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55
A Calculus for Overload Functions with Subtyping

, 1992
"... We present a simple extension of typed calculus where functions can be overloaded by putting different "branches of code" together. When the function is applied, the branch to execute is chosen according to a particular selection rule which depends on the type of the argument. The crucial featu ..."
Abstract

Cited by 139 (28 self)
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We present a simple extension of typed calculus where functions can be overloaded by putting different "branches of code" together. When the function is applied, the branch to execute is chosen according to a particular selection rule which depends on the type of the argument. The crucial feature of the present approach is that the branch selection depends on the "runtime type" of the argument, which may differ from its compiletime type, because of the existence of a subtyping relation among types. Hence overloading cannot be eliminated by a static analysis of code, but is an essential feature to be dealt with during computation. We obtain in this way a typedependent calculus, which differs from the various calculi where types do not play any role during computation. We prove Confluence and a generalized SubjectReduction theorem for this calculus. We prove Strong Normalization for a "stratified" subcalculus. The definition of this calculus is guided by the understand...
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
On the Security of MultiParty PingPong Protocols
, 1985
"... This paper is concerned with the model for security of cryptographic protocols suggested by Dolev and Yao. The Dolev and Yao model deals with a restricted class of protocols, known as TwoParty PingPong Protocols. In such a protocol, messages are exchanged in a memoryless manner. That is, the mess ..."
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Cited by 60 (1 self)
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This paper is concerned with the model for security of cryptographic protocols suggested by Dolev and Yao. The Dolev and Yao model deals with a restricted class of protocols, known as TwoParty PingPong Protocols. In such a protocol, messages are exchanged in a memoryless manner. That is, the message sent by each party results from applying a predetermined operator to the message he has received. The Dolev and Yao model is presented, generalized in various directions and the affect of these generalizations is extensively studied. First, the model is trivially generalized to deal with multiparty pingpong protocols. However, the problems which arise from this generalization are very far from being trivial. In particular, it is no longer clear how many saboteurs (adversaries) should be considered when testing the security of pparty pingpong protocols. We demonstrate an upper bound of 3(p \Gamma 2) + 2 and a lower bound of 3(p \Gamma 2) + 1 on this number. Thus, for every fixed p, th...
A GraphConstructive Approach to Solving Systems of Geometric Constraints
 ACM TRANSACTIONS ON GRAPHICS
, 1997
"... ..."
Correctness Proof Of A Geometric Constraint Solver
, 1993
"... We present a correctness proof of a graphdirected variational geometric constraint solver. First, we prove that the graph reduction that establishes the sequence in which to apply the construction steps defines a terminating confluent reduction system, in the case of wellconstrained graphs. For ov ..."
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Cited by 31 (7 self)
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We present a correctness proof of a graphdirected variational geometric constraint solver. First, we prove that the graph reduction that establishes the sequence in which to apply the construction steps defines a terminating confluent reduction system, in the case of wellconstrained graphs. For overconstrained problems there may not be a unique normal form. Underconstrained problems, on the other hand, do have a unique normal form. Second, we prove that all geometric solutions found using simple rootselection rules must place certain triples of elements in the same topological order, no matter which graph reduction sequence they are based on. Moreover, we prove that this implies that the geometric solutions derived by different reduction sequences must be congruent. Again, this result does not apply to overconstrained problems. Keywords: geometric constraint solving, computer aided design 1. Introduction Geometric constraint solving has broad applications in a wide range of subje...
Relating Innermost, Weak, Uniform and Modular Termination of Term Rewriting Systems
, 1993
"... We investigate restricted termination and confluence properties of term rewriting systems, in particular weak termination and innermost termination, and their interrelation. New criteria are provided which are sufficient for the equivalence of innermost / weak termination and uniform termination of ..."
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Cited by 28 (5 self)
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We investigate restricted termination and confluence properties of term rewriting systems, in particular weak termination and innermost termination, and their interrelation. New criteria are provided which are sufficient for the equivalence of innermost / weak termination and uniform termination of term rewriting systems. These criteria provide interesting possibilities to infer completeness, i.e. termination plus confluence, from restricted termination and confluence properties. Using these basic results we are also able to prove some new results about modular termination of rewriting. In particular, we show that termination is modular for some classes of innermost terminating and locally confluent term rewriting systems, namely for nonoverlapping and even for overlay systems. As an easy consequence this latter result also entails a simplified proof of the fact that completeness is a decomposable property of socalled constructor systems. Furthermore we show how to obtain similar re...
Persistency of Confluence
, 1997
"... A property P of term rewriting systems (TRSs, for short) is said to be persistent if for any manysorted TRS R, R has the property P if and only if its underlying unsorted TRS (R) has the property P. This notion was introduced by H. Zantema (1994). In this paper, it is shown that confluence is pers ..."
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Cited by 24 (6 self)
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A property P of term rewriting systems (TRSs, for short) is said to be persistent if for any manysorted TRS R, R has the property P if and only if its underlying unsorted TRS (R) has the property P. This notion was introduced by H. Zantema (1994). In this paper, it is shown that confluence is persistent.
MLISP: A RepresentationIndependent Dialect of LISP with Reduction Semantics
 ACM Transactions on Programming Languages and Systems
, 1992
"... In this paper we introduce MLISP, a simple new dialect of LISP which is designed with an eye toward reconciling LISP's metalinguistic power with the structural style of operational semantics advocated by Plotkin [Plo75]. We begin by reviewing the original denition of LISP [McC61] in an attempt t ..."
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Cited by 21 (2 self)
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In this paper we introduce MLISP, a simple new dialect of LISP which is designed with an eye toward reconciling LISP's metalinguistic power with the structural style of operational semantics advocated by Plotkin [Plo75]. We begin by reviewing the original denition of LISP [McC61] in an attempt to clarify the source of its metalinguistic power. We nd that it arises from a problematic clause in this denition. We then dene the abstract syntax and operational semantics of MLISP, essentially a hybrid of Mexpression LISP and Scheme. Next, we tie the operational semantics to the corresponding equational logic. As usual, provable equality in the logic implies operational equality. Having established this framework we then extend MLISP with the metalinguistic eval and reify operators (the latter is a nonstrict operator which converts its argument to its metalanguage representation.) These operators encapsulate the metalinguistic representation conversions that occur globall...