An Effective Method for Handling Initial Algebras

Given an arbitrary Term Rewriting System R, we compute a “conditional grammar” of the language of ground terms which are irreducible for R. Such a presentation provides a powerful tool for reasoning in non-free algebras. We sketch here two applications: 1. The decision of inductive reducibility (which is a key concept in automating proofs by induction) 2. The automatic transformation of non-free, many sorted algebraic specifications into free order-sorted specifications.

[1]  Paliath Narendran,et al.  Complexity of Sufficient-Completeness , 1986, FSTTCS.

[2]  Jean H. Gallier,et al.  Reductions in Tree Replacement Systems , 1985, Theor. Comput. Sci..

[3]  Philippe Schnoebelen,et al.  Refined Compilation of Pattern-Matching for Functional Languages , 1988, Sci. Comput. Program..

[4]  David A. Plaisted,et al.  Semantic Confluence Tests and Completion Methods , 1985, Inf. Control..

[5]  Simon J. Thompson.  Laws in Miranda , 1986, LFP '86.

[6]  Hubert Comon.  Unification et disunification : théorie et applications , 1988 .

[7]  Hubert Comon,et al.  How to characterize the language of ground normal forms , 1986 .

[8]  José Meseguer,et al.  Models and Equality for Logical Programming , 1987, TAPSOFT, Vol.1.

[9]  José Meseguer,et al.  Initiality, induction, and computability , 1986 .

[10]  Jean-Jacques Thiel.  Stop losing sleep over incomplete data type specifications , 1984, POPL '84.

[11]  Pierre Lescanne,et al.  Proving inductive equalities algorithms and implementation , 1986 .

[12]  Alain Colmerauer,et al.  Equations and Inequations on Finite and Infinite Trees , 1984, FGCS.

[13]  Tobias Nipkow,et al.  A decidability result about sufficient-completeness of axiomatically specified abstract data types , 1983 .

[14]  Michael J. Maher.  Complete axiomatizations of the algebras of finite, rational and infinite trees , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[15]  H. Comon.  Sufficient Completness, Term Rewriting Systems and Anti-Unification , 1986 .

[16]  Jean-Pierre Jouannaud,et al.  Proofs by induction in equational theories without constructors , 1985, Bull. EATCS.

[17]  Gérard P. Huet,et al.  Proofs by induction in equational theories with constructors , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[18]  Hubert Comon-Lundh,et al.  Equational Problems and Disunification , 1989, J. Symb. Comput..