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## Higher-order function

Not to be confused with Functor (category theory).

” (WP)

In mathematics and computer science, a higher-order function is a function that does at least one of the following:

All other functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function. Higher-order functions should not be confused with other uses of the word “functor” throughout mathematics, see Functor (disambiguation).

In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus, from which most functional programming languages are derived, higher-order functions that take one function as argument are values with types of the form {\displaystyle (\tau _{1}\to \tau _{2})\to \tau _{3}}.

## General examples

• map function, found in many functional programming languages, is one example of a higher-order function. It takes as arguments a function f and a collection of elements, and as the result, returns a new collection with f applied to each element from the collection.
• Sorting functions, which take a comparison function as a parameter, allowing the programmer to separate the sorting algorithm from the comparisons of the items being sorted. The C standard function qsort is an example of this.
• filter
• fold
• apply
• Function composition
• Integration
• Callback
• Tree traversal
• Montague grammar, a semantic theory of natural language, uses higher-order functions

## Support in programming languages

### Direct support

The examples are not intended to compare and contrast programming languages, but to serve as examples of higher-order function syntax

In the following examples, the higher-order function twice takes a function, and applies the function to some value twice. If twice has to be applied several times for the same f it preferably should return a function rather than a value. This is in line with the “don’t repeat yourself” principle.

#### APL

Further information: APL (programming language)

      twice←{⍺⍺ ⍺⍺ ⍵}

plusthree←{⍵+3}

g←{plusthree twice ⍵}

g 7
13


Or in a tacit manner:

      twice←⍣2

plusthree←+∘3

g←plusthree twice

g 7
13


#### C++

Further information: C++

Using std::function in C++11:

#include <iostream>
#include <functional>

auto twice = [](const std::function<int(int)>& f)
{
return [&f](int x) {
return f(f(x));
};
};

auto plus_three = [](int i)
{
return i + 3;
};

int main()
{
auto g = twice(plus_three);

std::cout << g(7) << '\n'; // 13
}


Or, with generic lambdas provided by C++14:

#include <iostream>

auto twice = [](const auto& f)
{
return [&f](int x) {
return f(f(x));
};
};

auto plus_three = [](int i)
{
return i + 3;
};

int main()
{
auto g = twice(plus_three);

std::cout << g(7) << '\n'; // 13
}


#### C#

Further information: C Sharp (programming language)

Using just delegates:

using System;

public class Program
{
public static void Main(string[] args)
{
Func<Func<int, int>, Func<int, int>> twice = f => x => f(f(x));

Func<int, int> plusThree = i => i + 3;

var g = twice(plusThree);

Console.WriteLine(g(7)); // 13
}
}


Or equivalently, with static methods:

using System;

public class Program
{
private static Func<int, int> Twice(Func<int, int> f)
{
return x => f(f(x));
}

private static int PlusThree(int i) => i + 3;

public static void Main(string[] args)
{
var g = Twice(PlusThree);

Console.WriteLine(g(7)); // 13
}
}


#### Clojure

Further information: Clojure

(defn twice [f]
(fn [x] (f (f x))))

(defn plus-three [i]
(+ i 3))

(def g (twice plus-three))

(println (g 7)) ; 13


#### ColdFusion Markup Language (CFML)

Further information: ColdFusion Markup Language

twice = function(f) {
return function(x) {
return f(f(x));
};
};

plusThree = function(i) {
return i + 3;
};

g = twice(plusThree);

writeOutput(g(7)); // 13


#### D

Further information: D (programming language)

import std.stdio : writeln;

alias twice = (f) => (int x) => f(f(x));

alias plusThree = (int i) => i + 3;

void main()
{
auto g = twice(plusThree);

writeln(g(7)); // 13
}


#### Elixir

Further information: Elixir (programming language)

In Elixir, you can mix module definitions and anonymous functions

defmodule Hof do
def twice(f) do
fn(x) -> f.(f.(x)) end
end
end

plus_three = fn(i) -> 3 + i end

g = Hof.twice(plus_three)

IO.puts g.(7) # 13


Alternatively, we can also compose using pure anonymous functions.

twice = fn(f) ->
fn(x) -> f.(f.(x)) end
end

plus_three = fn(i) -> 3 + i end

g = twice.(plus_three)

IO.puts g.(7) # 13


#### Erlang

Further information: Erlang (programming language)

or_else([], _) -> false;
or_else([F | Fs], X) -> or_else(Fs, X, F(X)).

or_else(Fs, X, false) -> or_else(Fs, X);
or_else(Fs, _, {false, Y}) -> or_else(Fs, Y);
or_else(_, _, R) -> R.

or_else([fun erlang:is_integer/1, fun erlang:is_atom/1, fun erlang:is_list/1], 3.23).


In this Erlang example, the higher-order function or_else/2 takes a list of functions (Fs) and argument (X). It evaluates the function F with the argument X as argument. If the function F returns false then the next function in Fs will be evaluated. If the function F returns {false, Y} then the next function in Fs with argument Y will be evaluated. If the function F returns R the higher-order function or_else/2 will return R. Note that XY, and R can be functions. The example returns false.

#### F#

Further information: F Sharp (programming language)

let twice f = f >> f

let plus_three = (+) 3

let g = twice plus_three

g 7 |> printf "%A" // 13


#### Go

Further information: Go (programming language)

package main

import "fmt"

func twice(f func(int) int) func(int) int {
return func(x int) int {
return f(f(x))
}
}

func main() {
plusThree := func(i int) int {
return i + 3
}

g := twice(plusThree)

fmt.Println(g(7)) // 13
}


Notice a function literal can be defined either with an identifier (twice) or anonymously (assigned to variable f).

twice :: (Int -> Int) -> (Int -> Int)
twice f = f . f

plusThree :: Int -> Int
plusThree = (+3)

main :: IO ()
main = print (g 7) -- 13
where
g = twice plusThree


#### J

Further information: J (programming language)

Explicitly,

   twice=.     adverb : 'u u y'

plusthree=. verb   : 'y + 3'

g=. plusthree twice

g 7
13


or tacitly,

   twice=. ^:2

plusthree=. +&3

g=. plusthree twice

g 7
13


#### Java (1.8+)

Further information: Java (programming language) and Java version history

Using just functional interfaces:

import java.util.function.*;

class Main {
public static void main(String[] args) {
Function<IntUnaryOperator, IntUnaryOperator> twice = f -> f.andThen(f);

IntUnaryOperator plusThree = i -> i + 3;

var g = twice.apply(plusThree);

System.out.println(g.applyAsInt(7)); // 13
}
}


Or equivalently, with static methods:

import java.util.function.*;

class Main {
private static IntUnaryOperator twice(IntUnaryOperator f) {
return f.andThen(f);
}

private static int plusThree(int i) {
return i + 3;
}

public static void main(String[] args) {
var g = twice(Main::plusThree);

System.out.println(g.applyAsInt(7)); // 13
}
}


#### JavaScript

Further information: JavaScript

"use strict";

const twice = f => x => f(f(x));

const plusThree = i => i + 3;

const g = twice(plusThree);

console.log(g(7)); // 13


#### Julia

Further information: Julia (programming language)

julia> function twice(f)
function result(x)
return f(f(x))
end
return result
end
twice (generic function with 1 method)

julia> plusthree(i) = i + 3
plusthree (generic function with 1 method)

julia> g = twice(plusthree)
(::var"#result#3"{typeof(plusthree)}) (generic function with 1 method)

julia> g(7)
13


#### Kotlin

Further information: Kotlin (programming language)

fun twice(f: (Int) -> Int): (Int) -> Int {
return { f(f(it)) }
}

fun plusThree(i: Int) = i + 3

fun main() {
val g = twice(::plusThree)

println(g(7)) // 13
}


#### Lua

Further information: Lua (programming language)

local function twice(f)
return function (x)
return f(f(x))
end
end

local function plusThree(i)
return i + 3
end

local g = twice(plusThree)

print(g(7)) -- 13


#### MATLAB

Further information: MATLAB

function result = twice(f)
result = @inner

function val = inner(x)
val = f(f(x));
end
end

plusthree = @(i) i + 3;

g = twice(plusthree)

disp(g(7)); % 13


#### OCaml

Further information: OCaml (programming language)

let twice f x =
f (f x)

let plus_three =
(+) 3

let () =
let g = twice plus_three in

print_int (g 7); (* 13 *)
print_newline ()


#### PHP

Further information: PHP

<?php

declare(strict_types=1);

function twice(callable $f): Closure { return function (int$x) use ($f): int { return$f($f($x));
};
}

function plusThree(int $i): int { return$i + 3;
}

$g = twice('plusThree'); echo$g(7), "\n"; // 13


or with all functions in variables:

<?php

declare(strict_types=1);

$twice = fn(callable$f): Closure => fn(int $x): int =>$f($f($x));

$plusThree = fn(int$i): int => $i + 3;$g = $twice($plusThree);

echo $g(7), "\n"; // 13  Note that arrow functions implicitly capture any variables that come from the parent scope,[1] whereas anonymous functions require the use keyword to do the same. #### Pascal Further information: Pascal (programming language) {$mode objfpc}

type fun = function(x: Integer): Integer;

function twice(f: fun; x: Integer): Integer;
begin
result := f(f(x));
end;

function plusThree(i: Integer): Integer;
begin
result := i + 3;
end;

begin
writeln(twice(@plusThree, 7)); { 13 }
end.


#### Perl

Further information: Perl

use strict;
use warnings;

sub twice {
my ($f) = @_; sub {$f->($f->(@_)); }; } sub plusThree { my ($i) = @_;
$i + 3; } my$g = twice(\&plusThree);

print $g->(7), "\n"; # 13  or with all functions in variables: use strict; use warnings; my$twice = sub {
my ($f) = @_; sub {$f->($f->(@_)); }; }; my$plusThree = sub {
my ($x) = @_;$x + 3;
};

my $g =$twice->($plusThree); print$g->(7), "\n"; # 13


#### Python

Further information: Python (programming language)

>>> def twice(f):
...     def result(x):
...         return f(f(x))
...     return result

>>> plusthree = lambda i: i + 3

>>> g = twice(plusthree)

>>> g(7)
13


Python decorator syntax is often used to replace a function with the result of passing that function through a higher-order function. E.g., the function g could be implemented equivalently:

>>> @twice
... def g(i):
...     return i + 3

>>> g(7)
13


#### R

Further information: R (programming language)

twice <- function(f) {
return(function(x) {
f(f(x))
})
}

plusThree <- function(i) {
return(i + 3)
}

g <- twice(plusThree)

> print(g(7))
[1] 13


#### Raku

Further information: Raku (programming language)

sub twice(Callable:D $f) { return sub {$f($f($^x)) };
}

sub plusThree(Int:D $i) { return$i + 3;
}

my $g = twice(&plusThree); say$g(7); # 13


In Raku, all code objects are closures and therefore can reference inner “lexical” variables from an outer scope because the lexical variable is “closed” inside of the function. Raku also supports “pointy block” syntax for lambda expressions which can be assigned to a variable or invoked anonymously.

#### Ruby

Further information: Ruby (programming language)

def twice(f)
->(x) { f.call f.call(x) }
end

plus_three = ->(i) { i + 3 }

g = twice(plus_three)

puts g.call(7) # 13


#### Rust

Further information: Rust (programming language)

fn twice(f: impl Fn(i32) -> i32) -> impl Fn(i32) -> i32 {
move |x| f(f(x))
}

fn plus_three(i: i32) -> i32 {
i + 3
}

fn main() {
let g = twice(plus_three);

println!("{}", g(7)) // 13
}


#### Scala

Further information: Scala (programming language)

object Main {
def twice(f: Int => Int): Int => Int =
f compose f

def plusThree(i: Int): Int =
i + 3

def main(args: Array[String]): Unit = {
val g = twice(plusThree)

print(g(7)) // 13
}
}


#### Scheme

Further information: Scheme (programming language)

(define (add x y) (+ x y))
(define (f x)
(lambda (y) (+ x y)))
(display ((f 3) 7))


In this Scheme example, the higher-order function (f x) is used to implement currying. It takes a single argument and returns a function. The evaluation of the expression ((f 3) 7) first returns a function after evaluating (f 3). The returned function is (lambda (y) (+ 3 y)). Then, it evaluates the returned function with 7 as the argument, returning 10. This is equivalent to the expression (add 3 7), since (f x) is equivalent to the curried form of (add x y).

#### Swift

Further information: Swift (programming language)

func twice(_ f: @escaping (Int) -> Int) -> (Int) -> Int {
return { f(f($0)) } } let plusThree = {$0 + 3 }

let g = twice(plusThree)

print(g(7)) // 13


#### Tcl

Further information: Tcl

set twice {{f x} {apply $f [apply$f $x]}} set plusThree {{i} {return [expr$i + 3]}}

# result: 13
puts [apply $twice$plusThree 7]


Tcl uses apply command to apply an anonymous function (since 8.6).

#### XACML

Further information: XACML

The XACML standard defines higher-order functions in the standard to apply a function to multiple values of attribute bags.

rule allowEntry{
permit
condition anyOfAny(function[stringEqual], citizenships, allowedCitizenships)
}


The list of higher-order functions in XACML can be found here.

#### XQuery

Further information: XQuery

declare function local:twice($f,$x) {
$f($f($x)) }; declare function local:plusthree($i) {
$i + 3 }; local:twice(local:plusthree#1, 7) (: 13 :)  ### Alternatives #### Function pointers Function pointers in languages such as C and C++ allow programmers to pass around references to functions. The following C code computes an approximation of the integral of an arbitrary function: #include <stdio.h> double square(double x) { return x * x; } double cube(double x) { return x * x * x; } /* Compute the integral of f() within the interval [a,b] */ double integral(double f(double x), double a, double b, int n) { int i; double sum = 0; double dt = (b - a) / n; for (i = 0; i < n; ++i) { sum += f(a + (i + 0.5) * dt); } return sum * dt; } int main() { printf("%g\n", integral(square, 0, 1, 100)); printf("%g\n", integral(cube, 0, 1, 100)); return 0; }  The qsort function from the C standard library uses a function pointer to emulate the behavior of a higher-order function. #### Macros Macros can also be used to achieve some of the effects of higher-order functions. However, macros cannot easily avoid the problem of variable capture; they may also result in large amounts of duplicated code, which can be more difficult for a compiler to optimize. Macros are generally not strongly typed, although they may produce strongly typed code. #### Dynamic code evaluation In other imperative programming languages, it is possible to achieve some of the same algorithmic results as are obtained via higher-order functions by dynamically executing code (sometimes called Eval or Execute operations) in the scope of evaluation. There can be significant drawbacks to this approach: • The argument code to be executed is usually not statically typed; these languages generally rely on dynamic typing to determine the well-formedness and safety of the code to be executed. • The argument is usually provided as a string, the value of which may not be known until run-time. This string must either be compiled during program execution (using just-in-time compilation) or evaluated by interpretation, causing some added overhead at run-time, and usually generating less efficient code. #### Objects In object-oriented programming languages that do not support higher-order functions, objects can be an effective substitute. An object’s methods act in essence like functions, and a method may accept objects as parameters and produce objects as return values. Objects often carry added run-time overhead compared to pure functions, however, and added boilerplate code for defining and instantiating an object and its method(s). Languages that permit stack-based (versus heap-based) objects or structs can provide more flexibility with this method. An example of using a simple stack based record in Free Pascal with a function that returns a function: program example; type int = integer; Txy = record x, y: int; end; Tf = function (xy: Txy): int; function f(xy: Txy): int; begin Result := xy.y + xy.x; end; function g(func: Tf): Tf; begin result := func; end; var a: Tf; xy: Txy = (x: 3; y: 7); begin a := g(@f); // return a function to "a" writeln(a(xy)); // prints 10 end.  The function a() takes a Txy record as input and returns the integer value of the sum of the record’s x and y fields (3 + 7). #### Defunctionalization Defunctionalization can be used to implement higher-order functions in languages that lack first-class functions: // Defunctionalized function data structures template<typename T> struct Add { T value; }; template<typename T> struct DivBy { T value; }; template<typename F, typename G> struct Composition { F f; G g; }; // Defunctionalized function application implementations template<typename F, typename G, typename X> auto apply(Composition<F, G> f, X arg) { return apply(f.f, apply(f.g, arg)); } template<typename T, typename X> auto apply(Add<T> f, X arg) { return arg + f.value; } template<typename T, typename X> auto apply(DivBy<T> f, X arg) { return arg / f.value; } // Higher-order compose function template<typename F, typename G> Composition<F, G> compose(F f, G g) { return Composition<F, G> {f, g}; } int main(int argc, const char* argv[]) { auto f = compose(DivBy<float>{ 2.0f }, Add<int>{ 5 }); apply(f, 3); // 4.0f apply(f, 9); // 7.0f return 0; }  In this case, different types are used to trigger different functions via function overloading. The overloaded function in this example has the signature auto apply. ## See also ## References 1. ^ “PHP: Arrow Functions – Manual”www.php.net. Retrieved 2021-03-01. ” (WP) #### Sources: Categories ## Limited hangout “A limited hangout or partial hangout is, according to former special assistant to the Deputy Director of the Central Intelligence Agency Victor Marchetti, “spy jargon for a favorite and frequently used gimmick of the clandestine professionals. When their veil of secrecy is shredded and they can no longer rely on a phony cover story to misinform the public, they resort to admitting—sometimes even volunteering—some of the truth while still managing to withhold the key and damaging facts in the case. The public, however, is usually so intrigued by the new information that it never thinks to pursue the matter further.”[1][2] (WP) ## Modified limited hangout “In a March 22, 1973, meeting between president Richard NixonJohn DeanJohn EhrlichmanJohn Mitchell, and H. R. Haldeman, Ehrlichman incorporated the term into a new and related one, “modified limited hangout“.[3][4] The phrase was coined in the following exchange:[5]” (WP) PRESIDENT: You think, you think we want to, want to go this route now? And the — let it hang out, so to speak? DEAN: Well, it’s, it isn’t really that — HALDEMAN: It’s a limited hang out. DEAN: It’s a limited hang out. EHRLICHMAN: It’s a modified limited hang out. PRESIDENT: Well, it’s only the questions of the thing hanging out publicly or privately. “Before this exchange, the discussion captures Nixon outlining to Dean the content of a report that Dean would create, laying out a misleading view of the role of the White House staff in events surrounding the Watergate burglary. In Ehrlichman’s words: “And the report says, ‘Nobody was involved,'”. The document would then be shared with the United States Senate Watergate Committee investigating the affair. The report would serve the administration’s goals by protecting the President, providing documentary support for his false statements should information come to light that contradicted his stated position. Further, the group discusses having information on the report leaked by those on the Committee sympathetic to the President, to put exculpatory information into the public sphere.[5]” (WP) “The phrase has been cited as a summation of the strategy of mixing partial admissions with misinformation and resistance to further investigation, and is used in political commentary to accuse people or groups of following a Nixon-like strategy.[6]” (WP) However, this “strategy” has been used since time immemorial. “Writing in The Washington PostMary McGrory described a statement by Pope John Paul II regarding sexual abuse by priests as a “modified, limited hangout”.[7] (WP) ## See also ## References 1. ^ Victor Marchetti (August 14, 1978) The Spotlight 2. ^ “720 F2d 631 Hunt v. Liberty Lobby Dc”. OpenJurist. 1983-11-28. Retrieved 2016-07-13. 3. ^ Frost/Nixon: The Complete Interviews. David Frost, Richard Nixon. Paradine Television, 1977. 4. ^ Safire, William (26 March 1989). “On Language; In Nine Little Words”New York Times. Retrieved 23 June 2013. 5. a b “Transcript of a recording of a meeting among the president, John Dean, John Erlichman, H. R. Haldeman, and John Mitchell on March 22, 1973 from 1:57 to 3:43 p.m.” History and Politics Out Loud. Retrieved 2006-08-27. 6. ^ Carrol, Jon (2002-05-01). “The Richard Nixon playbook”San Francisco Chronicle. Retrieved 2006-08-27. 7. ^ McGrory, Mary (2002-04-25). “From Rome, A ‘Limited Hangout'”The Washington Post. Washington, D.C. p. A29. Retrieved 2010-04-30. ” (WP) #### Sources: Categories ## Fair Credit Reporting Act – 1970 AD Return to Timeline of the History of Computers 1970 Fair Credit Reporting Act Alan Westin (1929–2013) “In March 1970, a (“limited hangout“) professor from Columbia University testified before the US Congress about shadowy American businesses that were maintaining secret databases on American citizens. These files, said Alan Westin, “may include ‘facts, statistics, inaccuracies and rumors’ . . . about virtually every phase of a person’s life: his marital troubles, jobs, school history, childhood, sex life, and political activities.” The files were used by American banks, department stores, and other firms to determine who should be given credit to buy a house, a car, or even a furniture set. The databanks, Westin explained, were also used by companies evaluating job applicants and underwriting insurance. And they couldn’t be outlawed: without credit and the ability to pay for major purchases with installments, many people couldn’t otherwise afford such things. Westin was well known to the US Congress: he had testified on multiple occasions before congressional committees investigating the credit-reporting industry, and he had published a book, Privacy and Freedom (1967), in which he argued that freedom in the information age required that individuals have control over how their data are used by governments and businesses. Westin defined privacy as “the claim of individuals, groups, or institutions to determine for themselves when, how, and to what extent information about them is communicated to others.” And he coined the phrase data shadow to describe the trail of information that people leave behind in the modern world. On October 26, 1970, Congress enacted the Fair Credit Reporting Act (FCRA), which gave Americans, for the first time, the right to see the consumer files that businesses used to decide who should get credit and insurance. The FCRA also gave consumers the right to force the credit bureaus to investigate a claim that the consumer felt was inaccurate, and the ability to insert a statement in the file, telling his or her side of the story. The FCRA was one of the first laws in the world regulating what private businesses could do with data that they collect—the beginning of what is now called data protection, an idea that eventually spread worldwide. Today there are privacy commissioners in almost every developed country. The passage of the European Union’s General Data Protection Regulation (GDPR) marked the most far-reaching privacy law on the planet.” SEE ALSO Relational Database (1970) Columbia professor Alan Westin was concerned about American businesses keeping secret databases on American citizens. Categories ## The Byte – 1956 AD Return to Timeline of the History of Computers 1956 The Byte Werner Buchholz (b. 1922), Louis G. Dooley (dates unavailable) “Designers of the early binary computers faced a fundamental question: how should the computers’ storage be organized? The computers stored information in bits, but computer users didn’t want to write programs that manipulated bits; they wanted to solve math problems, crack codes, and generally work with larger units of information. The memory of decimal computers such as ENIAC and the UNIVAC I was organized in groups of 10 alphanumeric digits, called words. The binary computers also organized their memory into words, but these groups of bits were called bytes.” “It appears that the word byte was coined simultaneously in 1956 by Werner Buchholz at IBM, working on the IBM STRETCH (the world’s first supercomputer), and by Louis G. Dooley and others at MIT Lincoln Lab working on the SAGE air-defense system. In both cases, they used the word byte to describe the inputs and outputs of machine instructions that could operate on less than a full word. The STRETCH had 60-bit words and used 8-bit bytes to represent characters for its input/output system; the SAGE had instructions that could operate on 4-bit bytes.” “The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer[1][2] and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as The Internet Protocol (RFC 791)(1981) refer to an 8-bit byte as an octet.[3] “Over the next 20 years, the definition of a byte was somewhat fluid. IBM used 8-bit bytes with its System/360 architecture, and 8-bit groups were the standard for AT&T’s long-distance digital telephone lines. DEC, on the other hand, successfully marketed a series of computers with 18-bit and 36-bit words, including the PDP-7 and the PDP-10, which both utilized 9-bit bytes.” “This lack of consistency resulted in the early Internet standards avoiding the word byte entirely. Instead, the word octet is used to describe a group of 8 bits sent over a computer network, a usage that survives to this day in Internet standards.” “Nevertheless, by the 1980s, the acceptance of 8-bit bytes was almost universal—largely a result of the microcomputer revolution, because micros used 8-bit bytes almost exclusively. In part, that’s because 8 bits is an even power of 2, which makes it somewhat easier to design computer hardware with 8-bit bytes than with 9-bit bytes.” “Today the era of 9-bit bytes is all but forgotten. And what about collections of 4 bits? Today these are called a nibble (sometimes spelled nybble).” Multiples of bytes: SEE ALSO: “Today’s computers most frequently use bytes consisting of 8 bits, represented by 1s and 0s.” Categories ## 2020s ## 2020 ## 2021 ## Deaths ### 2020 ### 2021 ” (WP) #### Sources: Categories ## 2010s ## 2010 ## 2011 ## 2012 • February 29 • Raspberry Pi, a bare-bones, low-cost credit-card sized computer created by volunteers mostly drawn from academia and the UK tech industry, is released to help teach children to code.[8][9] • September ?? (Date unknown) • October 4 • TDK demonstrates a 2 terabyte hard drive on a single 3.5-inch platter.[11] • October 26 • November 18 ## 2013 ## 2014 ## 2015 • July 29 • October 15 • AlphaGo was the first Go AI computer program developed by Google to defeat a professional human opponent on a full-sized board without handicap. ## 2016 ## 2017 ## 2019 ## References 1. ^ “Official: iPad Launching Here April 3, Pre-Orders March 12”GizmodoArchived from the original on 28 February 2014. Retrieved 4 October 2014. 2. ^ “iPad Available in US on April 3”. Apple.com. Archived from the original on 17 November 2017. Retrieved 17 November 2017. 3. ^ “iPhone 4 Release Date: New iPhone Release Set For Summer 2010”HuffPost. 7 June 2010. Archived from the original on 20 December 2016. Retrieved 17 November 2017. 4. ^ “Apple Presents iPhone 4”. Apple.com. Archived from the original on 3 September 2011. Retrieved 17 November 2017. 5. ^ Shimpi, Anand Lal (2011-05-04). “Intel Announces first 22nm 3D Tri-Gate Transistors, Shipping in 2H 2011”. AnandTech. Archived from the original on 2013-12-25. Retrieved 23 January 2014. 6. ^ “Official Google Blog: A new kind of computer: Chromebook”Official Google BlogArchived from the original on 6 October 2014. Retrieved 4 October 2014. 7. ^ Shimpi, Anand Lal (2011-09-07). “Seagate Ships World’s First 4TB External HDD”. AnandTech. Archived from the original on 2014-02-03. Retrieved 26 January 2014. 8. ^ “BBC News – The Raspberry Pi computer goes on general sale”BBC NewsArchived from the original on 14 October 2014. Retrieved 4 October 2014. 9. ^ “Raspberry Pi$35 miniature computer now on sale, $25 model going into production ‘immediately'”The Verge. 29 February 2012. Archived from the original on 6 October 2014. Retrieved 4 October 2014. 10. ^ Shimpi, Anand Lal (2012-09-11). “Intel’s Next Unit of Computing: 4″x4″, Core i3, Systems Targeted at$399”. AnandTech. Archived from the original on 2014-01-22. Retrieved 26 January 2014.
11. ^ Parrish, Kevin (2012-10-04). “TDK Finally Crams 2TB on One 3.5-inch HDD Platter”. Tom’s Hardware. Retrieved 26 January 2014.
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15. ^ “PlayStation 4 Release Date Confirmed for November 15th in North America, November 29th in Europe”. Archive.is. Archived from the original on 20 August 2013. Retrieved 4 October 2014.
16. ^ “Xbox One to Launch on November 22, 2013 in 13 Markets – Xbox Live’s Major Nelson”Xbox Live’s Major NelsonArchived from the original on 29 September 2013. Retrieved 4 October 2014.
17. ^ “PlayStation 4 Release Date Confirmed for November 15th in North America, November 29th in Europe”. Archive.is. Archived from the original on 20 August 2013. Retrieved 4 October 2014.
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19. ^ “Seagate ships first 8TB hard drive”. Techreport.com. Archived from the original on 6 October 2014. Retrieved 4 October 2014.
20. ^ “Seagate Ships World’s First 8TB Hard Drives”. Seagate.com. Archived from the original on 27 August 2014. Retrieved 4 October 2014.
21. ^ “Chromium Blog: 64 bits of awesome: 64-bit Windows Support, now in Stable!”Chromium BlogArchived from the original on 6 October 2014. Retrieved 4 October 2014.
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## References

1. ^ Newsroom, NVIDIA. “Home”NVIDIA Newsroom Newsroom.
2. ^ “Apple to Use Intel Microprocessors Beginning in 2006”. Apple. June 6, 2005.
3. ^ “Microsoft to Launch Xbox 360 November 22”pcworld.com. Retrieved 9 May 2017.
4. ^ “IBM, Georgia Tech Deep Freeze for Gigahertz | News | TechNewsWorld”www.technewsworld.com.
5. ^ Kanellos, Michael. “Chip breaks speed record in deep freeze”CNET.
6. ^ Krazit, Tom. “Intel pledges 80 cores in five years”CNET.
7. ^ “Asus Eee PC Series Announced – Laptoping”.
8. ^ “Announcing the Android 1.0 SDK, release 1”.
9. ^ “Five Years of Bitcoin in One Post”washingtonpost.com. Retrieved 9 May 2017.

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