Proofs and computations in conditional equational theories
G. Sivakumar · 1990
Conditional equations arise naturally in the algebraic speci cation of data types. They also provide an elegant computational paradigm that cleanly combines logic and functional programming. In this thesis, we study how to do proofs and computations in conditional equational theories, using rewriting techniques. We examine di erentformulations of conditional equations as rewrite systems and compare their expressive power. We identify a class of \\decreasing " systems for which most of the basic notions (like rewriting and computing normal forms) are decidable. We then study how to determine if a conditional rewrite system is \\con uent. " We settle negatively the question whether \\joinability of critical pairs " is, in general, su cient for con uence of terminating conditional systems. We also prove two positive results for systems having critical pairs and arbitrarily big terms in conditions. We discuss \\completion " methods to generate convergent conditional rewrite systems equivalent to a given set of conditional equations. Finally, we study equation solving methods and formulate a goal-directed approach that improves prior methods and detects more unsatis able equations. iii To my parents.