Pure: Difference between revisions

Revision as of 04:16, 12 April 2024

(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. This is in contrast to procedures or subroutines that, for example, 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.

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-A function is called '''pure''' if it corresponds to a function in the mathematical sense: it associates each possible input value with an output value, and does nothing else. In particular,
+(In contrast to <i>applied</i>, when distinguishing between applied and [https://web.archive.org/web/20221204080950/https://www.maynoothuniversity.ie/mathematics-and-statistics/undergraduate-studies/why-do-research-pure-mathematics pure mathematics]; the latter being <q>divorced from the real world</q>.)
-* it has no ''side effects'', that is to say, invoking it produces no observable effect other than the result it returns; it cannot also ''e.g.'' write to disk, or print to a screen.
+In mathematics, functions are <b>pure</b> - 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 [[Referential transparency|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. This is in contrast to <i>procedures</i> or <i>subroutines</i> that, for example, could also:
-A pure function is trivially [[Referential transparency|referentially transparent]] - it 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.
+* read from or write to [[Global variables|global variables]],
+* send data to a file,
+* or print to a screen.
-A programming language may be called '''purely functional''' if evaluation of expressions is pure.
+A programming language may sometimes be known as <i>purely functional</i> if:
-There has been some debate in the past as to the precise meaning of these terms. See also:
+* 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:
 * [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.7800 What is a Purely Functional Language?] a 1993 paper which presents a proposed formal definition of the concept,