Computing Constructor Forms with Non Terminating Rewrite Programs

Isabelle Gnaedig 1 Hélène Kirchner 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In the context of the study of rule-based programming, we focus in this paper on the property of C-reducibility, expressing that every term reduces to a constructor term on at least one of its rewriting derivations. This property implies completeness of function definitions, and enables to stop evaluations of a program on a constructor form, even if the program is not terminating. We propose an inductive procedure proving C-reducibility of rewriting. The rewriting relation on ground terms is simulated through an abstraction mechanism and narrowing. The induction hypothesis allows assuming that terms smaller than the starting terms rewrite into a constructor term. The existence of the induction ordering is checked during the proof process, by ensuring satisfiability of ordering constraints. The proof is constructive, in the sense that the branch leading to a constructor term can be computed from the proof trees establishing C-reducibility for every term.
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Submitted on : Tuesday, November 7, 2006 - 1:34:08 PM
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Isabelle Gnaedig, Hélène Kirchner. Computing Constructor Forms with Non Terminating Rewrite Programs. Symposium on Principles and Practice of Declarative Programming - PPDP'06, Jul 2006, Venise/Italie. ⟨inria-00112083⟩

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