This essay originally appeared in 2017. Eagle-eyed readers pointed out that the original implementation offoldrhad incorrect semantics. The essay has now been substantially revised to provide an implementation offoldrthat is much closer to the one we find in lazy languages like Haskell.When talking with people in the functional programming community, we often hear the termfold. Folding is an abstraction of operations to be carried out on linear collections, and it’s nearly always implemented as a higher-order function.In this essay we’re going to look at what “folding” does by writing our own ...继续阅读 (20)

Note well: This is an unfinished work-in-progress.Turing Machines and ToolingMuch is made of “functional” programming in JavaScript. People get very excited talking about how to manage, minimize, or even eliminate mutation and state. But what if, instead of trying to avoid state and mutation, weembraceit? What if we “turn mutation up to eleven?”We know the rough answer without even trying. We’d need a lot of tooling to manage our programs. Which is interesting in its own right, because we might learn a lot about tools for writing software.So with that in mind, let’s begin at the beginning.turi ...继续阅读 (29)

Note well: This is an unfinished work-in-progress.Turing Machines and Tooling, Part IMuch is made of “functional” programming in JavaScript. People get very excited talking about how to manage, minimize, or even eliminate mutation and state. But what if, instead of trying to avoid state and mutation, weembraceit? What if we “turn mutation up to eleven?”We know the rough answer without even trying. We’d need a lot of tooling to manage our programs. Which is interesting in its own right, because we might learn a lot about tools for writing software.So with that in mind, let’s begin at the beginn ...继续阅读 (21)

SINGERI’m a lumberjane and I’m OKI sleep all night and I code all dayNERD CHOIRShe’s a lumberjane and she’s OKShe sleeps all night and codes all dayI write clean code, I mentor youthI go to the lavatoryOn Wednesdays I race bicyclesMine’s espresso, if you pleaseShe writes clean code, mentors youthShe goes to the lavatoryOn Wednesdays she races bicyclesHers is espresso, if you pleaseShe’s a lumberjane and she’s OKShe sleeps all night and codes all dayI write clean code, I mentor youthI march against injusticeI can’t stand wearing high heelsAnd play roller derbyShe writes clean code, she mentors ...继续阅读 (24)

SINGERI’m a lumberjane and I’m OKI sleep all night and I code all dayNERD CHOIRShe’s a lumberjane and she’s OKShe sleeps all night and codes all dayI write clean code, I mentor youthI go to the lavatoryOn Wednesdays I race bicyclesMine’s espresso, if you pleaseShe writes clean code, mentors youthShe goes to the lavatoryOn Wednesdays she races bicyclesHers is espresso, if you pleaseShe’s a lumberjane and she’s OKShe sleeps all night and codes all dayI write clean code, I mentor youthI march against injusticeI can’t stand wearing high heelsAnd play roller derbyShe writes clean code, she mentors ...继续阅读 (24)

InWhy Recursive Data Structures?we usedmultirec, a recursive combinator, to implementquadtreesand coloured quadtrees (The full code for creating and rotating quadtrees and coloured quadtrees isbelow).Our focus was on the notion of an isomorphism between the data structures and the algorithms, more than on the performance of quadtrees. Today, we’ll take a closer look at taking advantage of their recursive structure to optimize for time and usingmemoizationandcanonicalization.Finally, we will look at the application of recursive algorithms and quadtrees to simulate the universe. Really.Recursion ...继续阅读 (15)

InWhy Recursive Data Structures?we usedmultirec, a recursive combinator, to implementquadtreesand coloured quadtrees (The full code for creating and rotating quadtrees and coloured quadtrees isbelow).Our focus was on the notion of an isomorphism between the data structures and the algorithms, more than on the performance of quadtrees. Today, we’ll take a closer look at taking advantage of their recursive structure to optimize for time and usingmemoizationandcanonicalization.Finally, we will look at the application of recursive algorithms and quadtrees to simulate the universe. Really.Recursion ...继续阅读 (24)

In this essay, we are going to look at recursive algorithms, and how sometimes, we can organize an algorithm so that it resembles the data structure it manipulates, and organize a data structure so that it resembles the algorithms that manipulate it.When algorithms and the data structures they manipulate areisomorphic,1the code we write is easier to understand for exactly the same reason that code like template strings and regular expressions are easy to understand: The code resembles the data it consumes or produces.We’ll finish up by observing that we also can employ optimizations that are o ...继续阅读 (16)

In this essay, we are going to look at recursive algorithms, and how sometimes, we can organize an algorithm so that it resembles the data structure it manipulates, and organize a data structure so that it resembles the algorithms that manipulate it.When algorithms and the data structures they manipulate areisomorphic,1the code we write is easier to understand for exactly the same reason that code like template strings and regular expressions are easy to understand: The code resembles the data it consumes or produces.We’ll finish up by observing that we also can employ optimizations that are o ...继续阅读 (22)

In this essay, we will take a look at higher-order functions, with an eye to seeing how they can be used to make our programs more expressive, while balancing that against the need to limit the perceived complexity of our programs.introduction: expressiveness and complexityConsiderStructured Programming, a technique arising in the late 1950s and exemplified in the ALGOL programming language. In structured programming, we write procedures that call other procedures by name. Structured programming allows us to decompose procedures, and to extract and share common procedures, DRY-ing up our code ...继续阅读 (17)

In this essay, we will take a look at higher-order functions, with an eye to seeing how they can be used to make our programs more expressive, while balancing that against the need to limit the perceived complexity of our programs.introduction: expressivenessOne of the most basic ideas in programming is that functions can invoke other functions.1When a function invokes other functions, and when one function can be invoked by more than one other function, we have a very good thing. When we have amany-to-manyrelationship between functions, we have a more expressive power than when we have aone-t ...继续阅读 (11)

In this essay, we will take a look at some higher-order functions, with an eye to seeing how they can be used to make our programs more expressive, while balancing that against the need to limit the perceived complexity of our programs.introduction: expressivenessOne of the most basic ideas in programming is that functions can invoke other functions.1When a function invokes other functions, and when one function can be invoked by more than one other function, we have a very good thing. When we have amany-to-manyrelationship between functions, we have a more expressive power than when we have a ...继续阅读 (20)

Unfolded, © 2011Regulla,Some rights reservedpreamble: unfolds and foldsAnamorphismsare functions that map from some object to a more complex structure containing the type of the object. For example, mapping from an integer to a list of integers.Here’s an anamorphism:functiononeTo(n){constlist=[];for(leti=1;i<=n;++i){list.push(i);}returnlist;}oneTo(5)//=> [ 1, 2, 3, 4, 5 ]An integer is our object, and the array containing integers is our “structure containing integers.” Maps from integers to arrays of integers are anamorphisms. “Anamorphism” is a very long word, and using it implies that ...继续阅读 (8)

Unfolded, © 2011Regulla,Some rights reservedpreamble: unfolds and foldsAnamorphismsare functions that map from some object to a more complex structure containing the type of the object. For example, mapping from an integer to a list of integers.Here’s an anamorphism:functiondownToOne(n){constlist=[];for(leti=n;i>0;--i){list.push(i);}returnlist;}downToOne(5)//=> [ 5, 4, 3, 2, 1 ]An integer is our object, and the array containing integers is our “structure containing integers.” Maps from integers to arrays of integers are anamorphisms. “Anamorphism” is a very long word, and using it implies that ...继续阅读 (23)

Preamble: Developing Products “Like This”In “Making sense of MVP,”Henrik Knibergexplains the salient distinction between fake-agile and real-agile development by contrasting two ways of developing a product iteratively,Not Like ThisandLike this.TheNot Like Thisway to develop software is to work in increments, each of which represents a portion of what we plan to build. In this way, nothing is expected to be “wasted,” since everything we build is a necessary part of the finished work.Not Like This…However, at each step along the way, we havepotentialvalue, but not realized value: Until the very ...继续阅读 (23)

InWhy Are Mixins Considered Harmful, we saw that concatenative sharing–as exemplified by mixins–leads to snowballing complexity because of three effects:Lack of EncapsulationImplicit DependenciesName ClashesWe looked at some variations on creating encapsulation to help reduce the “surface area” for dependencies to grow and names to clash, but noted that this merely slows down the growth of the problem, it does not fix it.That being said, that doesn’t mean that mixins are terrible. Mixins are simple to understand and to implement. As we’ll see in this essay, it is straightforward to refactor aw ...继续阅读 (32)

InWhy Are Mixins Considered Harmful, we saw that concatenative sharing–as exemplified by mixins–leads to snowballing complexity because of three effects:Lack of EncapsulationImplicit DependenciesName ClashesWe looked at some variations on creating encapsulation to help reduce the “surface area” for dependencies to grow and names to clash, but noted that this merely slows down the growth of the problem, it does not fix it.That being said, that doesn’t mean that mixins are terrible. Mixins are simple to understand and to implement. As we’ll see in this essay, it is straightforward to refactor aw ...继续阅读 (19)

(This is a work-in-progress, feel free to read and even submit an edit, but do not post on Reddit or Hacker News, thank you.)AreMixins Considered Harmful?Dan Abramov wrote something that sounds familiar to everyone1who works with legacy applications:However it’s inevitable that some of our code using React gradually became incomprehensible. Occasionally, the React team would see groups of components in different projects that people were afraid to touch. These components were too easy to break accidentally, were confusing to new developers, and eventually became just as confusing to the people ...继续阅读 (35)

(This is a work-in-progress, feel free to read and even submit an edit, but do not post on Reddit or Hacker News, thank you.)AreMixins Considered Harmful?Dan Abramov wrote something that sounds familiar to everyone1who works with legacy applications:However it’s inevitable that some of our code using React gradually became incomprehensible. Occasionally, the React team would see groups of components in different projects that people were afraid to touch. These components were too easy to break accidentally, were confusing to new developers, and eventually became just as confusing to the people ...继续阅读 (26)

update: Part II,From Mixins to Object Compositionis now available.InMixins Considered Harmful, Dan Abramov wrote something that sounds familiar to everyone1who works with legacy applications:Some of our code using React gradually became incomprehensible. Occasionally, the React team would see groups of components in different projects that people were afraid to touch. These components were too easy to break accidentally, were confusing to new developers, and eventually became just as confusing to the people who wrote them in the first place.This is not specific to “React:” All legacy applicati ...继续阅读 (21)

the hubris of blog post authorsAlthea and Ben were sipping feature espressos at their local indie coffee shop. “Althea,” Ben began, “I’m prepping for interviews with you-know-who, so I’ve been trying to read as many algorithm blog posts as I can, just to catch up on all the stuff I’ve forgotten now that Ive been working for a few years…” Althea died a little inside.That conversation. Programmers were notorious for taking interview questions extremely personally.“Oh?” Althea tried to discourage Ben with overt disinterest. It was futile, of course: Ben carried on.“Well, I was just reading a blog ...继续阅读 (34)

the hubris of blog post authorsAlthea and Ben were sipping feature espressos at their local indie coffee shop. “Althea,” Ben began, “I’m prepping for interviews with you-know-who, so I’ve been trying to read as many algorithm blog posts as I can, just to catch up on all the stuff I’ve forgotten now that Ive been working for a few years…” Althea died a little inside.That conversation. Programmers were notorious for taking interview questions extremely personally.“Oh?” Althea tried to discourage Ben with overt disinterest. It was futile, of course: Ben carried on.“Well, I was just reading a blog ...继续阅读 (20)

melissa e. o’neillthe unfaithful sieveIn thelastpost, we looked at theSieve of Eratosthenes. The definition is:We start with a table of numbers (e.g., 2, 3, 4, 5, . . . ) and progressively cross off numbers in the table until the only numbers left are primes. Specifically, we begin with the first number, p, in the table, and:Declare p to be prime, and cross off all the multiples of that number in the table, starting from p squared, then;Find the next number in the table after p that is not yet crossed off and set p to that number; and then repeat from step 1.The solution given was the most naï ...继续阅读 (20)

melissa e. o’neillalthea and ben have espressosAlthea and Ben were sipping feature espressos at their local indie coffee shop. “Althea,” Ben began, “I’m prepping for my interview with RealTime, and I did some googling for their interview questions…” Althea died a little insideThat conversation, they thought. Programmers were notorious for taking interview questions extremely personally.“Oh?” Althea tried to discourage Bob with overt disinterest. It was futile, of course: Bob carried on.“Well, they have five or six slots that they run, one phone screen and then the rest in a single-day onslaugh ...继续阅读 (27)

Inthe last post, we looked at theSieve of Eratosthenes.The definition is:We start with a table of numbers (e.g., 2, 3, 4, 5, . . . ) and progressively cross off numbers in the table until the only numbers left are primes. Specifically, we begin with the first number, p, in the table, and:Declare p to be prime, and cross off all the multiples of that number in the table, starting from p squared, then;Find the next number in the table after p that is not yet crossed off and set p to that number; and then repeat from step 1.The solution given was the most naïve possible mapping from words to code ...继续阅读 (17)

larry walllaziness and eagernessIn computing, “laziness” is a broad term, generally referring to not doing any work unless you need it. Whereas its opposite is “eagerness,” doing as much work as possible in case you need it later.For example, consider this JavaScript:functionifThen(a,b){if(a)returnb;}ifThen(1===0,2+3)//=> undefinedNow, here’s the question: Does JavaScript compute2+3? You probably know the answer: Yes it does. When it comes to passing arguments to a function invocation, JavaScript iseager, it evaluates all of the expressions, and it does so whether the value of the expressio ...继续阅读 (16)

larry walllaziness and eagernessIn computing, “laziness” is a broad term, generally referring to not doing any work unless you need it. Whereas its opposite is “eagerness,” doing as much work as possible in case you need it later.Consider this JavaScript:functionifThen(a,b){if(a)returnb;}ifThen(1===0,2+3)//=> undefinedNow, here’s the question: Does JavaScript evaluate2+3? You probably know the answer: Yes it does. When it comes to passing arguments to a function invocation, JavaScript iseager, it evaluates all of the expressions, and it does so whether the value of the expression is used or no ...继续阅读 (15)

hal abelsonthe fibonacci numbersIn mathematics, the Fibonacci numbers orFibonacci sequenceare numbers in the following integer sequence:0, 1, 1, 2, 3, 5, 8, 13, 21, ….1The rule for determining the sequence is quite simple to explain:The first number is0.The second number is1.Every subsequent number is the sum of the two previous numbers.Thus, the third number is1(0 + 1), the fourth number is2(1 + 1), and that makes the fifth number3(1 + 2), the sixth number5(2 + 3) and so onad infinitum.There are many ways to write a program that will output the Fibonacci numbers. each method optimizes for som ...继续阅读 (16)

hal abelsonthe fibonacci numbersIn mathematics, the Fibonacci numbers orFibonacci sequenceare numbers in the following integer sequence:0, 1, 1, 2, 3, 5, 8, 13, 21, ….1The rule for determining the sequence is quite simple to explain:The first number is0.The second number is1.Every subsequent number is the sum of the two previous numbers.Thus, the third number is1(0 + 1), the fourth number is2(1 + 1), and that makes the fifth number3(1 + 2), the sixth number5(2 + 3) and so onad infinitum.There are many ways to write a program that will output the Fibonacci numbers. each method optimizes for som ...继续阅读 (18)

forewardThis talk was given atNDC Londonon January 14, 2016.1. A selection of slides are shown here, along with some annotations explaining the ideas being presented. This is not a transcript, nor is it a blog post. Some slides are elided, especially those showing code. It will be most valuable to those who attended the talk or watch it when it is released on video.Part I: The Basics“In object-oriented programming, thecommand patternis a behavioural design pattern in which an object is used to encapsulate all information needed to perform an action or trigger an event at a later time.”We will ...继续阅读 (20)