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Under consideration for publication in J. Functional Programming 1 A Predicative Analysis of Structural Recursion
 

Summary: Under consideration for publication in J. Functional Programming 1
A Predicative Analysis of Structural Recursion
ANDREAS ABEL
Department of Computer Science, University of Munich, 80538 Munich, Germany
(e-mail: abel@tcs.informatik.uni-muenchen.de)
THORSTEN ALTENKIRCH
School of Computer Science & Information Technology, University of Nottingham,
Nottingham, NG8 1BB, UK
(e-mail: txa@cs.nott.ac.uk)
Abstract
We introduce a language based upon lambda calculus with products, coproducts and
strictly positive inductive types that allows the de nition of recursive terms. We present
the implementation (foetus) of a syntactical check that ensures that all such terms are
structurally recursive, i.e., recursive calls appear only with arguments structurally smaller
than the input parameters of terms considered. To ensure the correctness of the termina-
tion checker, we show that all structurally recursive terms are normalizing with respect
to a given operational semantics. To this end, we de ne a semantics on all types and a
structural ordering on the values in this semantics and prove that all values are accessible
with regard to this ordering. Finally, we point out how to do this proof predicatively using
set based operators.

  

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen

 

Collections: Computer Technologies and Information Sciences