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Rewriting Logic as a Logical and Semantic Framework
, 1993
"... Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are und ..."
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Cited by 169 (57 self)
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Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are understood as mappings L ! F that translate one logic into the other in a conservative way. The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of "sequent," is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L ! RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of...
Theorem Proving Modulo
 Journal of Automated Reasoning
"... Abstract. Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of much wider interest because it permits to separate computations and deductions in a clean way. The first ..."
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Cited by 112 (18 self)
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Abstract. Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of much wider interest because it permits to separate computations and deductions in a clean way. The first contribution of this paper is to define a sequent calculus modulo that gives a proof theoretic account of the combination of computations and deductions. The congruence on propositions is handled via rewrite rules and equational axioms. Rewrite rules apply to terms and also directly to atomic propositions. The second contribution is to give a complete proof search method, called Extended Narrowing and Resolution (ENAR), for theorem proving modulo such congruences. The completeness of this method is proved with respect to provability in sequent calculus modulo. An important application is that higherorder logic can be presented as a theory modulo. Applying the Extended Narrowing and Resolution method to this presentation of higherorder logic subsumes full higherorder resolution.
Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda ..."
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Cited by 109 (13 self)
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Higherorder unification is equational unification for &beta;&eta;conversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda;&sigma;calculus of explicit substitutions.
What Are Principal Typings and What Are They Good For?
, 1995
"... We demonstrate the pragmatic value of the principal typing property, a property more general than ML's principal type property, by studying a type system with principal typings. The type system is based on rank 2 intersection types and is closely related to ML. Its principal typing property ..."
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Cited by 102 (0 self)
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We demonstrate the pragmatic value of the principal typing property, a property more general than ML's principal type property, by studying a type system with principal typings. The type system is based on rank 2 intersection types and is closely related to ML. Its principal typing property provides elegant support for separate compilation, including "smartest recompilation" and incremental type inference, and for accurate type error messages. Moreover, it motivates a novel rule for typing recursive definitions that can type many examples of polymorphic recursion.
Deciding security of protocols against offline guessing attacks
 In Proc. 12th ACM Conference on Computer and Communications Security (CCS’05
, 2005
"... We provide an effective procedure for deciding the existence of offline guessing attacks on security protocols, for a bounded number of sessions. The procedure consists of a constraint solving algorithm for determining satisfiability and equivalence of a class of secondorder Eunification problems ..."
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Cited by 73 (4 self)
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We provide an effective procedure for deciding the existence of offline guessing attacks on security protocols, for a bounded number of sessions. The procedure consists of a constraint solving algorithm for determining satisfiability and equivalence of a class of secondorder Eunification problems, where the equational theory E is presented by a convergent subterm rewriting system. To the best of our knowledge, this is the first decidability result to use the generic definition of offline guessing attacks due to Corin et al. based on static equivalence in the applied pi calculus.
Completion of Rewrite Systems with Membership Constraints Part II: Constraint Solving
 J. Symbolic Computation
, 1992
"... this paper is to show how to solve the constraints that are involved in the deduction mechanism of the first part. This may be interesting in its own since this provides with a unification algorithm for an ordersorted logic with context variables and can be read independently of the first part. Thi ..."
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Cited by 70 (2 self)
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this paper is to show how to solve the constraints that are involved in the deduction mechanism of the first part. This may be interesting in its own since this provides with a unification algorithm for an ordersorted logic with context variables and can be read independently of the first part. This can also be compared with unification of term schemes of various kind (Chen & Hsiang, 1991; Salzer, 1992; Comon, 1995; R. Galbav'y and M. Hermann, 1992). Indeed,
Unification via Explicit Substitutions: The Case of HigherOrder Patterns
 PROCEEDINGS OF JICSLP'96
, 1998
"... In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient ..."
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Cited by 64 (18 self)
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In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient way to patterns. We also sketch an efficient implementation of the abstract algorithm and its generalization to constraint simplification, which has yielded good experimental results at the core of a higherorder constraint logic programming language.
Objective ML: An effective objectoriented extension to ML
 THEORY AND PRACTICE OF OBJECT SYSTEMS
, 1998
"... Objective ML is a small practical extension to ML with objects and top level classes. It is fully compatible with ML; its type system is based on ML polymorphism, record types with polymorphic access, and a better treatment of type abbreviations. Objective ML allows for most features of objectorien ..."
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Cited by 61 (5 self)
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Objective ML is a small practical extension to ML with objects and top level classes. It is fully compatible with ML; its type system is based on ML polymorphism, record types with polymorphic access, and a better treatment of type abbreviations. Objective ML allows for most features of objectoriented languages including multiple inheritance, methods returning self and binary methods as well as parametric classes. This demonstrates that objects can be added to strongly typed languages based on ML polymorphism.
Controlling Rewriting by Rewriting
"... In this paper, we investigate the idea of controlling rewriting by strategies and we develop a strategy language whose operational semantics is also based on rewriting. This language is described in ELAN, a language based on computational systems that are simply rewriting theories controlled by stra ..."
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Cited by 45 (12 self)
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In this paper, we investigate the idea of controlling rewriting by strategies and we develop a strategy language whose operational semantics is also based on rewriting. This language is described in ELAN, a language based on computational systems that are simply rewriting theories controlled by strategies. We illustrate the syntax, semantics and different features of this strategy language. Finally, we sketch its bootstrapping implementation by a transformation into a computational system, whose heart is a rewrite theory controlled by a lowerlevel strategy of ELAN. 1 Introduction Elegance and expressiveness of rewriting as a computational paradigm are no more to be stressed. What might be less evident, is the weakness that comes from the absence of controlling mechanism over rewriting. In many existing term rewriting systems, the term reduction strategy is hardwired and is not accessible to the designer of an application. The results of [KKV95a] and some experiences show that even f...
Unions of NonDisjoint Theories and Combinations of Satisfiability Procedures
 THEORETICAL COMPUTER SCIENCE
, 2001
"... In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint s ..."
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Cited by 44 (7 self)
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In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint satisfiability with respect to a constraint theory T2, produces a procedure that (semi)decides constraint satisfiability with respect to the union of T1 and T2. We provide a number of modeltheoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are nondisjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.