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Tait in one big step Thorsten Altenkirch and James Chapman
 

Summary: Tait in one big step
Thorsten Altenkirch and James Chapman
School of Computer Science, University of Nottingham
Jubilee Campus, Wollaton Road, Nottingham, NG8 1BB, UK
{txa,jmc}@cs.nott.ac.uk
Abstract
We present a Tait-style proof to show that a simple functional normaliser for a
combinatory version of System T terminates. The main interest in our construction
is methodological, it is an alternative to the usual small-step operational semantics
on the one side and normalisation by evaluation on the other. Our work is motivated
by our goal to verify implementations of Type Theory such as Epigram.
Keywords: Normalisation,Strong Computability
1. INTRODUCTION
Traditionally, decidability of equality for typed -calculi is established by showing strong
normalisation for a small-step reduction relation [19, 14]. However, this is not the only way to
establish this result, to show decidability it is sufficent to construct a normalisation function which,
for any term, calculates a normal form that is unique for the term's equivalence class. Indeed,
normalisation by evaluation (NBE) [7, 2, 3, 1, 6] uses a constructive denotational semantics
to construct a normalisation function by inverting the evaluation functional. While NBE has a
number of advantages, it is elegant and theoretically well understood, it is hard to tinker with the

  

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

 

Collections: Computer Technologies and Information Sciences