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Proving Security Protocols With Model Checkers By Data Independence Techniques
, 1999
"... Model checkers such as FDR have been extremely effective in checking for, and finding, attacks on cryptographic protocols  see, for example [16, 20] and many of the papers in [7]. Their use in proving protocols has, on the other hand, generally been limited to showing that a given small instanc ..."
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Cited by 63 (10 self)
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Model checkers such as FDR have been extremely effective in checking for, and finding, attacks on cryptographic protocols  see, for example [16, 20] and many of the papers in [7]. Their use in proving protocols has, on the other hand, generally been limited to showing that a given small instance, usually restricted by the finiteness of some set of resources such as keys and nonces, is free of attacks. While for specific protocols there are frequently good reasons for supposing that this will find any attack, it leaves a substantial gap in the method. The purpose of this paper is to show how techniques borrowed from data independence and related fields can be used to achieve the illusion that nodes can call upon an infinite supply of different nonces, keys, etc., even though the actual types used for these things remain finite. It is thus possible to create models of protocols in which nodes do not have to stop after a small number of runs, and to claim that a finitestate r...
Prelogical Relations
, 1999
"... this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results ..."
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Cited by 25 (5 self)
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this paper but which have some intriguing connections to some of our results and techniques, are [32] and [20]. We believe that the concept of prelogical relation would have a beneficial impact on the presentation and understanding of their results
The Impact of seq on Free TheoremsBased Program Transformations
 Fundamenta Informaticae
, 2006
"... Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, standard parametricity results — including socalled free theorems — fail for nonstrict ..."
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Cited by 17 (5 self)
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Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, standard parametricity results — including socalled free theorems — fail for nonstrict languages supporting a polymorphic strict evaluation primitive such as Haskell’s seq. A folk theorem maintains that such results hold for a subset of Haskell corresponding to a GirardReynolds calculus with fixpoints and algebraic datatypes even when seq is present provided the relations which appear in their derivations are required to be bottomreflecting and admissible. In this paper we show that this folklore is incorrect, but that parametricity results can be recovered in the presence of seq by restricting attention to leftclosed, total, and admissible relations instead. The key novelty of our approach is the asymmetry introduced by leftclosedness, which leads to “inequational” versions of standard parametricity results together with preconditions guaranteeing their validity even when seq is present. We use these results to derive criteria ensuring that both equational and inequational versions of short cut fusion and related program transformations based on free theorems hold in the presence of seq.
P.J.: Inductive types in constructive languages
, 1995
"... Logic grammar is used to partly define a formal mathematical language “ADAM”, that keeps close to informal mathematics and yet is reducible to a foundation of Constructive Type Theory (or Generalized Typed Lambda Calculus). This language is employed in making a study of inductive types and related s ..."
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Cited by 4 (0 self)
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Logic grammar is used to partly define a formal mathematical language “ADAM”, that keeps close to informal mathematics and yet is reducible to a foundation of Constructive Type Theory (or Generalized Typed Lambda Calculus). This language is employed in making a study of inductive types and related subjects, as they appear in languages for constructive mathematics and lambda calculi. The naturality property of objects with type parameters is described and employed. Cover diagram Behold the mathematical universe, developing from original unity into categorical duality. The central beam contains the initial and the final type, together with the remaining flat finite types. It is flanked by the dual principles of generalized sum and product, and of initial and final fixed point construction.
Program Equivalence in Linear Contexts
"... Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at contextual equivalence in the usual (nonlinear) functional l ..."
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Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at contextual equivalence in the usual (nonlinear) functional languages, and fail in capturing nontrivial equivalent programs in linear contexts, particularly when nondeterminism is present. We propose the notion of linear contextual equivalence to formally characterize such program equivalence, as well as a novel and general approach to studying it in higherorder languages, based on labeled transition systems specifically designed for functional languages. We show that linear contextual equivalence indeed coincides with trace equivalence. We illustrate our technique in both deterministic (a linear version of PCF) and nondeterministic (linear PCF in Moggi’s framework) functional languages.
IOS Press The Impact of seq on Free TheoremsBased Program Transformations ∗
"... Abstract. Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, standard parametricity results — including socalled free theorems — fail for ..."
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Abstract. Parametric polymorphism constrains the behavior of pure functional programs in a way that allows the derivation of interesting theorems about them solely from their types, i.e., virtually for free. Unfortunately, standard parametricity results — including socalled free theorems — fail for nonstrict languages supporting a polymorphic strict evaluation primitive such as Haskell’s seq. A folk theorem maintains that such results hold for a subset of Haskell corresponding to a GirardReynolds calculus with fixpoints and algebraic datatypes even when seq is present provided the relations which appear in their derivations are required to be bottomreflecting and admissible. In this paper we show that this folklore is incorrect, but that parametricity results can be recovered in the presence of seq by restricting attention to leftclosed, total, and admissible relations instead. The key novelty of our approach is the asymmetry introduced by leftclosedness, which leads to “inequational ” versions of standard parametricity results together with preconditions guaranteeing their validity even when seq is present. We use these results to derive criteria ensuring that both equational and inequational versions of short cut fusion and related program transformations based
and
"... We study a weakening of the notion of logical relations, called prelogical relations, that has many of the features that make logical relations so useful as well as further algebraic properties including composability. The basic idea is simply to require the reverse implication in the definition of ..."
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We study a weakening of the notion of logical relations, called prelogical relations, that has many of the features that make logical relations so useful as well as further algebraic properties including composability. The basic idea is simply to require the reverse implication in the definition of logical relations to hold only for pairs of functions that are expressible by the same lambda term. Prelogical relations are the minimal weakening of logical relations that gives composability for extensional structures and simultaneously the most liberal definition that gives the Basic Lemma. Prelogical predicates (i.e., unary prelogical relations) coincide with sets that are invariant under Kripke logical relations with varying arity as introduced by Jung and Tiuryn, and prelogical relations are the closure under projection and intersection of logical relations. These conceptually independent characterizations of prelogical relations suggest that the concept is rather intrinsic and robust. The use of prelogical relations gives an improved version of Mitchell’s representation independence theorem which characterizes observational equivalence for all signatures rather than just for firstorder signatures. Prelogical relations can be used in place of logical relations to give an account of data refinement where the fact that prelogical relations compose explains why stepwise refinement is sound.