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From: mob@mit-amt.MEDIA.MIT.EDU (Mario O. Bourgoin)
Newsgroups: comp.lang.scheme
Subject: The defintion of TRUE and FALSE in Scheme.
Message-ID: <152@mit-amt.MEDIA.MIT.EDU>
Date: 16 Jul 89 04:18:26 GMT
References: <8907141728.aa02609@mintaka.lcs.mit.edu>
Reply-To: mob@media-lab.media.mit.edu (Mario O. Bourgoin)
Organization: MIT Media Lab, Cambridge MA
Lines: 55

I've been wanting to replace the usual LISP definitions of TRUE and
FALSE by functions because that seems more in the spirit of Scheme.
Furthermore, with functions we can eliminate ``if'' and ``cond'' from
the essential syntax of Scheme which simplifies the analysis of
extensions to Scheme such as Zabih, McAllester, and Chapman's
non-deterministic operator, ``amb''.  I would like to get the Scheme
community's reaction to the specification of particular objects for
TRUE and FALSE, namely the functions:

(define true (lambda (iftrue iffalse) iftrue))
(define false (lambda (iftrue iffalse) iffalse))

Naturally, the constants #t and #f would always denote the appropriate
one of these two functions.

Given the above definitions for TRUE and FALSE, ``if'' statements can
be replaced according to the following pattern:

(if predicate iftrue iffalse) =>
((predicate (lambda () iftrue) (lambda () iffalse)))

And ``cond'' may be replaced thus:

(cond (predicate1 body1)
      (predicate2 body2)
      (predicate3 body3)
      (else bodyelse))

becomes:

((predicate1
  (lambda () body1)
  (lambda ()
    ((predicate2
      (lambda () body2)
      (lambda ()
        ((predicate3
          (lambda () body3)
          (lambda () bodyelse)))))))))

The logical connectives ``not'', ``and'', and ``or'' could be defined
as follows.

(not predicate) => (predicate false true)

(or predicate1 predicate2) => (predicate1 true predicate2)

(and predicate1 predicate2) => (predicate1 predicate2 false)

Naturally, the definitions for ``or'' and ``and'' can be extended to
handle a variable number of parameters.

Please tell me of any problems you see with such a definition.

--Mario O. Bourgoin