[Haskell-cafe] mathematical notation and functional
programming
Michael Matsko
msm at gwu.edu
Fri Jan 28 15:27:30 EST 2005
Also, Walter Noll of Carnegie Mellon Univ. wrote a book,
"Finite-Dimensional Spaces" in 1987 which basically presented
undergraduate math in a notationally and conceptually unified manner.
Some of the notation and terminology was strange, but consistent.
Mike Matsko
----- Original Message -----
From: Fritz Ruehr <fruehr at willamette.edu>
Date: Friday, January 28, 2005 3:10 pm
Subject: Re: [Haskell-cafe] mathematical notation and functional programming
> Well, I don't know about modern works which might appeal to
> knowledge
> of FP languages, but there is a well-known, 2-volume work by Cajori:
>
> Cajori, F., A History of Mathematical Notations, The Open
> Court
> Publishing Company, Chicago, 1929 (Available from Dover).
>
> I know it through Ken Iverson (may he rest in peace), the creator
> of
> APL. (Dr. Iverson's own notations were not to everyone's taste, but
> I
> think they were a bigger influence on Backus and the recent wave of
> FP
> than is generally acknowledged.)
>
> APL *did* have "implicit maps and zipWiths" in the sense that
> scalar
> functions would be automatically extended to vectors (and similarly
> for
> higher dimensions). I think my PhD advisor, Satish Thatte, did some
> work on extending this sort of "notational abuse" to Hindley-Milner
> systems, but I don't have the citations at hand.
>
> OK then, googling on Cajori yields this quote from a math history
> site:
> "He almost single-handedly created the history of mathematics as
> an
> academic subject in the United States
> and, particularly with his book on the history of mathematical
> notation, he is still one of the most quoted
> historians of mathematics today."
>
> More googling on "mathematical notation" reveals that there *are*
> people concerned about these issues, Steven Wolfram being an
> easily-recognized example (he refers to Cajori's work).
>
> -- Fritz
>
> On Jan 27, 2005, at 12:14 PM, Henning Thielemann wrote:
>
> > I wonder if
> > mathematical notation is subject of a mathematical branch and
> whether> there are papers about this topic, e.g. how one can
> improve common
> > mathematical notation with the knowledge of functional languages.
>
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