What is “Orthogonality”?

Question

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

What are some examples of Orthogonality?

Answer 1

Check orthogonality of matrices:

Orthogonality can also be with respect to matrices,

Matrix *(transpose of matrix)= identity matrix. 

Click the below link to view a YouTube video on Orthogonality.
https://youtu.be/tNekLaxnfW8

Answer 2

Most of the answers are very long-winded, and even obscure. The point is: if a tool is orthogonal, it can be added, replaced, or removed, in favor of better tools, without screwing everything else up.

It's the difference between a carpenter having a hammer and a saw, which can be used for hammering or sawing, or having some new-fangled hammer/saw combo, which is designed to saw wood, then hammer it together. Either will work for sawing and then hammering together, but if you get some task that requires sawing, but not hammering, then only the orthogonal tools will work. Likewise, if you need to screw instead of hammering, you won't need to throw away your saw, if it's orthogonal (not mixed up with) your hammer.

The classic example is unix command line tools: you have one tool for getting the contents of a disk (dd), another for filtering lines from the file (grep), another for writing those lines to a file (cat), etc. These can all be mixed and matched at will.

Answer 3

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 4

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 5

Orthogonality in a programming language means that a relatively small set of primitive constructs can be combined in a relatively small number of ways to build the control and data structures of the language. Furthermore, every pos- sible combination of primitives is legal and meaningful. For example, consider data types. Suppose a language has four primitive data types (integer, float, double, and character) and two type operators (array and pointer). If the two type operators can be applied to themselves and the four primitive data types, a large number of data structures can be defined. The meaning of an orthogonal language feature is independent of the context of its appearance in a program. (the word orthogonal comes from the mathematical concept of orthogonal vectors, which are independent of each other.) Orthogonality follows from a symmetry of relationships among primi- tives. A lack of orthogonality leads to exceptions to the rules of the language. For example, in a programming language that supports pointers, it should be possible to define a pointer to point to any specific type defined in the language. However, if pointers are not allowed to point to arrays, many potentially useful user-defined data structures cannot be defined. We can illustrate the use of orthogonality as a design concept by compar- ing one aspect of the assembly languages of the IBM mainframe computers and the VAX series of minicomputers. We consider a single simple situation: adding two 32-bit integer values that reside in either memory or registers and replacing one of the two values with the sum. The IBM mainframes have two instructions for this purpose, which have the forms

A Reg1, memory_cell
AR Reg1, Reg2

where Reg1 and Reg2 represent registers. The semantics of these are

Reg1 ← contents(Reg1) + contents(memory_cell)
Reg1 ← contents(Reg1) + contents(Reg2)

The VAX addition instruction for 32-bit integer values is

ADDL operand_1, operand_2

whose semantics is

operand_2 ← contents(operand_1) + contents(operand_2)

In this case, either operand can be a register or a memory cell. The VAX instruction design is orthogonal in that a single instruction can use either registers or memory cells as the operands. There are two ways to specify operands, which can be combined in all possible ways. The IBM design is not orthogonal. Only two out of four operand combinations possibilities are legal, and the two require different instructions, A and AR . The IBM design is more restricted and therefore less writable. For example, you cannot add two values and store the sum in a memory location. Furthermore, the IBM design is more difficult to learn because of the restrictions and the additional instruction. Orthogonality is closely related to simplicity: The more orthogonal the design of a language, the fewer exceptions the language rules require. Fewer exceptions mean a higher degree of regularity in the design, which makes the language easier to learn, read, and understand. Anyone who has learned a sig- nificant part of the English language can testify to the difficulty of learning its many rule exceptions (for example, i before e except after c).

Answer 6

While talking about project decisions on programming languages, orthogonality may be seen as how easy is for you to predict other things about that language for what you've seen in the past.

For instance, in one language you can have:

str.split

for splitting a string and

len(str)

for getting the lenght.

On a language more orthogonal, you would always use str.x or x(str).

When you would clone an object or do anything else, you would know whether to use

clone(obj)

or

obj.clone

That's one of the main points on programming languages being orthogonal. That avoids you to consult the manual or ask someone.

The wikipedia article talks more about orthogonality on complex designs or low level languages. As someone suggested above on a comment, the Sebesta book talks cleanly about orthogonality.

If I would use only one sentence, I would say that a programming language is orthogonal when its unknown parts act as expected based on what you've seen. Or... no surprises.

;)