In computer programming, M-expressions (or meta-expressions) were intended to be the expressions used to write functions in the Lisp programming language. Data to be manipulated using M-expressions was to be written using S-expressions. M-expressions were used for the original theoretical language in early papers about Lisp, but the first working implementation of Lisp interpreted encodings of M-expressions as S-expressions, and M-expressions were never actually implemented.

Historical relation to S-expressions

An S-expression represents data made up of atoms and pairs. As originally described, an atom was a symbol written in upper case, and a pair was delimited by parentheses. Shorthand list notation was described, though it originally separated list elements by commas rather than whitespace

Whitespace (computer science)

In computer science, whitespace is any single character or series of characters that represents horizontal or vertical space in typography. When rendered, a whitespace character does not correspond to a visual mark, but typically does occupy an area on a page...

. For example (using spaces rather than commas):

((A B) (C D) (E F))

which represents a list of three elements, each of which is a list of two symbols.

An M-expression could also use operator names, meta-variables, and argument lists. Operator names and meta-variable names were in lower case, to show that they were not symbols (i.e., not data). Argument lists were delimited by brackets, [], and their elements were separated by semicolons. For example:

car[cons[(A . B); x]]

which represents a two-part operation. The first part constructs a pair from the data structure (A . B) and whatever data is represented by the meta-variable called x. The second part extracts the first element of the constructed pair.

In McCarthy's original published paper on Lisp, as a demonstration of the theoretical universality of the language, he described a function eval, which would take as input an S-expression encoding of an M-expression, and execute the M-expression program encoded by that S-expression. Here are a few examples of M-expressions and their encodings as S-expressions (again using the modern list notation):

(A B C) (QUOTE (A B C))
car[x] (CAR X)
car[append[(A B C); (D E F)]] (CAR (APPEND (QUOTE (A B C)) (QUOTE (D E F))))

The initial implementation of Lisp was expected to be a very long process, as compilers at the time were expected to take years to write. Implementation began with hand-compiling particular functions while the M-expression sublanguage was still tentative. However, Stephen B. Russell

Steve Russell

Steve "Slug" Russell is a programmer and computer scientist most famous for creating Spacewar!, one of the earliest videogames, in 1961 with the fellow members of the Tech Model Railroad Club at MIT working on a DEC Digital PDP-1...

 and Daniel J. Edwards realized that an implementation of eval would be in effect a full implementation of S-expression-encoded Lisp as an interpreter. He hand-compiled function eval — a very easy task, compared to the anticipated huge many-year compiler construction — and a community of S-expression Lisp programmers quickly developed. M-expressions fell into neglect, and were never implemented.

Later use of M-expressions

While it is not uncommon for Lisp programmers to devise an alternate form for the language (of which MLISP

MLisp

MLISP is a variant of Lisp with an Algol-like syntax based on M-Expressions, which were the function syntax in the original description of Lisp by John McCarthy. McCarthy's M-expressions were never implemented....

 is one example), some of which use M-expressions, such dialects generally lack the homoiconicity

Homoiconicity

In computer programming, homoiconicity is a property of some programming languages, in which the primary representation of programs is also a data structure in a primitive type of the language itself, from the Greek words homo meaning the same and icon meaning representation...

 of S-expressions, which is considered an important part of the expressiveness of the language. As a result, virtually all mainstream Lisp dialects retain S-expressions as the main (or sole) syntax. Exceptions to this include Logo

Logo (programming language)

Logo is a multi-paradigm computer programming language used in education. It is an adaptation and dialect of the Lisp language; some have called it Lisp without the parentheses. It was originally conceived and written as functional programming language, and drove a mechanical turtle as an output...

, which could be considered (loosely) to be an M-expression Lisp. Several other languages, such as Dylan and Ruby

Ruby (programming language)

Ruby is a dynamic, reflective, general-purpose object-oriented programming language that combines syntax inspired by Perl with Smalltalk-like features. Ruby originated in Japan during the mid-1990s and was first developed and designed by Yukihiro "Matz" Matsumoto...

, borrow heavily from Lisp, but use an ALGOL

ALGOL

ALGOL is a family of imperative computer programming languages originally developed in the mid 1950s which greatly influenced many other languages and became the de facto way algorithms were described in textbooks and academic works for almost the next 30 years...

-like syntax that differs from both S-expressions and M-expressions.

There is also an implementation of a interpreter for M-LISP in Common Lisp

Common Lisp

Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard document ANSI INCITS 226-1994 , . From the ANSI Common Lisp standard the Common Lisp HyperSpec has been derived for use with web browsers...

, which evaluates M-Expressions.

Variants

The syntax of ML (Metalanguage), a functional programming language, provides somewhat similar syntax, as it is derived from math notation as well. However, additional concepts such as type annotations and regular expressions hide this similarity. The Mathematica

Mathematica

Mathematica is a computational software program used in scientific, engineering, and mathematical fields and other areas of technical computing...

 language uses a syntax similar to the original M-expression syntax, where lists can be written using braces (which can also be written using M-expression notation), and functions using M-expressions.

A more recent variant is I-expressions, which use indentation

Off-side rule

A computer programming language is said to adhere to the off-side rule if the scope of declarations in that language is expressed by their indentation. The term and the idea are attributed to Peter J. Landin, and the term can be seen as a pun on the offside law of football .- Definition :Peter J...

 to indicate parentheses implicitly, and are thus in some ways intermediate between S-expressions and M-expressions. I-expressions were introduced in Scheme Request For Implementation

Scheme Requests for Implementation

Scheme Requests for Implementation is an effort to coordinate libraries and extensions of standard Scheme, necessitated by Scheme's minimalistic design, and particularly the lack of a standard library prior to R6RS...

 49 as an auxiliary syntax for Scheme, but they have not been widely adopted.

External links

• Scheme Request For Implementation 49