Combinatory reduction systems: introduction and survey

Klop, Jan Willem; Oostrom, Vincent van; Raamsdonk, Femke van

doi:10.1016/0304-3975(93)90091-7

Cited by 191 publications

(171 citation statements)

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“…In other words, the rules defining the generic functions do not reuse variables in the left-hand side, and all functions are defined by cases on constructors, without superpositions. Left-linear and non-overlapping rules are confluent, even in the case of higher-order rewrite systems, as proved by Klop (see, for instance, [47]). Thus, we can give a sufficient condition for confluence derived from Klop's orthogonality theorem.…”

Section: Policy Analysis: Higher-order Operatorsmentioning

confidence: 73%

A metamodel of access control for distributed environments: Applications and properties

Bertolissi

Fernández

2014

Information and Computation

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We describe a metamodel for access control, designed to take into account the specific requirements of distributed environments. We see a distributed system consisting of several sites, each with its own resources to protect, as a federation, and propose a framework for the specification (and enforcement) of global access control policies that take into account the local policies specified by each member of the federation. The framework provides mechanisms to specify heterogeneous local access control policies, to define policy composition operators, and to use them to define conflict-free access authorisation decisions. We use a declarative formalism in order to give an operational semantics to the distributed metamodel. We then show how properties of policies can be directly obtained from standard results for the operational semantics of access request evaluation.

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Section: Policy Analysis: Higher-order Operatorsmentioning

confidence: 73%

A metamodel of access control for distributed environments: Applications and properties

Bertolissi

Fernández

2014

Information and Computation

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“…In contrast, higher-order rewriting systems (e.g. CRSs [22], HRSs [25], ERSs [21,20], HORSs [31], and the ρ-calculus [10,11]) extend first-order rewriting to include binders using higher-order substitutions and higher-order matching (i.e. matching modulo β) and therefore binders are allowed in left-hand sides.…”

Section: Related Workmentioning

confidence: 99%

“…A CRS [23,22] In CRSs a distinction is made between metaterms and terms. Metaterms are the expressions built from the symbols in the alphabet, in the usual way.…”

Section: Combinatory Reduction Systemsmentioning

confidence: 99%

“…Higher-order terms are built with higher-order functions and variables which can be free or bound. Several examples of higher-order systems can be found in the literature: Combinatory Reduction Systems (CRS) [22], Higherorder Rewrite Systems (HRS) [25], Expression Reduction Systems (ERS) [21,20], and the rewriting calculus [10,11], combine first-order rewriting with a notion of bound variable. The λ-calculus can be seen as a higher-order rewrite system with one binder: λ-abstraction.…”

Section: Introductionmentioning

confidence: 99%

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Nominal rewriting systems

Fernández

Gabbay

Mackie

2004

Proceedings of the 6th ACM SIGPLAN International Conference on Principles and Practice of Declarative Programming

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We present a generalisation of first-order rewriting which allows us to deal with terms involving binding operations in an elegant and practical way. We use a nominal approach to binding, in which bound entities are explicitly named (rather than using a nameless syntax such as de Bruijn indices), yet we get a rewriting formalism which respects α-conversion and can be directly implemented. This is achieved by adapting to the rewriting framework the powerful techniques developed by Pitts et al. in the FreshML project.Nominal rewriting can be seen as higher-order rewriting with a first-order syntax and built-in α-conversion. We show that standard (first-order) rewriting is a particular case of nominal rewriting, and that very expressive higher-order systems such as Klop's Combinatory Reduction Systems can be easily defined as nominal rewriting systems. Finally we study confluence properties of nominal rewriting.

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“…Indeed, the new σ-reduction rules are formulated in such a way that there are no critical pairs so the reduction relation is orthogonal and hence confluent [26].…”

Section: Properties Of the Extended Type Systemmentioning

confidence: 99%