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Graduate Seminar

Will Gunther
Carnegie Mellon University
Title: Rewriting: Bring Your Eraser

Abstract: A function is a sacred thing---a mythical machine. Consider $f(x) = x^2$. Put in a real number, turn a crank, and another number will be produced that is the square of the one you put in. Well, that's one way of looking at it. Another way, is that it is a rule written on the chalkboard. And whenever someone writes $f(x)$ on a chalkboard, you are allowed to erase it and replace it with $x^2$ (no matter what $x$ is, of course). This brings in the area of mathematical logic called rewriting. Rewriting gives a new meaning, or semantics, to many different concepts, such as that of a function. Stripping away all the cranks, machines, and frills from the classical semantics of mathematics, and looking just at the syntactic semantics (writing things, and allowing yourself to erase them and replace them with others) we see new and interesting questions we can pose.

Date: Tuesday, September 18, 2012
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell