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From: Florian Weimer <fw@deneb.enyo.de>
Newsgroups: comp.lang.ada
Subject: Re: Side-Effects in Functions [Rosen Trick]
Date: Tue, 06 Nov 2001 21:08:10 +0100
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Date: 2001-11-06T21:08:10+01:00
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"Nick Roberts" <nickroberts@adaos.worldonline.co.uk> writes:

> From a pedagogical point of view, care needs to be taken not to give the
> impression that a function in a procedural programming language (most
> programming languages, really) is the same thing as a mathematical function.
> Clearly it isn't: a mathematical function is a kind of relation called a
> 'bijection' (and is nowadays specifically defined as such, I think);

A function f : M -> N are two sets M, N and a subset G_f of the
Cartesian product M x N with the following property: for all m in M,
there exists exactly one n in N such that (m, n) in G_f.

> a programming function is really just an encapsulated computation.

Yes, such functions take an additional implicit argument (the machine
state before execution) and have an invisible result (the machine
state after execution).

However, there are programming languages which use only mathematical
functions, and a special construct for I/O, Haskell for example.