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:

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.

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