Scheme: An Interpreter for Extended Lambda Calculus/Section 1

by Gerald Jay Sussman and Guy L. Steele, Jr.

Section 1: The SCHEME Reference Manual

SCHEME is essentially a full-funarg LISP. LAMBDA expressions need not be QUOTEd, FUNCTIONed, or *FUNCTIONed when passed as arguments or returned as values; they will evaluate to closures of themselves.

All LISP functions (i.e., EXPRs, SUBRs, and LSUBRs, but not FEXPRs, FSUBRs, or MACROs) are primitive operators in SCHEME, and have the same meaning as they have in LISP. Like LAMBDA expressions, primitive operators and numbers are self-evaluating (they evaluate to trivial closures of themselves).

There are a number of special primitives known as AINTs which are to SCHEME as FSUBRs are to LISP. We will enumerate them here.

IF

This is the primitive conditional operator. It takes three arguments. If the first evaluates to non-NIL, it evaluates the second expression, and otherwise the third.

QUOTE

As in LISP, this quotes the argument form so that it will be passed verbatim as data. The abbreviation "'FOO" may be used instead of "(QUOTE FOO)".

DEFINE

This is analogous to the MacLISP DEFUN primitive (but note that the LAMBDA must appear explicitly!). It is used for defining a function in the "global environment" permanently, as opposed to LABELS (see below), which is used for temporary definitions in a local environment. DEFINE takes a name and a lambda expression; it closes the lambda expression in the global environment and stores the closure in the LISP value cell of the name (which is a LISP atom).

LABELS

We have decided not to use the traditional LABEL primitive in this interpreter because it is difficult to define several mutually recursive functions using only LABEL. The solution, which Hewitt [Smith and Hewitt] also uses, is to adopt an ALGOLesque block syntax:

(LABELS <function definition list> <expression>)

This has the effect of evaluating the expression in an environment where all the functions are defined as specified by the definitions list. Furthermore, the functions are themselves closed in that environment, and not in the outer environment; this allows the functions to call themselves and each other recursively. For example, consider a function which counts all the atoms in a list structure recursively to all levels, but which doesn't count the NILs which terminate lists (but NILs in the CAR of some list count). In order to perform this we use two mutually recursive functions, one to count the car and one to count the cdr, as follows:

(DEFINE COUNT
    (LAMBDA (L)
        (LABELS ((COUNTCAR
                  (LAMBDA (L)
                      (IF (ATOM L) 1
                          (+ (COUNTCAR (CAR L))
                             (COUNTCDR (CDR L))))))
                 (COUNTCDR
                  (LAMBDA (L)
                      (IF (ATOM L)
                          (IF (NULL L) 0 1)
                          (+ (COUNTCAR (CAR L))
                             (COUNTCDR (CDR L)))))))
                (COUNTCDR L))))         ;Note: COUNTCDR is defined here.

ASET

This is the side effect primitive. It is analogous to the LISP function SET. For example, to define a cell [Smith and Hewitt], we may use ASET as follows:

(DEFINE CONS-CELL
    (LAMBDA (CONTENTS)
        (LABELS ((THE-CELL
                  (LAMBDA (MSG)
                      (IF (EQ MSG 'CONTENTS?) CONTENTS
                          (IF (EQ MSG 'CELL?) 'YES
                              (IF (EQ (CAR MSG) '<-)
                                  (BLOCK (ASET 'CONTENTS (CADR MSG))
                                         THE-CELL)
                                  (ERROR '|UNRECOGNIZED MESSAGE - CELL|
                                          MSG
                                          'WRNG-TYPE-ARG)))))))
                THE-CELL)))

Those of you who may complain about the lack of ASETQ are invited to write (ASET' foo bar) instead of (ASET 'foo bar).

EVALUATE

This is similar to the LISP function EVAL. It evaluates its argument, and then evaluates the resulting s-expression as SCHEME code.

CATCH

This is the "escape operator" which gives the user a handle on the control structure of the interpreter. The expression:

(CATCH <identifier> <expression>)

evaluates <expression> in an environment where <identifier> is bound to a continuation which is "just about to return from the CATCH"; that is, if the continuation is called as a function of one argument, then control proceeds as if the CATCH expression had returned with the supplied (evaluated) argument as its value. For example, consider the following obscure definition of SQRT (Sussman's favorite style/Steele's least favorite):

(DEFINE SQRT
    (LAMBDA (X EPSILON)
        ((LAMBDA (ANS LOOPTAG)
             (CATCH RETURNTAG
                    (PROGN
                     (ASET 'LOOPTAG (CATCH M M))        ;CREATE PROG TAG
                     (IF (< (ABS (-$ (*$ ANS ANS) X)) EPSILON)
                         (RETURNTAG ANS)                ;RETURN
                         NIL)                           ;JFCL
                     (ASET 'ANS (//$ (+$ (//$ X ANS) ANS) 2.0))
                     (LOOPTAG LOOPTAG))))               ;GOTO
         1.0
         NIL)))

Anyone who doesn't understand how this manages to work probably should not attempt to use CATCH.

As another example, we can define a THROW function, which may then be used with CATCH much as they are in LISP:

(DEFINE THROW (LAMBDA (TAG RESULT) (TAG RESULT)))

CREATE!PROCESS

This is the process generator for multiprocessing. It takes one argument, an expression to be evaluated in the current environment as a separate parallel process. If the expression ever returns a value, the process automatically terminates. The value of CREATE!PROCESS is a process id for the newly generated process. Note that the newly created process will not actually run until it is explicitly started.

START!PROCESS

This takes one argument, a process id, and starts up that process. It then runs.

STOP!PROCESS

This also takes a process id, but stops the process. The stopped process may be continued from where it was stopped by using START!PROCESS again on it. The magic global variable **PROCESS** always contains the process id of the currently running process; thus a process can stop itself by doing (STOP!PROCESS **PROCESS**). A stopped process is garbage collected if no live process has a pointer to its process id.

EVALUATE!UNINTERRUPTIBLY

This is the synchronization primitive. It evaluates an expression uninterruptibly; i.e. no other process may run until the expression has returned a value. Note that if a funarg is returned from the scope of an EVALUATE!UNINTERRUPTIBLY, then that funarg will be uninterruptible when it is applied; that is, the uninterruptibility property follows the rules of variable scoping. For example, consider the following function:

(DEFINE SEMGEN
    (LAMBDA (SEMVAL)
        (LIST (LAMBDA ()
                  (EVALUATE!UNINTERRUPTIBLY
                      (ASET' SEMVAL (+ SEMVAL 1))))
              (LABELS (P (LAMBDA ()
                             (EVALUATE!UNINTERRUPTIBLY
                                 (IF (PLUSP SEMVAL)
                                     (ASET' SEMVAL (- SEMVAL 1))
                                     (P)))))
                      P))))

This returns a pair of functions which are V and P operations on a newly created semaphore. The argument to SEMGEN is the initial value for the semaphore. Note that P busy-waits by iterating if necessary; because EVALUATE!UNINTERRUPTIBLY uses variable-scoping rules, other processes have a chance to get in at the beginning of each iteration. This busy-wait can be made much more efficient by replacing the expression (P) in the definition of P with

((LAMBDA (ME)
         (BLOCK (START!PROCESS (CREATE!PROCESS '(START!PROCESS ME)))
                (STOP!PROCESS ME)
                (P)))
 **PROCESS**)

Let's see you figure this one out! Note that a STOP!PROCESS within an EVALUATE!UNINTERRUPTIBLY forces the process to be swapped out even if it is the current one, and so other processes get to run; but as soon as it gets swapped in again, others are locked out as before.

Besides the AINTs, SCHEME has a class of primitives known as AMACROs. These are similar to MacLISP MACROs, in that they are expanded into equivalent code before being executed. Some AMACROs supplied with the SCHEME interpreter:

COND

This is like the MacLISP COND statement, except that singleton clauses (where the result of the predicate is the returned value) are not allowed.

AND, OR

These are also as in MacLISP.

BLOCK

This is like the MacLISP PROGN, but arranges to evaluate its last argument without an extra net control frame (explained later), so that the last argument may involved in an iteration. Note that in SCHEME, unlike MacLISP, the body of a LAMBDA expression is not an implicit PROGN.

DO

This is like the MacLISP "new-style" DO; old-style DO is not supported.

AMAPCAR, AMAPLIST

These are like MAPCAR and MAPLIST, but they expect a SCHEME lambda closure for the first argument.

To use SCHEME, simply incant at DDT (on MIT-AI):

:LISP LIBLSP;SCHEME

which will load up the current version of SCHEME, which will announce itself and give a prompt. If you want to escape to LISP, merely hit ^G. To restart SCHEME, type (SCHEME). Sometimes one does need to use a LISP FSUBR such as UREAD; this may be accomplished by typing, for example,

(EVAL' (UREAD FOO BAR DSK LOSER))

After doing this, typing ^Q will, of course, cause SCHEME to read from the file.

This concludes the SCHEME Reference Manual.