On implicit program constructs

Session types are a well-established approach to ensuring protocol conformance and the absence of communication errors such as deadlocks in message passing systems. Implicit parameters, introduced by Haskell and popularised in Scala, are a mechanism to improve program readability and conciseness by allowing the programmer to omit function call arguments, and have the compiler insert them in a principled manner at compile-time. Scala recently gave implicit types first-class status (implicit functions), yielding an expressive tool for handling context dependency in a type-safe manner. DOT (Dependent Object Types) is an object calculus with path-dependent types and abstract type members, developed to serve as a theoretical foundation for the Scala programming language. As yet, DOT does not model all of Scala’s features, but a small subset. Among those features of Scala not yet modelled by DOT are implicit functions. We ask: can type-safe implicit functions be generalised from Scala’s sequential setting to message passing computation, to improve readability and conciseness of message passing programs? We answer this question in the affirmative by generalising the concept of an implicit function to an implicit message, its concurrent analogue, a programming language construct for session-typed concurrent computation. We explore new applications for implicit program constructs by integrating theminto four novel calculi, each demonstrating a new use case or theoretical result for implicits. Firstly, we integrate implicit functions and messages into the concurrent functional language LAST, Gay and Vasconcelos’s calculus of linear types for asynchronous sessions. We demonstrate their utility by example, and explore use cases for both implicit functions and implicit messages. We integrate implicit messages into two pi calculi, further demonstrating the robustness of our approach to extending calculi with implicits. We show that implicit messages are possible in the absence of lambda calculus, in languages with concurrency primitives only, and that they are sound not only in binary session-typed computation, but also in multi-party context. Finally we extend DOT to include implicit functions. We show type safety of the resulting calculus by translation to DOT, lending a higher degree of confidence to the correctness of implicit functions in Scala. We demonstrate that typical use cases for implicit functions in Scala are typably expressible in DOT when extended with implicit functions

On the Use of Underspecified Data-Type Semantics for Type Safety in Low-Level Code

In recent projects on operating-system verification, C and C++ data types are often formalized using a semantics that does not fully specify the precise byte encoding of objects. It is well-known that such an underspecified data-type semantics can be used to detect certain kinds of type errors. In general, however, underspecified data-type semantics are unsound: they assign well-defined meaning to programs that have undefined behavior according to the C and C++ language standards. A precise characterization of the type-correctness properties that can be enforced with underspecified data-type semantics is still missing. In this paper, we identify strengths and weaknesses of underspecified data-type semantics for ensuring type safety of low-level systems code. We prove sufficient conditions to detect certain classes of type errors and, finally, identify a trade-off between the complexity of underspecified data-type semantics and their type-checking capabilities.Comment: In Proceedings SSV 2012, arXiv:1211.587

A Bi-Directional Refinement Algorithm for the Calculus of (Co)Inductive Constructions

The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof terms directly written by the user or generated by using tactics, decision procedures or general automation. The terms are written in an "external syntax" meant to be user friendly that allows omission of information, untyped binders and a certain liberal use of user defined sub-typing. The refiner modifies the terms to obtain related well typed terms in the internal syntax understood by the kernel of the ITP. In particular, it acts as a type inference algorithm when all the binders are untyped. The proposed algorithm is bi-directional: given a term in external syntax and a type expected for the term, it propagates as much typing information as possible towards the leaves of the term. Traditional mono-directional algorithms, instead, proceed in a bottom-up way by inferring the type of a sub-term and comparing (unifying) it with the type expected by its context only at the end. We propose some novel bi-directional rules for CIC that are particularly effective. Among the benefits of bi-directionality we have better error message reporting and better inference of dependent types. Moreover, thanks to bi-directionality, the coercion system for sub-typing is more effective and type inference generates simpler unification problems that are more likely to be solved by the inherently incomplete higher order unification algorithms implemented. Finally we introduce in the external syntax the notion of vector of placeholders that enables to omit at once an arbitrary number of arguments. Vectors of placeholders allow a trivial implementation of implicit arguments and greatly simplify the implementation of primitive and simple tactics

Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parameterised models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented

The C++0x "Concepts" Effort

C++0x is the working title for the revision of the ISO standard of the C++ programming language that was originally planned for release in 2009 but that was delayed to 2011. The largest language extension in C++0x was "concepts", that is, a collection of features for constraining template parameters. In September of 2008, the C++ standards committee voted the concepts extension into C++0x, but then in July of 2009, the committee voted the concepts extension back out of C++0x. This article is my account of the technical challenges and debates within the "concepts" effort in the years 2003 to 2009. To provide some background, the article also describes the design space for constrained parametric polymorphism, or what is colloquially know as constrained generics. While this article is meant to be generally accessible, the writing is aimed toward readers with background in functional programming and programming language theory. This article grew out of a lecture at the Spring School on Generic and Indexed Programming at the University of Oxford, March 2010