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The HigherOrder Recursive Path Ordering
 FOURTEENTH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 1999
"... This paper extends the termination proof techniques based on reduction orderings to a higherorder setting, by adapting the recursive path ordering definition to terms of a typed lambdacalculus generated by a signature of polymorphic higherorder function symbols. The obtained ordering is wellfoun ..."
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Cited by 58 (12 self)
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This paper extends the termination proof techniques based on reduction orderings to a higherorder setting, by adapting the recursive path ordering definition to terms of a typed lambdacalculus generated by a signature of polymorphic higherorder function symbols. The obtained ordering is wellfounded, compatible with fireductions and with polymorphic typing, monotonic with respect to the function symbols, and stable under substitution. It can therefore be used to prove the strong normalizationproperty of higherorder calculi in which constants can be defined by higherorder rewrite rules. For example, the polymorphic version of Gödel's recursor for the natural numbers is easily oriented. And indeed, our ordering is polymorphic, in the sense that a single comparison allows to prove the termination property of all monomorphic instances of a polymorphic rewrite rule. Several other nontrivial examples are given which examplify the expressive power of the ordering.
Abstract Data Type Systems
 Theoretical Computer Science
, 1997
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 54 (10 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Code generation via higherorder rewrite systems
 In Functional and Logic Programming, 10th International Symposium: FLOPS 2010, volume 6009 of Lecture Notes in Computer Science
, 2010
"... Abstract. We present the metatheory behind the code generation facilities of Isabelle/HOL. To bridge the gap between the source (higherorder logic with type classes) and the many possible targets (functional programming languages), we introduce an intermediate language, MiniHaskell. To relate th ..."
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Cited by 46 (5 self)
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Abstract. We present the metatheory behind the code generation facilities of Isabelle/HOL. To bridge the gap between the source (higherorder logic with type classes) and the many possible targets (functional programming languages), we introduce an intermediate language, MiniHaskell. To relate the source and the intermediate language, both are given a semantics in terms of higherorder rewrite systems (HRSs). In a second step, type classes are removed from MiniHaskell programs by means of a dictionary translation; we prove the correctness of this step. Building on equational logic also directly supports a simple but powerful algorithm and data refinement concept. 1 Introduction and related work Like many theorem provers, Isabelle/HOL can generate functional programs from recursive functions specified in the logic. Many applications have taken advantage of this feature, e.g. the certified termination analysis tool CeTA [19] or the Quickcheck counterexample search [3]. The initial code generator [2] has since
Nominal rewriting
 Information and Computation
"... Nominal rewriting is based on the observation that if we add support for alphaequivalence to firstorder syntax using the nominalset approach, then systems with binding, including higherorder reduction schemes such as lambdacalculus betareduction, can be smoothly represented. Nominal rewriting ma ..."
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Cited by 32 (13 self)
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Nominal rewriting is based on the observation that if we add support for alphaequivalence to firstorder syntax using the nominalset approach, then systems with binding, including higherorder reduction schemes such as lambdacalculus betareduction, can be smoothly represented. Nominal rewriting maintains a strict distinction between variables of the objectlanguage (atoms) and of the metalanguage (variables or unknowns). Atoms may be bound by a special abstraction operation, but variables cannot be bound, giving the framework a pronounced firstorder character, since substitution of terms for variables is not captureavoiding. We show how good properties of firstorder rewriting survive the extension, by giving an efficient rewriting algorithm, a critical pair lemma, and a confluence theorem
HigherOrder Rewriting
 12th Int. Conf. on Rewriting Techniques and Applications, LNCS 2051
, 1999
"... This paper will appear in the proceedings of the 10th international conference on rewriting techniques and applications (RTA'99). c flSpringer Verlag. ..."
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Cited by 28 (1 self)
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This paper will appear in the proceedings of the 10th international conference on rewriting techniques and applications (RTA'99). c flSpringer Verlag.
Developing Developments
, 1994
"... Confluence of orthogonal rewriting systems can be proved using the Finite Developments Theorem. We present, in a general setting, several adaptations of this proof method for obtaining confluence of `not quite' orthogonal systems. 1. Introduction Rewriting as studied here is based on the an ..."
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Cited by 23 (2 self)
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Confluence of orthogonal rewriting systems can be proved using the Finite Developments Theorem. We present, in a general setting, several adaptations of this proof method for obtaining confluence of `not quite' orthogonal systems. 1. Introduction Rewriting as studied here is based on the analogy: rewriting = substitution + rules. This analogy is useful since it enables a clearcut distinction between the `designer' defined substition process, i.e. management of resources, and the `user' defined rewrite rules, of rewriting systems. For example, application of the `user' defined term rewriting rule 2 \Theta x ! x + x to the term 2 \Theta 3 gives rise to the duplication of the term 3 in the result 3 + 3. How this duplication is actually performed (for example, using sharing) depends on the `designer's' implementation of substitution. This decomposition has been shown useful in [OR94, Oos94] in the case of firstorder term rewriting systems (TRSs, [DJ90, Klo92]) and higherorder term r...
Termination and confluence of higherorder rewrite systems
 In Proc. RTA ’00, volume 1833 of LNCS
, 2000
"... Abstract: In the last twenty years, several approaches to higherorder rewriting have been proposed, among which Klop’s Combinatory Rewrite Systems (CRSs), Nipkow’s Higherorder Rewrite Systems (HRSs) and Jouannaud and Okada’s higherorder algebraic specification languages, of which only the last on ..."
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Cited by 19 (6 self)
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Abstract: In the last twenty years, several approaches to higherorder rewriting have been proposed, among which Klop’s Combinatory Rewrite Systems (CRSs), Nipkow’s Higherorder Rewrite Systems (HRSs) and Jouannaud and Okada’s higherorder algebraic specification languages, of which only the last one considers typed terms. The later approach has been extended by Jouannaud, Okada and the present author into Inductive Data Type Systems (IDTSs). In this paper, we extend IDTSs with the CRS higherorder patternmatching mechanism, resulting in simplytyped CRSs. Then, we show how the termination criterion developed for IDTSs with firstorder patternmatching, called the General Schema, can be extended so as to prove the strong normalization of IDTSs with higherorder patternmatching. Next, we compare the unified approach with HRSs. We first prove that the extended General Schema can also be applied to HRSs. Second, we show how Nipkow’s higherorder critical pair analysis technique for proving local confluence can be applied to IDTSs. 1
A code generator framework for Isabelle/HOL
 Department of Computer Science, University of Kaiserslautern
, 2007
"... Abstract. We present a code generator framework for Isabelle/HOL. It formalizes the intermediate stages between the purely logical description in terms of equational theorems and a programming language. Correctness of the translation is established by giving the intermediate languages (a subset of H ..."
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Cited by 15 (4 self)
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Abstract. We present a code generator framework for Isabelle/HOL. It formalizes the intermediate stages between the purely logical description in terms of equational theorems and a programming language. Correctness of the translation is established by giving the intermediate languages (a subset of Haskell) an equational semantics and relating it back to the logical level. To allow code generation for SML, we present and prove correct a (dictionarybased) translation eliminating type classes. The design of our framework covers different functional target languages. 1 Introduction and related work Executing formal specifications is a wellestablished topic and many theorem provers support this activity by generating code in a standard programming language from a logical description, typically by translating an internal functional language to an external one:
Finite Family Developments
"... Associate to a rewrite system R having rules l → r, its labelled version R ω having rules l ◦ m+1 → r • , for any natural number m m ∈ ω. These rules roughly express that a lefthand side l carrying labels all larger than m can be replaced by its righthand side r carrying labels all smaller than o ..."
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Cited by 15 (6 self)
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Associate to a rewrite system R having rules l → r, its labelled version R ω having rules l ◦ m+1 → r • , for any natural number m m ∈ ω. These rules roughly express that a lefthand side l carrying labels all larger than m can be replaced by its righthand side r carrying labels all smaller than or equal to m. A rewrite system R enjoys finite family developments (FFD) if R ω is terminating. We show that the class of higher order pattern rewrite systems enjoys FFD, extending earlier results for the lambda calculus and first order term rewrite systems.
Term rewriting for access control
 In Proc. DBSec’2006, volume 4127 of LNCS
, 2006
"... Abstract. We demonstrate how access control models and policies can be represented by using term rewriting systems, and how rewriting may be used for evaluating access requests and for proving properties of an access control policy. We focus on two kinds of access control models: discretionary model ..."
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Abstract. We demonstrate how access control models and policies can be represented by using term rewriting systems, and how rewriting may be used for evaluating access requests and for proving properties of an access control policy. We focus on two kinds of access control models: discretionary models, based on access control lists (ACLs), and rolebased access control (RBAC) models. For RBAC models, we show that we can specify several variants, including models with role hierarchies, and constraints and support for security administrator review querying. 1