Lecture given by David Mazières on April 1, 2014.

This course is taught by David Mazières and Bryan O'Sullivan, who together have done a lot of systems programming and research and Haskell. Meanwhile, the CA, David Terei, is a member of the Haskell language standards committee...

The goal of this class is to learn how to use Haskell to program systems with reduced upfront cost. Haskell is typically taught in the context of programming language research, but this course will adopt a systems perspective. It's a surprisingly flexible and effective language, and since it was created by and for programming language researchers, there are lots of interesting things to do, and it's extremely flexible (if you want to try something new, even if it's syntactical, this is as easy as using a library, unlike most programming languages).

The first week of this class will cover the basics of Haskell, though having some prior experience or a supplement (e.g. Real World Haskell or Learn You a Haskell) is helpful. After the basics, we will cover more advanced techniques. The class grade will be based on attendance and participation, with scribing one of the lectures, and also three warm-up programming assignments and a large final project and presentation, in groups of one to three people.

Now, let's talk about Haskell.

In order to use Haskell, one will want to install the Haskell platform or cabal, along with the Haskell compiler, ghc. The simplest program is

main = putStrLn "Hello, world!"

Unsurprisingly, this is a "Hello, world!" program. One can compile it, e.g. ghc -o hello hello.hs, but also load it into an interpreter ghci (in this regard, Haskell is much like Lisp).

The first thing you've noticed is the equals sign, which makes a binding, e.g.

x = 2       -- Two hyphens introduce a comment.
y = 3       -- Comments go until the end of a line.
main = let z = x + y -- let introduces local bindings.
       in print z

This program will print 5.

Bound names can't start with uppercase letters, and are separated by semicolons, which are usually automatically inserted as above. Functions can even be bound, e.g.:

add x y = x + y   -- defines function add
five = add 2 3    -- invokes function add

This is a good way to define functions.

Parentheses are important to eliminate ambiguity in function application.

bad = print add 2 3     -- error! (print should have only 1 argument)

main = print (add 2 3)  -- ok, calls print with 1 argument, 5

Haskell is a pure functional language. Thus, unlike variables in imperative languages, Haskell bindings are immutable: within a given scope, each symbol can be bound only once. In other words, the following is an error:

x = 5
x = 6 -- Error, cannot re-bind x

Bindings are thus order-independent; if any two are switched such that the program still makes sense (i.e. things aren't used after they are bound), the program behaves in the same way.

Another interesting fact is that bindings are lazy: definitions of symbols are only evaluated when they're needed. For example:

safeDiv x y =
    let q = div x y     -- safe as q isn't evaluated if y == 0
    in if y == 0 then 0 else q
main = print (safeDiv 1 0) -- prints 0

Notice this is completely different from C-like languages!

Another interesting aspect of bindings, which goes hand-in-hand with order-independence, is that bindings are recursive, so each binding is in scope within its own definition.

x = 5                   -- not used in main!

main = let x = x + 1    -- introduces a new x, defined in terms of itself
       in print x       -- loops forever, or stack overflows

In C, this would print 6, but here, x refers to itself! The runtime sometimes is able to detect the loop, however.

This means that writing things in Haskell requires thinking differently! For example, here's a factorial program in C:

long factorial(int n) {
    long result = 1;
    while (n > 1)
        result *= n--;
    return result;

But in Haskell, one uses recursion.

factorial n = if n > 1 then n * factorial (n-1)
                       else 1

However, the C function requires constant space, but the Haskell version requires n stack frames! But Haskell supports optimized tail recursion; if a function ends with a call to itself (i.e. is tail-recursive), then it can be optimized into a loop. However, the definition provided above isn't tail-recursive.

Using an accumulator, the factorial function can be made tail-recursive.

factorial n = let loop acc n' = if n' > 1
                                then loop (acc * n') (n' - 1)
                                else acc
              in loop 1 n

This uses an accumulator to keep track of the partial result. It's a bit clunky, but can be tidied up with Haskell's incredible concision. For example, one can use guards to shorten function declarations, e.g.

factorial n = let loop acc n' | n' > 1 = loop (acc * n') (n' - 1)
                              | otherwise = acc
              in loop 1 n

The guards (pipe symbols) are evaluated from top to bottom; the first one that evaluates to True is followed. otherwise is defined to be True, but it makes the code easier to read. One might also introduce a where clause, which is like let but can support multiple guarded definitions, and is thus convenient for use around guards.

factorial n = loop 1 n
    where loop acc n' | n' > 1    = loop (acc * n') (n' - 1)
                      | otherwise = acc

You'll notice that there will be plenty of inner functions, and their arguments are related to that of the outer functions. But it's easy to confuse n and n', so the following code compiles and throws a runtime error!

factorial n = loop 1 n
    where loop acc n' | n' > 1    = loop (acc * n) (n' - 1) -- bug, should be n'
                      | otherwise = acc

One way to work around that is to use a naming convention in which the outermost variable has the longer name; then, bugs like this are caught at compile time, due to scope.

Haskell is strongly typed, so we have types such as Bool, which is either True or False; Char, which is a Unicode code point; Int, a fixed-size integer; Integer, an arbitrary-sized integer; Double, which is like a double in C; and also functions. A function from type a to tybe b is denoted a -> b. We also have tuples: (a1, a2, a3), including the unit () (a zero tuple, kind of like void of C).

It's good practice to write the function's type on top of a function, e.g.

add :: Integer -> (Integer -> Integer)
add arg1 arg2 = arg1 + arg2

Well, here's something interesting. The arrow associates to the right, so these parentheses aren't strictly necessary, but they make an important point: all functions accept only one argument, so the above function takes an integer and returns a function! For example, add 2 3 is parsed as (add 2) 3, and add 2 is a function. Often, this behavior (called currying) is optimized out by the compiler, but can be useful. The compiler can infer types, and in the interpreter this can be queried by :t.

*Main> :t add
add :: Integer -> Integer -> Integer

The user can also define data types, using the data keyword.

data PointT = PointC Double Double deriving Show

This declares the type PointT with a constructor PointC containing two Doubles. The phrase deriving Show means that it can be printed, which is useful in the interpreter. Types and constructors must start with capital names, but live in different namespaces, so they can be given the same name.

Types may have multiple constructors, and said constructors don't actually need arguments (which makes them look sort of like enums in C).

data Point = Cartesian Double Double
           | Polar Double Double
             deriving Show

data Color = Red | Green | Blue | Violet deriving (Show, Eq, Enum)

Now, we can do things like myPoint = Cartesian 1.0 1.0 and so on.

One extracts this data using case statements and guards, as in the following example:

getX, getMaxCoord :: Point -> Double
getX point = case point of
               Point x y -> x       -- if only the Point x y constructor is around
getMaxCoord (Point x y) | x > y     = x
                        | otherwise = y

isRed :: Color -> Bool
isRed Red = True        -- Only matches constructor Red
isRed c   = False       -- Lower-case c just a variable

The latter notion is called pattern matching, which detects which constructor was used to create the object. For another example, consider the following:

whatKind :: Point -> String -- Cartesian or polar constructor as above
whatKind (Cartesian _ _) = "Cartesian"
whatKind (Polar _ _)     = "Polar"

This underscore indicates that the value is unused, or something we don't care about. The compiler can actually infer and optimize based on that. It's bound, but never used, which is quite helpful, especially given that the compiler warns about unused variables.

Given the following types for a rock-paper-scissors game:

data Move = Rock | Paper | Scissors
     deriving (Eq, Read, Show, Enum, Bounded)

data Outcome = Lose | Tie | Win deriving (Show, Eq, Ord)

Define a function outcome :: Move -> Move -> Outcome. The first move should be your own, the second your opponent's, and then the function should indicate whether one won, lost, or tied.


outcome :: Move -> Move -> Outcome
outcome Rock Scissors           = Win
outcome Paper Rock              = Win
outcome Scissors Paper          = Win
outcome us them | us == them    = Tie
                | otherwise     = Lose

There are plenty of other ways to do this.

Types, much like functions, can accept parameters, but type parameters start with lowercase letters. For example, within the standard Prelude:

data Maybe a = Just a
             | Nothing

data Either a b = Left a
                | Right b

Maybe is used to indicate the presence of an item, or some sort of error, and Either can provide more useful error information, etc. In this case, the convention is for Right to indicate the normal value, and Left some sort of sinister error. The interpreter can reason about these types, too:

Prelude> :t Just True
Just True :: Maybe Bool
Prelude> :t Left True
Left True :: Either Bool b

Often, one uses the underscore pattern matching mentioned above with these parameterized types to pass exceptions along. For example,

addMaybes mx my | Just x <- mx, Just y <- my = Just (x + y)
addMaybes _ _                                = Nothing

Equivalently (and more simply),

addMaybes (Just x) (Just y) = Just (x + y)
addMaybes _ _               = Nothing

Now, we have enough information to define lists, somewhat like the following.

data List a = Cons a (List a) | Nil

oneTwoThree = (Cons 1 (Cons 2 (Cons 3 Nil))) :: List Integer

But since lists are so common, there are some shortcuts: instead of List Integer, one writes [Integer], and the Cons function is written :, and is infix. The empty list is called [], so instead we could have written oneTwoThree = 1:2:3:[]. Alternatively, there is nicer syntax:

oneTwoThree' = [1, 2, 3]  -- comma-separated elements within brackets
oneTwoThree'' = [1..3]    -- define list by a range

Strings are just lists of characters.

Here are some useful list functions from the Prelude:

head :: [a] -> a -- first element of a list
head (x:_) = x
head []    = error "head: empty list"

tail :: [a] -> [a]             -- all but the first element
tail (_:xs) = xs
tail []     = error "tail: empty list"

a ++ b :: [a] -> [a] -> [a]  -- infix operator to concatenate lists
[] ++ ys     = ys
(x:xs) ++ ys = x : xs ++ ys

length :: [a] -> Int         -- This code is from language specification.
length []    =  0            -- GHC implements differently, because it's not tail-recursive.
length (_:l) =  1 + length l

filter :: (a -> Bool) -> [a] -> [a] -- returns a subset of a list matching a predicate.
filter pred [] = []
filter pred (x:xs)
    | pred x     = x : filter pred xs
    | otherwise  = filter pred xs

Note the function error :: String -> a, which reports assertion failures. filter is a higher-order function, i.e. one of its arguments is also a function. For example, one might define a function isOdd :: Integer -> Bool and then filter a list of Integers as filter isOdd listName.

In addition to deriving Show, one has deriving Read, allowing one to parse a value from a string at runtime. But parsing is tricky: there could be multiple possible values, or ambiguity. For example, suppose we have the following declaration:

data Point = Point Double Double deriving (Show, Read)

Then, the following would happen in the interpreter.

*Main> reads "invalid Point 1 2" :: [(Point, String)]
*Main> reads "Point 1 2" :: [(Point, String)]
[(Point 1.0 2.0,"")]
*Main> reads "Point 1 2 and some extra stuff" :: [(Point, String)]
[(Point 1.0 2.0," and some extra stuff")]
*Main> reads "(Point 1 2)" :: [(Point, String)] -- note parens OK
[(Point 1.0 2.0,"")]

Notice that reads returns a list of possibilities, along with the rest of the string. This is asymmetrical from show.

This isn't a language property, but the best way to search for functions (and their source code!) is Hoogle, at http://www.haskell.org/hoogle/. This is a good way to look up functions, their type signatures, and so on. Looking at the source is a great way to learn the good ways to do things in Haskell; in particular, notice just how short the functions are. Haskell has a steep learning curve, but it's pretty easy to understand what code is doing.

For another example of functional thinking, here's a function to count the number of lowercase letters in a string.

import Data.Char    -- brings function isLower into scope

countLowerCase :: String -> Int -- String is just [Char]
countLowerCase str = length (filter isLower str)

This looks absurd in C, but since Haskell is lazily evaluated, it doesn't actually copy the string; in some sense, values and function pointers are the same under lazy evaulation. But, of course, this can be written more concisely:

countLowerCase :: String -> Int
countLowerCase = length . filter isLower

Here, f . g means fg mathematically: this is function composition: (f . g) x = f (g x). But now, the argument isn't necessary. This can be used like a concise, right-to-left analogue to Unix pipelines. This is known as point-free programming.

Conversely, if one wants the arguments but not the function, you can just use lambda expressions. The notion is \variables -> body. For example:

countLowercaseAndDigits :: String -> Int
countLowercaseAndDigits =
    length . filter (\c -> isLower c || isDigit c)

This is useful for small functions that don't need to be used in more than one place.

Another neat syntactic trick is that any function can be made prefix or infix. For functions that start with a letter, underscore, digit, or apostrophe, prefix is the default, but they can be made infix with backticks, e.g. 1 `add` 2. For anything else, infix is default, adding parentheses makes them prefix: (+) 1 2 and so on. Infix functions can also be partially applied:

stripPunctuation :: String -> String
stripPunctuation = filter (`notElem` "!#$%&*+./<=>?@\\^|-~:")
-- Note above string the SECOND argument to notElem ^