In the refinement calculus, monotonic predicate transformers are used to model specifications for (imperative) programs. Together with a natural notion of simulation, they form a...
This paper presents a mathematical framework to exploit the semantic properties of matrix operations in loop-based numerical codes. The heart of this framework is an algebraic lan...
Using the language Z for more than specification is hindered by the fact that its algebra of schemas is not monotonic with respect to refinement; so specification is modular, but ...
We establish a monotonicity principle for convex functions that enables high-level reasoning about capacity in information theory. Despite its simplicity, this single idea is rema...
Selection bias, caused by preferential exclusion of samples from the data, is a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized exper...