Encoding monomorphic and polymorphic types

Most automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter. Here we pursue this approach systematically, analysing formally a variety of encodings that further improve on efficiency while retaining soundness and completeness. We extend the approach to rank-1 polymorphism and present alternative schemes that lighten the translation of polymorphic symbols based on the novel notion of “cover”. The new encodings are implemented, and partly proved correct, in Isabelle/HOL. Our evaluation finds them vastly superior to previous schemes

Inter-country exploration of factors associated with admission to long-term institutional dementia care: Evidence from the RightTimePlaceCare study

AimTo explore inter-country variation of factors associated with institutionalization of people with dementia. BackgroundThere is an urgent need for evidence on whether factors associated with admission to institutional dementia care are applicable across healthcare systems, as increasing evidence suggests that these factors could be country-specific. DesignA prospective cohort study. MethodPrimary data were collected in eight European countries, at baseline and after 3months follow-up (November 2010-April 2012). The sample included 2014 dyads of people with dementia and their informal caregivers; 791 patients were recently institutionalized, 1223 patients lived at home and were at risk of institutionalization. Associations between care setting (institution vs. home) and factors shown to influence institutionalization (e.g. cognition, independence in activities of daily life, behaviour) were studied. ResultsConsiderable differences were found between the eight countries in characteristics of people with dementia who had been recently admitted to ILTC. However, caregiver burden appeared the most consistent factor associated with institutionalization in all analyses. Indications for the importance of independence in activities of daily life were found as well, although country differences may be more prominent for this factor. ConclusionEvidence was found for two common factors, crucial in the process of institutionalization across countries: caregiver burden and independency in activities of daily life. However, this study also suggests that admission to institutional dementia care is context-specific, as wide variation exists in factors associated with institutionalization across countries. Tailored best-practice strategies are needed to reflect variations in response to these needs

Efficient E-matching for SMT solvers

Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrating theory reasoning. However, for numerous applications from program analysis and verification, the ground fragment is insufficient, as proof obligations often include quantifiers. A well known approach for quantifier reasoning uses a matching algorithm that works against an E-graph to instantiate quantified variables. This paper introduces algorithms that identify matches on E-graphs incrementally and efficiently. In particular, we introduce an index that works on E-graphs, called E-matching code trees that combine features of substitution and code trees, used in saturation based theorem provers. E-matching code trees allow performing matching against several patterns simultaneously. The code trees are combined with an additional index, called the inverted path index, which filters E-graph terms that may potentially match patterns when the E-graph is updated. Experimental results show substantial performance improvements over existing state-of-the-art SMT solvers