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Psicalculi: Mobile processes, nominal data, and logic
 In Proceedings of LICS 2009
"... A psicalculus is an extension of the picalculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard picalculus mechanism to allow for scope migr ..."
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A psicalculus is an extension of the picalculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard picalculus mechanism to allow for scope migrations. Other proposed extensions of the picalculus can be formulated as psicalculi; examples include the applied picalculus, the spicalculus, the fusion calculus, the concurrent constraint picalculus, and calculi with polyadic communication channels or pattern matching. Psicalculi can be even more general, for example by allowing structured channels, higherorder formalisms such as the lambda calculus for data structures, and a predicate logic for assertions. Our labelled operational semantics and definition of bisimulation is straightforward, without a structural congruence. We establish minimal requirements on the nominal data and logic in order to prove general algebraic properties of psicalculi. The proofs have been checked in the interactive proof checker Isabelle. We are the first to formulate a truly compositional labelled operational semantics for calculi of this calibre. Expressiveness and therefore modelling convenience significantly exceeds that of other formalisms, while the purity of the semantics is on par with the original picalculus. 1
Quotients Revisited for Isabelle/HOL
 the Proc. of the 26th ACM Symposium On Applied Computing
, 2011
"... HigherOrder Logic (HOL) is based on a small logic kernel, whose only mechanism for extension is the introduction of safe definitions and of nonempty types. Both extensions are often performed in quotient constructions. To ease the work involved with such quotient constructions, we reimplemented i ..."
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HigherOrder Logic (HOL) is based on a small logic kernel, whose only mechanism for extension is the introduction of safe definitions and of nonempty types. Both extensions are often performed in quotient constructions. To ease the work involved with such quotient constructions, we reimplemented in the Isabelle/HOL theorem prover the quotient package by Homeier. In doing so we extended his work in order to deal with compositions of quotients and also specified completely the procedure of lifting theorems from the raw level to the quotient level. The importance for theorem proving is that many formal verifications, in order to be feasible, require a convenient reasoning infrastructure for quotient constructions.
Proof Pearl: A New Foundation for Nominal Isabelle
"... Abstract. Pitts et al introduced a beautiful theory about names and binding based on the notions of permutation and support. The engineering challenge is to smoothly adapt this theory to a theorem prover environment, in our case Isabelle/HOL. We present a formalisation of this work that differs from ..."
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Abstract. Pitts et al introduced a beautiful theory about names and binding based on the notions of permutation and support. The engineering challenge is to smoothly adapt this theory to a theorem prover environment, in our case Isabelle/HOL. We present a formalisation of this work that differs from our earlier approach in two important respects: First, instead of representing permutations as lists of pairs of atoms, we now use a more abstract representation based on functions. Second, whereas the earlier work modeled different sorts of atoms using different types, we now introduce a unified atom type that includes all sorts of atoms. Interestingly, we allow swappings, that is permutations build up by two atoms, to be illsorted. As a result of these design changes, we can iron out inconveniences for the user, considerably simplify proofs and also drastically reduce the amount of custom MLcode. Furthermore we can extend the capabilities of Nominal Isabelle to deal with variables that carry additional information. We end up with a pleasing and formalised theory of permutations and support, on which we can build an improved and more powerful version of Nominal Isabelle. 1
General Bindings and AlphaEquivalence in Nominal Isabelle
"... Abstract. Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to deBruijn indices). In this paper we present an extension of Nominal Isabell ..."
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Abstract. Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to deBruijn indices). In this paper we present an extension of Nominal Isabelle for dealing with general bindings, that means termconstructors where multiple variables are bound at once. Such general bindings are ubiquitous in programming language research and only very poorly supported with single binders, such as lambdaabstractions. Our extension includes new definitions of αequivalence and establishes automatically the reasoning infrastructure for αequated terms. We also prove strong induction principles that have the usual variable convention already built in. 1
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"... Abstract. A psicalculus is an extension of the picalculus with nominal data types for data structures and for logical assertions and conditions. These can be transmitted between processes and their names can be statically scoped as in the standard picalculus. Psicalculi can capture the same phen ..."
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Abstract. A psicalculus is an extension of the picalculus with nominal data types for data structures and for logical assertions and conditions. These can be transmitted between processes and their names can be statically scoped as in the standard picalculus. Psicalculi can capture the same phenomena as other proposed extensions of the picalculus such as the applied picalculus, the spicalculus, the fusion calculus, the concurrent constraint picalculus, and calculi with polyadic communication channels or pattern matching. Psicalculi can be even more general, for example by allowing structured channels, higherorder formalisms such as the lambda calculus for data structures, and predicate logic for assertions. We provide ample comparisons to related calculi and discuss a few significant applications. Our labelled operational semantics and definition of bisimulation is straightforward, without a structural congruence. We establish minimal requirements on the nominal data and logic in order to prove general algebraic properties of psicalculi, all of which have been checked in the interactive theorem prover Isabelle. We are the first to formulate a truly compositional labelled operational semantics for calculi of this calibre. Expressiveness and therefore modelling convenience significantly exceeds that of other formalisms, while the purity of the semantics is on par with the original picalculus. Received by the editors February 1, 2010.
Editorial Manager(tm) for Journal of Automated Reasoning Manuscript Draft Manuscript Number: Title: A Canonical Locally Named Representation of Binding Article Type: Special Issue TAASN
"... Abstract: This paper is about completely formal representation of languages with binding. We have previously written about a representation following an approach going back to Frege, based on firstorder syntax using distinct syntactic classes for locally bound variables vs. \ global or free variabl ..."
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Abstract: This paper is about completely formal representation of languages with binding. We have previously written about a representation following an approach going back to Frege, based on firstorder syntax using distinct syntactic classes for locally bound variables vs. \ global or free variables. The present paper differs from our previous work by being more abstract. Whereas we previously gave a particular concrete function for canonically choosing the names of binders, here we characterize abstractly the properties required of such a choice function to guarantee canonical representation, and focus on the metatheory of the representation, proving that it is in substitution preserving isomorphism with the nominal Isabelle representation of pure lambda terms. This metatheory is formalized in Isabelle/HOL. The final section outlines a formalization in Matita of a challenging language with multiple binding and simultaneous substitution. The Isabelle and Matita proof files are available online. Click here to download Manuscript: paper.tex Click here to view linked References 1 2
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"... Psicalculi is a parametric framework for extensions of the picalculus; in earlier work we have explored their expressiveness and algebraic theory. In this paper we consider higherorder psicalculi through a technically surprisingly simple extension of the framework, and show how an arbitrary psi ..."
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Psicalculi is a parametric framework for extensions of the picalculus; in earlier work we have explored their expressiveness and algebraic theory. In this paper we consider higherorder psicalculi through a technically surprisingly simple extension of the framework, and show how an arbitrary psicalculus can be lifted to its higherorder counterpart in a canonical way. We illustrate this with examples and establish an algebraic theory of higherorder psicalculi. The formal results are obtained by extending our proof repositories in Isabelle/Nominal. Robin Milner in memoriam Robin Milner pioneered developments in process algebras, higherorder formalisms, and interactive theorem provers. We hope he would have been pleased to see the different strands of his work combined in this way. 1.
ACTA UNIVERSITATIS UPSALIENSIS Uppsala Dissertations from the Faculty of Science and Technology
"... Formalising process calculiAbstract page As the complexity of programs increase, so does the complexity of the models required to reason about them. Process calculi were introduced in the early 1980s and have since then been used to model communication protocols of varying size and scope. Whereas mo ..."
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Formalising process calculiAbstract page As the complexity of programs increase, so does the complexity of the models required to reason about them. Process calculi were introduced in the early 1980s and have since then been used to model communication protocols of varying size and scope. Whereas modeling sophisticated protocols in simple process algebras like CCS or the picalculus is doable, expressing the models required is often gruesome and error prone. To combat this, more advanced process calculi were introduced, which significantly reduce the complexity of the models. However, this simplicity comes at a price – the theories of the calculi themselves instead become gruesome and error prone, and establishing their mathematical and logical properties has turned out to be difficult. Many of the proposed calculi have later turned out to be inconsistent. The contribution of this thesis is twofold. Firstly we provide methodologies to formalise the metatheory of process calculi in an interactive theorem