What is “Orthogonality”?

Question

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

What are some examples of Orthogonality?

Answer 1

From Eric S. Raymond's "Art of UNIX programming"

Orthogonality is one of the most important properties that can help make even complex designs compact. In a purely orthogonal design, operations do not have side effects; each action (whether it's an API call, a macro invocation, or a language operation) changes just one thing without affecting others. There is one and only one way to change each property of whatever system you are controlling.

Answer 2

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)

Answer 3

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 4

Orthogonality means the degree to which language consists of a set of independent primitive constructs that can be combined as necessary to express a program. Features are orthogonal if there are no restrictions on how they may be combined

Example : non-orthogonality

PASCAL: functions can't return structured types. Functional Languages are highly orthogonal.

Answer 5

from wikipedia:

Computer science

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.

Answer 6

Orthogonality in Programming:

Orthogonality is an important concept, addressing how a relatively small number of components can be combined in a relatively small number of ways to get the desired results. It is associated with simplicity; the more orthogonal the design, the fewer exceptions. This makes it easier to learn, read and write programs in a programming language. The meaning of an orthogonal feature is independent of context; the key parameters are symmetry and consistency (for example, a pointer is an orthogonal concept).

from Wikipedia