SHRAD: A language for sequential real number computation

Since Di Gianantonio introduced his semantics for exact real number computation, there has always been a struggle to maintain data abstraction and efficiency as much as possible. The interval domain model - or its variations - can be regarded as the standard setting to obtain maximum data abstraction. As for efficiency there has been much focus on sequentially to the extent that these two terms have become almost synonymous. [2, 3] demonstrated that there is not much one can get by sequential computation in the interval domain model. In [4, 5] we reinforced this result by exposing the limited power of (some extensions of) the sequential fragment of Real-PCF. The previous argument suggests some sort of compromise in the beauty of the model in order to keep efficiency. One way forward is to try to sacrifice extensionality. This is exactly what we did in designing SHRAD [6]. There we succeeded in presenting a framework for exact real number computation which satisfies the following all at the same time: 1. It is sequential. 2. Multi-valuedness is carefully avoided. 3. A 'good degree' of expressivity is retained.