What is “Orthogonality”?

Question

What does \"orthogonality\" mean when talking about programming languages?

What are some examples of Orthogonality?

Answer 1

If you have a set of constructs. A langauge is said to be orthogonal if it allows the programmer to mix these constructs freely. For example, in C you can't return an array(static array), C is said to be unorthognal in this case:

int[] fun(); // you can't return a static array.
// Of course you can return a pointer, but the langauge allows passing arrays.
// So, it is unorthognal in case.

Answer 2

From Wikipedia:

Orthogonality is a system design property facilitating feasibility and compactness of complex designs. Orthogonality guarantees that modifying the technical effect produced by a component of a system neither creates nor propagates side effects to other components of the system. The emergent behavior of a system consisting of components should be controlled strictly by formal definitions of its logic and not by side effects resulting from poor integration, i.e. non-orthogonal design of modules and interfaces. Orthogonality reduces testing and development time because it is easier to verify designs that neither cause side effects nor depend on them.

For example, a car has orthogonal components and controls (e.g. accelerating the vehicle does not influence anything else but the components involved exclusively with the acceleration function). On the other hand, a non-orthogonal design might have its steering influence its braking (e.g. electronic stability control), or its speed tweak its suspension.[1] Consequently, this usage is seen to be derived from the use of orthogonal in mathematics: One may project a vector onto a subspace by projecting it onto each member of a set of basis vectors separately and adding the projections if and only if the basis vectors are mutually orthogonal.

An instruction set is said to be orthogonal if any instruction can use any register in any addressing mode. This terminology results from considering an instruction as a vector whose components are the instruction fields. One field identifies the registers to be operated upon, and another specifies the addressing mode. An orthogonal instruction set uniquely encodes all combinations of registers and addressing modes.

To put it in the simplest terms possible, two things are orthogonal if changing one has no effect upon the other.

Answer 3

Real life examples of orthogonality in programming languages

There are a lot of answers already that explain what orthogonality generally is while specifying some made up examples. E.g. this answer explains it well. I wanted to provide (and gather) some real life examples of orthogonal or non-orthogonal features in programming languages:

Orthogonal: C++20 Modules and Namespaces

On the cppreference-page about the new Modules system in c++20 is written:

Modules are orthogonal to namespaces

In this case they write that modules are orthogonal to namespaces because a statement like import foo will not import the module-namespace related to foo:

import foo;            // foo exports foo::bar()
bar ();                // Error
foo::bar ();           // Ok
using namespace foo;
bar ();                // Ok

(adapted from modules-cppcon2017 slide 9)

Answer 4

Broadly, orthogonality is a relationship between two things such that they have minimal effect on each other.

The term comes from mathematics, where two vectors are orthogonal if they intersect at right angles.

Think about a typical 2 dimensional cartesian space (you typical grid with X/Y axes). Plot two lines: x=1 and y=1. The two lines are orthogonal. You can change x=1 by changing x, and this will have no effect on the other line, and vice versa.

In software, the term can be appropriately used in situations where you're talking about two parts of a system which behave independently of each other.

Answer 5

The basic idea of orthogonality is that things that are not related conceptually should not be related in the system. Parts of the architecture that really have nothing to do with the other, such as the database and the UI, should not need to be changed together. A change to one should not cause a change to the other.

Answer 6

From Robert W. Sebesta's "Concepts of Programming Languages":

As examples of the lack of orthogonality in a high-level language, consider the following rules and exceptions in C. Although C has two kinds of structured data types, arrays and records (structs), records can be returned from functions but arrays cannot. A member of a structure can be any data type except void or a structure of the same type. An array element can be any data type except void or a function. Parameters are passed by value, unless they are arrays, in which case they are, in effect, passed by reference (because the appearance of an array name without a subscript in a C program is interpreted to be the address of the array’s first element)