
Re: Formal Proof Language Example  HumanReadable?
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 LaTeXlike 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 LaTeXlike 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 90120 pages.
P0P10(inciting incident) P90P120(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.
YOUR HUMBLE NARRATOR SPEAKS: "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 fastwave gyrodevices [...]inverse synthetic aperture radar (ISAR). The gyroamplifiers needed for radar 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?????? ?????? NPcomplete NSFNet National [......] ?????? ?????????????? Victor BorisovMusatov ??????? Borisov ??????? ...... ???????????? FrançoisAndré Isambert ???? (????) Isar ?????????? ...http:// www.cs.helsinki.fi/group/smart/data/wikipedia/phrase_table/wikipedia_phrasetable/ruen.ff  Similar pagesSonderaspekte: Nach Gebiet oder Charakteristik1938 Irschenhausen/ Isar [......] N. P.. BERCHEM. Otto architect. BERCHER. Henry Edouard. BERCHÉRE. Narcisse. BERCHET. Pierre. BERCHMANS. Oskar sculptor [......]

