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starting with Traversable example
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thma
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@ -18,6 +18,7 @@ executable LtuPatternFactory
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other-modules: Adapter
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, Builder
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, Composite
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, Iterator
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, NullObject
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, Pipeline
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, Singleton
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937
README.md
937
README.md
@ -1,3 +1,4 @@
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<<<<<<< HEAD
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# Lambda the Ultimate Pattern Factory
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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)).
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@ -932,3 +933,939 @@ https://staticallytyped.wordpress.com/2013/03/09/gang-of-four-patterns-with-type
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http://norvig.com/design-patterns/design-patterns.pdf
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[Scala Typeclassopedia](https://github.com/tel/scala-typeclassopedia)
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=======
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# Lambda the Ultimate Pattern Factory
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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)).
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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.
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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.
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I think this kind of exposition could be helpful if you are either:
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* a programmer with an OO background who wants to get a better grip on how to implement complexer designs in functional programming
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* a functional programmer who wants to get a deeper intuition for type classes.
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# The Patternopedia
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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.
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In this section I'm taking a tour through the Typeclassopedia from a design pattern perspective.
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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.
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## Strategy -> Functor
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> "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"
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> "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."
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>(quoted from https://en.wikipedia.org/wiki/Strategy_pattern)
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* in C a strategy would be modelled as a function pointer that can be used to dispatch calls to different functions.
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* 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.
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* in functional programming a strategy is just a higher order function, that is a parameter of a function that has a function type.
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```haskell
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-- first we define two simple strategies that map numbers to numbers:
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strategyId :: Num a => a -> a
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strategyId n = n
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strategyDouble :: Num a => a -> a
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strategyDouble n = 2*n
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-- now we define a context that applies a function of type Num a => a -> a to a list of a's:
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context :: Num a => (a -> a) -> [a] -> [a]
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context f l = map f l
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-- according to the rules of currying this can be abbreviated to:
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context = map
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```
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The `context` function uses higher order `map` function (`map :: (a -> b) -> [a] -> [b]`) to apply the strategies to lists of numbers:
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```haskell
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ghci> context strategyId [1..10]
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[1,2,3,4,5,6,7,8,9,10]
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ghci> context strategyDouble [1..10]
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[2,4,6,8,10,12,14,16,18,20]
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```
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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.
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In Haskell the application of a function in a computational context is generalized with the typeclass `Functor`:
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```haskell
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class Functor f where
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fmap :: (a -> b) -> f a -> f b
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```
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Actually `map` is the fmap implementation for the List Functor instance:
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```haskell
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instance Functor [] where
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fmap = map
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```
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Although it would be fair to say that the typeclass `Functor` captures the essential idea of the strategy pattern - namely the injecting 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.
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[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/Strategy.hs)
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## Singleton -> Pointed -> Applicative
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> "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."
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> (quoted from https://en.wikipedia.org/wiki/Singleton_pattern)
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The singleton pattern ensures that multiple requests to a given object always return one and the same singleton instance.
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In functional programming this semantics can be achieved by ```let```.
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```haskell
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let singleton = someExpensiveComputation
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in mainComputation
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--or in lambda notation:
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(\singleton -> mainComputation) someExpensiveComputation
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```
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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.
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Typeclasses provide several tools to make this kind of threading more convenient or even to avoid explicit threading of instances.
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### Using Pointed to create singletons
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> "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."
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> (quoted from the Typeclassopedia)
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```haskell
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class Functor f => Pointed f where
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pure :: a -> f a
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```
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### Using Applicative Functor for threading of singletons
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The following code defines a simple expression evaluator:
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```haskell
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data Exp e = Var String
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| Val e
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| Add (Exp e) (Exp e)
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| Mul (Exp e) (Exp e)
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-- the environment is a list of tupels mapping variable names to values of type e
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type Env e = [(String, e)]
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-- a simple evaluator reducing expression to numbers
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eval :: Num e => Exp e -> Env e -> e
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eval (Var x) env = fetch x env
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eval (Val i) env = i
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eval (Add p q) env = eval p env + eval q env
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eval (Mul p q) env = eval p env * eval q env
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```
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`eval` is a classic evaluator function that recursively evaluates sub-expression before applying `+` or `*`.
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Note how the explicit `env`parameter is threaded through the recursive eval calls. This is needed to have the
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environment avalailable for variable lookup at any recursive call depth.
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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`.
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```haskell
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main = do
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let exp = Mul (Add (Val 3) (Val 1))
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(Mul (Val 2) (Var "pi"))
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env = [("pi", pi)]
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print $ eval exp env
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```
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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`:
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```haskell
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class Functor f => Applicative f where
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pure :: a -> f a
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(<*>) :: f (a -> b) -> f a -> f b
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instance Applicative ((->) a) where
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pure = const
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(<*>) f g x = f x (g x)
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```
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This `Applicative` allows us to rewrite `eval` as follows:
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```haskell
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eval :: Num e => Exp e -> Env e -> e
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eval (Var x) = fetch x
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eval (Val i) = pure i
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eval (Add p q) = pure (+) <*> eval p <*> eval q
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eval (Mul p q) = pure (*) <*> eval p <*> eval q
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```
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Any explicit handling of the variable `env` is now removed.
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(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`.)
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[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/Singleton.hs)
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## Pipeline -> Monad
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> 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.
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> (Quoted from: https://en.wikipedia.org/wiki/Pipeline_(software))
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The concept of pipes and filters in Unix shell scripts is a typical example of the pipeline architecture pattern.
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```bash
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$ echo "hello world" | wc -w | xargs printf "%d*3\n" | bc -l
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6
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```
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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.
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On the first glance this might look like ordinary function composition. We could for instance come up with the following approximation in Haskell:
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```haskell
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((3 *) . length . words) "hello world"
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6
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```
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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:
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```bash
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$ echo "hello world" | wc -w
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```
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So we might say that `echo` *injects* the String `"hello world"` into the stream context.
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We can capture this behaviour in a functional program like this:
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```haskell
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-- The Stream type is a wrapper around an arbitrary payload type 'a'
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newtype Stream a = Stream a deriving (Show)
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-- echo injects an item of type 'a' into the Stream context
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echo :: a -> Stream a
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echo = Stream
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-- the 'andThen' operator used for chaining commands
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infixl 7 |>
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(|>) :: Stream a -> (a -> Stream b) -> Stream b
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Stream x |> f = f x
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-- echo and |> are used to create the actual pipeline
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pipeline :: String -> Stream Int
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pipeline str =
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echo str |> echo . length . words |> echo . (3 *)
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-- now executing the program in ghci repl:
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ghci> pipeline "hello world"
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Stream 6
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```
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The `echo` function injects any input into the `Stream` context:
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```haskell
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ghci> echo "hello world"
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Stream "hello world"
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```
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The `|>` (pronounced as "andThen") does the function chaining:
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```haskell
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ghci> echo "hello world" |> echo . words
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Stream ["hello","world"]
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```
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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 `|>`.
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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:
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> 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.
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There is an interesting paper available elaborating on the monadic nature of Unix pipes: http://okmij.org/ftp/Computation/monadic-shell.html.
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Here is the definition of the Monad typeclass in Haskell:
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```Haskell
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class Applicative m => Monad m where
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-- | Sequentially compose two actions, passing any value produced
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-- by the first as an argument to the second.
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(>>=) :: m a -> (a -> m b) -> m b
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-- | Inject a value into the monadic type.
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return :: a -> m a
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return = pure
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```
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By looking at the types of `>>=` and `return` it's easy to see the direct correspondence to `|>` and `echo` in the pipeline example above:
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```haskell
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(|>) :: Stream a -> (a -> Stream b) -> Stream b
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echo :: a -> Stream a
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```
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Mhh, this is nice, but still looks a lot like ordinary composition of functions, just with the addition of a wrapper.
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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:
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```haskell
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Stream x |> f = f x
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```
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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).
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So we could for instance change the semantic of `>>=` to keep a log along the execution pipeline.
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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 `>>=`.
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```haskell
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-- The DeriveFunctor Language Pragma provides automatic derivation of Functor instances
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{-# LANGUAGE DeriveFunctor #-}
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-- the Stream type is extened by an Int that keeps the counter state
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newtype Stream a = Stream (a, Int) deriving (Show, Functor)
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-- as any Monad must be an Applicative we also have to instantiate Applicative
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instance Applicative Stream where
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pure = return
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Stream (f, _) <*> r = fmap f r
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-- our definition of the Stream Monad
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instance Monad Stream where
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-- returns a Stream wrapping a tuple of the actual payload and an initial counter state of 0
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return a = Stream (a, 0)
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-- we define (>>=) to reach an incremented counter to the subsequent action
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m >>= k = let Stream(a, c1) = m
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next = k a
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Stream(b, c2) = next
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in Stream (b, c1 + 1 + c2)
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-- instead of echo and |> we now use the "official" monadic versions return and >>=
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pipeline :: String -> Stream Int
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pipeline str =
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return str >>= return . length . words >>= return . (3 *)
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-- when using this in GHCI we receive a Stream wrapping a tuple of the result of the
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-- actual pipeline plus the result of the counter:
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ghci> pipeline "hello world"
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Stream (6,2)
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```
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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.
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So in a sense Monads could be called [programmable semicolons](http://book.realworldhaskell.org/read/monads.html#id642960)
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To make this statement a bit clearer we will have a closer look at the internal workings of the `Maybe` Monad in the next section.
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[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/Pipeline.hs)
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### NullObject -> Maybe Monad
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>[...] a null object is an object with no referenced value or with defined neutral ("null") behavior. The null object design pattern describes the uses of such objects and their behavior (or lack thereof).
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> [Quoted from Wikipedia](https://en.wikipedia.org/wiki/Null_object_pattern)
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In functional programming the null object pattern is typically formalized with option types:
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> [...] an option type or maybe type is a polymorphic type that represents encapsulation of an optional value; e.g., it is used as the return type of functions which may or may not return a meaningful value when they are applied. It consists of a constructor which either is empty (named None or `Nothing`), or which encapsulates the original data type `A` (written `Just A` or Some A).
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> [Quoted from Wikipedia](https://en.wikipedia.org/wiki/Option_type)
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(See also: [Null Object as Identity](http://blog.ploeh.dk/2018/04/23/null-object-as-identity/))
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In Haskell the most simple option type is `Maybe`. Let's directly dive into an example. We define a reverse index, mapping songs to album titles.
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If we now lookup up a song title we may either be lucky and find the respective album or not so lucky when there is no album matching our song:
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```haskell
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import Data.Map (Map, fromList)
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import qualified Data.Map as Map (lookup) -- avoid clash with Prelude.lookup
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-- type aliases for Songs and Albums
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type Song = String
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type Album = String
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-- the simplified reverse song index
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songMap :: Map Song Album
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songMap = fromList
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[("Baby Satellite","Microgravity")
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,("An Ending", "Apollo: Atmospheres and Soundtracks")]
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```
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We can lookup this map by using the function `Map.lookup :: Ord k => k -> Map k a -> Maybe a`.
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If no match is found it will return `Nothing` if a match is found it will return `Just match`:
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```haskell
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ghci> Map.lookup "Baby Satellite" songMap
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Just "Microgravity"
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ghci> Map.lookup "The Fairy Tale" songMap
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Nothing
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```
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Actually the `Maybe` type is defined as:
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```haskell
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data Maybe a = Nothing | Just a
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deriving (Eq, Ord)
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```
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All code using the `Map.lookup` function will never be confronted with any kind of Exceptions, null pointers or other nasty things. Even in case of errors a lookup will always return a properly typed `Maybe` instance. By pattern matching for `Nothing` or `Just a` client code can react on failing matches or positive results:
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```haskell
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case Map.lookup "Ancient Campfire" songMap of
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Nothing -> print "sorry, could not find your song"
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Just a -> print a
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```
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Let's try to apply this to an extension of our simple song lookup.
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Let's assume that our music database has much more information available. Apart from a reverse index from songs to albums, there might also be an index mapping album titles to artists.
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And we might also have an index mapping artist names to their websites:
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```haskell
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type Song = String
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type Album = String
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type Artist = String
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type URL = String
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songMap :: Map Song Album
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songMap = fromList
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[("Baby Satellite","Microgravity")
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,("An Ending", "Apollo: Atmospheres and Soundtracks")]
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albumMap :: Map Album Artist
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albumMap = fromList
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[("Microgravity","Biosphere")
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,("Apollo: Atmospheres and Soundtracks", "Brian Eno")]
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artistMap :: Map Artist URL
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artistMap = fromList
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[("Biosphere","http://www.biosphere.no//")
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,("Brian Eno", "http://www.brian-eno.net")]
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loookup' :: Ord a => Map a b -> a -> Maybe b
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loookup' = flip Map.lookup
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|
||||
findAlbum :: Song -> Maybe Album
|
||||
findAlbum = loookup' songMap
|
||||
|
||||
findArtist :: Album -> Maybe Artist
|
||||
findArtist = loookup' albumMap
|
||||
|
||||
findWebSite :: Artist -> Maybe URL
|
||||
findWebSite = loookup' artistMap
|
||||
```
|
||||
|
||||
With all this information at hand we want to write a function that has an input parameter of type `Song` and returns a `Maybe URL` by going from song to album to artist to website url:
|
||||
```haskell
|
||||
findUrlFromSong :: Song -> Maybe URL
|
||||
findUrlFromSong song =
|
||||
case findAlbum song of
|
||||
Nothing -> Nothing
|
||||
Just album ->
|
||||
case findArtist album of
|
||||
Nothing -> Nothing
|
||||
Just artist ->
|
||||
case findWebSite artist of
|
||||
Nothing -> Nothing
|
||||
Just url -> Just url
|
||||
```
|
||||
|
||||
This code makes use of the pattern matching logic described before. It's worth to note that there is some nice circuit breaking happening in case of a `Nothing`. In this case `Nothing` is directly returned as result of the function and the rest of the case-ladder is not executed.
|
||||
What's not so nice is: "the dreaded ladder of code marching off the right of the screen" [(quoted from Real World Haskell)](http://book.realworldhaskell.org/).
|
||||
|
||||
For each find function we have to repeat the same ceremony of pattern matching on the result and either return `Nothing` or proceed with the next nested level.
|
||||
|
||||
The good news is that it is possible to avoid this ladder.
|
||||
We can rewrite our search by applying the `andThen` operator `>>=` as `Maybe` is an instance of `Monad`:
|
||||
```haskell
|
||||
findUrlFromSong' :: Song -> Maybe URL
|
||||
findUrlFromSong' song =
|
||||
findAlbum song >>= \album ->
|
||||
findArtist album >>= \artist ->
|
||||
findWebSite artist
|
||||
```
|
||||
or even shorter as we can eliminate the lambda expressions by applying [eta-conversion](https://wiki.haskell.org/Eta_conversion):
|
||||
```haskell
|
||||
findUrlFromSong'' :: Song -> Maybe URL
|
||||
findUrlFromSong'' song =
|
||||
findAlbum song >>= findArtist >>= findWebSite
|
||||
```
|
||||
Using it in GHCi:
|
||||
```haskell
|
||||
ghci> findUrlFromSong'' "All you need is love"
|
||||
Nothing
|
||||
ghci> findUrlFromSong'' "An Ending"
|
||||
Just "http://www.brian-eno.net"
|
||||
```
|
||||
|
||||
The expression `findAlbum song >>= findArtist >>= findWebSite` and the sequencing of actions in the [pipeline](#pipeline---monad) example `return str >>= return . length . words >>= return . (3 *)` have a similar structure.
|
||||
|
||||
But the behaviour of both chains is quite different: In the Maybe Monad `a >>= b` does not evaluate b if `a == Nothing` but stops the whole chain of actions by simply returning `Nothing`.
|
||||
|
||||
The pattern matching and 'short-circuiting' is directly coded into the definition of `(>>=)` in the Monad implementation of `Maybe`:
|
||||
```haskell
|
||||
instance Monad Maybe where
|
||||
(Just x) >>= k = k x
|
||||
Nothing >>= _ = Nothing
|
||||
```
|
||||
|
||||
This elegant feature of `(>>=)` in the `Maybe` Monad allows us to avoid ugly and repetetive coding.
|
||||
|
||||
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`. But that's a different story...
|
||||
|
||||
[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/NullObject.hs)
|
||||
|
||||
<!--
|
||||
#### TBD: Reimplementing the Evaluator with Writer-Monad
|
||||
-->
|
||||
|
||||
## Composite -> SemiGroup -> Monoid
|
||||
|
||||
>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):
|
||||
|
||||
```haskell
|
||||
-- the composite data structure: a Test can be either a single TestCase
|
||||
-- or a TestSuite holding a list of Tests
|
||||
data Test = TestCase TestCase
|
||||
| TestSuite [Test]
|
||||
|
||||
-- a test case produces a boolean when executed
|
||||
type TestCase = () -> Bool
|
||||
```
|
||||
The function `run` as defined below can either execute a single TestCase or a composite TestSuite:
|
||||
```haskell
|
||||
-- execution of a Test.
|
||||
run :: Test -> Bool
|
||||
run (TestCase t) = t () -- evaluating the TestCase by applying t to ()
|
||||
run (TestSuite l) = all (True ==) (map run l) -- running all tests in l and return True if all tests pass
|
||||
|
||||
-- a few most simple test cases
|
||||
t1 :: Test
|
||||
t1 = TestCase (\() -> True)
|
||||
t2 :: Test
|
||||
t2 = TestCase (\() -> True)
|
||||
t3 :: Test
|
||||
t3 = TestCase (\() -> False)
|
||||
-- collecting all test cases in a TestSuite
|
||||
ts = TestSuite [t1,t2,t3]
|
||||
```
|
||||
As run is of type `run :: Test -> Bool` we can use it to execute single `TestCases` or complete `TestSuites`.
|
||||
Let's try it in GHCI:
|
||||
```
|
||||
ghci> run t1
|
||||
True
|
||||
ghci> run ts
|
||||
False
|
||||
```
|
||||
|
||||
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.
|
||||
```haskell
|
||||
-- adding Tests
|
||||
addTest :: Test -> Test -> Test
|
||||
addTest t1@(TestCase _) t2@(TestCase _) = TestSuite [t1,t2]
|
||||
addTest t1@(TestCase _) (TestSuite list) = TestSuite ([t1] ++ list)
|
||||
addTest (TestSuite list) t2@(TestCase _) = TestSuite (list ++ [t2])
|
||||
addTest (TestSuite l1) (TestSuite l2) = TestSuite (l1 ++ l2)
|
||||
```
|
||||
|
||||
If we take a closer look at `addTest` we will see that it is a associative binary operation on the set of `Test`s.
|
||||
|
||||
In mathemathics a set with an associative binary operation is a [Semigroup](https://en.wikipedia.org/wiki/Semigroup).
|
||||
|
||||
We can thus make our type `Test` an instance of the typeclass `Semigroup` with the following declaration:
|
||||
|
||||
```haskell
|
||||
instance Semigroup Test where
|
||||
(<>) = addTest
|
||||
```
|
||||
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.
|
||||
Here are the changes we have to add to our code:
|
||||
```haskell
|
||||
-- the composite data structure: a Test can be Empty, a single TestCase
|
||||
-- or a TestSuite holding a list of Tests
|
||||
data Test = Empty
|
||||
| TestCase TestCase
|
||||
| TestSuite [Test]
|
||||
|
||||
-- execution of a Test.
|
||||
run :: Test -> Bool
|
||||
run Empty = True -- empty tests will pass
|
||||
run (TestCase t) = t () -- evaluating the TestCase by applying t to ()
|
||||
--run (TestSuite l) = foldr ((&&) . run) True l
|
||||
run (TestSuite l) = all (True ==) (map run l) -- running all tests in l and return True if all tests pass
|
||||
|
||||
-- addTesting Tests
|
||||
addTest :: Test -> Test -> Test
|
||||
addTest Empty t = t
|
||||
addTest t Empty = t
|
||||
addTest t1@(TestCase _) t2@(TestCase _) = TestSuite [t1,t2]
|
||||
addTest t1@(TestCase _) (TestSuite list) = TestSuite ([t1] ++ list)
|
||||
addTest (TestSuite list) t2@(TestCase _) = TestSuite (list ++ [t2])
|
||||
addTest (TestSuite l1) (TestSuite l2) = TestSuite (l1 ++ l2)
|
||||
```
|
||||
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)
|
||||
|
||||
|
||||
With haskell we can declare `Test` as an instance of the `Monoid` typeclass by defining:
|
||||
```haskell
|
||||
instance Monoid Test where
|
||||
mempty = Empty
|
||||
```
|
||||
We can now use all functions provided by the `Monoid` typeclass to work with our `Test`:
|
||||
|
||||
```haskell
|
||||
compositeDemo = do
|
||||
print $ run $ t1 <> t2
|
||||
print $ run $ t1 <> t2 <> t3
|
||||
```
|
||||
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.
|
||||
|
||||
We need just one more hint from our mathematician friends:
|
||||
|
||||
> Functions are monoids if they return monoids
|
||||
> [Quoted from blog.ploeh.dk](http://blog.ploeh.dk/2018/05/17/composite-as-a-monoid-a-business-rules-example/)
|
||||
|
||||
Currently our `TestCases` are defined as functions yielding boolean values:
|
||||
```haskell
|
||||
type TestCase = () -> Bool
|
||||
```
|
||||
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`):
|
||||
|
||||
```haskell
|
||||
-- | Boolean monoid under conjunction ('&&').
|
||||
-- >>> getAll (All True <> mempty <> All False)
|
||||
-- False
|
||||
-- >>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
|
||||
-- False
|
||||
newtype All = All { getAll :: Bool }
|
||||
|
||||
instance Semigroup All where
|
||||
(<>) = coerce (&&)
|
||||
|
||||
instance Monoid All where
|
||||
mempty = All True
|
||||
```
|
||||
|
||||
Making use of `All` our improved definition of TestCases is as follows:
|
||||
```haskell
|
||||
type SmartTestCase = () -> All
|
||||
```
|
||||
Now our test cases do not directly return a boolean value but an `All` wrapper, which allows automatic conjunction of test results to a single value.
|
||||
Here are our redefined TestCases:
|
||||
```haskell
|
||||
tc1 :: SmartTestCase
|
||||
tc1 () = All True
|
||||
tc2 :: SmartTestCase
|
||||
tc2 () = All True
|
||||
tc3 :: SmartTestCase
|
||||
tc3 () = All False
|
||||
```
|
||||
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.
|
||||
|
||||
```haskell
|
||||
run' :: SmartTestCase -> Bool
|
||||
run' tc = getAll $ tc ()
|
||||
```
|
||||
|
||||
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.
|
||||
|
||||
```haskell
|
||||
compositeDemo = do
|
||||
-- execute a single test case
|
||||
print $ run' tc1
|
||||
|
||||
--- execute a complex test suite
|
||||
print $ run' $ mconcat [tc1,tc2]
|
||||
print $ run' $ mconcat [tc1,tc2,tc3]
|
||||
```
|
||||
For more details on Composite as a Monoid please refer to the following blog:
|
||||
http://blog.ploeh.dk/2018/03/12/composite-as-a-monoid/
|
||||
|
||||
[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/Composite.hs)
|
||||
|
||||
## Visitor -> Foldable
|
||||
|
||||
> [...] 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))
|
||||
|
||||
|
||||
In functional languages - and Haskell in particular - we have a whole armada of tools serving this purpose:
|
||||
* higher order functions like map, fold, filter and all their variants allow to "visit" lists
|
||||
* The Haskell typeclasses `Functor`, `Foldable`, `Traversable`, etc. provide a generic framework to allow visiting any algebraic datatype by just deriving one of these typeclasses.
|
||||
### Using Foldable
|
||||
```haskell
|
||||
-- we are re-using the Exp data type from the Singleton example
|
||||
-- and transform it into a Foldable type:
|
||||
instance Foldable Exp where
|
||||
foldMap f (Val x) = f x
|
||||
foldMap f (Add x y) = foldMap f x `mappend` foldMap f y
|
||||
foldMap f (Mul x y) = foldMap f x `mappend` foldMap f y
|
||||
|
||||
filterF :: Foldable f => (a -> Bool) -> f a -> [a]
|
||||
filterF p = foldMap (\a -> if p a then [a] else [])
|
||||
|
||||
visitorDemo = do
|
||||
let exp = Mul (Add (Val 3) (Val 2))
|
||||
(Mul (Val 4) (Val 6))
|
||||
putStr "size of exp: "
|
||||
print $ length exp
|
||||
putStrLn "filter even numbers from tree"
|
||||
print $ filterF even exp
|
||||
```
|
||||
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.
|
||||
|
||||
`foldMap` can for example be used to write a filtering function `filterF`that collects all elements matching a predicate into a list.
|
||||
|
||||
#### Alternative approaches
|
||||
http://blog.ploeh.dk/2018/06/25/visitor-as-a-sum-type/
|
||||
|
||||
[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/Visitor.hs)
|
||||
|
||||
## Iterator -> Traversable
|
||||
|
||||
> [...] 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;
|
||||
> [Quoted from Wikipedia] (https://en.wikipedia.org/wiki/Iterator_pattern)
|
||||
|
||||
TBD: Traversable Demo
|
||||
|
||||
|
||||
## Typeclasses Category, Arrow & Co.
|
||||
Theses typeclasses aim at generalizing elements of Monads or Functors.
|
||||
|
||||
If you have ideas how these typeclasses map to specific design patterns please let me know!
|
||||
|
||||
# Beyond Typeclass patterns
|
||||
|
||||
TBD:
|
||||
- Chain of Responsibility: ADT + pattern matching the ADT (at least the distpatch variant)
|
||||
|
||||
- Currying / Partial application
|
||||
|
||||
## Dependency Injection -> Parameter Binding
|
||||
> [...] 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:
|
||||
```haskell
|
||||
ghci> closure = generatePage htmlRenderer
|
||||
:type closure
|
||||
closure :: String -> Html
|
||||
```
|
||||
|
||||
|
||||
|
||||
## Adapter -> Function Composition
|
||||
> "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`.
|
||||
`adapter` will then look like follows:
|
||||
```haskell
|
||||
adapter :: a -> b
|
||||
adapter = unmarshal . backend . marshal
|
||||
```
|
||||
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`:
|
||||
|
||||
```haskell
|
||||
-- a 24:00 hour clock representation of time
|
||||
newtype WallTime = WallTime (Int, Int) deriving (Show)
|
||||
|
||||
-- this is our backend. It can add minutes to a WallTime representation
|
||||
addMinutesToWallTime :: Int -> WallTime -> WallTime
|
||||
addMinutesToWallTime x (WallTime (h, m)) =
|
||||
let (hAdd, mAdd) = x `quotRem` 60
|
||||
hNew = h + hAdd
|
||||
mNew = m + mAdd
|
||||
in if mNew >= 60
|
||||
then
|
||||
let (dnew, hnew') = (hNew + 1) `quotRem` 24
|
||||
in WallTime (24*dnew + hnew', mNew-60)
|
||||
else WallTime (hNew, mNew)
|
||||
|
||||
-- this is our time representation in Minutes that we want to use in the frontend
|
||||
newtype Minute = Minute Int deriving (Show)
|
||||
|
||||
-- convert a Minute value into a WallTime representation
|
||||
marshalMW :: Minute -> WallTime
|
||||
marshalMW (Minute x) =
|
||||
let (h,m) = x `quotRem` 60
|
||||
in WallTime (h `rem` 24, m)
|
||||
|
||||
-- convert a WallTime value back to Minutes
|
||||
unmarshalWM :: WallTime -> Minute
|
||||
unmarshalWM (WallTime (h,m)) = Minute $ 60 * h + m
|
||||
|
||||
-- this is our frontend that add Minutes to a time of a day
|
||||
-- measured in minutes
|
||||
addMinutesAdapter :: Int -> Minute -> Minute
|
||||
addMinutesAdapter x = unmarshalWM . addMinutesToWallTime x . marshalMW
|
||||
|
||||
adapterDemo = do
|
||||
putStrLn "Adapter vs. function composition"
|
||||
print $ addMinutesAdapter 100 $ Minute 400
|
||||
putStrLn ""
|
||||
```
|
||||
|
||||
[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/Adapter.hs)
|
||||
|
||||
## Template Method -> Typeclass default functions
|
||||
|
||||
> 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:
|
||||
```haskell
|
||||
addMinutesTemplate :: (Int -> WallTime -> WallTime) -> Int -> Minute -> Minute
|
||||
addMinutesTemplate f x =
|
||||
unmarshalWM .
|
||||
f x .
|
||||
marshalMW
|
||||
```
|
||||
`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
|
||||
linearTimeAdd :: Int -> Minute -> Minute
|
||||
linearTimeAdd = addMinutesTemplate addMinutesToWallTime
|
||||
|
||||
-- implements cyclic addition, respecting a 24 hour (1440 Min) cycle
|
||||
cyclicTimeAdd :: Int -> Minute -> Minute
|
||||
cyclicTimeAdd = addMinutesTemplate addMinutesToWallTime'
|
||||
```
|
||||
|
||||
where `addMinutesToWallTime'` implements a silly 24 hour cyclic addition:
|
||||
|
||||
```haskell
|
||||
-- a 24 hour (1440 min) cyclic version of addition: 1400 + 100 = 60
|
||||
addMinutesToWallTime' :: Int -> WallTime -> WallTime
|
||||
addMinutesToWallTime' x (WallTime (h, m)) =
|
||||
let (hAdd, mAdd) = x `quotRem` 60
|
||||
hNew = h + hAdd
|
||||
mNew = m + mAdd
|
||||
in if mNew >= 60
|
||||
then WallTime ((hNew + 1) `rem` 24, mNew-60)
|
||||
else WallTime (hNew, mNew)
|
||||
```
|
||||
|
||||
And here is how we use it to do actual computations:
|
||||
```haskell
|
||||
templateMethodDemo = do
|
||||
putStrLn $ "linear time: " ++ (show $ linearTimeAdd 100 (Minute 1400))
|
||||
putStrLn $ "cyclic time: " ++ (show $ cyclicTimeAdd 100 (Minute 1400))
|
||||
```
|
||||
|
||||
### 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)
|
||||
|
||||
[Full Sourcecode for this section](https://github.com/thma/LtuPatternFactory/blob/master/src/TemplateMethod.hs)
|
||||
|
||||
## TBD: Factory -> Function Currying
|
||||
|
||||
## TBD: A Table of Patterns
|
||||
TBD: a comprehensive list of patterns with their functional counterpart
|
||||
|
||||
## TBD: Conclusion
|
||||
> While we (me included) have been on an a thirty-odd year long detour around object-orientation, I don't think all is lost.
|
||||
> [Quoted from blog.ploeh.dk](http://blog.ploeh.dk/2018/03/05/some-design-patterns-as-universal-abstractions/)
|
||||
|
||||
> 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)
|
||||
|
||||
http://blog.ploeh.dk/2018/03/05/some-design-patterns-as-universal-abstractions/
|
||||
http://blog.ploeh.dk/2017/10/04/from-design-patterns-to-category-theory/
|
||||
|
||||
|
||||
# some interesting links
|
||||
https://www.ibm.com/developerworks/library/j-ft10/index.html
|
||||
|
||||
http://blog.ezyang.com/2010/05/design-patterns-in-haskel/
|
||||
|
||||
https://staticallytyped.wordpress.com/2013/03/09/gang-of-four-patterns-with-type-classes-and-implicits-in-scala/
|
||||
|
||||
http://norvig.com/design-patterns/design-patterns.pdf
|
||||
|
||||
[Scala Typeclassopedia](https://github.com/tel/scala-typeclassopedia)
|
||||
>>>>>>> starting with Traversable example
|
||||
|
||||
27
src/Iterator.hs
Normal file
27
src/Iterator.hs
Normal file
@ -0,0 +1,27 @@
|
||||
module Iterator where
|
||||
import Singleton (Exp (..))
|
||||
import Visitor
|
||||
|
||||
instance Functor Exp where
|
||||
fmap f (Var x) = Var x
|
||||
fmap f (Val a) = Val $ f a
|
||||
fmap f (Add x y) = Add (fmap f x) (fmap f y)
|
||||
fmap f (Mul x y) = Mul (fmap f x) (fmap f y)
|
||||
|
||||
instance Traversable Exp where
|
||||
---traverse g Empty = pure Empty
|
||||
traverse g (Var x) = pure $ Var x
|
||||
traverse g (Val x) = Val <$> g x
|
||||
traverse g (Add l r) = Add <$> traverse g l
|
||||
<*> traverse g r
|
||||
traverse g (Mul l r) = Mul <$> traverse g l
|
||||
<*> traverse g r
|
||||
|
||||
iteratorDemo = do
|
||||
putStrLn "Iterator -> Traversable"
|
||||
let exp = Mul (Add (Val 3) (Val 1))
|
||||
(Mul (Val 2) (Var "pi"))
|
||||
env = [("pi", pi)]
|
||||
print env
|
||||
--print $ traverse id exp
|
||||
|
||||
@ -9,6 +9,7 @@ import Adapter
|
||||
import Builder
|
||||
import TemplateMethod
|
||||
import NullObject
|
||||
import Iterator
|
||||
|
||||
main :: IO ()
|
||||
main = do
|
||||
@ -22,3 +23,4 @@ main = do
|
||||
builderDemo
|
||||
templateMethodDemo
|
||||
nullObjectDemo
|
||||
iteratorDemo
|
||||
|
||||
Loading…
Reference in New Issue
Block a user