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From: Julieta Shem <jshem@yaxenu.org>
Newsgroups: comp.lang.lisp
Subject: Re: Lisp history: IF, etc.
Date: Wed, 03 Apr 2024 20:30:14 -0300
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Alan Bawden <alan@csail.mit.edu> writes:

> Kaz Kylheku <643-408-1753@kylheku.com> writes:
>
>    On 2024-04-03, Alan Bawden <alan@csail.mit.edu> wrote:
>    > Lisp doesn't really have statements _because_ McCarthy invented the
>    > conditional expression.  That's kind of the point.  Other programming
>    > languages at the time (e.g. FORTRAN and ALGOL) only had conditional
>    > statements.  McCarthy invented the conditional expression and thus
>    > created the first expression-only programming language.
>
>    However, conditional expressions ultimately come from math. E.g for
>    specifying a discontinuous function:
>
>       f(x) = { x, if x >= 0
>              { 0, if x < 0
>
>    If you think about it, it's actually kind of ignorant to invent a
>    programming language with imperative if statements, but in which where
>    the math conditional is missing.
>
> If you think like a historian, you don't describe this as "ignorant".
> It's just not something that was above the horizon in the mind set of
> the time.  After all, that mathematical notation you are referring to
> isn't something that mathematicians get very formal about.

So true.

> It has a status that's midway between being able to define something
> using a simple equation, and having to resort to a definition in the
> form of a paragraph of words.  Realizing that you could tighten that
> notation up and use it in a programming language _as a kind of
> expression_ is actually a bit of a leap.

There's a paper from 1961--1963 in which he defines the conditional
expression with the intention of being able to define functions
recursively.

--8<---------------cut here---------------start------------->8---
  A BASIS FOR A MATHEMATICAL THEORY OF COMPUTATION
  JOHN McCARTHY
  1961--1963

  [This 1963 paper was included in Computer Programming and Formal Sys-
  tems, edited by P. Braffort and D. Hirshberg and published by
  North-Holland.  An earlier version was published in 1961 in the
  Proceedings of the Western Joint Computer Conference.]

  [...]

  The present paper is an attempt to create a basis for a mathematical
  theory of computation.  [...]

  [...]

  2.1 Functions Computable in Terms of Given Base Functions

  Suppose we are given a base collection F of functions (including
  predicates) having certain domains and ranges. [...] Our object is to
  define a class of functions C{F} which we shall call the class of
  functions computable in terms of F.  Before developing C{F} formally,
  we wish to give an example, and in order to give the example, we first
  need the concept of conditional expression. In our notation a
  conditional expression has the form

                  (p1 → e1, p2 → e2, . . . , pn → en)

  which corresponds to the ALGOL 60 reference language (12) expression

       if p1 then e1 else if p2 then e2 . . . else if pn then en.

  [...]

  Some examples of the conditional expressions for well known functions
  are |x| = (x < 0 → -x, x >= 0 → x) [...]

  Now we are ready to use conditional expressions to define functions
  recursively. For example, we have 

                 n! = (n = 0 → 1, n =/= 0 → n · (n − 1)!)

  [...]
--8<---------------cut here---------------end--------------->8---