Pure

(In contrast to applied, when distinguishing between applied and pure mathematics; the latter being divorced from the real world.)

In mathematics, functions are pure - they merely associate each possible input value with an output value, and nothing more. In Haskell, most functions uphold this principle. As a result, they usually are referentially transparent - each of them does not depend on anything other than its parameters, so when invoked in a different context or at a different time with the same arguments, it will produce the same result. In comparison, procedures or subroutines are more complicated - for example, they could also:

• read from or write to global variables,
• send data to a file,
• or print to a screen.

A programming language may sometimes be known as purely functional if:

• it only permits programs to be defined in terms of pure definitions,
• and functions are its primary means of abstraction.

However there has been some debate in the past as to the precise meaning of these terms - see also:

• What is a Purely Functional Language? a 1993 paper which presents a proposed formal definition of the concept,
• The C language is purely functional (some satire intended),
• Is Haskell a purely functional language?
• Purity vs Referential transparency, Stack Overflow.