Improving statistical skills through students’ participation in the development of resources

This paper summarizes the evaluation of a project that involved undergraduate mathematics students in the development of teaching and learning resources for statistics modules taught in various departments of a university. This evaluation regards students’ participation in the project and its impact on their learning of statistics, as characterized in terms of statistical reasoning, statistical thinking, and skills for statistical consultancy. The participation of students is evaluated from the viewpoint of communities of practice. The evaluation resulted in a characterization of the benefits of such a project and suggestions for implementations of future projects, and in addition brought to light new theoretical elements both as regards the learning of statistics and as regards communities of practice. In particular, the analysis highlighted contributions of the students involved to resource development practice in the community of university statistics teachers, as well as contributions to students’ learning as a result of participation in this community

Synthesizing Short-Circuiting Validation of Data Structure Invariants

This paper presents incremental verification-validation, a novel approach for checking rich data structure invariants expressed as separation logic assertions. Incremental verification-validation combines static verification of separation properties with efficient, short-circuiting dynamic validation of arbitrarily rich data constraints. A data structure invariant checker is an inductive predicate in separation logic with an executable interpretation; a short-circuiting checker is an invariant checker that stops checking whenever it detects at run time that an assertion for some sub-structure has been fully proven statically. At a high level, our approach does two things: it statically proves the separation properties of data structure invariants using a static shape analysis in a standard way but then leverages this proof in a novel manner to synthesize short-circuiting dynamic validation of the data properties. As a consequence, we enable dynamic validation to make up for imprecision in sound static analysis while simultaneously leveraging the static verification to make the remaining dynamic validation efficient. We show empirically that short-circuiting can yield asymptotic improvements in dynamic validation, with low overhead over no validation, even in cases where static verification is incomplete

GPUVerify: A Verifier for GPU Kernels

We present a technique for verifying race- and divergence-freedom of GPU kernels that are written in mainstream ker-nel programming languages such as OpenCL and CUDA. Our approach is founded on a novel formal operational se-mantics for GPU programming termed synchronous, delayed visibility (SDV) semantics. The SDV semantics provides a precise definition of barrier divergence in GPU kernels and allows kernel verification to be reduced to analysis of a sequential program, thereby completely avoiding the need to reason about thread interleavings, and allowing existing modular techniques for program verification to be leveraged. We describe an efficient encoding for data race detection and propose a method for automatically inferring loop invari-ants required for verification. We have implemented these techniques as a practical verification tool, GPUVerify, which can be applied directly to OpenCL and CUDA source code. We evaluate GPUVerify with respect to a set of 163 kernels drawn from public and commercial sources. Our evaluation demonstrates that GPUVerify is capable of efficient, auto-matic verification of a large number of real-world kernels