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Topic: Formal Proof Language Example - Human-Readable?
Replies: 39   Last Post: Jun 27, 2009 11:09 PM

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Andrew Tomazos

Posts: 137
Registered: 8/1/05
Re: Formal Proof Language Example - Human-Readable?
Posted: Jun 21, 2009 3:34 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jun 21, 9:11 pm, Jan Burse <janbu...@fastmail.fm> wrote:
> For example your theorem could also be formalize as follows:
>
>      forall a, b, c in nat
>         (a^2 + b^2 = c^2 &
>          rel_prim(a,b) &
>          odd(a) => exists m, n in nat
>           (m<=n &
>            a = n^2 - m^2 &
>            b = 2*m*n &
>            c = n^2 + m^2))
>
> And I think this is better than distributing conjuncts
> over C like statements separated by semicolon ";". First
> of all because this language has already been 100-times
> formally introduces in logic books.


Are you sure the way you have written it is really clearer?

When you think about it - if I state that a series of propositions:

A
B
C
D

are individually true in some context, than it is exactly the same as
saying:

A and B and C and D

This also mirrors the way that (what I suspect to be) at the core of
every proof:

Axiom A
A'
A''
A'''
Theorem X

ie Truth-preseving transformations of an axiom(s) to a theorem.

..is identical on some level to:

Axiom A and A' and A'' and A''' and Thereom X

Also the way you have indented and spaced out the theorem doesn't seem
to follow any logical pattern. It is almost like you have written it
on one line and randomly inserted carriage returns.

The way I formatted it was deliberate, to indicate the relevant scope
connections and compound statements. This is an important
consideration when complexity increases.
-Andrew.



Date Subject Author
6/21/09
Read Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/24/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/25/09
Read Re: Formal Proof Language Example - Human-Readable?
MeAmI.org
6/25/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/26/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/27/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/27/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/27/09
Read Re: Formal Proof Language Example - Human-Readable?
Jan Burse
6/27/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/27/09
Read Re: Formal Proof Language Example - Human-Readable?
Joshua Cranmer
6/27/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Marshall
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Spiros Bousbouras
6/24/09
Read Re: Formal Proof Language Example - Human-Readable?
Tim Smith
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
Charlie-Boo
6/21/09
Read Re: Formal Proof Language Example - Human-Readable?
William Elliot
6/22/09
Read Re: Formal Proof Language Example - Human-Readable?
MeAmI.org
6/22/09
Read Re: Formal Proof Language Example - Human-Readable?
MeAmI.org
6/23/09
Read Re: Formal Proof Language Example - Human-Readable?
Slawomir
6/24/09
Read Re: Formal Proof Language Example - Human-Readable?
David Bernier
6/24/09
Read Re: Formal Proof Language Example - Human-Readable?
MeAmI.org
6/24/09
Read Re: Formal Proof Language Example - Human-Readable?
MeAmI.org
6/24/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/24/09
Read Re: Formal Proof Language Example - Human-Readable?
Andrew Tomazos
6/25/09
Read Re: Formal Proof Language Example - Human-Readable?
Slawomir

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