Gradual Certified Programming in Coq

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We explore gradual certified programming in Coq, providing the possibility to postpone the proofs of selected properties, and to check "at runtime" whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq to support implicit cast insertion a la gradual typing. Additionally, when extracting Coq functions to mainstream languages, our encoding of casts supports lifting assumed properties into runtime checks. Much to our surprise, it is not necessary to extend Coq in any way to support gradual certified programming. A simple mix of type classes and axioms makes it possible to bring gradual certified programming to Coq in a straightforward manner.Comment: DLS'15 final version, Proceedings of the ACM Dynamic Languages Symposium (DLS 2015

MELT - a Translated Domain Specific Language Embedded in the GCC Compiler

The GCC free compiler is a very large software, compiling source in several languages for many targets on various systems. It can be extended by plugins, which may take advantage of its power to provide extra specific functionality (warnings, optimizations, source refactoring or navigation) by processing various GCC internal representations (Gimple, Tree, ...). Writing plugins in C is a complex and time-consuming task, but customizing GCC by using an existing scripting language inside is impractical. We describe MELT, a specific Lisp-like DSL which fits well into existing GCC technology and offers high-level features (functional, object or reflexive programming, pattern matching). MELT is translated to C fitted for GCC internals and provides various features to facilitate this. This work shows that even huge, legacy, software can be a posteriori extended by specifically tailored and translated high-level DSLs.Comment: In Proceedings DSL 2011, arXiv:1109.032

Automated code generation for discontinuous Galerkin methods

A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates efficient code in a standard programming language. This facilitates the rapid generation of efficient code for general equations in varying spatial dimensions. Key concepts underlying the compiler approach and the automated generation of computer code are elaborated. The approach is demonstrated for a range of common problems, including the Poisson, biharmonic, advection--diffusion and Stokes equations