A Higher-Order Implementation of Rewriting

Polynomial Interpretations for Higher-Order Rewriting

The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative formalism of algebraic functional systems, where the simply-typed λ-calculus is combined with algebraic reduction. Using this theory, we define higher-order ...

Programming Research Group an Implementation of Higher-order Rewriting (extended Abstract)

Higher-Order Families

A redex family is a set of redexes which arècreated in the same way'. Families specify which redexes should be shared in any so-called optimal implementation of a rewriting system. We formalise the notion of family for orthogonal higher-order term rewriting systems (OHRSs). In order to comfort our formalisation of the intuitive concept of family, we actually provide three conceptually diierent ...

A Logic Programming Approach to Implementing Higher-Order Term Rewriting

Term rewriting has proven to be an important technique in theorem proving. In this paper, we illustrate that rewrite systems and strategies for higher-order term rewriting, which includes the usual notion of rst-order rewriting, can be naturally speciied and implemented in a higher-order logic programming language. We adopt a notion of higher-order rewrite system which uses the simply typed-cal...

R O M a Elfrw: a Tool for Higher-order Dependently Typed Rewriting (system Description)

We report on an extension of the SML implementation of the logic programming language Elf Pfe to support the check of convergence for higher order critical pairs Since Elf is based on the Edinburgh Logical Framework HHP it utilizes dependent types Therefore in the implementation a generalization of the critical pair lemma to this case as done in Vir had to be employed