getRawData’ fn 
                return (dropEmpty d)

2.3.8 Step 8: Cleaning up the data

So far we have read and parsed the data set to obtain a list of lists of strings. However, the data are numerical, so String is not an appropriate data type. We need to clean it up, and parse the strings containing numbers into a numeric data type.

Each row in the CSV file includes several values which would form the input vector to a perceptron, plus a class which determines the the correct output.

Look at the «attribute information» in the presentation of the data set, as well as the data file. What is the meaning of the individual columns? Which are input? Which is output?

Cleaning up the data is a multi-step process, which we consider in the next problem.

2.4 Problem 3: Cleaning up the data

The data set (CSV) file consists of rows. Each row consists of an ID, a class label, and a feature vector. The feature vector is in turn made up of individual features.

The raw data that you have read is [[String]], so each row is a list of strings, where one string is class label, some strings may be ignored (the ID), and the rest is the feature vector.

We want to reformat the data set so that it has type [(Double,[Double])]. Thus each row is a pair, where the first element is the class label (Double) and the other is the feature vector ([Double]). Thus, we need the function

formatData :: [[String]] > [(Double,[Double])]

It is easiest to work bottom up. So we will do formatData last, and start with the class label and individual features.

2.4.1 Step 1: Formatting the class label

The class label is a string "M" or "B", while it should be numeric, typically 0 or 1. Let’s map "M" to 1 and "B" to 0. We need a function numericLabel to do the conversion

Write a type declaration for numericLabel
Write an implementation for numericLabel
Test the function numericLabel "M" 
numericLabel "B" 
numericLabel "q" 
numericLabel "Bonnie"

For the time being, it is ok if the last two tests cause an error. In a production system we would have to handle such errors appropriately. Our time, in contrast, is better spent on exploring the learning algorithm, than handling input which we do not want to see.

2.4.2 Step 2: Formatting the feature vector

The features are strings representing numeric data. We have to parse it to get floating point data. We need a function numericFeatures to do the conversion.

We need read function to do the conversion. Open ghci and get familiar with it. Try the following: read "6.12" What happens?
You get a rather cryptic error message. What it essentially says is that GHCI does not know which data type you want for the return value. You have to specify this explicitely. Try the following: read "6" :: Integer 
read "6" :: Double 
read "6.12" :: Double

What happens now?

Write the type declaration for numericFeatures.
We can define numericFeatures using map and read as follows: numericFeatures = map read

If you have a precise type declaration for numericFeature, GHCi can deduce the return type required from read; thus you do not need to specify the type again.

Test the function numericFeatures ["6.12","8.11","0","2"] 
numericFeatures ["B","6.12","8.11","0","2"]

For the time being, it is ok if the last test causes an error. As before, a production system would require adequate error handling.

2.4.3 Step 3: Formatting the record

Using the helper functions from Steps 1-2, we are ready to write a function processItem taking a row ([String]) from the parsed CSV data and return a pair with class label and feature vector for the perceptron.

Write a type declaration for processItem in the ANNData module.
Add a function definition for processItem, using the helper functions from Steps 1-2.
Test the function, e.g. processItem ["9898","M","6.12","8.11","0","2"]

2.4.4 Step 4: Formatting the complete data set

Now we need a function formatData taking [[String]] as input and applying processItem on each row. The output should be a list of class label/feature vector pairs. This is an obvious case for map.

Write a type declaration for formatData.
Write a definition for formatData.
Test the function on data from the getRawData function.

2.4.5 Step 5: Putting it all together

Now, at last, we can make a single getData function which does it all. Starting with file name as input, it reads the file, parses CSV data, and formats it properly using formatData.

Write a type declaration for getData in the ANNData module.
Using all the functions you have implemented above, add a definition of the getData function.
Test the getData function on the breast cancer data set in GHCi. Are you happy with the output?

2.5 Problem 4: Refinement (optional)

As you see in the API documentation, the CSV library has several functions to parse CSV data. The one we used is very simple and provides no error handling.

Revise the functions above to use parseCSV, and handle error values properly.

7th April 2017
Hans Georg Schaathun /