[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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