Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 MeAmI.org Posts: 405 Registered: 6/14/09
Re: Formal Proof Language Example - Human-Readable?
Posted: Jun 24, 2009 3:42 AM

slawekk wrote:
> Yes, I can understand the meaning of the (assertion of) the theorem.
> I think a good formal proof language has to have the following
> features:
>
> 1. Be readable for people with general mathematical education, without
> having the study the language. Readability is of course relative and
> depends on the reader's experience. For some people a proof is
> readable if it looks like Lisp. For most mathematicians though the
> proof is readable if it looks similar to what they can see in a
> standard journal. I think your syntax does have this feature.
>
> 2. Provide ways to cope with excessive verbosity. Formal proofs are
> typically very verbose. A proof language should provide ways to
> structure the proofs so that at least in a web presentation the reader
> can choose how detailed the proof she wants to see. Your syntax is too
> verbose.
>
> 3. Should support LaTeX-like mathematical symbols and notation. This
> can be done by a presentation layer, but there has to be way to render
> the proofs so that they look like math. This is also needed for 2.
>
> 4. Should support some notion of context to be able to limit the scope
> of introduced notation, independent of the defined notions. For
> example you should be able to talk about groups using both
> multiplicative and additive notation (in different contexts), or use
> the same \cdot symbol to denote both general group operation and
> multiplication of real numbers (again in different contexts). How
> important this need is becomes obvious only when you reach certain
> scale.
>
> Isar is a proof language that has all these features to some extent.
> <plug> See formalmath.org site for an examples </plug>.

Musatov wrote:

slawekk wrote:
> Yes, I can understand the meaning of the (assertion of) the theorem.
> I think a good formal proof language has to have the following
> features:
>
> 1. Be readable for people with general mathematical education, without
> having the study the language. Readability is of course relative and
> depends on the reader's experience. For some people a proof is
> readable if it looks like Lisp. For most mathematicians though the
> proof is readable if it looks similar to what they can see in a
> standard journal. I think your syntax does have this feature.
>
> 2. Provide ways to cope with excessive verbosity. Formal proofs are
> typically very verbose. A proof language should provide ways to
> structure the proofs so that at least in a web presentation the reader
> can choose how detailed the proof she wants to see. Your syntax is too
> verbose.
>
> 3. Should support LaTeX-like mathematical symbols and notation. This
> can be done by a presentation layer, but there has to be way to render
> the proofs so that they look like math. This is also needed for 2.
>
> 4. Should support some notion of context to be able to limit the scope
> of introduced notation, independent of the defined notions. For
> example you should be able to talk about groups using both
> multiplicative and additive notation (in different contexts), or use
> the same \cdot symbol to denote both general group operation and
> multiplication of real numbers (again in different contexts). How
> important this need is becomes obvious only when you reach certain
> scale.
>
> Isar is a proof language that has all these features to some extent.
> <plug> See formalmath.org site for an examples </plug>.

"First off, I am terribly sorry for all the bulk behind me. Be it
necessary these days to a fellow to make a point, however, it is."

Well, like much of Hollywood these days the story starts trying to
grab your attention really quickly! If it can do it and keep you on
your toes too it is best.

In Screenwriting we call it the "inciting incident". It usually
happens by page 10.

Consider a script for a feature length movie is on average between
90-120 pages.

P0-P10(inciting incident)
P90-P120(story complete)

The above framework agrees with Aristotle in three act structure and
meshes also with Shakespeare. Proportionately we are in good company.

What happens "next" in the story? (To answer the question flashed
before my eyes then disappeared into a vaccuous drum beyond the tiny
machine, have I hold in unweary hands.)

It is my story we are telling here, the story of I, your humble
narrator, to pay homage to an old great.

(A bit of the old Ludwig Van...)

Betthoven's 9th begins to fill the space. At first from a distant din
to a quiet hum till sound as full as water fills our ears with sweet
sweet symphony.

"While all of this was going on I couldn't help but tell them ahead of
time how pleased I was to see 'Sade' make an appearance in this my
very own algorithm."

The music crescendos and continues in full glorious fidelity.

(Note: the vowels strike the chords in time as they apear on screen)

AAB AABANDONED AABB AABBOT AABEL AABENRAA AABERG AABHORRENT AABOVE
[......] ISANMAALINEN ISANTIM ISAO ISAOKA ISAQ ISAR ISARD ISAREL
ISARELI ISARELIS [......] MUSASHI MUSASHIC MUSATELLI MUSATOV MUSAVI
MUSAVIAN MUSAWA MUSAWI MUSBACH [......] PNH PNI PNIN PNINA PNN PNNR
PNO PNOISILY PNOM PNOMH PNP PNR PNS PNT PNTA [...]http://
jph.durand.free.fr/propres.txt

Characteristics and applications of fast-wave gyrodevices [...]inverse
applications must [......] [24] P. Sprangle and A. Drobot, ?The linear
and selfconsistent [....] [69] G. G. Denisov, A. N. Kutfin, V. I.
Malygin, N. P. Venediktov, [.....] V. K. Yulpatov, L. A. Aksenova, A.
P. Keyer, V. S. Musatov, [...]http://ieeexplore.ieee.org/
iel4/5/16414/00757254.pdf%3Farnumber%3D757254

'68 Comeback Special (????????????? ???????) Elvis Presley's '68
[......] code M ATC ??? N ATC code N ATC ??? P ATC code P ATC ??? R
ATC code P ATC ??? S [......] No Ordinary Love (Sade single) NP-??????
?????? NP-complete NSFNet National [......] ?????? ??????????????
Victor Borisov-Musatov ??????? Borisov ??????? ...... ???????-?????
François-André Isambert ???? (????) Isar ?????????? ...http://
www.cs.helsinki.fi/group/smart/data/wikipedia/phrase_table/wikipedia_phrasetable/ru-en.ff
- Similar pagesSonderaspekte: Nach Gebiet oder Charakteristik1938
Irschenhausen/ Isar [......] N. P.. BERCHEM. Otto architect. BERCHER.
Henry Edouard. BERCHÉRE. Narcisse. BERCHET. Pierre. BERCHMANS. Oskar
sculptor [......]

Date Subject Author
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Jan Burse
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Andrew Tomazos
6/21/09 Jan Burse
6/21/09 Jan Burse
6/24/09 Andrew Tomazos
6/25/09 MeAmI.org
6/25/09 Jan Burse
6/26/09 Andrew Tomazos
6/27/09 Jan Burse
6/27/09 Andrew Tomazos
6/27/09 Jan Burse
6/27/09 Andrew Tomazos
6/27/09 Joshua Cranmer
6/27/09 Andrew Tomazos
6/21/09 Marshall
6/21/09 Spiros Bousbouras
6/24/09 Tim Smith
6/21/09 Charlie-Boo
6/21/09 William Elliot
6/22/09 MeAmI.org
6/22/09 MeAmI.org
6/23/09 Slawomir
6/24/09 David Bernier
6/24/09 MeAmI.org
6/24/09 MeAmI.org
6/24/09 Andrew Tomazos
6/24/09 Andrew Tomazos
6/25/09 Slawomir