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Under consideration for publication in J. Functional Programming 1 Big-Step Normalisation
 

Summary: Under consideration for publication in J. Functional Programming 1
Big-Step Normalisation
THORSTEN ALTENKIRCH and JAMES CHAPMAN
School of Computer Science,
University of Nottingham, UK
Abstract
Traditionally, decidability of conversion for typed -calculi is established by showing that
small-step reduction is confluent and strongly normalising. Here we investigate an alter-
native approach employing a recursively defined normalisation function which we show
to be terminating and which reflects and preserves conversion. We apply our approach to
the simply-typed -calculus with explicit substitutions and -equality, a system which is
not strongly normalising. We also show how the construction can be extended to System
T with the usual -rules for the recursion combinator. Our approach is practical, since
it does verify an actual implementation of normalisation which, unlike normalisation by
evaluation, is first order. An important feature of our approach is that we are using logical
relations to establish equational soundness (identity of normal forms reflects the equa-
tional theory), instead of the usual syntactic reasoning using the Church-Rosser property
of a term rewriting system.
1 Introduction
Traditionally, decidability of conversion for typed -calculi is established by showing

  

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

 

Collections: Computer Technologies and Information Sciences