Higher-order rewrite systems and their confluence

Higher-Order Rewrite Systems and Their Confluence

We introduce Higher-Order Rewrite Systems (HRS) which extend term rewriting to-terms. HRS can describe computations on arbitrary terms with bound variables. We show that rewriting is closely related to undirected equational reasoning , and extend three connuence results from term rewriting to HRS: the critical pair lemma by Knuth and Bendix, connuence of rewriting modulo equations a la Huet, an...

Higher-order Rewrite Systems and Their Connuence

We study Higher-Order Rewrite Systems (HRSs) which extend term rewriting to-terms. HRSs can describe computations over terms with bound variables. We show that rewriting with HRSs is closely related to undirected equational reasoning. We deene Pattern Rewrite Systems (PRSs) as a special case of HRSs and extend three connuence results from term rewriting to PRSs: the critical pair lemma by Knuth...

Higher - Order Rewrite Systems and their

Confluence of Conditional Rewrite Systems

Conditional rewriting has been studied both from the point of view of algebraic data type specifications and as a computational paradigm combining logic and functional programming. An important issue, in either case, is determining whether a rewrite system has the Church-Rosser, or confluence, property. In this paper, we settle negatively the question whether "joinabihty of critical pairs" is, ...

Orthogonal Higher-Order Rewrite Systems are Confluent

Two important aspects of computation are reduction, hence the current infatuation with termrewriting systems (TI~Ss), and abstraction, hence the study of A-calculus. In his groundbreaking thesis, Klop [10] combined both areas in the framework of combinatory reduction systems (ClaSs) and lifted many results from the A-calculus to the CRS-level. More recently [15], we proposed a different althoug...