Andrew Cave

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belugais a proof environment that provides a rich sophisticated infrastructure for implementing formal systems based on the logical framework LF together with a first-order reasoning language for implementing inductive proofs about them following the Curry-Howard isomorphism. In this paper we describe four significant extensions to beluga: 1) we enrich our(More)
Breast cancer incidence differs by ethnicity in New Zealand (NZ) with Māori (the indigenous people) women having the highest rates followed by Pakeha (people primarily of British/European descent), Pacific and Asian women, who experience the lowest rates. The reasons for these differences are unclear. Breast density, an important risk factor for breast(More)
BACKGROUND Parents play a central role in preventing childhood obesity. There is a need for innovative, scalable, and evidence-based interventions designed to enhance parents' motivation to support and sustain healthy lifestyle behaviors in their children, which can facilitate obesity prevention. OBJECTIVE (1) Develop an online screening, brief(More)
We consider the normalization proof for a simply-typed lambda calculus with Mendler-style recursion using logical relations. This language is powerful enough to encode total recursive functions using recursive types. A key feature of our proof is the semantic interpretation of recursive types, which requires higher-kinded polymorphism in the reasoning(More)
Indexed data types allow us to specify and verify many interesting invariants about finite data in a general purpose programming language. In this paper we investigate the dual idea: indexed codata types, which allow us to describe data-dependencies about infinite data structures. Unlike finite data which is defined by constructors, we define infinite data(More)
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