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Processes and Games
, 2003
"... A general theory of computing is important, if we wish to have a common mathematical footing based on which diverse scienti c and engineering eorts in computing are uniformly understood and integrated. A quest for such a general theory may take dierent paths. As a case for one of the possible paths ..."
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A general theory of computing is important, if we wish to have a common mathematical footing based on which diverse scienti c and engineering eorts in computing are uniformly understood and integrated. A quest for such a general theory may take dierent paths. As a case for one of the possible paths towards a general theory, this paper establishes a precise connection between a gamebased model of sequential functions by Hyland and Ong on the one hand, and a typed version of the calculus on the other. This connection has been instrumental in our recent eorts to use the calculus as a basic mathematical tool for representing diverse classes of behaviours, even though the exact form of the correspondence has not been presented in a published form. By redeeming this correspondence we try to make explicit a convergence of ideas and structures between two distinct threads of Theoretical Computer Science. This convergence indicates a methodology for organising our understanding on computation and that methodology, we argue, suggests one of the promising paths to a general theory.
Under consideration for publication in J. Functional Programming 1 From Process Logic to Program Logic Kohei Honda
"... We present a process logic for the πcalculus with the linear/affine type discipline (Berger et al. ..."
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We present a process logic for the πcalculus with the linear/affine type discipline (Berger et al.
Process Logic and Duality  Part I: Sequential Processes
"... We present typed process logics for the πcalculus with linear/affine type disciplines. Built on the preceding studies on logics for programs and processes, simple systems of assertions are developed, capturing the classes of behaviours ranging from purely functional interactions to those with de ..."
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We present typed process logics for the πcalculus with linear/affine type disciplines. Built on the preceding studies on logics for programs and processes, simple systems of assertions are developed, capturing the classes of behaviours ranging from purely functional interactions to those with destructive update, local state and genericity. A central feature of the logic is representation of the environments' behaviour as the dual of those of processes in assertions, which is crucial for obtaining compositional proof systems. This paper develops typed process logics starting from purely functional behaviours and treating increasingly complex ones, and illustrate their usage by deriving program logics for higherorder languages. The embedding of the proof rules in the derived logics into the process logics gives a simple proof of the soundness of the former. Some of the derived logics correspond to known program logics, including Hoare logic for imperative programs.
Completeness
, 2003
"... Abstract We prove a full completeness theorem for multiplicativeadditive linear logic (i.e. MALL) using a double gluing construction applied to Ehrhard's \Lambdaautonomous category of hypercoherences. This is the first nongametheoretic full completeness theorem for this fragment. Our main r ..."
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Abstract We prove a full completeness theorem for multiplicativeadditive linear logic (i.e. MALL) using a double gluing construction applied to Ehrhard's \Lambdaautonomous category of hypercoherences. This is the first nongametheoretic full completeness theorem for this fragment. Our main result is that every dinatural transformation between definable functors arises from the denotation of a cutfree MALL proof. Our proof consists of three steps. We show: ffl Dinatural transformations on this category satisfy Joyal's softness property for products and coproducts. ffl Softness, together with multiplicative full completeness, guarantees that every
Full Abstraction for Nominal Scott Domains
, 2013
"... We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbitfinite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely m ..."
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We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbitfinite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojańczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and ‘definite description ’ over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallelor, to a programming language for recursively defined higherorder functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin’s classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higherorder functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.