Editing M-expression (section)

==Background==
[[John McCarthy (computer scientist)|John McCarthy]] published the first paper on Lisp in 1960 while a research fellow at the [[Massachusetts Institute of Technology]]. In it he described a language of symbolic expressions ([[S-expression]]s) that could represent complex structures as lists. Then he defined a set of primitive operations on the S-expressions, and a language of meta-expressions (M-expressions) that could be used to define more complex operations. Finally, he showed how the meta-language itself could be represented with S-expressions, resulting in a system that was potentially [[Self-hosting (compilers)|self-hosting]].<ref name="lisp1960">McCarthy, John (April 1960) "Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I"</ref> The draft version of this paper is known as "AI Memo 8".<ref>{{cite web |last1=McCarthy |first1=John |title=Recursive Functions of Symbolic Expressions and Their Computation by Machine (AI Memo 8) |url=https://www.informatimago.com/develop/lisp/com/informatimago/small-cl-pgms/aim-8/index.html |date=March 1959 |url-status=dead |archive-url=https://web.archive.org/web/20210307145003/https://www.informatimago.com/develop/lisp/com/informatimago/small-cl-pgms/aim-8/index.html |archive-date=7 March 2021 }}</ref>

{| class="wikitable"
|+ Example M-expressions (LISP 1.5, 1965)<ref name=LISP15/>
! Expression type
! Mathematical notation
! M-expression
! Modern Lisp S-expression
|-
| List value
| <math>(1, 2, 3)</math>
| {{code|(1, 2, 3)}}
| {{code|2=lisp|(quote (1 2 3))}}
|-
| Function application
| <math>f(x, y)</math>
| {{code|f[x;y]}}
| {{code|2=lisp|(f x y)}}
|-
| Function definition
| <math>\mathrm{square}: x \mapsto x \cdot x</math>
| {{code|1=label[square;λ[[x];times[x;x]]]}}
| {{code|2=lisp|(define square (lambda (x) (* x x)))}}
|-
| Conditional expression
| <math>\begin{cases}
  -x, & \text{if } x < 0 \\
  x,  & \text{otherwise} 
\end{cases}
</math>
| {{code|[lessp[x;0] → minus[x]; T → x]}}
| {{code|2=lisp|(cond ((< x 0) (- x)) (t x))}}
|}

McCarthy had planned to develop an automatic Lisp compiler ([[LISP 2]]) using M-expressions as the language syntax and S-expressions to describe the compiler's internal processes. [[Steve Russell (computer scientist)|Stephen B. Russell]] read the paper and suggested to him that S-expressions were a more convenient syntax. Although McCarthy disapproved of the idea, Russell and colleague Daniel J. Edwards hand-coded an [[Interpreter (computing)|interpreter]] program that could execute S-expressions.<ref name=LISP15>{{cite web |url=http://community.computerhistory.org/scc/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf |date=1965|title=LISP 1.5 Programmer's Manual |publisher=Community.computerhistory.org |access-date=2013-09-02 |url-status=dead |archive-url=https://web.archive.org/web/20060211020233/http://community.computerhistory.org/scc/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf |archive-date=2006-02-11 }}</ref> This program was adopted by McCarthy's research group, establishing S-expressions as the dominant form of Lisp.

McCarthy reflected on the fate of M-expressions in 1979:

{{quote|The project of defining M-expressions precisely and compiling them or at least translating them into S-expressions was neither finalized nor explicitly abandoned. It just receded into the indefinite future, and a new generation of programmers appeared who preferred internal notation to any FORTRAN-like or ALGOL-like notation that could be devised.<ref>{{cite web|url=http://www-formal.stanford.edu/jmc/history/lisp/node3.html |title=The implementation of LISP |publisher=Formal.stanford.edu |date=1979-02-12 |access-date=2013-08-24}}</ref>|''[http://www-formal.stanford.edu/jmc/history/lisp/lisp.html History of Lisp]''}}

The book ''Anatomy of LISP'' by John Allen explains the definition of M-expressions and uses them throughout the book to explain Lisp and its implementation.<ref name=AOL>{{cite web |url=https://dl.acm.org/doi/10.5555/542865 |date=1978|title=Anatomy of LISP |publisher=McGraw-Hill, Inc.}}</ref>