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A Proof Search Specification of the πCalculus
 IN 3RD WORKSHOP ON THE FOUNDATIONS OF GLOBAL UBIQUITOUS COMPUTING
, 2004
"... We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic. Since we ..."
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Cited by 21 (11 self)
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We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic. Since we
Consistency of the Theory of Contexts
, 2001
"... The Theory of Contexts is a typetheoretic axiomatization which has been recently proposed by some of the authors for giving a metalogical account of the fundamental notions of variable and context as they appear in Higher Order Abstract Syntax. In this paper, we prove that this theory is consistent ..."
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Cited by 12 (3 self)
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The Theory of Contexts is a typetheoretic axiomatization which has been recently proposed by some of the authors for giving a metalogical account of the fundamental notions of variable and context as they appear in Higher Order Abstract Syntax. In this paper, we prove that this theory is consistent by building a model based on functor categories. By means of a suitable notion of forcing, we prove that this model validates Classical Higher Order Logic, the Theory of Contexts, and also (parametrised) structural induction and recursion principles over contexts. The approach we present in full detail should be useful also for reasoning on other models based on functor categories. Moreover, the construction could be adopted, and possibly generalized, also for validating other theories of names and binders. Contents 1 The object language 4 2 The metalanguage (Framework System #) 6 2.1 Syntax 6 2.2 Typing and logical judgements 7 2.3 Adequacy of the encoding 8 2.4 Remarks on the design of # 9 3 Categorytheoretic preliminaries 11 4.1 The ambient categories 4.2 Interpreting types 16 4.3 Interpreting environments 18 4.4 Interpreting the typing judgement of terms 19 4.5 Interpreting logical judgements 21 is a model of # 22 5.1 Forcing 22 5.2 Characterisation of Leibniz equality 23 models logical axioms and rules 26 models the Theory of Contexts 27 6 Recursion 28 6.1 Firstorder recursion 28 6.2 Higherorder recursion 31 7 Induction 33 7.1 Firstorder induction 34 7.2 Higherorder induction 37 8 Connections with tripos theory 38 9 Related work 41 9.1 Semantics based on functor categories 41 9.2 Logics for nominal calculi 44 10 Conclusions 45 A Proofs 46 A.1 Proof of Proposition 4.2 46 A.2 Proof of Proposition 4.3 47 A.3 Proof of Theorem 5.1 48 A.4 Proof of...
Encoding Generic Judgments
 In Proceedings of FSTTCS. Number 2556 in LNCS
, 2002
"... The operational semantics of a computation system is often presented as inference rules or, equivalently, as logical theories. Specifications can be made more declarative and highlevel if syntactic details concerning bound variables and substitutions are encoded directly into the logic using te ..."
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Cited by 3 (2 self)
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The operational semantics of a computation system is often presented as inference rules or, equivalently, as logical theories. Specifications can be made more declarative and highlevel if syntactic details concerning bound variables and substitutions are encoded directly into the logic using termlevel abstractions (#abstraction) and prooflevel abstractions (eigenvariables). When one wishes to reason about relations defined using termlevel abstractions, generic judgment are generally required.
A FirstOrder Syntax for the piCalculus in Isabelle/HOL using Permutations
"... . A formalized theory of alphaconversion for the #calculus in ..."
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Cited by 2 (0 self)
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. A formalized theory of alphaconversion for the #calculus in
TOSCA 2001 Preliminary Version
"... Syntax Furio Honsell and Marino Miculan and Ivan Scagnetto Dipartimento di Matematica e Informatica, Universita di Udine Via delle Scienze 206, 33100 Udine, Italy. honsell,miculan,scagnett@dimi.uniud.it Abstract We present two case studies in formal reasoning about untyped #calculus in Coq, us ..."
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Syntax Furio Honsell and Marino Miculan and Ivan Scagnetto Dipartimento di Matematica e Informatica, Universita di Udine Via delle Scienze 206, 33100 Udine, Italy. honsell,miculan,scagnett@dimi.uniud.it Abstract We present two case studies in formal reasoning about untyped #calculus in Coq, using both firstorder and higherorder abstract syntax. In the first case, we prove the equivalence of three definitions of #equivalence; in the second, we focus on properties of substitution. In both cases, we deal with contexts, which are rendered by means of higherorder terms (functions) in the metalanguage. These are successfully handled by using the Theory of Contexts.
The Australian National University
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode
Mechanical Verification of Distributed Algorithms
, 2004
"... We report the current state of the mechanisation, in Isabelle and HOL Light, of a paper [EM03] from the area of distributed algorithms. As well as the contribution of the mechanisation itself, we address several issues in theorem proving. For example, we have developed several tools which make the p ..."
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We report the current state of the mechanisation, in Isabelle and HOL Light, of a paper [EM03] from the area of distributed algorithms. As well as the contribution of the mechanisation itself, we address several issues in theorem proving. For example, we have developed several tools which make the process of mechanisation easier, such as tools to handle context during a mechanisation, which greatly facilitates the expression of proofs.