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no. 7957786 filed  3.54.24  mon 27 jun 1994
from eem
to   uclapl
subj Chwastyk's request for Mathematica help

Subj: Distributivity of the 16 logical dyadic functions

This has nothing to do with the Mathematica part of Chwastyk's
question, but it has some small amount of relevance to his request.  

K. E. Iverson's paper "Formalism in Programming Languages", was based
on work he did on a Harvard sabbatical, and was presented at a
"Working Conference on Language Structures" in August, 1963, and
appeared in CACM in 1964. This work predates APL, using the form of
the notation that appeared in his 1962 book "A Programming Language".
It includes Table 6, "Properties of the Binary Logical Operators".
Part of Table 6 is a 16 by 16 table of the distributivity of the 16
boolean functions with respect to each other. It is noteworthy that it
disagrees with the tables provided by Chwastyk and Rubin. This may be
because Iverson prepared the table by hand, since there was no
implementation available in 1963.  

This paper has been reprinted in the APL Press publication "A Source
Book in APL" (pp 17-25), and includes in the Discussion a question by
R. A. Brooker, "Why do you insist on using a notation which is a
nightmare for typist and compositor and impossible to implement with
punching and printing equipment currently available?" Brooker goes on
to say "It is not obvious to me that these two symbols for FLOOR and
CEILING have a great deal of mnemonic value." It is a fitting irony
that of all of Iverson's contributions to notation, these two have
been the most outstandingly successful, being widely used by both
computer scientists and mathematicians.  

The Source Book may be available from Renaissance Press in New York.  

Eugene McDonnell  

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