Term rewriting and all that

  title={Term rewriting and all that},
  author={Franz Baader and Tobias Nipkow},

A Functional Approach to String Rewriting and Gröbner bases

An algebraic formulation of completion is given and it is shown that such a completion exists using the lattice structure and the notions of confluence and of Church-Rosser property are equivalent.

Confluence and Normalization in Reduction Systems Lecture Notes

We study confluence and normalization in abstract reduction systems and apply the results to combinatory logic and an abstract version of the lambda beta calculus. For both systems we obtain the

Introduction to Term Rewriting Systems

The confluence property is introduced, which is certainly one of the most fundamental properties ofterm rewriting theory, and applications of term rewriting systems to the field of automated theorem proving are presented.

On some slowly terminating term rewriting systems

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano

Term Rewriting

This tutorial gives an introduction to term rewriting, which is an important computational model with applications in algebra, software engineering, declarative programming, and theorem proving.

Joint Spectral Radius Theory for Automated Complexity Analysis of Rewrite Systems

This paper strengthens and unifies improvements based on the theory of weighted automata and linear algebra by using joint spectral radius theory on the derivational complexity of (compatible) rewrite systems.

Semantic Matching for Left-Linear Convergent Rewrite Systems

A calculus for solving the semantic matching problem with respect to left-linear or variable-preserving convergent termrewriting systems is presented and the approach to designing a special calculus for special goals is proposed.

Relative Undecidability in Term Rewriting: II. The Confluence Hierarchy

For a hierarchy of properties of term rewriting systems related to confluence we prove relative undecidability, i.e., for implications X ↠ Y in the hierarchy the property X is undecidable for term

Confluence and Termination of Simply Typed Term Rewriting Systems

A simple proof method for confluence is studied which employs a characterization of the diamond property of a parallel reduction and a new confluence result is obtained for orthogonal conditional STTRSs.

A Coinductive Framework for Infinitary Rewriting and Equational Reasoning

A coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way that has neither the need for ordinals nor for metric convergence, making the framework especially suitable for formalizations in theorem provers.