If we assumed procedural languages, we might have included design patterns called 'Inheritance,' 'Encapsulation,' and 'Polymorphism. What is easy and what is hard to implement in a functional programming language?
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I decided to revisit all 23 original Gang of Four design patterns under that lense. My hope is that these results will be useful to Object Oriented Programmers seeking to learn the ways of Functional Programming. First class functions and lambdas. Any extra data that might be placed as class members is traditionally implemented using closures which stash the data in a lambda function's environment or currying which create implicit closures for function's arguments. Strategies are also powerful because they are polymorphic; type synonyms for function types can play a similar role.
Java has recognized anonymous functions as a good idea, and have added facilities for anonymous classes, which are frequently used in this capacity. Factory Method and Template Method.
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Higher-order functions. Instead of making a subclass, just pass the the function you'd like to vary the behavior of with the function. Abstract Factory , Builder and Bridge. Type classes and smart constructors. If you're not just constructing values but manipulating them with the general type class interface, you have a Bridge. Smart constructors are functions built on top of the basic data constructor that can do "more", whether this is invariant checking, encapsulation or an easier API, this can correspond to more advanced methods that a factory provides.
Adapter , Decorator and Chain of Responsibility. Composition and lifting. Function composition can be used to form a pipeline of data between functions; a foreign function can be sandwiched between two functions that convert to and from the type the function expects, or a function can be composed with another to make it do more things. If the signature stays the same, one or more of the functions was endomorphic. If the functions have side effect, it may be Kleisli arrow composition more plainly spoken as monadic function composition. Multiple functions can handle the same input using the Reader monad.
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Frequently foldable. Many functional languages favor grouping the same operation on different data constructors together, in a mathematical equational style. This means similar behaviors are grouped together. Traditional grouping of behavior by "class" is implemented with type classes. Visitors typically collapse the data structures they operate on into smaller values, this is seen in the fold family of functions.
Frequently circumvented with an embedded domain specific language. Algebraic data types make light-weight abstract syntax trees easy to formulate. Just as Visitor is often used with Interpeter, you'll probably write your interpreting functions with pattern matching. Even better, don't come up with another data type; just use functions and infix operators to say what you mean. Closely related to See also algebraic data types , frequently generalized GADT. What you could say here is something like "the morphisms are what you work with if you want to achieve elegant, compact programs expressing complex relationships.
Thanks for the kind words! I've actually been learning from Awodey's book since I don't have a very strong mathematical background for MacLane's book, yet, but I plan to work through it eventually. I was plan on doing a follow-up post discussing objects mainly in the context of Haskell types.
Even in my own code with long composition chains, I often annotate the type of each intermediate step as a comment to help keep track of what is going on. Are they Haskell types, just like in Hask? Are the objects on either side of the Pipe morphism represented by 'a' and 'b' in "Pipe a b r"?
If not, how far off the mark am I, exactly? You are correct.
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The a and b are the objects and they are Haskell types. So, interestingly, when you generalize pipes to proxies then you get two extra categories see the Interact class in Control. Class and they do make use of the r parameter. Hi Gabriel, nice post. I was planning to write something on the same topic, but in french, sometime in the near future. Haskell documentation is lacking in this dialect, and I hope that adding more content will create more opportunities for people to get into the purely functional way of programming.
If you agree, I could also translate this good article, and credit it clearly of course. What do you think about that? Thank you very much! I understand enough French to know you did an excellent job of translation. By the way, talking about "order of grouping" is a little awkward composition is generally not commutative.
I think if you rephrase to something like "nesting of groups" the flow will be more natural for the reader. Great post. I really love math and especially category theory, so to see it applied to Haskell means I'm immediately going to take another look at the language.
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Just a question though. I really want to learn haskell but the Rubyist in me just finds it easier to bang out a quick script when I need something. Is there any like things I can do with Haskell while I'm learning?
Like I find it helpful to learn by building so any ideas. Thanks and awesome post. As a matter of fact, there is a scripting library I wrote which is specifically geared towards people who have no prior Haskell knowledge. Awesome post. To me, this explains the monad laws: they arise naturally if you want to define a category where monadic functions compose. Is that fair to say? The monad laws follow exactly from the desire to ensure that monadic function composition is associative and has an identity. This is truly an awesome post! In the end you've mentioned a few follow up posts.
Can you point me to those? So far I've only found 'Functor Design Pattern'. The functor design pattern was the only follow-up post I wrote. I haven't gotten around to writing the other posts, yet. Are you planning on writing them? These two posts were very insightful and I'm looking forward to the rest of them. I eventually plan on writing a book, but that is still a couple of years away before I will begin writing in earnest. Saturday, August 18, The category design pattern. Functional programming is all the rage these days, but in this post I want to emphasize that functional programming is a subset of a more important overarching programming paradigm: compositional programming.
If you've ever used Unix pipes, you'll understand the importance and flexibility of composing small reusable programs to get powerful and emergent behaviors. Similarly, if you program functionally, you'll know how cool it is to compose a bunch of small reusable functions into a fully featured program. Category theory codifies this compositional style into a design pattern, the category. Moreover, category theory gives us a precise prescription for how to create our own abstractions that follow this design pattern: the category laws.
These laws differentiate category theory from other design patterns by providing rigorous criteria for what does and does not qualify as compositional. One could easily dismiss this compositional ideal as just that: an ideal, something unsuitable for "real-world" scenarios.
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However, the theory behind category theory provides the meat that shows that this compositional ideal appears everywhere and can rise to the challenge of messy problems and complex business logic. This post is just one of many posts that I will write over time where I will demonstrate how to practically use this compositional style in your programs, even for things that may seem like they couldn't possibly lend themselves to compositional programming. This first post starts off by introducing the category as a compositional design pattern. Categories I'm going to give a slightly different introduction to category theory than most people give.
I'm going to gloss over the definition of what a morphism or an object is and skip over domains and codomains and instead just go straight to composition, because from a programmer's point of view a category is just a compositional design pattern.
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Category theory says that for any given category there must be some sort of composition operator, which I will denote. The first rule is that this composition operator is associative: f. Being an identity means that: id. Notice that the definition of a category does not define: what. Instead, category theory leaves it up to us to discover what they might be. The brilliance behind the category design pattern is that any composition operator that observes these laws will be: easy to use, intuitive, and free from edge cases.
This is why we try to formulate abstractions in terms of the category design pattern whenever possible. The function category Let's define our first category: the category of Haskell functions! I guess we just give up, right?
Monad provides both of the above functions. Monadic functions just generalize ordinary functions and the Kleisli category demonstrates that monadic functions are composable, too. They just use a different composition operator: , and a different identity: return. Well, let's assume that category theorists aren't bullshitting us and that really is some sort of composition and return really is its identity. If that were true, we'd expect the following laws to hold: return Well, we already have the definition for : f Those are just the monad laws , which all Monad instances are required to satisfy.
If you have ever wondered where those monad laws came from, now you know! They are just the category laws in disguise. Consequently, every new Monad we define gives us a category for free!
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