# Re: A Simple Notation

From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 05 Jul 2007 14:36:33 GMT
Message-ID: <Rl7ji.89241\$xq1.85813_at_pd7urf1no>

David Cressey wrote:
> In Boolean algebra, you could, if you wanted to, express everything by just
> using brackets, as follows:
>
> [A B] means NOT (A AND B)
>
> This notation can be extended to 3 or more operands, as follows:
>
> [A B C] means NOT (A AND B AND C)
>
> "AND" is associative, so there's no confusion.
>
> You can reduce the notation to 1 operand as follows:
>
> [A] means NOT (A)
>
> And to zero operands as follows:
>
> [] means TRUE
> [[]] means FALSE
>
> You can build up everything else from there. For example,
>
> [[A B]] = A AND B
> [[A] [B]] = A OR B
>
> Now my question is, can you do the corresponding thing in the RA, using
> <NOT> and <AND>? I don't see why not.
>
> So you would get (for example)
>
> [[A B]] = A <AND> B
> [[A] [B]] = A <OR> B
>
> As written text, this notation is rather unwieldy, but you can represent it
> fairly tightly in internal data structures. And its simplicity does make
> some things easier.
>

Just playing with eg., De Morgan:
<NOT> (A <AND> B) = (<NOT> A) <OR> (<NOT> B) ->
[[[A B]]] = [[A] [B]].

```A = A <AND> [] ->
A = A [] ->
A = [[A []]].

```

Have to admit I like brackets because on my keyboard, I can type them without a shift key. At first glance, I imagine that a practical engine operating on "tuples" could simply reverse its tests whenever it encountered a leading bracket, eg. test 'not equal' instead of 'equal', assume <OR> whenever a leading bracket immediately follows a trailing bracket and so forth. I know that the electronic engineers like NAND because transistor-like circuit devices emulate it precisely. Does a language like Lisp make the same emulation easy? Another thing I wonder is what a debugging traceback of intermediate results would look like! Also, is it the case that one would never need more than three leading or trailing brackets in succession?

p Received on Thu Jul 05 2007 - 16:36:33 CEST

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