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John McCarthy

Computer Science Department

Stanford University

Stanford, CA 94305



1999 Mar 22, 5:09 p.m.


LISP has survived for 21 years because it is an approximate lo-

cal optimum in the space of programming languages. However, it

has accumulated some barnacles that should be scraped off, and some

long-standing opportunities for improvement have been neglected. It

would benefit from some co-operative maintenance especially in cre-

ating and maintaining program libraries. Computer checked proofs

of program correctness are now possible for pure LISP and some ex-

tensions, but more theory and some smoothing of the language itself

are required before we can take full advantage of LISP’s mathematical


1999 note: This article was included in the 1980 Lisp conference

held at Stanford. Since it almost entirely corresponds to my present

opinions, I should have asked to have it reprinted in the 1998 Lisp

users conference proceedings at which I gave a talk with the same



On LISP’s approximate 21st anniversary, no doubt something could be said

about coming of age, but it seems doubtful that the normal life expectancy of

a programming language is three score and ten. In fact, LISP seems to be the

second oldest surviving programming language after Fortran, so maybe we

should plan on holding one of these newspaper interviews in which grandpa

is asked to what he attributes having lived to 100. Anyway the early history

of LISP was already covered in [McC81], reprinted from the Proceedings of

the 1977 ACM conference on the history of programming languages.

Therefore, these notes first review some of the salient features of LISP and

their relation to its long survival, noting that it has never been supported by

a computer company. LISP has a partially justified reputation of being more

based on theory than most computer languages, presumably stemming from

its functional form, its use of lambda notation and basing the interpreter on

a universal function.

From the beginning, I have wanted to develop techniques for making com-

puter checkable proofs of LISP programs, and now this is possible for a large

part of LISP. Still other present and proposed facilities are in a theoretically

more mysterious state. I will conclude with some remarks on improvements

that might be made in LISP and the prospects for replacing it by something

substantially better.

2 The Survival of LISP

As a programming language, LISP is characterized by the following ideas:

  1. Computing with symbolic expressions rather than numbers.
  2. Representation of symbolic expressions and other information by list structure in computer memory.
  3. Representation of information on paper, from keyboards and in other external media mostly by multi-level lists and sometimes by S-expressions.It has been important that any kind of data can be represented by a

    single general type.

  4. A small set of selector and constructor operations expressed as func- tions, i.e. car, cdr and cons.
  5. Composition of functions as a tool for forming more complex functions.
  6. The use of conditional expressions for getting branching into function definitions.
  7. The recursive use of conditional expressions as a sufficient tool for build- ing computable functions.
  8. The use of λ-expressions for naming functions.
  9. The storage of information on the property lists of atoms. 10. The representation of LISP programs as LISP data that can be manip-

    ulated by object programs. This has prevented the separation between

    system programmers and application programmers. Everyone can “im-

    prove” his LISP, and many of these “improvements” have developed

    into improvements to the language.

    11. The conditional expression interpretation of Boolean connectives.

    12. The LISP function eval that serves both as a formal definition of the

    language and as an interpreter.

    13. Garbage collection as the means of erasure.

    14. Minimal requirements for declarations so that LISP statements can be

    executed in an on-line environment without preliminaries.

    15. LISP statements as a command language in an on-line environment.

    Of course, the above doesn’t mention features that LISP has in common

    with most programming languages in its “program feature”.

    All these features have remained viable and the combination must be

    some kind of approximate local optimum in the space of programming lan-

    guages, because LISP has survived several attempts to replace it, some rather

    determined. It may be worthwhile to review a few of these and guess why

    they didn’t make it.

  10. SLIP included list processing in Fortran. It used bidirectional lists

    and didn’t allow recursive functions or conditional expressions. The

    bidirectional lists offered advantages in only a few applications but

    otherwise took up space and time.

    It didn’t encourage on-line use,

    since Fortran doesn’t.

  11. Formac was another Fortran based language that was pushed for a while by part of IBM. It was dedicated to manipulating a class of

    algebraic formulas written in Fortran style and was also oriented to

    batch processing.

  12. Formula Algol was dedicated to the linguistic pun that the elementary operations can be regarded as operating on numbers or on formulas.

    The idea was that if a variable x has no value, then operations on

    expressions involving x must be regarded as operating on the formula.

    A few programs could be written, but the pun proved an inadequate

    basis for substantial programs.

  13. One of the more interesting rivals to LISP is (or was) POP-2. It has everything that LISP has except that its statements are written in an

    Algol-like form and don’t have any list structure internal form. Thus

    POP-2 programs can produce other POP-2 programs only as charac-

    ter strings. This makes a much sharper distinction between system

    programmers and application programmers than in LISP. In LISP, for

    example, anyone can make his own fancy macro recognizer and ex-


  14. Microplanner is an attempt to make a higher level general purpose lan- guage than LISP. The higher level involves both data (pattern match-

    ing) and control (goal seeking and failure mechanisms). Unfortunately,

    both proved inadequately general, and programmers were forced to

    very elaborate constructions, to new languages like CONNIVER with

    even more elaborate control features, and eventually many went back

    to LISP.

    One generic trouble seems to be that no-one adequately understands

    pattern directed computation which always works very nicely on simple

    examples, but which leads to over complicated systems when general-

    ized. We can see this in LISP in certain macro expansion systems like

    that of the LISP machine [WM78].

  15. I should mention Prolog, but I don’t understand it well enough to comment. 1

    11999 note: The ideas of Prolog are similar to a subset of the ideas of Microplanner.

    However, Prolog was designed systematically and has survived, while Microplanner didn’t.


    Like most everything, LISP is subject to improvement. The various versions

    of LISP have accumulated many barnacles with time, and these would have to

    be scraped off before a definitive standardizable language could be achieved

  • a worthwhile but long term goal. Meanwhile here are a few directions for improvement. Some are purely operational and others have more conceptual


  1. Incorporating more standard functions into the language and rational- izing the standard functions in the present versions.

    Designers of programming languages often propose omitting from the

    definition of the language facilities that can be defined within the lan-

    guage on the grounds that the user can do it for himself. The result is

    often that users cannot use each other’s programs, because each instal-

    lation and user performs various common tasks in different ways. In so

    far as programmers use local libraries without rewriting the functions,

    they are using different languages if they use different local libraries.

    Compatibility between users of LISP would be much enhanced if there

    were more standard functions.

  2. Syntax directed input and output. A notation for representing symbolic information can be optimized from

    three points of view: One can try to make it easy to write. One can try

    to make it easy and pleasant to read. One can make easy to manipulate

    with computer programs. Unfortunately, these desiderata are almost

    always grossly incompatible. LISP owes most of its success to optimiz-

    ing the third. LISP lists and S-expressions in which the car of an item

    identifies its kind have proved most suitable as data for programming.

    When the amount of input and output is small, users are inclined to

    accept the inconvenience of entering the input and seeing the output as

    lists or S-expressions. Otherwise they write read and print programs

    of varying elaborateness. Input and output programs are often a large

    part of the work and a major source of bugs. Moreover, input programs

    often must detect and report errors in the syntax of input.

    The key permanent idea of Prolog is that a certain subset of logic (Horn clauses) are

    executable as programs doing backtracking search. It seems to me that this discovery has

    as much permanent importance as the ideas behind Lisp.

    LISP would be much improved by standard facilities for syntax directed

    input and output. Some years ago Lynn Quam implemented a system

    that used the same syntax description for both input and output, but

    this was rather constraining. Probably one wants different syntaxes

    for input and output, and input syntaxes should specify ways of com-

    plaining about errors. The idea is to provide standard facilities for a

    programmer to describe correspondences between data in an external

    medium and S-expressions, e.g. he should be able to say something like

    (P LU S x . . . z) → x + . . . + z,

    (DIF F EREN CE x y) → x − y,

    although I hold no brief for this particular notation.

  3. Syntax directed computation in general. It isn’t clear whether this would be a feature to be added to LISP or a

    new language. However, it seems likely that both the functional form

    of computation that LISP has now and syntax directed features are

    wanted in one language.

  4. LISP might benefit if we could find a way to finance and manage a central agency that could keep libraries, make agreed on machine in-

    dependent improvements, maintain a standard subset, and co-ordinate

    pressure on computer manufacturers to develop and maintain adequate

    LISPs on their machines. It shouldn’t get too powerful.2

    4 Proving Correctness of LISP Programs

    This can be done by taking Advantage of LISP’s Theoretical Foundation.

    As soon as pure LISP took its present form, it became apparent that

    properties of LISP functions should be provable by algebraic manipulation

    together with an appropriate form of mathematical induction. This gave rise

    to the goal of creating a mathematical theory of computation that would lead

    to computer checked proofs [McC62] that programs meet their specifications.

    Because LISP functions are functions, standard logical techniques weren’t im-

    mediately applicable, although recursion induction [McC63] quickly became

    available as an informal method. The methods of [Kle52] might have been

    21999: Only the part about standardization happened.

    adopted to proving properties of programs had anyone who understood them

    well been properly motivated and understood the connections.

    The first adequate formal method was based on Cartwright’s thesis [Car77],

    which permits a LISP function definition such as

    append[u, v] ← if null u then v

    else cons[car u, append[cdr u, v]]

    to be replaced by a first order sentence

    (∀u v)(append(u, v) = if null u then v

    else cons(car u, append(cdr u, v)))

    without first having to prove that the program terminates for any lists u and

    v. The proof of termination has exactly the same form as any other inductive

    proof. See also [CM79].

    The Elephant formalism (McCarthy 1981 forthcoming)3 supplies a second

    method appropriate for sequential LISP programs. Boyer and Moore [BM79]

    provide proof finding as well as proof checking in a different formalism that

    requires a proof that a function is total as part of the process of accepting

    its definition.

    I should say that I don’t regard the LCF methods as adequate, because

    the “logic of computable functions” is too weak to fully specify programs.

    These methods (used informally) have been succesfully taught as part of

    the LISP course at Stanford and will be described in the textbook (McCarthy

    and Talcott 1980).4 It is also quite feasible to check the proofs by machine

    using Richard Weyhrauch’s FOL interactive proof-checker for first order logic,

    but practical use requires a LISP system that integrates the proof checker

    with the interpreter and compiler.56

    31999: The 1981 ideas have been combined with other ideas, e.g. about speech acts,

    and elaborated. See [McC96]. The Elephant idea referred to was to avoid data structures

    by allowing direct reference to the past.

    41999: That textbook didn’t appear, mainly because of a difference of opinion among

    the authors about the most appropriate proof formalism

    51999: FOL was succeeded in the Lisp course by Jussi Ketonen’s EKL prover, but the

    proposed integrated system hasn’t happened.

    61999: NQTHM (aka the Boyer-Moore prover) was used by Shankar when he taught the

    course. This prover is designed to use induction to prove properties of total Lisp functions.

    Using the Eval function of the logic and the representation of function definitions as

    Sexpressions properties of partial functions can also be proved. NQTHM has evolved

    The ultimate goal of computer proof-checking is a system that will be used

    by people without mathematical inclination simply because it leads more

    quickly to programs without bugs. This requires further advances that will

    make possible shorter proofs and also progress in writing the specifications

    of programs.

    Probably some parts of the specifications such as that the program termi-

    nates are almost syntactic in their checkability. However, the specifications

    of programs used in AI work require new ideas even to formulate. I think

    that recent work in non-monotonic reasoning will be relevant here, because

    the fact that an AI program works requires jumping to conclusions about the

    world in which it operates.

    While pure LISP and the simple form of the “program feature” are readily

    formalized, many of the fancier features of the operational LISP systems such

    as Interlisp, Maclisp and Lisp Machine LISP [WM78] are harder to formalize.

    Some of them like FEXPRs require more mathematical research, but others

    seem to me to be kludges and should be made more mathematically neat

    both so that properties of programs that use them can be readily proved and

    also to reduce ordinary bugs.

    The following features of present LISP systems and proposed extensions

    require new methods for correctness proofs:

  5. Programs that involve re-entrant list structure. Those that don’t in- volve rplaca and rplacd such as search and print programs are more

    accessible than those that do.

    I have an induction method on finite

    graphs that applies to them, but I don’t yet know how to treat rplaca,

    etc. Induction on finite graphs also has applications to proving theo-

    rems about flowchart programs.7

  6. No systematic methods are known for formally stating and proving properties of syntax directed computations.8
  7. Programs that use macro expansions are in principle doable via ax- iomatizations of the interpreter, but I don’t know of any actual formal

    into ACL2 which supports a large applicative subset of Common Lisp and is programmed

    almost entirely within that subset. [see http://www.cs.utexas.edu/users/moore/acl2/acl2-


    71999: Ian Mason’s thesis[Mas86] gave some principles for reasoning about first-order

    Lisp including rplacx.

    81999: Maybe this is still the case.



  8. No techniques exist for correctness proofs of programs involving lazy
  9. Programs with functional arguments are in principle accessible by Dana Scott’s methods, but the different kinds of functional arguments have

    been treated only descriptively and informally.9

  10. Probably the greatest obstacle to making proof-checking a useful tool is our lack of knowledge of how to express the specifications of programs.

    Many programs have useful partial specifications - they shouldn’t loop

    or modify storage that doesn’t belong to them. A few satisfy algebraic

    relations, and this includes compilers. However, programs that interact

    with the world have specifications that involve assumptions about the

    world. AI programs in general are difficult to specify; most likely their

    very specification involves default and other non-monotonic reasoning.

    (See [McC80].)

    5 Mysteries and other Matters

  11. Daniel Friedman and David Wise have argued that cons should not evaluate its arguments and have shown that this allows certain infinite

    list structures to be regarded as objects. Trouble is avoided, because

    only as much of the infinite structure is created as is necessary to get the

    answers to be printed. Exactly what domain of infinite list structures

    is assumed is unclear to me. While they give interesting examples of

    applications, it isn’t clear whether the proposed extension has practical


  12. Many people have proposed implementations of full lambda calculus. This permits higher level functions, i.e. functions of functions of func-

    tions etc., but allows only manipulations based on composition and

    lambda conversions, not general manipulations of the symbolic form of

    91999: A logic for reasoning about Lisp-Scheme-ML like programs with functions and

    mutable data structures has been developed by Mason and Talcott [HMST95]. This logic

    has a relatively complete axiomatization of primitives for mutable data as well as a variety

    of induction principles and methods for proving properties of programs.

    functions. While conditional expressions are not directly provided, they

    can be imitated by writing (as proposed by Dana Scott in an unpub-

    lished note) true as (λx y.x), false as (λx y.y) and if p then a else b

    as p(a)(b). Another neat idea of Scott’s (improved from one of Church)

    is to identify the natural number n with the operation of taking the

    (n+1)th element of a list. The mystery is whether extension to lambda

    calculus has any practical significance, and the current best guess is no,

    although the Scott’s notational idea suggests changing the notation of

    LISP and writing 0 for car, 1 for cadr, 2 for caddr, etc.

  13. Pure LISP would be much simpler conceptually if all list structure were represented uniquely in memory. This can be done using a hash cons,

    but then rplaca and friends don’t work. Can’t we somehow have the

    best of both worlds?

  14. It seems to me that LISP will probably be superseded for many pur- poses by a language that does to LISP what LISP does to machine lan-

    guage. Namely it will be a higher level language than LISP that, like

    LISP and machine language, can refer to its own programs. (However,

    a higher level language than LISP might have such a large declarative

    component that its texts may not correspond to programs. If what re-

    places the interpreter is smart enough, then the text written by a user

    will be more like a declarative description of the facts about a goal and

    the means available for attaining it than a program per se).10

    An immediate problem is that both the kinds of abstract syntax presentlyavailable and present pattern matching systems are awkward for ma-

    nipulating expressions containing bound variables.

    6 References

    Lisp was first described in [McC60] and the first manual was [ML+66] the

    first version of which appeared in 1962.11

    101999: An example is Maude [Gro99, CDE+98, Wil97], a language based on Rewriting

    Logic. In Maude, actions and effects are expressed in a declarative manner, and using

    the reflective capability, Maude programs and computations can be represented, reasoned

    about, modified and executed in Maude.

    111999: I thank Carolyn Talcott for additonal references.




    Robert Boyer and J. Strother Moore. A Computational Logic.

    Academic Press, 1979.

    Robert S. Cartwright. A practical formal semantic definition and

    verification system for typed lisp. Phd dissertation, stanford uni-

    versity, 1977.

    [CDE+98] M. Clavel, F. Dur´an, S. Eker, P. Lincoln, N. Marti-Oliet, and

    J. Meseguer. Metalevel Computation in Maude.

    In C. Kirch-

    ner and H. Kirchner, editors, 2nd International Workshop on

    Rewriting Logic and its Applications, WRLA’98, volume 15 of

    Electronic Notes in Theoretical Computer Science, 1998. URL:



    Robert Cartwright and John McCarthy. Recursive programs as

    functions in a first order theory. In Proceedings of the Interna-

    tional Conference on Mathematical Studies of Information Pro-

    cessing, Kyoto, Japan, 1979.


    The Maude Group.


    The Maude system,



    [HMST95] F. Honsell, I. A. Mason, S. F. Smith, and C. L. Talcott. A Variable

    Typed Logic of Effects. Information and Computation, 119(1):55–

    90, 1995.



    Stephen C. Kleene. Introduction to Metamathematics. Van Nos-

    trand, 1952.

    I. A. Mason. The Semantics of Destructive Lisp. PhD thesis,

    Stanford University, 1986. Also available as CSLI Lecture Notes

    No. 5, Center for the Study of Language and Information, Stan-

    ford University.


    J. McCarthy. Recursive functions of symbolic expressions and

    their computation by machine, part 1. Comm. A.C.M., 3:184–

    195, 1960.







    John McCarthy. Checking mathematical proofs by computer.

    In Proceedings Symposium on Recursive Function Theory (1961).

    American Mathematical Society, 1962.

    John McCarthy. A Basis for a Mathematical Theory of Com-

    putation12. In P. Braffort and D. Hirschberg, editors, Computer

    Programming and Formal Systems, pages 33–70. North-Holland,

    Amsterdam, 1963.

    John McCarthy. Circumscription—A Form of Non-Monotonic

    Reasoning13. Artificial Intelligence, 13:27–39, 1980. Reprinted in


    John McCarthy. History of lisp. In Richard L. Wexelblat, ed-

    itor, History of programming languages. Academic Press, 1981.

    Reprinted from Proceedings of the ACM Conference on the His-

    tory of Programming Languages, Los Angeles, 1977.

    John McCarthy. Formalizing Common Sense: Papers by John

    McCarthy. Ablex Publishing Corporation, 355 Chestnut Street,

    Norwood, NJ 07648, 1990.

    John McCarthy. elephant 200014. Technical report, Stanford

    Formal Reasoning Group, 1996. Available only as http://www-



    John McCarthy, Michael Levin, et al. LISP 1.5 Programmer’s

    Manual. MIT, 1966.

    [Wil97] Wilson97. Cars and their enemies. Commentary, pages 17–23,

    July 1997.

    [WM78] Daniel Weinreb and David Moon. Lisp machine manual. Techni-

    cal report, M.I.T. Artificial Intelligence Laboratory, 1978.

    /@steam.stanford.edu:/u/ftp/jmc/lisp20th.tex: begun Mon Feb 1 17:36:27 1999, latexed March 22, 1999 at 5:09 p.m.