We introduce a type theoretical framework in which canon ical term rewriting systems can be represented faithfully both from the logical and the computational points of view The framework is based on congruence types a new syntax which combines inductive algebraic and quotient types Congruence types improve on existing work to combine type theories with algebraic rewriting by making explicit th...

Contents 1 Abstract Reduction Systems Abstract Term Rewriting Systems play an important role in various areas, such as abstract data type speciications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic concepts and facts for TRS's. Speciically, we discuss Abstract Reduction Systems; general Term Rewriting Systems incl...

Conditional narrowing is underlying computational mechanism of most functional-logic programming languages. It is important to ensure completeness of conditional narrowing for conditional term rewriting systems without assumption of termination because termination is a too severe restriction for programming languages. In this paper we show completeness of conditional narrowing for a kind of ort...

A property P of term rewriting system is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (R), which results from R by omitting its sort information, has the property P. It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sorts. This is the positi...

Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term rewrite systems. Recent results provide confluence criteria for conditional term rewrite systems via transformations, yet they are restricted to CTRSs with ...

Ground confluence of term rewriting systems guarantees that all ground terms are confluent. Recently, interests in proving confluence of term rewriting systems automatically has grown, and confluence provers have been developed. But they mainly focus on confluence and not ground confluence. In fact, little interest has been paid to developing tools for proving ground confluence automatically. W...

We investigate modular properties of term rewriting systems, the basic operational formalism for equational speciications. First we study suucient conditions for the preservation of the termination property under disjoint (and more general) combinations of term rewriting systems. By means of a reened analysis of existing approaches we show how to prove several new asymmetric preservation result...

Learning from examples is an important characteristic feature of intelligence in both natural and artificial intelligent agents. In this paper, we study learnability of term rewriting systems from positive examples alone. We define a class of linear-bounded term rewriting systems that are inferable from positive examples. In linear-bounded term rewriting systems, nesting of defined symbols is a...

We carry out a detailed analysis of Thatte’s transformation of term rewriting systems. We refute an earlier claim that this transformation preserves confluence for weakly persistent systems. We prove the preservation of weak normalization, and of confluence in weakly normalizing systems and in nonoverlapping systems with linear subtemplates. We conclude by proving that weak persistence is an un...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...