My first programming languages were Lisp, Scheme, and ML. When I later started to work in OO languages like C++ and Java I noticed that idioms that are standard vocabulary in functional programming (fp) were not so easy to achieve and required sophisticated structures. Books like [Design Patterns: Elements of Reusable Object-Oriented Software](https://en.wikipedia.org/wiki/Design_Patterns) were a great starting point to reason about those structures. One of my earliest findings was that several of the GoF-Patterns had a stark resemblance of structures that are built into in functional languages: for instance the strategy pattern corresponds to higher order functions in fp (more details see [below](#strategy)).
Recently, while re-reading through the [Typeclassopedia](https://wiki.haskell.org/Typeclassopedia) I thought it would be a good exercise to map the structure of software [design-patterns](https://en.wikipedia.org/wiki/Software_design_pattern#Classification_and_list) to the concepts found in the Haskell typeclass library and in functional programming in general.
By searching the web I found some blog entries studying specific patterns, but I did not come across any comprehensive study. As it seemed that nobody did this kind of work yet I found it worthy to spend some time on it and write down all my findings on the subject.
The [Typeclassopedia](https://wiki.haskell.org/wikiupload/8/85/TMR-Issue13.pdf) is a now classic paper that introduces the Haskell type classes by clarifying their algebraic and category-theoretic background. In particular it explains the relationships among those type classes.
In this section I'm taking a tour through the Typeclassopedia from a design pattern perspective.
For each of the Typeclassopedia type classes (at least up to Traversable) I try to explain how it corresponds to structures applied in design patterns.
I believe this kind of exposition could be helpful if you are either:
> "The strategy pattern [...] is a behavioral software design pattern that enables selecting an algorithm at runtime. Instead of implementing a single algorithm directly, code receives run-time instructions as to which in a family of algorithms to use"
> "In the above UML class diagram, the `Context` class doesn't implement an algorithm directly. Instead, `Context` refers to the `Strategy` interface for performing an algorithm (`strategy.algorithm()`), which makes `Context` independent of how an algorithm is implemented. The `Strategy1` and `Strategy2` classes implement the `Strategy` interface, that is, implement (encapsulate) an algorithm."
>(quoted from https://en.wikipedia.org/wiki/Strategy_pattern)
* in C a strategy would be modelled as a function pointer that can be used to dispatch calls to different functions.
* In an OO language like Java a strategy would be modelled as a single strategy-method interface that would be implemented by different strategy classes that provide implementations of the strategy method.
* in functional programming a strategy is just a higher order function, that is a parameter of a function that has a function type.
```haskell
-- first we define two simple strategies that map numbers to numbers:
strategyId :: Num a => a -> a
strategyId n = n
strategyDouble :: Num a => a -> a
strategyDouble n = 2*n
-- now we define a context that applies a function of type Num a => a -> a to a list of a's:
context :: Num a => (a -> a) -> [a] -> [a]
context f l = map f l
-- according to the rules of currying this can be abbreviated to:
context = map
```
The `context` function uses higher order `map` function (`map :: (a -> b) -> [a] -> [b]`) to apply the strategies to lists of numbers:
Instead of map we could use just any other function that accepts a function of type `Num a => a -> a` and applies it in a given context.
In Haskell the application of a function in a computational context is generalized with the typeclass `Functor`:
```haskell
class Functor f where
fmap :: (a -> b) -> f a -> f b
```
Actually `map` is the fmap implementation for the List Functor instance:
```haskell
instance Functor [] where
fmap = map
```
Although it would be fair to say that the typeclass `Functor` captures the essential idea of the strategy pattern - namely the lifting into and the execution in a computational context of a function - the usage of higher order functions (or strategies) is of course not limited to `Functors` - we could use just any higher order function fitting our purpose. Other typeclasses like `Foldable` or `Traversable` can serve as helpful abstractions when dealing with typical use cases of applying variable strategies within a computational context.
> "The singleton pattern is a software design pattern that restricts the instantiation of a class to one object. This is useful when exactly one object is needed to coordinate actions across the system."
> (quoted from https://en.wikipedia.org/wiki/Singleton_pattern)
The singleton pattern ensures that multiple requests to a given object always return one and the same singleton instance.
In functional programming this semantics can be achieved by ```let```.
Via the `let`-Binding we can thread the singleton through arbitrary code in the `in` block. All occurences of `singleton` in the `mainComputation`will point to the same instance.
Typeclasses provide several tools to make this kind of threading more convenient or even to avoid explicit threading of instances.
### Using Pointed to create singletons
> "Given a Functor, the Pointed class represents the additional ability to put a value into a “default context.” Often, this corresponds to creating a container with exactly one element, but it is more general than that."
> (quoted from the Typeclassopedia)
```haskell
class Functor f => Pointed f where
pure :: a -> f a
```
### Using Applicative Functor for threading of singletons
The following code defines a simple expression evaluator:
```haskell
data Exp e = Var String
| Val e
| Add (Exp e) (Exp e)
| Mul (Exp e) (Exp e)
-- the environment is a list of tupels mapping variable names to values of type e
type Env e = [(String, e)]
-- a simple evaluator reducing expression to numbers
eval :: Num e => Exp e -> Env e -> e
eval (Var x) env = fetch x env
eval (Val i) env = i
eval (Add p q) env = eval p env + eval q env
eval (Mul p q) env = eval p env * eval q env
```
`eval` is a classic evaluator function that recursively evaluates sub-expression before applying `+` or `*`.
Note how the explicit `env`parameter is threaded through the recursive eval calls. This is needed to have the
environment avalailable for variable lookup at any recursive call depth.
If we now bind `env` to a value as in the following snippet it is used as an imutable singleton within the recursive evaluation of `eval exp env`.
Experienced Haskellers will notice the ["eta-reduction smell"](https://wiki.haskell.org/Eta_conversion) in `eval (Var x) env = fetch x env` which hints at the possibilty to remove `env` as an explicit parameter. We can not do this right away as the other equations for `eval` do not allow eta-reduction. In order to do so we have to apply the combinators of the `Applicative Functor`:
```haskell
class Functor f => Applicative f where
pure :: a -> f a
(<*>) :: f (a -> b) -> f a -> f b
instance Applicative ((->) a) where
pure = const
(<*>) f g x = f x (g x)
```
This `Applicative` allows us to rewrite `eval` as follows:
```haskell
eval :: Num e => Exp e -> Env e -> e
eval (Var x) = fetch x
eval (Val i) = pure i
eval (Add p q) = pure (+) <*> eval p <*> eval q
eval (Mul p q) = pure (*) <*> eval p <*> eval q
```
Any explicit handling of the variable `env` is now removed.
(I took this example from the classic paper [Applicative programming with effects](http://www.soi.city.ac.uk/~ross/papers/Applicative.pdf) which details how `pure` and `<*>` correspond to the combinatory logic combinators `K` and `S`.)
> In software engineering, a pipeline consists of a chain of processing elements (processes, threads, coroutines, functions, etc.), arranged so that the output of each element is the input of the next; the name is by analogy to a physical pipeline.
This works exactly as stated in the wikipedia definition of the pattern: the output of `echo "hello world"` is used as input for the next command `wc -w`. The ouptput of this command is then piped as input into `xargs printf "%d*3\n"` and so on.
On the first glance this might look like ordinary function composition. We could for instance come up with the following approximation in Haskell:
```haskell
((3 *) . length . words) "hello world"
6
```
But with this design we missed an important feature of the chain of shell commands: The commands do not work on elementary types like Strings or numbers but on input and output streams that are used to propagate the actual elementary data around. So we can't just send a String into the `wc` command as in `"hello world" | wc -w`. Instead we have to use `echo` to place the string into a stream that we can then use as input to the `wc` command:
```bash
$ echo "hello world" | wc -w
```
So we might say that `echo`*lifts* the String `"hello world"` into the stream context.
We can capture this behaviour in a functional program like this:
```haskell
-- The Stream type is a wrapper around an arbitrary payload type 'a'
newtype Stream a = Stream a deriving (Show)
-- echo lifts an item of type 'a' into the Stream context
echo :: a -> Stream a
echo = Stream
-- the 'andThen' operator used for chaining commands
infixl 7 |>
(|>) :: Stream a -> (a -> Stream b) -> Stream b
Stream x |> f = f x
-- echo and |> are used to create the actual pipeline
pipeline :: String -> Stream Int
pipeline str =
echo str |> echo . length . words |> echo . (3 *)
-- now executing the program in ghci repl:
ghci> pipeline "hello world"
Stream 6
```
The `echo` function lifts any input into the `Stream` context:
```haskell
ghci> echo "hello world"
Stream "hello world"
```
The `|>` (pronounced as "andThen") does the function chaining:
```haskell
ghci> echo "hello world" |> echo . words
Stream ["hello","world"]
```
The result of `|>` is of type `Stream b` that's why we cannot just write `echo "hello world" |> words`. We have to use echo to create a `Stream` output that can be digested by a subsequent `|>`.
The interplay of a Context type `Stream a` and the functions `echo` and `|>` is a well known pattern from functional languages: it's the legendary *Monad*. As the [Wikipedia article on the pipeline pattern](https://en.wikipedia.org/wiki/Pipeline_(software)) states:
> Pipes and filters can be viewed as a form of functional programming, using byte streams as data objects; more specifically, they can be seen as a particular form of monad for I/O.
There is an interesting paper available elaborating on the monadic nature of Unix pipes: http://okmij.org/ftp/Computation/monadic-shell.html.
Here is the definition of the Monad typeclass in Haskell:
```Haskell
class Applicative m => Monad m where
-- | Sequentially compose two actions, passing any value produced
-- by the first as an argument to the second.
(>>=) :: m a -> (a -> m b) -> m b
-- | Inject a value into the monadic type.
return :: a -> m a
return = pure
```
By looking at the types of `>>=` and `return` it's easy to see the direct correspondence to `|>` and `echo` in the pipeline example above:
```haskell
(|>) :: Stream a -> (a -> Stream b) -> Stream b
echo :: a -> Stream a
```
Mhh, this is nice, but still looks a lot like ordinary composition of functions, just with the addition of a wrapper.
In this simplified example that's true, because we have designed the `|>` operator to simply unwrap a value from the Stream and bind it to the formal parameter of the subsequent function:
```haskell
Stream x |> f = f x
```
But we are free to implement the `andThen` operator in any way that we seem fit as long we maintain the type signature and the [monad laws](https://en.wikipedia.org/wiki/Monad_%28functional_programming%29#Monad_laws).
So we could for instance change the semantic of `>>=` to keep a log along the execution pipeline.
In the following snippet I have extended `>>=` to increment a counter so that at the and of the pipeline we are informed about the number of invocations of `>>=`.
```haskell
-- The DeriveFunctor Language Pragma provides automatic derivation of Functor instances
{-# LANGUAGE DeriveFunctor #-}
-- the Stream type is extened by an Int that keeps the counter state
newtype Stream a = Stream (a, Int) deriving (Show, Functor)
-- as any Monad must be an Applicative we also have to instantiate Applicative
instance Applicative Stream where
pure = return
Stream (f, _) <*> r = fmap f r
-- our definition of the Stream Monad
instance Monad Stream where
-- returns a Stream wrapping a tuple of the actual payload and an initial counter state of 0
return a = Stream (a, 0)
-- we define (>>=) to reach an incremented counter to the subsequent action
m >>= k = let Stream(a, c1) = m
next = k a
Stream(b, c2) = next
in Stream (b, c1 + 1 + c2)
-- instead of echo and |> we now use the "official" monadic versions return and >>=
What's noteworthy here is that Monads allow to make the mechanism of chaining functions *explicit*. We can define what `andThen` should mean in our pipeline by choosing a different Monad implementation.
So in a sense Monads could be called [programmable semicolons](http://book.realworldhaskell.org/read/monads.html#id642960)
There are several predefined Monads available in the Haskell curated libraries and it's also possible to combine their effects by making use of `MonadTransformers`.
>In software engineering, the composite pattern is a partitioning design pattern. The composite pattern describes a group of objects that is treated the same way as a single instance of the same type of object. The intent of a composite is to "compose" objects into tree structures to represent part-whole hierarchies. Implementing the composite pattern lets clients treat individual objects and compositions uniformly.
> (Quoted from [Wikipedia](https://en.wikipedia.org/wiki/Composite_pattern))
A typical example for the composite pattern is the hierarchical grouping of test cases to TestSuites in a testing framework. Take for instance the following class diagram from the [JUnit cooks tour](http://junit.sourceforge.net/doc/cookstour/cookstour.htm) which shows how JUnit applies the Composite pattern to group `TestCases` to `TestSuites` while both of them implement the `Test` interface:
In Haskell we could model this kind of hierachy with an algebraic data type (ADT):
In order to aggregate TestComponents we follow the design of JUnit and define a function `addTest`. Adding two atomic Tests will result in a TestSuite holding a list with the two Tests. If a Test is added to a TestSuite, the test is added to the list of tests of the suite. Adding TestSuites will merge them.
What's not visible from the JUnit class diagram is how typical object oriented implementations will have to deal with null-references. That is the implementations would have to make sure that the methods `run` and `addTest` will handle empty references correctly.
With Haskells algebraic data types we would rather make this explicit with a dedicated `Empty` element.
From our additions it's obvious that `Empty` is the identity element of the `addTest` function. In Algebra a Semigroup with an identity element is called *Monoid*:
> In abstract algebra, [...] a monoid is an algebraic structure with a single associative binary operation and an identity element.
> [Quoted from Wikipedia](https://en.wikipedia.org/wiki/Monoid)
We can also use the function `mconcat :: Monoid a => [a] -> a` on a list of `Tests`: mconcat composes a list of Tests into a single Test. That's exactly the mechanism of forming a TestSuite from atomic TestCases.
```haskell
compositeDemo = do
print $ run $ mconcat [t1,t2]
print $ run $ mconcat [t1,t2,t3]
```
This particular feature of `mconcat :: Monoid a => [a] -> a` to condense a list of Monoids to a single Monoid can be used to drastically simplify the design of our test framework.
If `Bool` was a `Monoid` we could use `mconcat` to form test suite aggregates. `Bool` in itself is not a Monoid; but together with a binary associative operation like `(&&)` or `(||)` it will form a Monoid.
The intuitive semantics of a TestSuite is that a whole Suite is "green" only when all enclosed TestCases succeed. That is the conjunction of all TestCases must return `True`.
So we are looking for the Monoid of boolean values under conjunction `(&&)`. In Haskell this Monoid is called `All`):
We now implement a new evaluation function `run'` which evaluates a `SmartTestCase` (which may be either an atomic TestCase or a TestSuite assembled by `mconcat`) to a single boolean result.
This version of `run` is much simpler than the original and we can completely avoid the rather laborious `addTest` function. We also don't need any composite type `Test`.
By just sticking to the Haskell built-in typeclasses we achieve cleanly designed functionality with just a few lines of code.
> [...] the visitor design pattern is a way of separating an algorithm from an object structure on which it operates. A practical result of this separation is the ability to add new operations to existent object structures without modifying the structures. It is one way to follow the open/closed principle.
> (Quoted from [Wikipedia](https://en.wikipedia.org/wiki/Visitor_pattern))
* The Haskell typeclasses `Functor`, `Foldable`, `Traversable`, etc. provide a generic framework to allow visiting any algebraic datatype by just deriving one of these typeclasses.
By virtue of the instance declaration Exp becomes a Foldable instance an can be used with arbitrary functions defined on Foldable like `length` in the example.
> [...] the iterator pattern is a design pattern in which an iterator is used to traverse a container and access the container's elements. The iterator pattern decouples algorithms from containers; in some cases, algorithms are necessarily container-specific and thus cannot be decoupled.
> [Quoted from Wikipedia] (https://en.wikipedia.org/wiki/Iterator_pattern)
> [...] Dependency injection is a technique whereby one object (or static method) supplies the dependencies of another object. A dependency is an object that can be used (a service). An injection is the passing of a dependency to a dependent object (a client) that would use it. The service is made part of the client's state. Passing the service to the client, rather than allowing a client to build or find the service, is the fundamental requirement of the pattern.
>
> This fundamental requirement means that using values (services) produced within the class from new or static methods is prohibited. The client should accept values passed in from outside. This allows the client to make acquiring dependencies someone else's problem.
> (Quoted from [Wikipedia](https://en.wikipedia.org/wiki/Dependency_injection))
In functional languages this is simply achieved by binding a functions formal parameters to values.
See the following example where the function `generatePage :: (String -> Html) -> String -> Html` does not only require a String input but also a rendering function that does the actual conversion from text to Html.
```haskell
data Html = ...
generatePage :: (String -> Html) -> String -> Html
generatePage renderer text = renderer text
htmlRenderer :: String -> Html
htmlRenderer = ...
```
With partial application its even possible to form a closure that incorporates the rendering function:
> "The adapter pattern is a software design pattern (also known as wrapper, an alternative naming shared with the decorator pattern) that allows the interface of an existing class to be used as another interface. It is often used to make existing classes work with others without modifying their source code."
> (Quoted from https://en.wikipedia.org/wiki/Adapter_pattern)
An example is an adapter that converts the interface of a Document Object Model of an XML document into a tree structure that can be displayed.
What does an adapter do? It translates a call to the adapter into a call of the adapted backend code. Which may also involve translation of the argument data.
Say we have some `backend` function that we want to provide with an adapter. we assume that `backend` has type `c -> d`:
```haskell
backend :: c -> d
```
Our adapter should be of type `a -> b`:
```haskell
adapter :: a -> b
```
In order to write this adapter we have to write two function. The first is:
```haskell
marshal :: a -> c
```
which translated the input argument of `adapter` into the correct type `c` that can be digested by the backend.
And the second function is:
```haskell
unmarshal :: d -> b
```
which translates the result of the `backend`function into the correct return type of `adapter`.
So in essence the Adapter Patterns is just function composition.
Here is a simple example. Say we have a backend that understands only 24 hour arithmetics (eg. 23:50 + 0:20 = 0:10).
But in our frontend we don't want to see this ugly arithmetics and want to be able to add minutes to a time representation in minutes (eg. 100 + 200 = 300).
We solve this by using the above mentioned function composition of `unmarshal . backend . marshal`:
> In software engineering, the template method pattern is a behavioral design pattern that defines the program skeleton of an algorithm in an operation, deferring some steps to subclasses.
> It lets one redefine certain steps of an algorithm without changing the algorithm's structure.
> [Quoted from Wikipedia](https://en.wikipedia.org/wiki/Template_method_pattern)
The TemplateMethod pattern is quite similar to the [StrategyPattern](#strategy---functor). The main difference is the level of granularity.
In Strategy a complete block of functionality - the Strategy - can be replaced.
In TemplateMethod the overall layout of an algorithm is predefined and only specific parts of it may be replaced.
In functional programming the answer to this kind of problem is again the usage of higher order functions.
In the following example we come back to the example for the [Adapter](#adapter---function-composition).
The function `addMinutesAdapter` lays out a structure for interfacing to some kind of backend:
1. marshalling the arguments into the backend format
2. apply the backend logic to the marshalled arguments
3. unmarshal the backend result data into the frontend format
```haskell
addMinutesAdapter :: Int -> Minute -> Minute
addMinutesAdapter x = unmarshalWM . addMinutesToWallTime x . marshalMW
```
In this code the backend functionality - `addMinutesToWallTime` - is a hardcoded part of the overall structure.
Let's assume we want to use different kind of backend implementations - for instance a mock replacement.
In this case we would like to keep the overall structure - the template - and would just make a specific part of it flexible.
This sounds like an ideal candidate for the TemplateMethod pattern:
`addMinutesTemplate` has an additional parameter f of type `(Int -> WallTime -> WallTime)`. This parameter may be bound to `addMinutesToWallTime` or alternative implementations:
```haskell
-- implements linear addition (the normal case) even for values > 1440
### Typeclass minimal implementations as template method
> The template method is used in frameworks, where each implements the invariant parts of a domain's architecture,
> leaving "placeholders" for customization options. This is an example of inversion of control.
> [Quoted from Wikipedia](https://en.wikipedia.org/wiki/Template_method_pattern)
The Typeclasses in Haskells base library apply this template approach frequently to reduce the effort for implementing typeclass instances and to provide a predefined structure with specific 'customization options'.
As an example let's extend the type `WallTime` by an associative binary operation `addWallTimes` to form an instance of the `Monoid` typeclass
```haskell
addWallTimes :: WallTime -> WallTime -> WallTime
addWallTimes a@(WallTime (h,m)) b =
let aMin = h*60 + m
in addMinutesToWallTime aMin b
instance Semigroup WallTime where
(<>) = addWallTimes
instance Monoid WallTime where
mempty = WallTime (0,0)
```
Even though we specified only `mempty` and `(<>)` we can now use the functions `mappend :: Monoid a => a -> a -> a` and `mconcat :: Monoid a => [a] -> a` on WallTime instances:
```haskell
templateMethodDemo = do
let a = WallTime (3,20)
print $ mappend a a
print $ mconcat [a,a,a,a,a,a,a,a,a]
```
By looking at the definition of the `Monoid` typeclass we can see how this 'magic' is made possible:
```haskell
class Semigroup a => Monoid a where
-- | Identity of 'mappend'
mempty :: a
-- | An associative operation
mappend :: a -> a -> a
mappend = (<>)
-- | Fold a list using the monoid.
mconcat :: [a] -> a
mconcat = foldr mappend mempty
```
For `mempty` only a type requirement but no definition is given.
But for `mappend` and `mconcat` default implementations are provided.
So the Monoid typeclass definition forms a *template* where the default implementations define the 'invariant parts' of the typeclass and the part specified by us form the 'customization options'.
(please note that it's generally possible to override the default implementations)
> In the functional-programming world, traditional design patterns generally manifest in one of three ways:
> - The pattern is absorbed by the language.
> - The pattern solution still exists in the functional paradigm, but the implementation details differ.
> - The solution is implemented using capabilities other languages or paradigms lack. (For example, many solutions that use metaprogramming are clean and elegant — and they're not possible in Java.)
>
> [Quoted from IBM developerworks](https://www.ibm.com/developerworks/library/j-ft10/index.html)
