A Stream Calculus of Bottomed Sequences for Real Number Computation

Dag-Calculus: A Calculus for Parallel Computation

This appendix consists of two main parts: in the first, we prove correct the translations of parallel primitives into the dag calculus, in the second, we prove that the scheduling algorithm implements the rules of the dag calculus. Concretely, Appendix A provides auxiliary definitions and properties for the translations; Appendices B, C and D provide the proofs of translations of fork-join, asy...

A Universal Calculus for Stream Processing Languages

Stream processing applications such as algorithmic trading, MPEG processing, and web content analysis are ubiquitous and essential to business and entertainment. Language designers have developed numerous domain-specific languages that are both tailored to the needs of their applications, and optimized for performance on their particular target platforms. Unfortunately, the goals of generality ...

Real number computation through Gray code embedding

Comparing Functional Paradigms for Exact Real-Number Computation

We compare the definability of total functionals over the reals in two functional-programming approaches to exact real-number computation: the extensional approach, in which one has an abstract datatype of real numbers; and the intensional approach, in which one encodes real numbers using ordinary datatypes. We show that the type hierarchies coincide up to second-order types, and we relate this...

A machine model for data stream computation

We consider online and space-bounded computations in the data stream processing model where a stream is a sequence of records of the form (i, 1) signifying insertion of item i, or, (i,−1), signifying deletion of item i, where, i ∈ {1, 2, . . . , n}. This model finds applications in network monitoring, approximate query answering in databases, computational geometry, where, items signify points ...