Question

1b. Explain each of the following with an example in two languages of your choice for each item. (25 points)

• Orthogonality

• Generality

• Uniformity

Answer 1

Orthogonality:

• In geometry, orthogonal means "involving right angles", but the term has been extended to general use, meaning the property of being independent (relative to something else)
• Language constructs should not behave differently in different contexts.
• The language constructs can be combined in a meaningful way.
• The interactions of constructs, or the context of use, should not cause unexpected restrictions or behavior.
• There should be no strange interactions!

In the context of a programming language, a set of features/constructs is said to be orthogonal if those features can be used freely in combination with each other. In particular, the degree of orthogonality is lessened if

• particular combinations are forbidden (as exceptional cases) or
• the meaning of a particular combination is not evident from the meanings of its component parts, each one considered without regard to context.

Examples of non-orthogonality :

• C passes all parameters by value, except arrays, which are passed by reference.
• In Java, primitive data types are passed by value, the rest by reference, yet they look the same! (This is also non-uniformity)
• In Java, assigning objects is an assignment of references, while assigning primitive data types is done by value.
• In C and C++, values of all data types, except array types, can be returned from a function.
• In C, local variables must be defined at the beginning of a block, in C++ variable definitions can occur anywhere inside a block, but before use of course.

Example from assembly languages:

• In VAX assembler, the instruction for 32-bit integer addition is of the form

ADDL op₁ op₂

where each of the op_i's can refer to either a register or a memory location. This is nicely orthogonal.

• In contrast, in the assembly languages for IBM mainframes, there are two separate analogous ADD instructions, one of which requires op₁ to refer to a register and op₂ to refer to a memory location, the other of which requires both to refer to registers. This is lacking in orthogonality.

Generality:

• Avoiding special cases in the availability or use of constructs.
• Combining closely related constructs into a single more general one.
• Too much generality is bad!

Examples of Lack of Generality:

• C lacks nested function definitions.
• Pascal has no variable-length arrays, arrays lack generality.
• In C, two structures or arrays cannot be directly compared using the equality (==) operator, but must be compared element by element. Ada on the other hand allows totally new operators to be defined. C++ can overload operators.
• In Pascal, constants may not be expressions, opposite to Ada.
• Java does not have multiple inheritance, but interface inheritance implementation is a good enough substitute.

Uniformity:

• Similar things should look similar and have similar meanings
• Inversely, different things should look different i.e. consistency of appearance and behavior.
• Non-uniformity and non-orthogonality may be very closely related in some instances.

Examples of lack of uniformity:

• In C++, a semicolon is necessary after a class definition but forbidden after a function definition.  class A { … }; int f() { … }
• This non-uniformity was forced to allow C++ to be compatible with C.
• Returned values from functions in Pascal look like assignments

function f : boolean;

begin

…

f :=true;

end;