Tait in one big step

Authors:
Thorsten Altenkirch;James Chapman
Affiliations:
School of Computer Science and IT, University of Nottingham, Nottingham, UK;School of Computer Science and IT, University of Nottingham, Nottingham, UK
Venue:
MSFP'06 Proceedings of the 2006 international conference on Mathematically Structured Functional Programming
Year:
2006

Citing 11
Cited 4

Proofs and types

Proofs and types
An algorithm for testing conversion in type theory

Logical frameworks
Program Extraction from Normalization Proofs

TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Finite Axiomatization of Inductive-Recursive Definitions

TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Nested General Recursion and Partiality in Type Theory

TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Categorical Reconstruction of a Reduction Free Normalization Proof

CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
Reduction-free normalisation for a polymorphic system

LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Normalization by Evaluation for Typed Lambda Calculus with Coproducts

LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Intuitionistic model constructions and normalization proofs

Mathematical Structures in Computer Science
The view from the left

Journal of Functional Programming
Epigram: practical programming with dependent types

AFP'04 Proceedings of the 5th international conference on Advanced Functional Programming

Type Theory Should Eat Itself

Electronic Notes in Theoretical Computer Science (ENTCS)
Big-step normalisation

Journal of Functional Programming
A formalisation of a dependently typed language as an inductive-recursive family

TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Hereditary substitutions for simple types, formalized

Proceedings of the third ACM SIGPLAN workshop on Mathematically structured functional programming

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Abstract

We present a Tait-style proof to show that a simple functional normaliser for a combinatory version of System T terminates. Using a technique pioneered by Bove and Capretta, we can implement the normaliser in total Type Theory. 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. The present work is motivated by our longer term goal to verify implementations of Type Theory such as Epigram.