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Today's Topics:
1. Constrained polymorphic functions as natural transformations
(Matt R)
2. Raumzeit formulae in Haskell (Roman Czyborra)
----------------------------------------------------------------------
Message: 1
Date: Wed, 30 Oct 2013 09:50:03 +0000
From: Matt R <[email protected]>
To: [email protected]
Subject: [Haskell-beginners] Constrained polymorphic functions as
natural transformations
Message-ID:
<CA+ixoL=c22yAzzzvx=-sXO4h2V=lmkegjn_4pjuqasj-cg-...@mail.gmail.com>
Content-Type: text/plain; charset="iso-8859-1"
I read this excellent blog article on natural transformations[1], which
helped me gain one intuition as to what they are: "functions that don't
make too many assumptions about their arguments". In the article, natural
transformations make "no assumptions at all" about their arguments.
However, it's often the case that a Haskell function will require a type
argument constrained by a type class, e.g. show :: Show a => a -> String. I
wondered if it was possible to characterise these functions using category
theory too. Below is my attempt, and I'm hoping people can tell me whether
I'm in the right ballpark (or point me in the direction of a better
ball-park...)
For a particular type class T, we can form a subcategory Hask_T of Hask
consisting of all the instances of the type class as objects, with the
arrows just those functions that "commute" with the signature of the type
class. For example, in Hask_Show, the arrows would be all the functions f:
A -> B such that:
show == show . f
Or for Data.Monoid, all the monoid homomorphisms f:
mappend (f x) (f y) == f (mappend x y)
mempty == f mempty
In general, for any type class, we can formulate two functors f and g and a
function sig :: f a -> g a that captures the operations in the type class,
and then the condition is that:
fmap f . sig == sig . fmap f.
Then we have that the polymorphic functions with a type class constraint of
T are just the same thing as natural transformations in this subcategory
Hask_T.
Is the above correct / along the right lines?
Thanks,
-- Matt
[1] "You Could Have Defined Natural Transformations",
http://blog.sigfpe.com/2008/05/you-could-have-defined-natural.html
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Message: 2
Date: Wed, 30 Oct 2013 11:56:51 +0100 (CET)
From: Roman Czyborra <[email protected]>
To: [email protected]
Cc: [email protected]
Subject: [Haskell-beginners] Raumzeit formulae in Haskell
Message-ID:
<[email protected]>
Content-Type: text/plain; charset="utf-8"; Format="flowed"
Dear fellow beginning Haskellers,
I am delurking today because I think this might be of interest to you and
you might be of help to get more proofs out of the pudding since
information wants to be free and life wants to live and I would love to
have someone helping me here to transform this formulation into a
time-travel movie generating bioscope.
---------- Forwarded message ----------
Date: Wed, 30 Oct 2013 11:05:54
From: Roman Czyborra <[email protected]>
To: Prof Dr Magdalena Bushart <[email protected]>,
Sigrid Krajewski <[email protected]>,
Aris Dreismann <[email protected]>,
Prof Dr Debora Weber-Wulff <[email protected]>,
Stephan Voelker <[email protected]>,
Sabine Glesner <[email protected]>,
Peter Pepper <[email protected]>, Horst Voelz <[email protected]>,
Marie Neubert <[email protected]>,
Barbara Jochum <[email protected]>,
Prof Dr Dr Beier <[email protected]>,
Universiteit van Amsterdam <[email protected]>
Cc: Philippe Verdy <[email protected]>, Doug Ewell <[email protected]>,
Paul Hardy <[email protected]>, Donald Buczek <[email protected]>,
/dev/fd/0 <[email protected]>, Di Benedikt Homann <[email protected]>,
Dr Juergen Hoehn <[email protected]>,
Drs ?? Ilja Schmelzer <[email protected]>,
Marsha Linehan <[email protected]>,
Dbiol Dr med MSc PhD Mark Benecke <[email protected]>,
Die PARTEI <[email protected]>, Wolfgang Baitz <[email protected]>,
Andreschka Grossmann <[email protected]>, Reinhard Knoppka
<[email protected]>,
Db Lieselotte Juergensen <[email protected]>,
Daniela Czyborra Pacolli <[email protected]>,
bipolaris eV <[email protected]>,
Monika Schaefer-Ligustro <[email protected]>,
Robert Sengl <[email protected]>, Werner Fuss <[email protected]>,
Behindertenbeauftragte <[email protected]>,
Angela Merkel <[email protected]>, Ulrike Pohl
<[email protected]>,
Cornelia Otto <[email protected]>,
Kandidat Rhotep <[email protected]>, Sven Guckes
<[email protected]>,
Felix von Leitner <[email protected]>, OS X Survivors
<[email protected]>,
Ulf Kasch <[email protected]>, Marek Czyborra <[email protected]>,
Konrad Opitz <[email protected]>, Carbo Kuo <[email protected]>,
Richard Stallman <[email protected]>, Jacob Appelbaum <[email protected]>,
Claudia Schreck <[email protected]>,
Kurt Hartmann <[email protected]>, Mayra Hartmann
<[email protected]>
Subject: Antrag auf Promotion zum Doktor der Naturwissenschaft (Dr sci ?? Roma
Czyborra)
Verehrte Professor(inn)en,
als Tr?ger des durch Ihr http://czyborra.com/diplom/diplom.pdf verliehenen
akademischen Grades, welchen ich bereits 2001 wieder zur?ckzugeben m?ssen
glaubte, als mich nach dem Einbruch des Werbekommerzes ins Internet die Welt
nicht mehr verstand,
beantrage ich hiermit, schnellstm?glich zur wissenschaftlichen Verteidigung
meiner in http://czyborra.com/diplom/plank.hs ausformulierten
Dissertationsthese (f?r Sehbehinderungsfetischisten auch als
http://czyborra.com/diplom/plank.hs.unifont.pdf gecryptet verf?gbar) geladen zu
werden,
um noch 2013 die mir zustehende Erlaubnis zum F?hren des akademischen Titels
Doktor der Naturwissenschaft (gerne cum maxima laude) erteilt zu
bekommen und nutzbringend zu verwenden d?rfen.
Ich versichere Ihnen hiermit mit Eideskraft, dass ich Ihnen keinerlei
Fremdleistung betr?gerisch als eigene vorgaukele, sondern meine wesentlichen
Vorarbeiter_innen mit den mir bekanntesten Namen attributiert und meine den
menschlichen Erkenntnisgewinn schallmauerbrechend f?rdernde kleine
Synthese allein mithilfe eigener geistiger Arbeit und im Dialog mit unter
Zuhilfenahme meines Internetterminals zugreifbarer automatischer
Informationen selbst produziert habe.
Zur Formwahrung noch einen weiteren tabellarischer Lebenslauf, welcher
eigentlich Zeit vergeudet, solange Herr P?tz einem st?ndig Millionenwerte von
der Platte putzt, und man heutzutage einfach nur noch
http://facebook.com/roman.czyborra/about ins Adressfeld einzutragen braucht:
1970 http://czyborra.com/diplom/kopfgeburt.pdf
1976 http://czyborra.com/diplom/scheidungsurteil.pdf
1980-1984 http://czyborra.com/diplom/kinderausweis.jpg
1986-1989 http://czyborra.com/diplom/abitur.pdf
1989-? http://czyborra.com/diplom/fahrerlaubnis.pdf
1990-1992 http://czyborra.com/asf/p.pdf
1989-1993 http://czyborra.com/diplom/vordiplom.pdf
1993-??http://czyborra.com/bisexy/
1994-1995 http://www.cs.tu-berlin.de/www/
1994-1996 http://www.cs.tu-berlin.de/~czyborra/job.html
1996-1997 http://tal.cs.tu-berlin.de/lehre/thegi1/
1998 http://czyborra.com/diplom/abgabe.html
1999-2002 [email protected] mit http://woffs.de/
2003 http://czyborra.com/diplom/zeugnis.pdf
2003 http://czyborra.com/diplom/wolisz1.pdf?>>= http://czyborra.com/chemnitz/
2004-2005 Versauern in Depressionen verursacht durch
2001-2012 millionenschwere Psychiatrieeinweisungen durch ?rzte und Richter in
Cantor-G?delschem Ausma?
2006-2007 http://de.boywiki.org/wiki/Archiv:WP/Benutzersperrung/Roman_Czyborra
2007-2012 Systemadminstration in der WfbM?http://via-werkstaetten.de/
2011-2012?http://czyborra.com/zeta/
2012-??http://czyborra.com/diplom/reimmatrikulation.pdf
2013-??http://czyborra.com/diplom/marriagecertificate.pdf
2013 http://www.unicode.org/mail-arch/unicode-ml/y2013-m07/0015.html
2013?http://czyborra.wordpress.com/2013/07/05/hacking-the-universe-with-weltformel-c/
2013 http://czyborra.com/diplom/plank.hs
Ihren Antworten freudig entgegensehend verbleibe ich als: Ihr Roman Czyborra,
doctorandus informaticae, tel:+491789794164
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