Why Haskell Matters

This is an early draft of a work in progress article.

Haskell doesn't solve different problems than other languages. But it solves them differently.

-- unknown

Abstract

In this article I'm presenting some of the most important and distinguishing features of the Haskell programming language.

The target audience are developers with a background in non-functional languages who are eager to learn about concepts of functional programming and Haskell in particular.

The presentation aims to be self-contained and does not require any previous knowledge of the language. I will also try to keep the learning curve moderate and to limit the scope of the presentation; nevertheless this article is not meant to be a full introduction to the language.

(If you looking for an enjoyable tutorial have a look at Learn You a Haskell

Table of contents

• Introduction
• Functions are first class
• Pattern matching (part 1)
• Algebraic Data Types
• Polymorphic Data Types
  • Lists
• Immutability
• Declarative programming
• Non-strict Evaluation
• Type Classes

Introduction

Exactly thirty years ago, on April 1st 1990, the original Haskell language report was published by a small group of academic researchers in the field of non-strict functional programming.

Haskell never became one of the most popular languages in the software industry or part of the mainstream but it has been and still is quite influential in the software development community.

In this article I want to explain why Haskell keeps to be such an important language by presenting some of its most distinguishing features and detailing them with working code examples.

But before diving directly into the technical details I'd like to first have a closer look on the reception of Haskell in the software developers community:

A strange development over time

In a talk in 2017 on the Haskell journey since its beginnings in the 1980ies Simon Peyton Jones speaks about the rather unusual life story of Haskell.

First he talks about the typical life cycle of research languages. They are often created by a single researcher (who is also the single user) and most of them will be abandoned after just a few years.

A more successful research language might gain some interest in a larger community but will still not escape the ivory tower and typically will be given up within ten years.

On the other hand we have all those popular programming languages that are quickly adopted by large numbers of users and thus reach "the threshold of immortality". That is the base of existing code will grow so large that the language will be in use for decades.

A little jokingly he then depicts the sad fate of languages designed by committees by flat line through zero: They simply never take off.

Finally he presents a chart showing the Haskell timeline:

The development shown in this chart seems rather unexpected: Haskell started as a research language and was even designed by a committee; so in all probability it should have been abandoned long before the millennium!

But instead it gained some momentum in its early years followed by a rather quiet phase during the decade of OO hype (Java was released in 1995). And then again we see a continuous growth of interest since about 2005. I'm writing this in early 2020 and we still see this trend!

Being used versus being discussed

Then Simon Peyton Jones points out another interesting characteristic of the reception of Haskell in recent years: In statics that rank programming languages by actual usage Haskell is typically not under the 30 most active languages. But in statistics that instead rank languages by the volume of discussions on the internet Haskell typically scores much better (often in the top ten).

So why does Haskell keep to be a hot topic in the software development community?

A very short answer might be: Haskell has a number of features that are clearly different from those of most other programming languages. Many of these features have proven to be powerful tools to solve basic problems of software development elegantly.

Therefore over time other programming languages have adopted parts of these concepts (e.g. pattern matching or type classes). In discussions about such concepts the Haskell heritage is mentioned and differences between the original Haskell concepts and those of other languages are discussed. Sometimes people are encouraged to have a closer look at the source of these concepts to get a deeper understanding of their original intentions. That's why we see a growing number of developers working in Python, Typescript, Scala, Rust, C++, C# or Java starting to dive into Haskell.

A further essential point is that Haskell is still an experimental laboratory for research in areas such as compiler construction, programming language design, theorem-provers, type systems etc. So inevitably Haskell will be a topic in the discussion about these approaches.

In the following sections we will try to find the longer answer by studying some of the most distinguishing features of Haskell.

Functions are First-class

In computer science, a programming language is said to have first-class functions if it treats functions as first-class citizens. This means the language supports passing functions as arguments to other functions, returning them as the values from other functions, and assigning them to variables or storing them in data structures.[1] Some programming language theorists require support for anonymous functions (function literals) as well.[2] In languages with first-class functions, the names of functions do not have any special status; they are treated like ordinary variables with a function type.

quoted from Wikipedia

We'll go through this one by one:

functions can be assigned to variables exactly as any other other values

Let's have a look how this looks like in Haskell. First we define some simple values:

-- define constant `aNumber` with a value of 42. 
aNumber :: Integer
aNumber = 42

-- define constant `aString` with a value of "hello world"
aString :: String
aString = "Hello World"

In the first line we see a type signature that defines the constant aNumber to be of type Integer. In the second line we define the value of aNumber to be 42. In the same way we define the constant aString to be of type String.

Next we define a function square that takes an integer argument and returns the square value of the argument:

square :: Integer -> Integer
square x = x * x

Definition of a function works exactly in the same way as the definition of any other value. The only thing special is that we declare the type to be a function type by using the -> notation. So :: Integer -> Integer represents a function from Integer to Integer. In the second line we define function square to compute x * x for any Integer argument x.

Ok, seems not too difficult, so let's define another function double that doubles its input value:

double :: Integer -> Integer
double n = 2 * n

support for anonymous functions

Anonymous functions, also known as lambda expressions, can be defined in Haskell like this:

\x -> x * x

This expression denotes an anonymous function that takes a single argument x and returns the square of that argument. The backslash is read as λ (the greek letter lambda).

You can use such as expressions everywhere where you would use any other function. For example you could apply the anonymous function \x -> x * x to a number just like the named function square:

-- use named function:
result = square 5

-- use anonymous function:
result' = (\x -> x * x) 5

We will see more useful applications of anonymous functions in the following section.

Functions can be returned as values from other functions

function composition

Do you remember function composition from your high-school math classes? Function composition is an operation that takes two functions f and g and produces a function h such that h(x) = g(f(x)) The resulting composite function is denoted h = g ∘ f where (g ∘ f )(x) = g(f(x)). Intuitively, composing functions is a chaining process in which the output of function f is used as input of function g.

So looking from a programmers perspective the ∘ operator is a function that takes two functions as arguments and returns a new composite function.

In Haskell this operator is represented as the dot operator .:

(.) :: (b -> c) -> (a -> b) -> a -> c
(.) f g x = f (g x)

The brackets around the dot are required as we want to use a non-alphabetical symbol as an identifier. In Haskell such identifiers can be used as infix operators (as we will see below). Otherwise (.) is defined as any other function. Please also note how close the syntax is to the original mathematical definition.

Using this operator we can easily create a composite function that first doubles a number and then computes the square of that doubled number:

squareAfterDouble :: Integer -> Integer
squareAfterDouble = square . double

Currying and Partial Application

In this section we look at another interesting example of functions producing other functions as return values. We start by defining a function add that takes two Integer arguments and computes their sum:

-- function adding two numbers 
add :: Integer -> Integer -> Integer
add x y = x + y

This look quite straightforward. But still there is one interesting detail to note: the type signature of add is not something like

add :: (Integer, Integer) -> Integer

Instead it is:

add :: Integer -> Integer -> Integer

What does this signature actually mean? It can be read as "A function taking an Integer argument and returning a function of type Integer -> Integer". Sounds weird? But that's exactly what Haskell does internally. So if we call add 2 3 first add is applied to 2 which return a new function of type Integer -> Integer which is then applied to 3.

This technique is called Currying

Currying is widely used in Haskell as it allows another cool thing: partial application.

In the next code snippet we define a function add5 by partially applying the function add to only one argument:

-- partial application: applying add to 5 returns a function of type Integer -> Integer
add5 :: Integer -> Integer
add5 = add 5

The trick is as follows: add 5 returns a function of type Integer -> Integer which will add 5 to any Integer argument.

Partial application thus allows us to write functions that return functions as result values. This technique is frequently used to provide functions with configuration data.

Functions can be passed as arguments to other functions

I could keep this section short by telling you that we have already seen an example for this: the function composition operator (.). It accepts two functions as arguments and returns a new one as in:

squareAfterDouble :: Integer -> Integer
squareAfterDouble = square . double

But I have another instructive example at hand.

Let's imagine we have to implement a function that doubles any odd Integer:

ifOddDouble :: Integer -> Integer
ifOddDouble n =
  if odd n
    then double n
    else n

The Haskell code is straightforward: new ingredients are the if ... then ... else ... and the odd odd which is a predicate from the Haskell standard library that returns True if an integral number is odd.

Now let's assume that we also need another function that computes the square for any odd number. As you can imagine we can use the standard library predicate even:

ifOddSquare :: Integer -> Integer
ifOddSquare n =
  if odd n
    then square n
    else n

As vigilant developers we immediately detect a violation of the Don't repeat yourself principle as both functions only vary in the usage of a different growth functions double versus square.

So we are looking for a way to refactor this code by a solution that keeps the original structure but allows to vary the used growth function.

What we need is a function that takes a growth function (of type (Integer -> Integer)) as first argument, an Integer as second argument and returns an Integer. The specified growth function will be applied in the then clause:

ifOdd :: (Integer -> Integer) -> Integer -> Integer
ifOdd growthFunction n =
  if odd n
    then growthFunction n
    else n

With this approach we can refactor ifOddDouble and ifOddSquare as follows:

ifOddDouble :: Integer -> Integer
ifOddDouble n = ifOdd double n

ifOddSquare :: Integer -> Integer
ifOddSquare n = ifOdd square n

Now imagine that we have to implement new function ifEvenDouble and ifEvenSquare, that will work only on even numbers. Instead of repeating ourselves we come up with a function ifPredGrow that takes a predicate function of type (Integer -> Bool) as first argument, a growth function of type (Integer -> Integer) as second argument and an Integer as third argument, returning an Integer.

The predicate function will be used to determine whether the growth function has to be applied:

ifPredGrow :: (Integer -> Bool) -> (Integer -> Integer) -> Integer -> Integer
ifPredGrow predicate growthFunction n =
  if predicate n
    then growthFunction n
    else n

Using this higher order function that even takes two functions as arguments we can write the two new functions and further refactor the existing ones without breaking the DRY principle:

ifEvenDouble :: Integer -> Integer
ifEvenDouble n = ifPredGrow even double n

ifEvenSquare :: Integer -> Integer
ifEvenSquare n = ifPredGrow even square n

ifOddDouble'' :: Integer -> Integer
ifOddDouble'' n = ifPredGrow odd double n

ifOddSquare'' :: Integer -> Integer
ifOddSquare'' n = ifPredGrow odd square n

Pattern matching (part 1)

With the things that we have learnt so far, we can now start to implement some more interesting functions. So what about implementing the recursive factorial function?

The factorial function can be defined as follows:

For all n ∈ ℕ₀:

0! = 1
n! = n * (n-1)!

With our current knowledge of Haskell we can implement this as follows:

factorial :: Natural -> Natural
factorial n =
  if n == 0
    then 1
    else n * factorial (n - 1)

We are using the Haskell data type Natural to denote the set of non-negative integers ℕ₀. Using the literal factorial within the definition of the function factorial works as expected and denotes a recursive function call.

As these kind of recursive definition of functions are typical for functional programming, the language designers have added a useful feature called pattern matching that allows to define functions by a set of equations:

fac :: Natural -> Natural
fac 0 = 1
fac n = n * fac (n - 1)

This style comes much closer to the mathematical definition and is typically more readable, as it helps to avoid nested if ... then ... else ... constructs.

Pattern matching can not only be used for numeric values but for any other data types. We'll see some more examples shortly.

Algebraic Data Types

Haskell supports user-defined data types by making use of a very thought out concept. Let's start with a simple example:

data Status = Green | Yellow | Red

This declares a data type Status which has exactly three different instances. For each instance a data constructor is defined that allows to create a new instance of the data type.

Each of those data constructors is a function (in this simple case a constant) that returns a Status instance.

The type Status is a so called sum type as it is represents the set defined by the sum of all three instances Green, Yellow, Red. In Java this corresponds to Enumerations.

Let's assume we have to create a converter that maps our Status values to Severity values representing severity levels in some other system. This converter can be written using the pattern matching syntax that we already have seen above:

-- another sum type representing severity:
data Severity = Low | Middle | High deriving (Eq, Show)

severity :: Status -> Severity
severity Green  = Low
severity Yellow = Middle
severity Red    = High

The compiler will tell us when we did not cover all instances of the Status type (by making use of the -fwarn-incomplete-patterns pragma).

Now we look at data types that combine multiple different elements, like pairs n-tuples, etc. Let's start with a PairStatusSeverity type that combines two different elements:

data PairStatusSeverity = P Status Severity

This can be understood as: data type PairStatusSeverity can be constructed from a data constructor P that takes a value of type Status and a value of type Severity and returns a Pair instance.

So for example P Green High returns a PairStatusSeverity instance (the data constructor P has the signature P :: Status -> Severity -> PairStatusSeverity).

The type PairStatusSeverity can be interpreted as the set of all possible ordered pairs of Status and Severity values, that is the cartesian product of Status and Severity.

That's why such a data type is called product type.

Haskell allows you to create arbitrary data types by combining sum types and product types. The complete range of data types that can be constructed in this way is called algebraic data types or ADT in short.

Using algebraic data types has several advantages:

• Pattern matching can be used to analyze any concrete instance to select different behaviour based on input data. as in the example that maps Status to Severity there is no need to use if..then..else.. constructs.
• The compiler can detect incomplete patterns matching or other flaws.
• The compiler can derive many complex functionality automatically for ADTs as they are constructed in such a regular way.

We will cover the interesting combination of ADTs and pattern matching in the following sections.

Polymorphic Data Types

Forming pairs or more generally n-tuples is a very common task in programming. Therefore it would be inconvenient and repetitive if we were forced to create new Pair or Tuple types for each concrete usage. consider the following example:

data PairStatusSeverity = P Status Severity

data PairStatusString   = P' Status String

data PairSeverityStatus = P'' Severity Status

Luckily data type declarations allow to use type variables to avoid this kind of cluttered code. So we can define a generic data type Pair that allows us to freely combine different kinds of arguments:

-- a simple polymorphic type
data Pair a b = P a b

This can be understood as: data type Pair uses two elements of (potentially) different types a and b; the data constructor P takes a value of type a and a value of type b and returns a Pair a b instance (the data constructor P has the signature P :: a -> b -> Pair a b). The type Pair can now be used to create many different concrete data types it is thus called a polymorphic data type.

As pairs and n-tuples are so frequently used, the Haskell language designers have added some syntactic sugar to work effortlessly with them.

So you can simply write tuples like this:

tuple :: (Status, Severity, String)
tuple = (Green, Low, "All green")

Lists

Another very useful polymorphic type is the List.

A list can either be the empty list (denoted by the data constructor []) or some element of a data type a followed by a list with elements of type a, denoted by [a].

This intuition is reflected in the following data type definition:

data [a] = [] | a : [a]

The cons operator (:) (which is an infix operator like (.) from the previous section) is declared as a data constructor to construct a list from a single element of type a and a list of type [a].

So a list containing only a single element 1 is constructed by:

1 : []

A list containing the three numbers 1, 2, 3 is constructed like this:

1 : 2 : 3 : []

Luckily the Haskell language designers have been so kind to offer some syntactic sugar for this. So the first list can simply be written as [1] and the second as [1,2,3].

Polymorphic type expressions describe families of types. For example, (forall a)[a] is the family of types consisting of, for every type a, the type of lists of a. Lists of integers (e.g. [1,2,3]), lists of characters (['a','b','c']), even lists of lists of integers, etc., are all members of this family.

Function that work on lists can use pattern matching to select behaviour for the [] and the a:[a] case.

Take for instance the definition of the function length that computes the length of a list:

length :: [a] -> Integer
length []     =  0
length (x:xs) =  1 + length xs

We can read these equations as: The length of the empty list is 0, and the length of a list whose first element is x and remainder is xs is 1 plus the length of xs.

In our next example we want to work with a of some random integers:

someNumbers :: [Integer]
someNumbers = [49,64,97,54,19,90,934,22,215,6,68,325,720,8082,1,33,31]

Now we want to select all even or all odd numbers from this list. We are looking for a function filter that takes two arguments: first a predicate function that will be used to check each element and second the actual list of elements. The function will return a list with all matching elements. And of course our solution should work not only for Integers but for any other types as well. Here is the type signature of such a filter function:

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

In the implementation we will use pattern matching to provide different behaviour for the [] and the (x:xs) case:

filter :: (a -> Bool) -> [a] -> [a]
filter pred []     = []
filter pred (x:xs)
  | pred x         = x : filter pred xs
  | otherwise      = filter pred xs

The [] case is obvious. To understand the (x:xs) case we have to know that in addition to simple matching of the type constructors we can also use pattern guards to perform additional testing on the input data. In this case we compute pred x if it evaluates to True, x is a match and will be cons'ed with the result of filter pred xs. If it does not evaluate to True, we will not add x to the result list and thus simply call filter recursively on the remainder of the list.

Now we can use filter to select elements from our sample list:

someEvenNumbers :: [Integer]
someEvenNumbers = filter even someNumbers

-- predicates may also be lambda-expresssions
someOddNumbers :: [Integer]
someOddNumbers = filter (\n -> n `rem` 2 /= 0) someNumbers  

Of course we don't have to invent functions like filter on our own but can rely on the extensive set of predefined functions working on lists in the Haskell base library.

Arithmetic sequences

There is a nice feature that often comes in handy when dealing with lists of numbers. It's called arithmetic sequences and allows you to define lists of numbers with a concise syntax:

upToHundred :: [Integer]
upToHundred = [1..100]

As expected this assigns upToHundred with a list of integers from 1 to 100.

It's also possible to define a step width that determines the increment between the subsequent numbers. If we want only the odd numbers we can construct them like this:

oddsUpToHundred :: [Integer]
oddsUpToHundred = [1,3..100]

Arithmetic sequences can also be used in more dynamic cases. For example we can define the factorial function like this:

n! = 1 * 2 * 3 ... (n-2) * (n-1) * n, for integers > 0

In Haskell we can use an arithmetic sequence to define this function:

fac' n   = prod [1..n]

Immutability

In object-oriented and functional programming, an immutable object is an object whose state cannot be modified after it is created. This is in contrast to a mutable object (changeable object), which can be modified after it is created.

Quoted from Wikipedia

This is going to be a very short section. In Haskell all data is immutable. Period.

Let's look at some interactions with the Haskell GHCi REPL:

λ> a = [1,2,3]
λ> a
[1,2,3]
λ> reverse a
[3,2,1]
λ> a
[1,2,3]

In Haskell there is no way to change the value of a after its initial creation. There are no destructive operations available as in some other functional languages like Lisp, Scheme or ML.

The huge benefit of this is that refactorings become much simpler as in languages where every function or method might mutate data. Thus it will also be more easy to reason about a given piece of code.

Of course this also makes programming of concurrent operations much easier. With a shared nothing approach, Haskell programs will automatically be thread-safe.

Declarative programming

In this section I want to explain how programming with higher order functions can be used to factor out many basic control structures and algorithms from the user code.

This will result in a more declarative programming style where the developer can simply declare what she wants to achieve but is not required to write down how it is to be achieved.

Code that applies this style will be much denser and it will be more concerned with the actual elements of the problem domain than with the technical implementation details.

We'll demonstrate this with some examples working on lists. First we get the task to write a function that doubles all elements of a [Integer] list. We want to reuse the double function we have already defined above.

With all that we have learnt so far writing a function doubleAll isn't that hard:

-- compute the double value for all list elements
doubleAll :: [Integer] -> [Integer]
doubleAll [] = []
doubleAll (n:rest) = double n : doubleAll rest

Next we are asked to implement a similar function squareAll that will use square to compute the square of all elements in a list. The naive way would be to implement it in the WET (We Enjoy Typing) approach:

-- compute squares for all list elements
squareAll :: [Integer] -> [Integer]
squareAll [] = []
squareAll (n:rest) = square n : squareAll rest

Of course this is very ugly: both function use the same pattern matching and apply the same recursive iteration strategy. They only differ in the function applied to each element.

As role model developers we don't want to repeat ourselves. We are thus looking for something that captures the essence of mapping a given function over a list of elements:

map :: (a -> b) -> [a] -> [b]
map f []     = []
map f (x:xs) = f x : map f xs

This function abstracts away the implementation details of iterating over a list and allows to provide a user defined mapping function as well.

Now we can use map to simply declare our intention (the 'what') and don't have to detail the 'how':

doubleAll' :: [Integer] -> [Integer]
doubleAll' = map double

squareAll' :: [Integer] -> [Integer]
squareAll' = map square

folding or reducing

Now let's have a look at some related problem. Our first task is to add up all elements of a [Integer] list. First the naive approach which uses the already familiar mix of pattern matching plus recursion:

sumUp :: [Integer] -> Integer
sumUp [] = 0
sumUp (n:rest) = n + sumUp rest

By looking at the code for a function that computes the product of all elements of a [Integer] list we can again see that we are repeating ourselves:

prod :: [Integer] -> Integer
prod [] = 1
prod (n:rest) = n * prod rest

So what is the essence of both algorithms? At the core of both algorithms we have a recursive function which

• takes a binary operator ((+)or (*) in our case),
• an initial value that is used as a starting point for the accumulation (typically the identity element (or neutral element) of the binary operator),
• the list of elements that should be reduced to a single return value
• performs the accumulation by recursively applying the binary operator to all elements of the list until the [] is reached, where the neutral element is returned.

This essence is contained in the higher order function foldr which again is part of the Haskell standard library:

foldr :: (a -> b -> b) -> b -> [a] -> b
foldr f acc []     =  acc
foldr f acc (x:xs) =  f x (foldr f acc xs)

Now we can use foldr to simply declare our intention (the 'what') and don't have to detail the 'how':

sumUp' :: [Integer] -> Integer
sumUp' = foldr (+) 0

prod' :: [Integer] -> Integer
prod' = foldr (*) 1

With the functions map and foldr (or reduce) we have now two very powerful tools at hand that can be used in many situation where list data has to be processed.

Both functions can even be composed to form yet another very important programming concept: Map/Reduce. In Haskell this operation is provided by the function foldMap.

I won't go into details here as it would go beyond the scope of this article. But I'll invite you to read my introduction to Map/Reduce in Haskell.

Non-strict Evaluation

Now we come to topic that was one of the main drivers for the Haskell designers: they wanted to get away from the then standard model of strict evaluation.

Non-Strict Evaluation (aka. normal order reduction) has one very important property.

If a lambda expression has a normal form, then normal order reduction will terminate and find that normal form.

Church-Rosser Theorem II

This property does not hold true for other reduction strategies (like applicative order or call-by-value reduction).

This result from mathematical research on the lambda calculus is important as Haskell maintains the semantics of normal order reduction.

The real-world benefits of lazy evaluation include:

• Avoid endless loops in certain edge cases
• The ability to define control flow (structures) as abstractions instead of primitives.
• The ability to define potentially infinite data structures. This allows for more straightforward implementation of some algorithms.

So let's have a closer look at those benefits:

Avoid endless loops in certain edge cases

Consider the following example function:

ignoreY :: Integer -> Integer -> Integer
ignoreY x y = x

It takes two integer arguments and returns the first one unmodified. The second argument is simply ignored.

In most programming languages both arguments will be evaluated before the function body is executed: they use applicative order reduction aka. eager evaluation or call-by-value semantics.

In Haskell on the other hand it is save to call the function with a non-terminating expression in the second argument. First we create a non-terminating expression viciousCircle. Any attempt to evaluate it will result in an endless loop:

-- it's possible to define non-terminating expressions like
viciousCircle :: a
viciousCircle = viciousCircle

But if we use viciousCircle as second argument to the function ignoreY it will simply be ignored and the first argument is returned:

-- trying it in GHCi:
λ> ignoreY 42 viciousCircle
42

Define potentially infinite data structures

In the section on lists we have already met arithmetic sequences like [1..10].

Arithmetic sequences can also be used to define infinite lists of numbers. Here are a few examples:

-- all natural numbers
naturalNumbers = [1..]

-- all even numbers
evens = [2,4..]

-- all odd numbers
odds  = [1,3..]

Defining those infinite lists is rather easy. But can we do with them? Are they useful for any purpose? In the viciousCircle example above we have learnt that defining that expression is fine but any attempt to evaluate it will result in an infinite loop.

If we try to print naturalNumbers we will also end up in an infinite loop of integers printed to the screen.

But if we are bit less greedy than asking for all natural numbers everything will be OK.

λ> take 10 naturalNumbers
[1,2,3,4,5,6,7,8,9,10]

λ> take 10 evens
[2,4,6,8,10,12,14,16,18,20]

λ> take 10 odds
[1,3,5,7,9,11,13,15,17,19]

We can also peak at a specific position in such an infinite list, using the (!!) operator:

λ> odds !! 5000
10001

λ> evens !! 10000
20002

List comprehension

Do you remember set comprehension notation from your math classes?

As simple example would be the definition of the set of even numbers:

Evens = {i | i = 2n ∧ n ∊ ℕ}

Which can be read as: Evens is defined as the set of all i where i = 2*n and n is an element of the set of natural numbers.

The Haskell list comprehension allows us to define - potentially infinite - lists with a similar syntax:

evens' = [2*n | n <- [1..]]

Again we can avoid infinite loops by evaluating only a finite subset of evens':

λ> take 10 evens'
[2,4,6,8,10,12,14,16,18,20]

List comprehension can be very useful for defining numerical sets and series in a (mostly) declarative way that comes close to the original mathematical definitions.

Take for example the set PT of all pythagorean triples

PT = {(a,b,c) | a,b,c ∊ ℕ ∧ a² + b² = c² }

The Haskell definition looks like this:

pt :: [(Natural,Natural,Natural)]
pt = [(a,b,c) | c <- [1..],
                b <- [1..c],
                a <- [1..b],
                a^2 + b^2 == c^2]

define control flow structures as abstractions instead of primitives

In most languages it is not possible to define new conditional operations, e.g. your own myIf statement. A conditional operation will evaluate some of its arguments only if certain conditions are met. This is very hard - if not impossible - to implement in language with call-by-value semantics which evaluates all function arguments before actually evaluating the function body.

As Haskell implements call-by-need semantics, it is possible to define new conditional operations. In fact this is quite helpful when writing domain specific languages.

Here comes a very simple version of myIf:

myIf :: Bool -> b -> b -> b
myIf p x y = if p then x else y 

λ> myIf (4 > 2) "true" viciousCircle
"true"

A somewhat more useful control-structure is the cond (for conditional) function that stems from LISP and Scheme languages. It allows you to define a more table-like decision structure, somewhat resembling a switch statement from C-style languages:

cond :: [(Bool, a)] -> a
cond []                 = error "make sure that at least one condition is true"
cond ((True,  v):rest)  = v
cond ((False, _):rest)  = cond rest

With this function we can implement a signum function sign as follows:

sign :: (Ord a, Num a) => a -> a
sign x = cond [(x > 0     , 1 )
              ,(x < 0     , -1)
              ,(otherwise , 0 )]

λ> sign 5
1
λ> sign 0
0
λ> sign (-4)
-1

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This is my scrap book (don't look at it)

• Funktionen sind 1st class citizens (higher order functions, Funktionen könen neue Funktionen erzeugen und andere Funktionen als Argumente haben)

• Abstraktion über Resource management und Abarbeitung (=> deklarativ)

• Immutability ("Variables do not Vary")

• Seiteneffekte müssen in Funktions signaturen explizit gemacht werden. D.H wenn keine Seiteneffekt angegeben ist, verhindert der Compiler, dass welche auftreten ! Damit lässt sich Seiteneffektfreie Programmierung realisieren ("Purity")

• Evaluierung in Haskell ist "non-strict" (aka "lazy"). Damit lassen sich z.B. abzählbar unendliche Mengen (z.B. alle Primzahlen) sehr elegant beschreiben. Aber auch kontrollstrukturen lassen sich so selbst bauen (super für DSLs)

• Static and Strong typing (Es gibt kein Casting)

• Type Inferenz. Der Compiler kann die Typ-Signaturen von Funktionen selbst ermitteln. (Eine explizite Signatur ist aber möglich und oft auch sehr hilfreich für Doku und um Klarheit über Code zu gewinnen.)

• Polymorphie (Z.B für "operator overloading", Generische Container Datentypen, etc. auf Basis von "TypKlassen")

• Algebraische Datentypen (Summentypen + Produkttypen) AD helfen typische Fehler, die man von OO Polymorphie kenn zu vermeiden. Sie erlauben es, Code für viele Oerationen auf Datentypen komplett automatisch vom Compiler generieren zu lassen).

• Pattern Matching erlaubt eine sehr klare Verarbeitung von ADTs

• Eleganz: Viele Algorithmen lassen sich sehr kompakt und nah an der Problemdomäne formulieren.

• Data Encapsulation durch Module

• Weniger Bugs durch

  • Purity, keine Seiteneffekte

  • Starke typisierung. Keine NPEs !

  • Hohe Abstraktion, Programme lassen sich oft wie eine deklarative Spezifikation des Algorithmus lesen

  • sehr gute Testbarkeit durch "Composobility"

    • das "ports & adapters" Beispiel: https://github.com/thma/RestaurantReservation

    • TDD / DDD

  • Memory Management (sehr schneller GC)

  • Modulare Programme. Es gibt ein sehr einfaches aber effektive Modul System und eine grosse Vielzahl kuratierter Bibliotheken.

  ("Ich habe in 5 Jahre Haskell noch nicht ein einziges Mal debuggen müssen")

• Performance: keine VM, sondern sehr optimierter Maschinencode. Mit ein wenig Feinschliff lassen sich oft Geschwindigkeiten wie bei handoptimiertem C-Code erreichen.

toc for code chapters (still in german)

• Werte

• Funktionen

• Listen

• Lazyness

  • List comprehension
  • Eigene Kontrollstrukturen

• Algebraische Datentypen

  • Summentypen : Ampelstatus
  • Produkttypen (int, int) Beispiel: Baum mit Knoten (int, Ampelstatus) dann mit map ein Ampelstatus

• deriving (Show, Read) für einfache Serialisierung

• Homoiconicity (Kind of)

• Maybe Datentyp

  • totale Funktionen
  • Verkettung von Maybe operationen
    (um die "dreadful Staircase" zu vermeiden) => Monoidal Operations

• explizite Seiten Effekte -> IO Monade

• TypKlassen

  • Polymorphismus z.B. Num a, Eq a
  • Show, Read => Homoiconicity bei Serialisierung
  • Automatic deriving (Functor mit Baum Beispiel)

• Testbarkeit

  • TDD, higher order functions assembly, Typklassen dispatch (https://jproyo.github.io/posts/2019-03-17-tagless-final-haskell.html)