Symbolic Computation Group

David R. Cheriton School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada

Expressions as Functions
Jacques Carette, Maplesoft
Friday, January 5, 2001, at U. of Western Ontario.


For at least 2 centuries now mathematicians have routinely written down expressions such as sin(2*Pi*x) + arctan(y) and called them "functions". In this talk we will examine what it could mean to treat an expression as a function and, more specifically, different ways to give a semantic/functional interpretation to expressions with an eye towards exceptional cases such as x/x, x*sin(1/x) and diff(sqrt(x^2),x). In particular, we will consider pointwise, local and global interpretations, and show that all of them lead to undesirable behaviour in certain circumstances.


Last modified on Sunday, 04 November 2012, at 15:42 hours.