Polynomial approximations of the relational semantics of imperative programs

AbstractWe present a static analysis that approximates the relational semantics of imperative programs by systems of low-degree polynomial equalities. Our method is based on Abstract Interpretation in a lattice of polynomial pseudo ideals — finite-dimensional vector spaces of degree-bounded polynomials that are closed under degree-bounded products. For a fixed degree bound, the sizes of bases of pseudo ideals and the lengths of chains in the lattice of pseudo ideals are bounded by polynomials in the number of program variables. Despite the approximate nature of our analysis, for several programs taken from the literature on non-linear polynomial invariant generation our method produces results that are as precise as those produced by methods based on polynomial ideals and Gröbner bases

Enabling Operator Reordering in Data Flow Programs Through Static Code Analysis

In many massively parallel data management platforms, programs are represented as small imperative pieces of code connected in a data flow. This popular abstraction makes it hard to apply algebraic reordering techniques employed by relational DBMSs and other systems that use an algebraic programming abstraction. We present a code analysis technique based on reverse data and control flow analysis that discovers a set of properties from user code, which can be used to emulate algebraic optimizations in this setting.Comment: 4 pages, accepted and presented at the First International Workshop on Cross-model Language Design and Implementation (XLDI), affiliated with ICFP 2012, Copenhage

Programming with Purity Reflection: Peaceful Coexistence of Effects, Laziness, and Parallelism

We present purity reflection, a programming language feature that enables higher-order functions to inspect the purity of their function arguments and to vary their behavior based on this information. The upshot is that operations on data structures can selectively use lazy and/or parallel evaluation while ensuring that side effects are never lost or re-ordered. The technique builds on a recent Hindley-Milner style type and effect system based on Boolean unification which supports both effect polymorphism and complete type inference. We illustrate that avoiding the so-called \u27poisoning problem\u27 is crucial to support purity reflection. We propose several new data structures that use purity reflection to switch between eager and lazy, sequential and parallel evaluation. We propose a DelayList, which is maximally lazy but switches to eager evaluation for impure operations. We also propose a DelayMap which is maximally lazy in its values, but also exploits eager and parallel evaluation. We implement purity reflection as an extension of the Flix programming language. We present a new effect-aware form of monomorphization that eliminates purity reflection at compile-time. And finally, we evaluate the cost of this new monomorphization on compilation time and on code size, and determine that it is minimal

Polynomial Invariants for Affine Programs

We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose assignments are given by affine expressions). Our main tool is an algebraic result of independent interest: given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate

Abstract interpretation

Abstract. Abstract interpretation has been widely used for verifying properties of computer systems. Here, we present a way to extend this framework to the case of probabilistic systems. The probabilistic abstraction framework that we propose allows us to systematically lift any classical analysis or verification method to the probabilistic setting by separating in the program semantics the probabilistic behavior from the (non-)deterministic behavior. This separation provides new insights for designing novel probabilistic static analyses and verification methods. We define the concrete probabilistic semantics and propose different ways to abstract them. We provide examples illustrating the expressiveness and effectiveness of our approach.

Transforming semantics by abstract interpretation

In 1997, Cousot introduced a hierarchy where semantics are related with each other by abstract interpretation. In this field we consider the standard abstract domain transformers, devoted to refine abstract domains in order to include attribute independent and relational information, respectively the reduced product and power of abstract domains, as domain operations to systematically design and compare semantics of programming languages by abstract interpretation. We first prove that natural semantics can be decomposed in terms of complementary attribute independent observables, leading to an algebraic characterization of the symmetric structure of the hierarchy. Moreover, we characterize some structural property of semantics, such as their compositionality, in terms of simple abstract domain equations. This provides an equational presentation of most well known semantics, which is parametric on the observable and structural property of the semantics, making it possible to systematically derive abstract semantics, e.g. for program analysis, as solutions of abstract domain equations

Temporal Data Modeling and Reasoning for Information Systems

Temporal knowledge representation and reasoning is a major research field in Artificial Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to model and process time and calendar data is essential for many applications like appointment scheduling, planning, Web services, temporal and active database systems, adaptive Web applications, and mobile computing applications. This article aims at three complementary goals. First, to provide with a general background in temporal data modeling and reasoning approaches. Second, to serve as an orientation guide for further specific reading. Third, to point to new application fields and research perspectives on temporal knowledge representation and reasoning in the Web and Semantic Web