Higher-Order and Symbolic Computation

, Volume 19, Issue 2, pp 231–262

An initial algebra approach to term rewriting systems with variable binders


DOI: 10.1007/s10990-006-8747-5

Cite this article as:
Hamana, M. Higher-Order Symb Comput (2006) 19: 231. doi:10.1007/s10990-006-8747-5


We present an extension of first-order term rewriting systems. It involves variable binding in the term language. We develop systems called binding term rewriting systems (BTRSs) in a stepwise manner. First we present the term language, then formulate equational logic. Finally, we define rewriting systems. This development is novel because we follow the initial algebra approach in an extended notion of Σ-algebras in various functor categories. These are based on Fiore-Plotkin-Turi’s presheaf semantics of variable binding and Lüth-Ghani’s monadic semantics of term rewriting systems. We characterise the terms, equational logic and rewrite systems for BTRSs as initial algebras in suitable categories. Then, we show an important rewriting property of BTRSs: orthogonal BTRSs are confluent. Moreover, by using the initial algebra semantics, we give a complete characterisation of termination of BTRSs. Finally, we discuss our design choice of BTRSs from a semantic perspective.


Term rewriting systemsAbstract syntax with variable bindingHigher-order abstract syntaxInitial algebra semantics

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Computer ScienceGunma UniversityJapan