Full abstraction for fair testing in CCS

In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent presheaf semantics and as a concurrent game semantics. It is here proved that a behavioural equivalence induced by this semantics on CCS processes is fully abstract for fair testing equivalence. The proof relies on a new algebraic notion called playground, which represents the 'rule of the game'. From any playground, two languages, equipped with labelled transition systems, are derived, as well as a strong, functional bisimulation between them.Comment: 15 pages, to appear in CALCO '13. To appear Lecture notes in computer science (2013

Normalization by Evaluation in the Delay Monad: A Case Study for Coinduction via Copatterns and Sized Types

In this paper, we present an Agda formalization of a normalizer for simply-typed lambda terms. The normalizer consists of two coinductively defined functions in the delay monad: One is a standard evaluator of lambda terms to closures, the other a type-directed reifier from values to eta-long beta-normal forms. Their composition, normalization-by-evaluation, is shown to be a total function a posteriori, using a standard logical-relations argument. The successful formalization serves as a proof-of-concept for coinductive programming and reasoning using sized types and copatterns, a new and presently experimental feature of Agda.Comment: In Proceedings MSFP 2014, arXiv:1406.153

Classifying topoi in synthetic guarded domain theory

Several different topoi have played an important role in the development and applications of synthetic guarded domain theory (SGDT), a new kind of synthetic domain theory that abstracts the concept of guarded recursion frequently employed in the semantics of programming languages. In order to unify the accounts of guarded recursion and coinduction, several authors have enriched SGDT with multiple "clocks" parameterizing different time-streams, leading to more complex and difficult to understand topos models. Until now these topoi have been understood very concretely qua categories of presheaves, and the logico-geometrical question of what theories these topoi classify has remained open. We show that several important topos models of SGDT classify very simple geometric theories, and that the passage to various forms of multi-clock guarded recursion can be rephrased more compositionally in terms of the lower bagtopos construction of Vickers and variations thereon due to Johnstone. We contribute to the consolidation of SGDT by isolating the universal property of multi-clock guarded recursion as a modular construction that applies to any topos model of single-clock guarded recursion.Comment: To appear in the proceedings of the 38th International Conference on Mathematical Foundations of Programming Semantics (MFPS 2022

Guarded Dependent Type Theory with Coinductive Types

We present guarded dependent type theory, gDTT, an extensional dependent type theory with a `later' modality and clock quantifiers for programming and proving with guarded recursive and coinductive types. The later modality is used to ensure the productivity of recursive definitions in a modular, type based, way. Clock quantifiers are used for controlled elimination of the later modality and for encoding coinductive types using guarded recursive types. Key to the development of gDTT are novel type and term formers involving what we call `delayed substitutions'. These generalise the applicative functor rules for the later modality considered in earlier work, and are crucial for programming and proving with dependent types. We show soundness of the type theory with respect to a denotational model.Comment: This is the technical report version of a paper to appear in the proceedings of FoSSaCS 201

Sequentiality vs. Concurrency in Games and Logic

Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc

FICS 2010

International audienceInformal proceedings of the 7th workshop on Fixed Points in Computer Science (FICS 2010), held in Brno, 21-22 August 201

Denotational semantics in Synthetic Guarded Domain Theory

In functional programming, features such as recursion, recursive types and general references are central. To define semantics of this kind of languages one needs to come up with certain definitions which may be non-trivial to show well-defined. This is because they are circular. Domain theory has been used to solve this kind of problems for specific languages, unfortunately, this technique does not scale for more featureful languages, which prevented it from being widely used. Step-indexing is a more general technique that has been used to break circularity of definitions. The idea is to tweak the definition by adding a well-founded structure that gives a handle for recursion. Guarded dependent Type Theory (gDTT) is a type theory which implements step-indexing via a unary modality used to guard recursive definitions. Every circular definition is well-defined as long as the recursive variable is guarded. In this thesis we show that gDTT is a natural setting to give denotational semantics of typed functional programming languages with recursion and recursive types. We formulate operational semantics and denotational semantics and prove computational adequacy entirely inside the type theory. Furthermore, our interpretation is synthetic: types are interpreted as types in the type theory and programs as type-theoretical terms. Moreover, working directly in gDTT has advantages compared with existing set-theoretic models. Finally, this work builds the foundations for doing denotational semantics of languages with much more challenging features, for example, of general references for which denotational techniques were previously beyond reach

Thermal Conductivity of Fiber-Reinforced Lightweight Cement Composites

This dissertation describes the development of a multiscale mathematical model to predict the effective thermal conductivity (ETC) of fiber-reinforced lightweight cement composites. At various stages in the development of the model, the results are compared to experimental values and the model is calibrated when appropriate. Additionally at each stage the proposed model and its results are compared to physical upper and lower bounds placed on the ETC for the different types of structural models. Fiber-reinforced lightweight cement mortar is a composite material that contains various components at different scales. The model development begins with a study of neat cement paste and is then extended to include normal weight fine aggregate, lightweight aggregate, and reinforcing fibers. This is accomplished by first considering cement mortar, then models for lightweight cement mortar and fiber-reinforced cement mortar are considered separately, and finally these two are joined together to study fiber-reinforced lightweight cement mortar. Two different experimental techniques are used to determine the ETC of the different materials. The flash method is used to determine the ETC of the neat cement paste and cement mortar samples, and a recently developed transient technique is used for the remainder of the samples. The model for the ETC of cement paste is derived from a lumped parameter model considering the water-cement ratio and saturation of the paste. The results are calibrated using experimental data generated during this project and are in good agreement with values found in the literature. The models for the ETC of cement mortar, fiber-reinforced cement mortar, lightweight cement mortar, and fiber-reinforced lightweight cement mortar are all based on a differential multiphase model (DM model). This is capable of predicting the ETC of a composite material with various ellipsoidal inclusion phases. It is shown how the DM model can be modified to include information about the maximum volume fraction of the inclusions. A linear packing model is introduced which allows the gradation of the different inclusion phases to be considered. Additionally other factors that affect the ETC are discussed, including the presence of an interfacial transition zone around the inclusions and the relative size of the different constituent phases. The model developed in this report is not only able to predict the effective thermal conductivity for a material, but it can also be used to minimize the effective thermal conductivity by optimizing the structure of the composite. This is done through proper selection of the types and amounts of the various constituents, along with their size, shape, and gradation