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Under consideration for publication in J. Functional Programming 1 FUNCTIONAL PEARLS
 

Summary: Under consideration for publication in J. Functional Programming 1
FUNCTIONAL PEARLS
-conversion is easy
THORSTEN ALTENKIRCH
School of Computer Science & Information Technology, University of Nottingham,
Nottingham, NG8 1BB, UK
(e-mail: txa@cs.nott.ac.uk)
Abstract
We present a new and simple account of -conversion suitable for formal reasoning. Our
main tool is to define -conversion as a a structural congruence parametrized by a partial
bijection on free variables. We show a number of basic properties of substitution. e.g. that
substitution is monadic which entails all the usual substitution laws. Finally, we relate
-equivalence classes to de Bruijn terms.
1 Introduction
When reasoning about -terms we usually want to identify terms which only differ
in the names of bound variables, such as x.zx and y.zy. We say that these terms
are -convertible and write x.zx y.zy. We want that all operations on -terms
preserve . The first potential problem is substitution, if we naively substitute z
by x in the terms above we obtain (x.zx)[z x] = x.xx and (y.zy)[z x] =
y.xy but x.xx y.xy. To avoid this behaviour we introduce capture avoiding

  

Source: Altenkirch, Thorsten - School of Computer Science, University of Nottingham

 

Collections: Computer Technologies and Information Sciences