 
Summary: Pattern Matching vs. Elimination Rules
A Case Study in LEGO
Andreas Abel
abel@informatik.unimuenchen.de
http://www.tcs.informatik.unimuenchen.de/~abel/
Department of Computer Science
University of Munich
September 30, 1999
1 Introduction
In Type Theory there are two paradigms of how to obtain functions over
recursive types: Either by recursion resp. elimination rules or as the xed
point of a structural recursive denition. In [Gim94] Eduardo Gimenez has
shown that both methods are equivalent. On the one hand one can codify
the elimiation rules as structural recursive functions. On the other hand he
describes a method of how from a function f dened as a xedpoint one
obtains an extensionally equal function f 0 using only elimination rules.
In the following we exercise his method on a small example. Doing this
we want to demonstrate that pattern matching denitons are often much
more straight forward and understandable than elimination style denitions
are. (In my case, it took me a quater of an hour to do the pattern matching
