A MICRO-MANUAL FOR LISP - NOT THE WHOLE T R U T H
John McCarthy
Artificial Intelligence Laboratory
Stanford University

L I S P data are symbolic expressions that can be either atoms
ol lists. Atoms are s~tittgs of letters and digits and other characters

10. Here's the hard one. value ((LABEL f (LAMBDA (o I ...
e)) e I . . . en) is the same as value ((LAMBDA (v I ... vn) e) e I
e n) with the additional rule that whenever ~¢al
an) must
evaluated, f is replaced by (LABEL/" (LAMBDA (v I ... vn)
Lists b e g i n n i n g with L A B E L define functions recursively.

not otherwise used in LISP. A list consists of a left parenthesis
followed by zero or more atoms or lists separated by spaces and
e n d i n g with a right parenthesis. Examples: A, ONION, 0, (A), (A
O N I O N A), ( P L U S B (TIMES X PI) i), (CAR ( Q U O T E CA B))).

v,)
...
be
e)).

T h i s is the core of LISP, and here are more examples:

T h e LISP programming language is defined by rules
w h e r e b y certain LISP expressions have other LISP expressions as
values. T h e function called value that we will use in giving these
rules is not part of the LISP language but rather part of the
informal m3tbematical language u;ed to define LISP. Likewise,
the italic letters • and a (sometimes with subscripts) denote LISP
expressions, the letter v (usually subscripted) denotes an atom
s e r v i n g as a variable, and the letter f stands for a LISP expression
serving as a function name.

value ( C A R X) = (A B) if value X ~ ((A B) C), and value
( ( L A B E L FF ( L A M B D A (X) (GOND ((ATOM X) X) ((QUOTE

T ) (FF (CAR X)))))) ( Q U O T E ((A B) C))) - A. Thus ((LABEL
FF ( L A M B D A (X) ( C O N D ((ATOM X) X) ((QUOTE T) (FF
( C A R X)))))), is the LISP name of a function f f such that f f e is
the first atom in the written form of e. Note that the list f f is
substituted for the atom FF twice.

1. value ( Q U O T E e) = e. T h u s the value of ( Q U O T E A) is A.

Difficult mathematical type exercise: Find a list e such that
value e = e.

2. value (CAR e), where value e is a non-empty list, is the first
element of value e. T h u s value (CAR ( Q U O T E (A B C))) - A.

Abbreviations

3. value (CDR e), where value e is a non-empty list, is the the list
that remains when the first element of value e is deleted. T h u s
value (CDR ( Q U O T E (A B C))) = (B C).

T h e above LISP needs some abbreviations for practical use.
1. T h e variables T and NIL are permanently assigned the values T
and NIL, and NIL is the name of the null list 0.

4. value ( C O N S el e2), is the list that results from prefixing
value el
onto
the
list
value e2.
Thus
value ( C O N S ( Q U O T E A) ( Q U O T E (B C))) = (A B C).

2. So as not to describe a LISP function each time it is used, we
d e f i n e it permanently by typing (DEFUN f CaI ... vn) e).
T h e r e a f t e r ~f e I . . . e n) is evaluated by evaluating e with the
variables v I . . . . , v n taking the values value el, . . . , v a l u e en
respectively. Thus, after we define (DEFUN FF (X) (COND
( ( A T O M X) X) (T (FF (CAR X))))), typing (FF ( Q U O T E (CA B)
C))), gets A from LISP.

5. value ( E Q U A L el e2) is T if value el = value e2. Otherwise, its

value

is

NIL.

Thus

value ( E Q U A L (CAR ( Q U O T E (A B))) ( Q U O T E A)) = T,
6. value CATOM e) - T if value e is an atom; otherwise its value Is

NIL.

3. W e have the permanent function definitions

7. value ( C O N D ( p t e I) ... (PB en)) = value ei, where Pi is the the
first of the p's whose value is not NIL. Thus

( D E F U N N U L L (X) ( E Q U A L X NIL)) and
( D E F U N C A D R (X) (CAR (CDR X))),

value ( C O N D ( ( A T O M ( Q U O T E A)) ( Q U O T E B)) ((QUOTE T)

( Q U O T E C))) = B.

and similarly for arbitrary combinations of A and D.

8. A n atom v, regarded as a variable, may have a value.

4. ( L I S T e I . . . en) is defined for each n to be (CONS e I (CONS ...
( C O N S e n NIL))).

9. value ( ( L A M B D A (v I ... v,) e) e I ... ea) is the same as value e

but in an environment in which the variables v I ... vn take the
values of the expressions e I ... en in the original environment.
Thus

5. ( A N D p q) abbreviates (COND (p q) (T NIL)). ANDs with
more terms are defined similarly, and the propositional connectives
O R and N O T are used in abbreviating corresponding conditional
expressions.

value ( ( L A M B D A (X Y) (CONS (CAR X) Y)) (OJJOTE (A B))

(CDR ( Q U O T E (C D)))) = (A D).

¢1978 Association for Computing Machinery, Inc.

H e r e are m o r e examples o f L I S P function definitions:

'2..1.5

ACM SIGPLAN Notices, Vol. 13, No. 8, August 1978

Here is EVAL.

(DEFUN A L T (X) (COND ((OR (NULL X) (NULL (CDR X)))
X) (T (CONS (CAR X) (ALT (CDDR X))))))
defines

(LRBEL EVBL (LRnBDB (E R)
(CONO ((ATOM E)
(CONO ((EQ E Nil.) NIL)
((EQ E T) T)
(T (CDR ((LRBEL
RSSOC
(LflMBDfl (E fl)
(COND ((NULL R) NIL)
((EQ E (CflgR R)) (CflR R))
(T (RSSOC E (CDR f l ) ) ) ) ) )
E
R)))))
((ATOM (CAR E))
(COND ((EQ (CRR E) (QUOTEQUOTE)) (CflgR E))
((EQ (CRR E) (QUOTECRR))
(CflR (EVRL (CRDR E) R)))
((EQ (CAR E) (QUOTECUR))
(CDR (EVRL (CRDR E) R)))
((EQ (CAR E) (QUOTECAOR))
(CflDR (EVRL (CAOR E) fl)))
((EQ (CRR E) (QUOTECRODR))
(CRDDR (EVRL (CRDR E) R)))
((EQ (CRR E) (QUOTECRflR))
(CRflR (EVflL (CADR E) A)))
((EQ (CRR E) (QUOTECADflR))
(CRDRR (EVRL (CROR E) A)))
((EQ (CflR E) (QUOTECADOAR))
(CRDDRR (EVRL (CflDR E) R)))
((EQ (CAR E) (QUOTEATOfl))
(RTOM (EVRL (CRDR E) A)))
((EQ (CAR E) (QUOTENULL))
(NULL (EVRL (CADR E) A)))
((EQ (CflR E) (QUOTECONS))
(CONS (EVRL (CRORE) R) (EVRL (CflDDR E) R)))
((EQ (CRR E) (QUOTEEO))
(EQ (EVflL (CROR E) R) (EVRL (CROONE) R)))
((EQ (CRR E) (QUOTECOND))
((LRBEL EVCUNO
(LRMBDA (U A) (COND ((EVRL (CflAR U) R)
(EVAL (CflORR U)
A))
(T (EVCONO (CDR U)

a f u n c t i o n t h a t gives alternate elements o f a list starting

with the first element. Thus (ALT (QUOTE (A B C D E))) = (A

c E)
(DEFUN SUBST (X Y Z) (COND ((ATOM Z) (COND ((EQUAL
Z Y) X) (T Z))) (T (CONS (SUBST X Y (CAR Z)) (SUBST X Y
( C D R Z)))))),

where Y is an atom, gives the result of substituting X for Y in Z.
Thus
(SUBST ( q U O T E (PLUS X Y)) ( q U O T E V) ( q U O T E (TIMES
X V))) = (TIMES X (PLUS X Y)).
You may now program in LISP. Call LISP on a timesharing computer, define some functions, type in a LISP
expression, and LISP will output its value on your terminal.

T H E LISP INTERPRETER WRITTEN IN LISP
The

r u l e s we h a v e g i v e n f o r e v a l u a t i n g L I S P expressions

can themselves be expressed as a LISP function (EVAL e a),
where e is an expression to be evaluated, and a is a list of
variable-value pairs, a is used in the recursion and is often
initially NIL. The long LISP expression that follows is just such
an evaluator. It is presented as a single LABEL expressions with
all auxiliary functions also defined by LABEL expressions
internally, so that it references only the basic function of LISP and
some of abbreviations like CADR and friends. It knows about all
the functions that are used in its own definition so that it can
e v a l u a t e i t s e l f e v a l u a t i n g some o t h e r expression.

A)))))
(CDR E)
A))
(T (EVRL (CONS (CDR ((LRBEL
RSSOC
(LflMBOR (E fl)
(COND
((NULL R) NIL)
((EQ E (CRRR fl))
(CRR R))
(T (RSSOC E
(CUR R))))))
(CflR E)

I t does n o t k n o w

about DEFUNs or any features of LISP not explained in this
micro-manual such as functional arguments, property list functions,
input-output, or sequential programs.
T h e function EVAL can serve as an interpreter f o r LISP,
and LISP interpreters are actually made by hand-compiling EVAL
into machine language or by cross-compiling it on a machine for
which a LISP system already exists.

R))))

R))
(CDR E))

((EQ (CRRR E) (QUOTELRMBDfl)
(EVRL (CRDORRE)
((LABEL FFflPPEND

T h e definition would have been easier to follow had we
defined auxiliary functions separately rather than include them
using LABEL. However, we would then have needed property list
functions in order to make the EVAL self-applicable. These
auxiliary functions are EVLIS which evaluates lists of expressions,
E V C O N D which evaluates conditional expressions, ASSOC which
finds the value associated with a variable in the environment, and
P A I R U P which pairs up the corresponding elements of two lists.

(LAflBDA (U V)

(COND ((NULL U) V)
(T (CONS (CRR U)
(FFflPPEND (COR U)
V))))))
((LRBEL
PRIRUP
(LflMBUA (U V)
(COND ((NULL U) NIL)
iT (CONS (CONS (CRR U) (CAN V))
'-(PR]RUP (CDR U)
(CON V ) ) ) ) ) ) )
(CflDflR E)
((LRBEL
EVLIS
(LRflBDR (U A)
(COND ((NULL U) NIL)
(T (CONS (EVflL (CAR U) R)
(EVL]S (CDR O)
A))))))
(CON E)
R))
A)))
((EQ (CRAR E) (QUOTELABEL))
(EVAL (CONS (CADOARE) (CDR E))
(CONS (CONS (CRORRE) (CRR E)) fl)))))

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