Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas

In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f. Type systems defined in this way are idealized, since in the most interesting instantiations both the terms of the coinductive Herbrand universe and goal derivations cannot be finitely represented. However, sound and quite expressive approximations can be implemented by considering only regular terms and derivations. In doing so, it is essential to introduce a proper subtyping relation formalizing the notion of approximation between types. In this paper we study a subtyping relation on coinductive terms built on union and object type constructors. We define an interpretation of types as set of values induced by a quite intuitive relation of membership of values to types, and prove that the definition of subtyping is sound w.r.t. subset inclusion between type interpretations. The proof of soundness has allowed us to simplify the notion of contractive derivation and to discover that the previously given definition of subtyping did not cover all possible representations of the empty type

Link-time static analysis for efficient separate compilation of object-oriented languages

International audienc

A Correspondence between Two Approaches to Interprocedural Analysis in the Presence of Join

Many interprocedural static analyses perform a lossy join for reasons of termination or efficiency. We study the relationship between two predominant approaches to interprocedural analysis, the summary- based (or functional) approach and the call-strings (or k-CFA) approach, in the presence of a lossy join. Despite the use of radically different ways to distinguish procedure contexts by these two approaches, we prove that post-processing their results using a form of garbage collection ren- ders them equivalent. Our result extends the classic result by Sharir and Pnueli that showed the equivalence between these two approaches in the setting of distributive analysis, wherein the join is lossless. We also empirically compare these two approaches by applying them to a pointer analysis that performs a lossy join. Our experiments on ten Java programs of size 400K{900K bytecodes show that the summary-based approach outperforms an optimized implementation of the k-CFA approach: the k-CFA implementation does not scale beyond k=2, while the summary-based approach proves up to 46% more pointer analysis client queries than 2-CFA. The summary-based approach thus enables, via our equivalence result, to measure the precision of k-CFA with unbounded k, for the class of interprocedural analyses that perform a lossy join

Shape Analysis in the Absence of Pointers and Structure

discover properties of dynamic and/or mutable structures. We ask, “Is there an equivalent to shape analysis for purely functional programs, and if so, what ‘shapes ’ does it discover? ” By treating binding environments as dynamically allocated structures, by treating bindings as addresses, and by treating value environments as heaps, we argue that we can analyze the “shape ” of higher-order functions. To demonstrate this, we enrich an abstract-interpretive control-flow analysis with principles from shape analysis. In particular, we promote “anodization ” as a way to generalize both singleton abstraction and the notion of focusing, and we promote “binding invariants ” as the analog of shape predicates. Our analysis enables two optimizations known to be beyond the reach of control-flow analysis (globalization and super-β inlining) and one previously unknown optimization (higher-order rematerialization).

Comparison of treatment with insulin degludec and glargine U100 in patients with type 1 diabetes prone to nocturnal severe hypoglycaemia:The HypoDeg randomized, controlled, open-label, crossover trial

AIM: To investigate whether the long‐acting insulin analogue insulin degludec compared with insulin glargine U100 reduces the risk of nocturnal symptomatic hypoglycaemia in patients with type 1 diabetes (T1D). METHODS: Adults with T1D and at least one episode of nocturnal severe hypoglycaemia during the last 2 years were included in a 2‐year prospective, randomized, open, multicentre, crossover trial. A total of 149 patients were randomized 1:1 to basal‐bolus therapy with insulin degludec and insulin aspart or insulin glargine U100 and insulin aspart. Each treatment period lasted 1 year and consisted of 3 months of run‐in or crossover followed by 9 months of maintenance. The primary endpoint was the number of blindly adjudicated nocturnal symptomatic hypoglycaemic episodes. Secondary endpoints included the occurrence of severe hypoglycaemia. We analysed all endpoints by intention‐to‐treat. RESULTS: Treatment with insulin degludec resulted in a 28% (95% CI: 9%‐43%; P = .02) relative rate reduction (RRR) of nocturnal symptomatic hypoglycaemia at level 1 (≤3.9 mmol/L), a 37% (95% CI: 16%‐53%; P = .002) RRR at level 2 (≤3.0 mmol/L), and a 35% (95% CI: 1%‐58%; P = .04) RRR in all‐day severe hypoglycaemia compared with insulin glargine U100. CONCLUSIONS: Patients with T1D prone to nocturnal severe hypoglycaemia have lower rates of nocturnal symptomatic hypoglycaemia and all‐day severe hypoglycaemia with insulin degludec compared with insulin glargine U100