October 11, 2015

A teardown of a basic Haskell example, with line by line explanations of what and why. No warranty as to correctness.

The prolific Gabriel Gonzalez wrote a post last week about basic Haskell examples. Regarding the state of example Haskell code, often using advanced langauge idioms:

So I would like to swing the pendulum in the other direction by just writing five small but useful programs without any imports, language extensions, or advanced features. These are programs that you could write in any other language and that’s the point: you can use Haskell in the same way that you use other languages.

Followed by five examples:

a todo program a TSV to CSV converter a calendar printing utility an RNA decoder a bedtime story generator

I imagine 4 & 5 could be combined in some way for very precocious children.

Haskell has had my interest for a while but I’ve made far less progress learning the language than seems reasonable for someone who can tie his own shoes, in no small part because it’s much more difficult to get started doing anything productive compared to a host of other languages. It’s a much more interesting language than Go, for example, but Go fulfills it’s promise of programmer productivity almost immediately. The resolution, for me at least, is to find basic programs that actually do things (i.e. IO). So for my own benefit, and perhaps yours, too, if you’re in my boat, is to work with these examples, explaining and extending to the more uniquely usable tools.

I’m going to examine the todo example and walk through it line by line to examine and explain what it’s doing. Keep in mind that unlike Haskell I make no claims on my own correctness (my mother would be surprised to hear that, I’m sure). That includes explanation of concept as well as my language, which is almost certainly insufficiently precise even when it is accurate.

Here’s the full example as originally presented (the code on Gabriel’s site has been updated a bit). In my walkthrough I’ve rearragned the order to start with the entry point and go from there.

putTodo :: ( Int , String ) -> IO ( ) putTodo ( n , todo ) = putStrLn ( show n ++ ": " ++ todo ) prompt :: [ String ] -> IO ( ) prompt todos = do putStrLn "" putStrLn "Current TODO list:" mapM_ putTodo ( zip [ 0 .. ] todos ) command <- getLine interpret command todos interpret :: String -> [ String ] -> IO ( ) interpret ( '+' : ' ' : todo ) todos = prompt ( todo : todos ) interpret ( '-' : ' ' : num ) todos = case delete ( read num ) todos of Nothing -> do putStrLn "No TODO entry matches the given number" prompt todos Just todos ' -> prompt todos ' interpret "q" todos = return ( ) interpret command todos = do putStrLn ( "Invalid command: `" ++ command ++ "`" ) prompt todos delete :: Int -> [ a ] -> Maybe [ a ] delete 0 ( _ : as ) = Just as delete n ( a : as ) = do let n ' = n - 1 as ' <- n ' ` seq ` delete n ' as return ( a : as ' ) delete _ [ ] = Nothing main = do putStrLn "Commands:" putStrLn "+ <String> - Add a TODO entry" putStrLn "- <Int> - Delete the numbered entry" putStrLn "q - Quit" prompt [ ]

Do something: the entrypoint

A program is useless if you can’t do anything with it, and every Haskell program has a main function. In the example it’s written at the bottom of the Haskell code, and while that’s a reasonable and typical place for an entrypoint in other languages, too, it’s going to be our starting point.

main = do putStrLn "Commands:" putStrLn "+ <String> - Adda TODO entry" putStrLn "- <Int> - Delete the numbered entry" putStrLn "q - Quit" prompt [ ]

The first line assigns some stuff to main with a do statement. Here’s what I know about do : it’s syntactic sugar around monadic code which could be rewritten without the do statement; writing the monadic code is makes it clearer if you understand it, but the do statement looks nicer for us folks more used to imperative paradigms. I’m pretty sure this is true because I read it on the Internet.

Monadic means related to monads. And a monad is either a burrito or a calzone. A little bit more on this later.

The next four lines are function calls to the putStrLn function. In the context of this do block this is pretty obvious to the unitiated: the function prints the string argument to the screen. Of course that’s only superficially true - that is, it describes what happens, but doesn’t really describe the putStrLn function. Output is a side effect, so how can a function do that?

As defined in [the] Prelude (what’s available without import in Haskell), putStrLn has the following type signature:

putStrLn :: String -> IO ( )

I’m sure that clears it right up. It says that the function takes an argument of type String and returns a value that implements the IO monad. It prints to the screen with a new line, where as putStr simply prints the string without a newline. putStr is to putStrLn as Ruby’s print is to puts , roughly.

The last line of the main function calls the prompt function an empty list.

do or then

As I mentioned, it’s possible to write this kind of code without using do . Here’s the main function written without the benefit of do notation.

main = putStrLn "Commands:" >> putStrLn "+ <String> - Adda TODO entry" >> putStrLn "- <Int> - Delete the numbered entry" >> putStrLn "q - Quit" >> prompt [ ]

The “then” operator is used to chain operations. Here’s the type signature of the >> or “then” operator:

( >> ) :: Monad m => m a -> m b -> m b

The description from the Haskell docs is reasonably helpful:

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

That’s exactly what we want to happen here.

So, what’s a monad?

There’s a slew of explanations of what a monad is. An infamous attempt compares monads to burritos. Maybe this makes sense once you grok the concept of monads already, but I didn’t find the explanation terribly helpful.

A monad has a precise definition with regard to category theory, but better or at least shallower explanations are that monads are sequenced operations. Functions in Haskell are not sequentially applied, and monads allow you to do this. They also provide a way out when it comes to dealing with side effects which a pure functional programming otherwise prohibits.

My suspicion is that it’s possible to get reasonably far reading and writing Haskell code without fully grokking monads, and that once that is achieved they won’t look half as complicated as they’re presented.

For now let’s hold that a monad is a type class that sequences operations - even if that’s terribly wrong.

Type classes

Short aside about type classes: the best analogy for type classes in Python are abstract base classes, or if you’re not familiar with abstact base classes, in practice the use of dunder methods. For instance you might write a function in Python that iterates over an object - we call this “iteration” - without needing to know what class the object is an instance of. It could be a string, a generator object, a class of your own creation - anything that defines a __next__ method. So if a class defines a __next__ method as well as an __iter__ method then it’s an iterator. This is conceptually similar to a type class.

Or in Go, an interface.

Prompt for input

The prompt function below is responsible for outputting a prompt to the user, waiting for input, and then doing something with that input.

prompt :: [ String ] -> IO ( ) prompt todos = do putStrLn "" putStrLn "Current TODO List:" mapM_ putTodo ( zip [ 0 .. ] todos ) command <- getLine interpret command todos

This function takes a list of String instances (which means it’s a list of lists, since a String is a list of Char instances) and returns an IO monad (calzone). The particular input it’s getting for the list of strings is a list of our todos.

This function uses the do notation as well, which is a good indicator that it’s doing some IO (edit: this is false, it only indicates that the block is “monadic” not necessarily IO related). The first two lines we can now already understand. The function is outputting some text. It could be condensed into one line if we wanted (same in pretty much any language) but the putStrLn function call with the blank string is nicely explicit.

putStrLn "

Current TODO List:"

List output by function mapping

The third line of the function is more interesting. Here’s the type signature for mapM_ :

mapM_ :: Monad m => ( a -> m b ) -> [ a ] -> m ( )

Looking across the signature we can see three different type references, a , b , and m . m is the only one with a type class specified; m must implement type class Monad . Types a and b can be any type.

So mapM_ takes a function and a list and returns a burrito/monad. The function argument to mapM_ takes an instance of type a and returns a monad of type b . Let’s look at how we’re using this function and then come back to it.

The prompt function calls the mapM_ function with two parameters: the putTodo function, which is defined later, and the result of calling the zip function on what looks like some kind of auto populating list of numbers and our list of todos. This part’s making a bit more sense. mapM_ is mapping the putTodo function over the result of the zip function.

The zip function looks pretty familiar:

zip :: [ a ] -> [ b ] -> [ ( a , b ) ]

It takes a list of instances of type a and a list of instances of type b and returns a list of tuples each with an instance of type a and b respectively. Some implementation of a zip -like function is in the standard libary of every high-level language with few exceptions.

Here zip is provided with the aforementioned integer list and our list of todos. The integer list is constructed with the range syntax .. . This is pretty nice, as it can be used to produce a list without verbosely writing it out.

ghci > [ 1 .. 10 ] [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ]

The neat part is that by leaving off the end of the range, we get an infinite list! That’s sounds like a somewhat scary thing, but here it’s of no concern, as long as todos is finite. That’s because given lists of unequal length, zip will produce a list only as long as the shortest input. This is lazy evaluation at work (if you’re working in Python you can often get the same general benefit by using generators).

The next line is quite short, but introduces new functionality and syntax.

command <- getLine

The left pointing arrow - certainly how I interpret it - binds getLine to command . Here’s the helpful type signature:

getLine :: IO String

getLine just returns an IO String . It doesn’t take any arguments, although it does take some input via IO. That’s why it returns an IO String . I’m not entirely sure what’s going on under the hood, but it reminds me of using cin in C++:

cin >> command ;

Execution is going to stop until input - marked as finalized by the return key

is streamed into command .

And in the last line, our input in command and the todos list are sent as arguments to the interpret function.

Output a todo item

The putTodo function prints to the screen a todo prefaced by it’s numeric index in the list of todos.

putTodo :: ( Int , String ) -> IO ( ) putTodo ( n , todo ) = putStrLn ( show n ++ ": " ++ todo )

In slightly unidiomatic Python, it would look like this:

def putTodo ( n , todo ) : print ( n + ": " + todo )

So it’s not really all that different. String concatenation is performed with the ++ operator, not the + operator. Python’s + operator can be used with mixed types (thanks, dunder methods!) but we can’t do that in Haskell.

Let’s look at why. Operators are just infix functions - functions written between the parameters - so let’s look at the type signature for the + operator:

( + ) :: Num a => a -> a -> a

What that shows us is that it takes an instance of type a and another instance of type a and returns an instance of type a . a here is a placeholder for any type that satisfies the requirements of the Num type class (more on that below).

Let’s compare to the ++ concatenation operator:

( ++ ) :: [ a ] -> [ a ] -> [ a ]

Notice that it doesn’t specify the type class for a . Concatenation operator don’t care. It’s operating on the boxes containing type a . All that matters is that the things in each box being concatenated are of the same type. Lists are expected to hold one type.

Side note: lists must hold the same type, but this is a good practice even in dynamically typed languages like Python. Otherwise you’ll sow confusion, write complicated code, and if you’re lucky enjoy some high quality runtime errors.

Since we want a string, we need to coerce the Int into a String . That’s what show does here.

The show function has the following type signature:

show :: Show a => a -> String

That is, it takes an instance of type a and returns a String . Pretty simple. As long as the type a is of the Show type class. One way or another, type definitions will define the show function, declaring the type to be an instance of Show , and this function can be called when the show function is called from the Prelude.

Back to our putTodo function, the show function uses the Int type’s show funtion to return a String representation of the Int value. This can then be concatenated with the spacer string and the todo itself, and the resulting String is used as a parameter for the putStrLn function.

Parantheses and function parameters

Another sidenote: parantheses are unnecessary for calling functions in Haskell. When they’re used it’s either for readability (human’s sake) or ensuring parameters are interpreted correctly (compiler’s sake).

If you try to evaluate this code in ghci you’ll get a type error:

let n = 0 let todo = "Walk the dog" putStrLn show n ++ ": " ++ todo

Thinking as best I can as a compiler, I’d not necessarily recognize the evaluation order - does show need to be evaluated first before calling putStrLn ? - so it needs to be syntactically enforced. An alternative way of writing this, and seemingly more idiomatic from the Haskell code I’ve seen, is to use the $ operator:

putStrLn $ show n ++ ": " ++ todo

Handling user input

Now we get to the engine of the program. It’s also our first example using pattern matching for function definition.

interpret :: String -> [ String ] -> IO ( ) interpret ( '+' : ' ' : todo ) todos = prompt ( todo : todos ) interpret ( '-' : ' ' : num ) todos = case delete ( read num ) todos of Nothing -> do putStrLn "No TODO entry matches the given number" prompt todos Just todos ' -> prompt todos ' interpret "q" todos = return ( ) interpret command todos = do putStrLn ( "Invalid command: `" ++ command ++ "`" ) prompt todos

Pattern matching is one of those language features that I saw in Haskell and thought, okay, that looks kind of neat, and then found myself refactoring code in another language and thought, ”$@#! this would be simpler with pattern matching”. Pattern matching allows us to apply function bodies based not just on the name of the function but on specific argument values. It’s implemented by specifying values of one kind or another in the place of or inserted into the “shape” of an argument.

divide :: Num -> Num -> Num divide x 0 = 0 divide x y = x / y

That’s not mathematically sound but it illustrates the point. And at first it doesn’t look that dissimilar from an unnecessary mess, after all, there’s all of these definitions. But it makes for function bodies that “do” only what they need to, and it’s nicer than a rats nest of if statements.

Back to the function itself, it takes a string and a list of strings and it returns an IO monad.

The first pattern uses a new operator, : , to create a string matching the user input. Here’s the type signature for the operator:

( : ) :: a -> [ a ] -> [ a ]

It’s takes a single element of type class a , a list of type class a , and returns a list of type class a . The way it’s written here works because of how the arguments are interpreted. Substituting cons for : and as a non-infix function, it might look like this in Python:

cons ( "+" , cons ( " " , todo ) )

Or more appropriately in Clojure:

( cons "+" ( cons " " todo ) )

The choice of quotation mark is significant, as well. Single quotes ' are used for characters, double quotes " for strings. (Also, the String type is just an alias to a list of characters, e.g. [Char] .) If you try this in ghci you’ll encounter an error:

( "+" : " " : "My new todo" )

When the correct pattern is matched here though, a string starting with ”+ ” and followed by a non-empty string, then the first function body definition is used. In that case it simply returns the previously examined prompt function, prepending our new todo to the existing todo list.

Now the second pattern looks quite similar, albeit with a different preface character and different variable name. That’s legal and as you’ll notice very helpful. It’s the same type signature, and the name is local to the function body following this pattern.

The function body introduces the use of case which as you mgiht imagine isn’t all that conceptually different from case in other languages. Why use case rather than another pattern? Because case is applied against the result of a function call. Now, it’s true that the first two patterns are as well, after all, the : operator is a function. However the result of prepending those values is determinate, whereas the delete function returns a Maybe value, having either a value wrapped in a Just or a Nothing .

As such, if the result of delete (read num) todos is Nothing then the next two lines are invoked, and if the result in a list of todos wrapped in a Just, which gets labeled todos' , then the list is used as an argument back to the prompt function.

The interpret function can return a call to the prompt function because the latter returns an IO monad, just like the former.

The function call in the case statement introduces another function, read . Here’s the type signature:

read :: Read a => String -> a

It takes a string as input and returns an a where type a implements the Read type class. Okay, so that means that the type a must implement a read function. Of what use is this?

Well, if you look back to the pattern and the function signature of : , we know that num must be a String . However delete requires an Int . The effect of read is to coerce the value of num into an Int . It’s basically the inverse of show .

The third pattern and function body are pretty straightforward. If the entry is nothing more than a lower case “q” the return value is an empty monad.

The fourth value is akin to the “default” condition in a case statement (at least in a C like language). All of the valid inputs have been handled so anything else is handled here. The function body consists of another monadic block in which the user is alerted to their error and then the prompt function is once again called.

Remove an item

Lastly we come to the delete function. We see pattern matching employed here, too, and an interesting return value, Maybe . This function takes an Int and a list of a type a and it returns a list of a type a wrapped in a Maybe .

delete :: Int -> [ a ] -> Maybe [ a ] delete 0 ( _ : as ) = Just as delete n ( a : as ) = do let n ' = n - 1 as ' <- n ' ` seq ` delete n ' as return ( a : as ' ) delete _ [ ] = Nothing

Maybe , e.g. Maybe Int , is a way of noting that the value might be an Int or it might be nothing. Just as a list itself could have items or be empty, any value, whether a collection type or not, can be wrapped in a Maybe - either Just , e.g. Just 5 to indicate that there is an integer which can be unwrapped or unboxed from the Maybe , or Nothing .

This whole Maybe business seems to beg the question that this is better than returning, say, nil or None . At first pass it doesn’t seem any better. Couldn’t you just - pardon me, I had to - check for whether the value returned back is nil or length of 0 or something of that sort? You could. It’d bet a little messier though, just look at pattern matching. This nil or zero status has to be checked differently for every type. Here we have a consistent type based wrapper and, bonus, you an use it for pattern matching (see the interpret function).

Speaking of pattern matching, let’s look at the function’s pattern defintions. Looking through the different patterns for the function, it becomes clear how and why each is applied.

The first pattern matches against the first argument as the integer 0, and the second argument is the list of a typed instances. The second argument is further defined with a range. Here the : operator splits the list on the head, the first item in the list, and the tail, everything after that. These are named separately and can be referenced in the function body. The _ for the head means that it’s irrelevant - it’s going to be thrown away. If you’ve programmed in Go you’ve seen the same thing. If you’ve seen this in Python you’ve seen an anti-pattern.

The function body for the first pattern returns the tail of the input function. Well this makes sense! If you want to delete the first item, the 0-indexed item, in a list, then you should end up with the tail of the original list.

The third pattern (I’m skipping) simply matches an empty list. The index value is totally irrelevant, no matter what, and the return value is Nothing . Looking only at this pattern, we could have just returned an empty list. However the Nothing value is more generalizable. Any missing value should be treated the same way in the user interface whether the list is empty or not, and this return value greatly simplifies that. If a user tries to delete an item from a list, whether it’s missing because it cannot be found or because the list is empty, this should be handled in the same way.

The second pattern is pretty similar to the first, except that the first parameter is given a value name so that it can be referenced (and meaning that it should match any non-specified value) and the head of the list is likewise referenced. The second function body definition is quite different.

The do keyword tells us that there’s some sort of monadic magic at work here. Looking into the first line of this block it names a value n' - the apostrophe doesn’t have any special syntactical meaning to the compiler, it’s for the programmer’s benefit - and this named value is assigned n - 1. So if there are five items in the list, and I want to delete the third item, indexed 2, then n' will have a value of 1.

In the next line there’s what briefly looks like another value assignment, but it’s actually a value binding. The left pointing arrow <- binds everything to the right to the value on the left. So what’s on the right side?

Notice first the call to seq here using backticks seq . Here’s the type signature of seq :

seq :: a -> b -> b

The backticks allow seq to be used as in infix function. You can do this with any function that takes two arguments (subject to restrictions about which I’m ignorant, so grain of salt on the ‘any’ there). The seq function returns the second argument, b , unless a is “bottom” in which case it returns a . Insert head scratching here I supposed.

The Haskell wiki describes seq as “the most basic method of introducing strictness”. It seems that it must make a comparison and so requires that each argument is evaluated. There’s some controversy around this that represents a very fine rabbit hole I’ve no intention of investigating right now. At any rate we should look at what “bottom” means here. The Haskell wiki introduces bottom thusly:

The term bottom refers to a computation which never completes successfully. That includes a computation that fails due to some kind of error, and a computation that just goes into an infinite loop (without returning any data).

Note the conditions, that it fails due to an error or a compution that goes into an infinite loop without returning any data. If you try using seq in ghci you can see here you’d get 9.

Prelude > seq [ 0 .. ] 9 True

9 is not bottom. Maybe that infinite range is though.

Prelude > seq 9 [ 0 .. ] [ 0 , 1 , 2 , 3 ... ]

Nope! Hope you hit Ctrl+c. That infinite expansion returns values, so it’s not bottom. Even Nothing isn’t bottom.

Prelude > seq 9 Nothing Nothing

In any event, seq is used here to compare n' and the value of delete n' as , just like so without the infix syntax:

seq n ' ( delete n ' as )

Let’s walk through an example to understand how this recursion is working. Here’s my todo list:

Current TODO List: 0 : Edit blog post 1 : Sweep the garage 2 : Mow the lawn 3 : Make lunch 4 : Walk the dog

Normally it would involve more adventure, I promise. I’d like to remove the todo “Mow the lawn” because I hate mowing the lawn. Since I enter 2 , the value of n is 2 , a is “Edit blog post” and as is a list of the next four todos.

Now n' is 1 , and to as' we have bound the result of seq with values 1 and delete 1 as where as is todos starting at index 1. This means another recursive call to delete .

Since n is non-zero and the list is non-empty, this once again uses the second function definition. And now n' is 0, the seq line with a recursive call to delete is evaluated with as equal to the part of the list of todos starting from the second indexed item, “Mow the lawn”, which is the one I want to delete. The first pattern is now matched against this recursive call, because the n value is 0, and the tail of the passed list is returned, in this case the list starting from the todo after the one I wanted to delete.

Going back up the chain of recursion, the value Just as where as is the last two items in our list, is bound to as .

Make lunch Walk the dog

The value of a is “Sweep the garage”, and using the list appending operator : we can effectively put the former head back onto the new tail and return it.

The return statement should look odd, since functions in Haskell neither need nor use return . Instead it is used to ”[i]nject a value into the monadic type.” It’s synonymous, at least in this case, with this line:

Just ( a : as ' )

return is a function with this type signautre:

return :: Monad m => a -> m a

Given that Just is an instance of Maybe which is a Monad , we can see the equivalence - at least in this specific case. The explicit use of Just makes more sense to me, but having seen the return used enough in similar looking blocks of code, it smells like there’s probably a reason to use return - I just couldn’t tell you what it is.

Updated: I made a few minor edits after publishing this, thanks to everyone who gave feedback after taking the time to read.