# Scheme: An Interpreter for Extended Lambda Calculus/Section 1

Scheme: An Interpreter for Extended Lambda Calculus

Section 1: The SCHEME Reference Manual

## Section 1: The SCHEME Reference Manual

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

All LISP functions (i.e., `EXPR`s, `SUBR`s, and `LSUBR`s, but not `FEXPR`s, `FSUBR`s, or `MACRO`s) 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 `AINT`s which are to SCHEME as `FSUBR`s 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 `NIL`s which terminate lists (but `NIL`s 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) '<-)
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 `AINT`s, SCHEME has a class of primitives known as `AMACRO`s. These are similar to MacLISP `MACRO`s, in that they are expanded into equivalent code before being executed. Some `AMACRO`s 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.