Assessing the Economics of Obesity and Obesity Interventions

Examines projections for healthcare costs associated with the obesity epidemic; policy solutions and proven cost-effective interventions for addressing it; and the need to improve the Congressional Budget Office's projections

An Improved Implementation and Abstract Interface for Hybrid

Hybrid is a formal theory implemented in Isabelle/HOL that provides an interface for representing and reasoning about object languages using higher-order abstract syntax (HOAS). This interface is built around an HOAS variable-binding operator that is constructed definitionally from a de Bruijn index representation. In this paper we make a variety of improvements to Hybrid, culminating in an abstract interface that on one hand makes Hybrid a more mathematically satisfactory theory, and on the other hand has important practical benefits. We start with a modification of Hybrid's type of terms that better hides its implementation in terms of de Bruijn indices, by excluding at the type level terms with dangling indices. We present an improved set of definitions, and a series of new lemmas that provide a complete characterization of Hybrid's primitives in terms of properties stated at the HOAS level. Benefits of this new package include a new proof of adequacy and improvements to reasoning about object logics. Such proofs are carried out at the higher level with no involvement of the lower level de Bruijn syntax.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Partiality, revisited: the partiality monad as a quotient inductive-inductive type

Capretta's delay monad can be used to model partial computations, but it has the "wrong" notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the "right" notion of equality, weak bisimilarity. However, recent work by Chapman et al. suggests that it is impossible to define a monad structure on the resulting construction in common forms of type theory without assuming (instances of) the axiom of countable choice. Using an idea from homotopy type theory - a higher inductive-inductive type - we construct a partiality monad without relying on countable choice. We prove that, in the presence of countable choice, our partiality monad is equivalent to the delay monad quotiented by weak bisimilarity. Furthermore we outline several applications

A coalgebraic view of bar recursion and bar induction

We reformulate the bar recursion and induction principles in terms of recursive and wellfounded coalgebras. Bar induction was originally proposed by Brouwer as an axiom to recover certain classically valid theorems in a constructive setting. It is a form of induction on non- wellfounded trees satisfying certain properties. Bar recursion, introduced later by Spector, is the corresponding function defnition principle. We give a generalization of these principles, by introducing the notion of barred coalgebra: a process with a branching behaviour given by a functor, such that all possible computations terminate. Coalgebraic bar recursion is the statement that every barred coalgebra is recursive; a recursive coalgebra is one that allows defnition of functions by a coalgebra-to-algebra morphism. It is a framework to characterize valid forms of recursion for terminating functional programs. One application of the principle is the tabulation of continuous functions: Ghani, Hancock and Pattinson defned a type of wellfounded trees that represent continuous functions on streams. Bar recursion allows us to prove that every stably continuous function can be tabulated to such a tree where by stability we mean that the modulus of continuity is also continuous. Coalgebraic bar induction states that every barred coalgebra is well-founded; a wellfounded coalgebra is one that admits proof by induction

From coinductive proofs to exact real arithmetic: theory and applications

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps

Recursive Definitions of Monadic Functions

Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming extension, which results in a convenient definition principle for imperative programs, which were previously hard to define. For such monadic functions, the recursion equation can always be derived without preconditions, even if the function is partial. The construction is easy to automate, and convenient induction principles can be derived automatically.Comment: In Proceedings PAR 2010, arXiv:1012.455

Generic point-free lenses

Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with view-update, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a backward transformation instructing how to translate an abstract view to an update over concrete models. In this paper we show that most of the standard point-free combinators can be lifted to lenses with suitable backward semantics, allowing us to use the point-free style to define powerful bidirectional transformations by composition. We also demonstrate how to define generic lenses over arbitrary inductive data types by lifting standard recursion patterns, like folds or unfolds. To exemplify the power of this approach, we “lensify” some standard functions over naturals and lists, which are tricky to define directly “by-hand” using explicit recursion

Quotienting the Delay Monad by Weak Bisimilarity

The delay datatype was introduced by Capretta as a means to deal with partial functions (as in computability theory) in Martin-Löf type theory. It is a monad and it constitutes a constructive alternative to the maybe monad. It is often desirable to consider two delayed computations equal, if they terminate with equal values, whenever one of them terminates. The equivalence relation underlying this identification is called weak bisimilarity. In type theory, one commonly replaces quotients with setoids. In this approach, the delay monad quotiented by weak bisimilarity is still a monad. In this paper, we consider Hofmann's alternative approach of extending type theory with inductive-like quotient types. In this setting, it is difficult to define the intended monad multiplication for the quotiented datatype. We give a solution where we postulate some principles, crucially proposition extensionality and the (semi-classical) axiom of countable choice. We have fully formalized our results in the Agda dependently typed programming language

Economic Model of a Birth Cohort Screening Program for Hepatitis C Virus

Recent research has identified high hepatitis C virus (HCV) prevalence among older U.S. residents who contracted HCV decades ago and may no longer be recognized as high risk. We assessed the cost-effectiveness of screening 100% of U.S. residents born 1946-1970 over 5 years (birth-cohort screening), compared with current risk-based screening, by projecting costs and outcomes of screening over the remaining lifetime of this birth cohort. A Markov model of the natural history of HCV was developed using data synthesized from surveillance data, published literature, expert opinion, and other secondary sources. We assumed eligible patients were treated with pegylated interferon plus ribavirin, with genotype 1 patients receiving a direct-acting antiviral in combination. The target population is U.S. residents born 1946-1970 with no previous HCV diagnosis. Among the estimated 102 million (1.6 million chronically HCV infected) eligible for screening, birth-cohort screening leads to 84,000 fewer cases of decompensated cirrhosis, 46,000 fewer cases of hepatocellular carcinoma, 10,000 fewer liver transplants, and 78,000 fewer HCV-related deaths. Birth-cohort screening leads to higher overall costs than risk-based screening ($80.4 billion versus$53.7 billion), but yields lower costs related to advanced liver disease ($31.2 billion versus$39.8 billion); birth-cohort screening produces an incremental costeffectiveness ratio (ICER) of $37,700 per quality-adjusted life year gained versus riskbased screening. Sensitivity analyses showed that reducing the time horizon during which health and economic consequences are evaluated increases the ICER; similarly, decreasing the treatment rates and efficacy increases the ICER. Model results were relatively insensitive to other inputs. Conclusion: Birth-cohort screening for HCV is likely to provide important health benefits by reducing lifetime cases of advanced liver disease and HCV-related deaths and is cost-effective at conventional willingness-topay thresholds. (HEPATOLOGY 2012;55:1344-1355 H epatitis C virus (HCV) is the most common blood-borne viral infection in the United States, 1 affecting an estimated 3.6 million U.S. residents. 2 The majority of infected individuals develop chronic hepatitis; persistent liver injury leads to cirrhosis in 5$5 billion per year, 4 with projected HCV-related societal costs for the years 2010-2019 estimated to total $54.2 billion. 5 For the last decade, the standard of care for treating HCV has been the combination of pegylated interferon (Peg-IFN) and ribavirin (RBV), 6 which successfully eradicates virus (sustained virologic response; SVR) in 40%-80% of treated patients