Programming Graphics Processors Functionally

Proceedings of the 2004 Haskell Workshop

See also the Vertigo home page

Conal Elliott


Graphics cards for personal computers have recently undergone a radical transformation from fixed-function graphics pipelines to multi-processor, programmable architectures. Multi-processor architectures are clearly advantageous for graphics for the simple reason that graphics computations are naturally concurrent, mapping well to stateless stream processing. They therefore parallelize easily and need no random access to memory with its problematic latencies.

This paper presents Vertigo, a purely functional, Haskell-embedded language for 3D graphics and an optimizing compiler that generates graphics processor code. The language integrates procedural surface modeling, shading, and texture generation, and the compiler exploits the unusual processor architecture. The shading sub-language is based on a simple and precise semantic model, in contrast to previous shading languages. Geometry and textures are also defined via a very simple denotational semantics. The formal semantics yields not only programs that are easy to understand and reason about, but also very efficient implementation, thanks to a compiler based on partial evaluation and symbolic optimization, much in the style of Pan.

Haskell's overloading facility is extremely useful throughout Vertigo. For instance, math operators are used not just for floating point numbers, but also expressions (for differentiation and compilation), tuples, and functions. Typically, these overloadings cascade, as in the case of surfaces, which may be combined via math operators, though they are really functions over tuples of expressions on floating point numbers. Shaders may be composed with the same notational convenience. Functional dependencies are exploited for vector spaces, cross products, and derivatives.

Full paper: PDF (441K), Postscript (12.5M), gzipped Postscript (632K).

  author = 	 {Conal Elliott},
  title = 	 {Programming Graphics Processors Functionally},
  url =          {},
  booktitle = 	 {Proceedings of the 2004 Haskell Workshop},
  publisher =    {ACM Press},
  year =	 2004