# [Haskell-cafe] mathematical notation and functional programming

Henning Thielemann lemming at henning-thielemann.de
Thu Jan 27 15:14:41 EST 2005

Over the past years I became more and more aware that common mathematical
notation is full of inaccuracies, abuses and stupidity. I wonder if
mathematical notation is subject of a mathematical branch and whether
mathematical notation with the knowledge of functional languages.

Things I'm unhappy about are for instance

f(x) \in L(\R)
where f \in L(\R) is meant

F(x) = \int f(x) \dif x
where x shouldn't be visible outside the integral

O(n)
which should be O(\n -> n) (a remark by Simon Thompson in
The Craft of Functional Programming)

a < b < c
which is a short-cut of a < b \land b < c

f(.)
which means \x -> f x or just f

All of these examples expose a common misunderstanding of functions, so I
assume that the pioneers of functional programming also must have worried