A predicative strong normalisation proof for a -calculus with interleaving inductive types. submitted for publication, see http://www.tcs.informatik.uni-muenchen.de/~alti/drafts/snpred. dvi (1999) [3 citations — 3 self]
Download:
|
|
by Andreas Abel, Thorsten Altenkirch
Types for Proof and Programs, Inter40 A. Abel and T. Altenkirch national Workshop, TYPES '99, Selected Papers. Lecture Notes in Computer Science
http://www.tcs.informatik.uni-muenchen.de/~alti/drafts/sn-pred.ps
Add To MetaCart
Abstract:
Abstract. We present a new strong normalisation proof for a -calculus with interleaving strictly positive inductive types which avoids the use of impredicative reasoning, i.e., the theorem of Knaster-Tarski. Instead it only uses predicative, i.e., strictly positive inductive denitions on the metalevel. To achieve this we show that every strictly positive operator on types gives rise to an operator on saturated sets which is not only monotone but also (deterministically) set based { a concept introduced by Peter Aczel in the context of intuitionistic set theory. We also extend this to coinductive types using greatest xpoints of strictly monotone
Citations
| 54 | Infinite objects in Type Theory – Coquand - 1993 |
| 47 | Monadic presentations of lambda-terms using generalized inductive types – Altenkirch, Reus - 1999 |
| 47 | Abstract Data Type Systems – Jouannaud, Okada - 1997 |
| 33 | A predicative analysis of structural recursion – Abel, Altenkirch - 2000 |
| 21 | Logical relations and inductive/coinductive types – Altenkirch - 1998 |
| 9 | Inductive Types and Strong Normalization – Constructions - 1993 |
| 6 | Inductively de types – Coquand, Paulin - 1990 |
| 5 | Notes on constructive set theory. Available from the WWW – Aczel - 1997 |
| 5 | The !+1 -rule – Buchholz - 1981 |
| 4 | Normalisierung fur die Heyting-Arithmetik mit induktiven Typen – Starke - 1998 |
