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Logical Concepts in Cryptography
, 2006
"... This paper is about the exploration of logical concepts in cryptography and their linguistic abstraction and modeltheoretic combination in a logical system, called CPL (for Cryptographic Protocol Logic). ..."
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Cited by 5 (3 self)
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This paper is about the exploration of logical concepts in cryptography and their linguistic abstraction and modeltheoretic combination in a logical system, called CPL (for Cryptographic Protocol Logic).
A User Guide to Bedwyr
, 2006
"... Some recent theoretical work in proof search has illustrated that it is possible to combine the following two computational principles into one computational logic. 1. A symmetric treatment of finite success and finite failure. This allows capturing both aspects of may and must behavior in operation ..."
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Cited by 4 (2 self)
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Some recent theoretical work in proof search has illustrated that it is possible to combine the following two computational principles into one computational logic. 1. A symmetric treatment of finite success and finite failure. This allows capturing both aspects of may and must behavior in operational semantics and mixing model checking and logic programming. 2. Direct support for λtree syntax, as in λProlog, via termlevel λbinders, higherorder pattern unification, and the ∇quantifier. All these features have a clean proof theory. The combination of these features allow, for example, specifying rather declarative approaches to model checking syntactic expressions containing bindings. The Bedwyr system is intended as an implementation of these computational logic principles. Why the name Bedwyr? In the legend of King Arthur and the round table, several knights shared in the search for the holy grail. The name of one of them, Parsifal, is used for an INRIA team associated with the “Slimmer ” effort. Bedwyr was another one of those knights. Wikipedia (using the spelling “Bedivere”) mentions that Bedwyr appears in Monty Python and the Holy Grail where he is “portrayed as a master of the extremely odd logic in the ancient times, whom occasionally blunders. ” Bedwyr is a reimplementation and rethinking ∗ Support has been obtained for this work from the following sources: from INRIA through
The Representational Adequacy of HYBRID
"... The Hybrid system (Ambler et al., 2002b), implemented within Isabelle/HOL, allows object logics to be represented using higher order abstract syntax (HOAS), and reasoned about using tactical theorem proving in general and principles of (co)induction in particular. The form of HOAS provided by Hybrid ..."
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Cited by 2 (1 self)
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The Hybrid system (Ambler et al., 2002b), implemented within Isabelle/HOL, allows object logics to be represented using higher order abstract syntax (HOAS), and reasoned about using tactical theorem proving in general and principles of (co)induction in particular. The form of HOAS provided by Hybrid is essentially a lambda calculus with constants. Of fundamental interest is the form of the lambda abstractions provided by Hybrid. The user has the convenience of writing lambda abstractions using names for the binding variables. However each abstraction is actually a definition of a de Bruijn expression, and Hybrid can unwind the user’s abstractions (written with names) to machine friendly de Bruijn expressions (without names). In this sense the formal system contains a hybrid of named and nameless bound variable notation. In this paper, we present a formal theory in a logical framework which can be viewed as a model of core Hybrid, and state and prove that the model is representationally adequate for HOAS. In particular, it is the canonical translation function from λexpressions to Hybrid that witnesses adequacy. We also prove two results that characterise how Hybrid represents certain classes of λexpressions. The Hybrid system contains a number of different syntactic classes of expression, and associated abstraction mechanisms. Hence this paper also aims to provide a selfcontained theoretical introduction to both the syntax and key ideas of the system; background in automated theorem proving is not essential, although this paper will be of considerable interest to those who wish to work with Hybrid in Isabelle/HOL.
3.5. Deep Inference and Categorical Axiomatizations 5 3.6. Proof Nets and Combinatorial Characterization of Proofs 5
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