Simple Type System Research Articles

Subtyping and intersection types revisited

Church's system of simple types has proven to be remarkably robust: call-by-name, call-by-need, and call-by-value languages, with or without effects, and even logical frameworks can be based on the same typing rules. When type systems become more expressive, this unity fractures. An early example is the value restriction for parametric polymorphism which is necessary for ML but not Haskell; a later manifestation is the lack of distributivity of function types over intersections in call-by-value languages with effects. In this talk we reexamine the logical justification for systems of subtyping and intersection types and then explore the consequences in two different settings: logical frameworks and functional programming. In logical frameworks functions are pure and their definitions observable, but complications could arise from the presence of dependent types. We show that this is not the case, and that we can obtain soundness and completeness theorems for a certain axiomatization of subtyping. We also sketch a connection to the type-theoretic notion of proof irrelevance. In functional programming we investigate how the encapsulation of effects in monads interacts with subtyping and intersection types, providing an updated analysis of the value restriction and related phenomena. While at present this study is far from complete, we believe that its origin in purely logical notions will give rise to a uniform theory that can easily be adapted to specific languages and their operational interpretations.

A New Helicobacter pylori Vacuolating Cytotoxin Determinant, the Intermediate Region, Is Associated With Gastric Cancer

Helicobacter pylori is the main cause of peptic ulceration and gastric adenocarcinoma. The vacuolating cytotoxin gene, vacA, is a major determinant of virulence. Two naturally polymorphic sites in vacA, the signal region and midregion, are well-characterized determinants of toxicity and markers of pathogenesis. The aim of this study was to characterize a new vacA polymorphic site, the intermediate (i) region. The vacA i-region was identified and characterized by constructing isogenic vacA exchange mutants and determining their vacuolating activity on HeLa, AGS, and RK13 cell lines. The vacA i-region types of H pylori isolates from patients undergoing routine endoscopy were determined by nucleotide sequencing and allele-specific polymerase chain reaction. Two i-region types were identified, i1 and i2, and both were common among 42 Western clinical isolates. Interestingly, only naturally occurring s1/m2 strains varied in i-type; s1/m1 and s2/m2 strains were exclusively i1 and i2, respectively. Vacuolation assays showed that i-type determined vacuolating activity among these s1/m2 strains, and exchange mutagenesis confirmed that the i-region itself was directly responsible. Using a simple i-region polymerase chain reaction-based typing system, it was shown for 73 Iranian patients that i1-type strains were strongly associated with gastric adenocarcinoma (P < 10(-3)). Finally, logistic regression analysis showed this association to be independent of, and larger than, associations of vacA s- or m-type or cag status with gastric adenocarcinoma. Together these data show that the vacA i-region is an important determinant of H pylori toxicity and the best independent marker of VacA-associated pathogenicity.

Program verification with interacting analysis plugins

Abstract In this paper we propose and argue for a modular framework for interprocedural program analysis, where multiple program analysis tools are combined in order to exploit the particular advantages of each. This allows for “plugging together” such tools as required by each verification task and makes it easy to integrate new analyses. Our framework automates the sharing of information between plugins using a first order logic with transitive closure, in a way inspired by the open product of Cortesi et al. We describe a prototype implementation of our framework, which performs static assertion checking on a simple language for heap-manipulating programs. This implementation includes plugins for three existing approaches—predicate abstraction, 3-valued shape analysis and a decidable pointer analysis—and for a simple type system. We demonstrate through a detailed example the increase in precision that our approach can provide. Finally we discuss the design decisions we have taken, in particular the tradeoffs involved in the choice of language by which the plugins communicate, and identify some future directions for our work.

Epidemiological typing of methicillin-resistant Staphylococcus aureus strains by Fourier transform infrared spectroscopy

A rapid and simple typing system is needed for controlling the spread of epidemic methicillin-resistant Staphylococcus aureus (MRSA), currently one of the most widespread multi-resistant nosocomial pathogens in Canadian hospitals. Fourier transform infrared (FTIR) spectroscopy was used to subtype 85 isolates representing five strains of epidemic Canadian MRSA (CMRSA). Spectral fingerprints of whole cells grown on Que-Bact® Universal Medium No. 2 were transformed to first derivative peak-height normalized files and examined visually and by singular-value decomposition (SVD). Distinguishing spectral regions were processed by principal component analysis (PCA), self-organizing map and K-nearest neighbor supervised cluster analysis. Among the visually identified regions, 1070–1050 and 1155–1137 cm − 1 were found suitable for discrimination of CMRSA-4 and CMRSA-2 respectively, while CMRSA-1, CMRSA-3, and CMRSA-5 each exhibited distinctive spectral profiles in the 1123–1094 cm − 1 region. The combination, 1123–1094, 1174–1154 and 2904–2864 cm − 1 separated the five CMRSA with 84.6% correct classification by PCA. Five clusters were also obtained using the SVD-selected regions 1096–1066, 1118–1090 and 2914–2880 cm − 1 , with 87.8% correct classification based on visual examination of the PCA scores plot and 97% based on supervised cluster analysis. These results demonstrate that FTIR spectroscopy has considerable potential as a rapid (1-hour) and simple method for MRSA strain typing and monitoring in clinical settings.

The Use of the Free Metal – Temperature ‘Phase Diagrams’ for Studies of Single Site Metal Binding Proteins

Typical physico-chemical studies of metal binding proteins are usually aimed at determination of the metal binding constant K for a native protein (Kn), while the significance of the K value for the thermally denatured protein (Ku) is usually underestimated. Meanwhile, metal binding induced shift of thermal denaturation transition of a single site metal binding protein is defined by Kn to Ku ratio, implying that knowledge of both K values is required for full characterization of the system. In the present work, the most universal approach to the studies of single site metal binding proteins, namely construction of a protein "phase diagram" in coordinates of free metal ion concentration - temperature, is considered in detail. The detailed algorithm of construction of the phase diagrams along with underlying mathematic procedures developed here may be of use for studies of other simple protein-target type systems, where target represents low molecular weight ligand. Analysis of the simplest protein-ligand system reveals that thermodynamic properties of apo-protein dictate the maximal possible increase of its affinity to any simple ligand upon thermal denaturation of the protein. Experimental and general problems coupled with the use of the phase diagrams are discussed.

A verifiable SSA program representation for aggressive compiler optimization

We present a verifiable low-level program representation to embed, propagate, and preserve safety information in high perfor-mance compilers for safe languages such as Java and C#. Our representation precisely encodes safety information via static single-assignment (SSA) [11, 3] proof variables that are first-class constructs in the program.We argue that our representation allows a compiler to both (1) express aggressively optimized machine-independent code and (2) leverage existing compiler infrastructure to preserve safety information during optimization. We demonstrate that this approach supports standard compiler optimizations, requires minimal changes to the implementation of those optimizations, and does not artificially impede those optimizations to preserve safety. We also describe a simple type system that formalizes type safety in an SSA-style control-flow graph program representation. Through the types of proof variables, our system enables compositional verification of memory safety in optimized code. Finally, we discuss experiences integrating this representation into the machine-independent global optimizer of STARJIT, a high-performance just-in-time compiler that performs aggressive control-flow, data-flow, and algebraic optimizations and is competitive with top production systems.

Communication and mobility control in boxed ambients

Boxed Ambients (BA) replace Mobile Ambients’ open capability with communication primitives acting across ambient boundaries. The expressiveness of the new communication model is achieved at the price of communication interferences whose resolution requires synchronisation of activities at multiple, distributed locations. We study a variant of BA aimed at controlling communication as well as mobility interferences. Our calculus modifies the communication mechanism of BA, and introduces a new form of co-capability, inspired from Safe Ambients (SA) (with passwords), that registers incoming agents with the receiver ambient while at the same time performing access control. We prove that the new calculus has a rich semantics theory, including a sound and complete coinductive characterisation, and an expressive, yet simple type system. Through a set of examples, and an encoding, we characterise its expressiveness with respect to both BA and SA.

Intersection and Union Types in the [formula omitted]-calculus

The original λ¯μμ˜ of Curien and Herbelin has a system of simple types, based on sequent calculus, embodying a Curry-Howard correspondence with classical logic. We introduce and discuss three type assignment systems that are extensions of λ¯μμ˜ with intersection and union types. The intrinsic symmetry in the λ¯μμ˜ calculus leads to an essential use of both intersection and union types.

Simple relational correctness proofs for static analyses and program transformations

We show how some classical static analyses for imperative programs, and the optimizing transformations which they enable, may be expressed and proved correct using elementary logical and denotationaltechniques. The key ingredients are an interpretation of program properties as relations, rather than predicates, and a realization that although many program analyses are traditionally formulated in very intensional terms, the associated transformations are actually enabled by more liberal extensional properties.We illustrate our approach with formal systems for analysing and transforming while-programs. The first is a simple type system which tracks constancy and dependency information and can be used to perform dead-code elimination, constant propagation and program slicing as well as capturing a form of secure information flow. The second is a relational version of Hoare logic, which significantly generalizes our first type system and can also justify optimizations including hoisting loop invariants. Finally we show how a simple available expression analysis and redundancy elimination transformation may be justified by translation into relational Hoare logic.

A simple and powerful type system for programming languages

A type system serves to guarantee that programs mix data of distinct types only as allowed by programmer declared rules. For example, a function declaration corresponds to one of these rules, providing a way to mix data of distinct types, possibly producing data of another type as a result. A type system also discovers the type of each (sub)expression throughout a program. This paper introduces a type system where types are parts of speech, and all relations among types are represented by a grammar, a grammar whose rules are written in terms of the types. In order to resolve types, i.e., discover which type each (sub)expression is, the type grammar may be used to parse a given program, as a second pass. A brief, Polish postfix programming language rich in types is presented, called the type grammar, as well as a way to translate down from a more natural syntax. We show how to extend the type grammar with new rules based on program declarations. By parsing with this postfix type grammar, unrestricted overloading (more powerful than Java’s) and unrestricted programmer-defined coercions (in some ways more powerful than multiple inheritance) may be implemented and understood in a straightforward manner. To realize these, a powerful parser like Earley’s efficient context-free parser, or others, which tolerate ambiguity efficiently, are required. We conclude by showing how a pair of coercions, in a cycle, proves useful.

Water detection in fuel tanks using the microwave reflection technique

Water is often present in fuel tanks due to night and day temperature changes,resulting in a build-up of condensed water within the inner surface of the tank. Theexpectancy of water infiltration in fuel tanks is even higher in flooding proneareas. Water settlement at the bottom of the tank causes internal corrosion. Inthis work, a simple, low cost and accurate microwave reflection type system fordetection of water in fuel tanks has been developed. A module consisting of amicrowave generator and a detecting diode is used to measure the microwavereflection coefficient at various positions through the fuel tank. In the course ofthe study, a motion control and data acquisition system has been developed.Software written using the LabVIEW programming language is used to control themovement of the sensor and for the data acquisition. Theoretical and experimentalresults show the ability of the system to detect the presence of a water level downto approximately 1 mm. A simple theoretical model for power prediction of thereflected signal at various positions of the sensor in the tank is also presented.

Lexically scoped distribution: what you see is what you get

We define a lexically scoped, asynchronous and distributed π-calculus, with local communication and process migration. This calculus adopts the network-awareness principle for distributed programming and follows a simple model of distribution for mobile calculi: a lexical scope discipline combines static scoping with dynamic linking, associating channels to a fixed site throughout computation. This discipline provides for both remote invocation and process migration. A simple type system is a straightforward extension of that of the π-calculus, adapted to take into account the lexical scope of channels. An equivalence law captures the essence of this model: a process behavior depends on the channels it uses, not on where it runs.

The receptive distributed π-calculus

We study an asynchronous distributed π-calculus, with constructs for localities and migration. We show that a static analysis ensures the receptiveness of channel names, which, together with a simple type system, guarantees the message deliverability property. This property states that any migrating message will find an appropriate receiver at its destination locality. We argue that this distributed, receptive calculus is still expressive enough while allowing for an effective type inference à la ML.

The logical approach to stack typing

We develop a logic for reasoning about adjacency and separation of memory blocks, as well as aliasing of pointers. We provide a memory model for our logic and present a sound set of natural deduction-style inference rules. We deploy the logic in a simple type system for a stack-based assembly language. The connectives for the logic provide a flexible yet concise mechanism for controlling allocation, deallocation and access to both heap-allocated and stack-allocated data.

Resistotyping of Campylobacter jejuni

The principal objective of typing in epidemiology is to trace a strain as it passes from one individual to another. Resistotyping is a phenotypic method that consists of testing bacterial strains against a set of arbitrarily chosen chemical agents, whereby, a resistance pattern that is characteristic of a strain is generated and, is believed to describe the isolates for epidemiological purposes. This simple typing system is described for campylobacter isolated in Lagos, Nigeria. Resistotyping was performed with twenty chemical agents incorporated into disc. The resistotyping results revealed that the twenty isolates from human and chickens belonged to 14 different resistotypes with the largest group comprising 25% of the isolates. The human strains were distinctly differentiated into eight resistotypes. All the Campylobacter Jejuni isolates were resistant to potassium chloride (A), Boric acid (B), Sodium biselenite (C), potassium dischromate (F), potassium permanganate (I) ferrous sulphate (N), magnesium sulphate (O), sodium hydrogen phosphate (P), sodium sulphate (Q), and magnesium chloride (R). Only one strain was resistant to mercuric chloride (M) while three of the strains were sensitive to disodium orthophosphate (H), sodium azide (J), and metronidazole (T). The method seems to be adequate for defining the relatedness of our isolates in epidemiologic situation and has proven promising for Campylobacter jejuni in our environment.

An Operational Approach to the Semantics of Classes: Application to Type Checking

This paper presents a simple and natural semantics for object-oriented languages with classes and multiple inheritance. The model, called the Formal Class model, is an intermediate level between the algebraic specification of data type, and the implementation within an object-oriented language. Our model is equipped with an operational semantics based on conditional term rewriting. One important characteristic is the use of conditional selectors. It allows one to define a type with a flat or an ordered design. In this context, we define a safe and simple type system with single dispatch and simply covariant methods. This type system is extended to some practical aspects, such as abstract classes, abstract methods, protected methods, and super methods. We describe and compare flat and ordered designs and prove that the latter is finer than the former one. We also look at multicovariant methods and show ways to fix type-checking problems using single dispatch. We describe the least pessimistic solution. Lastly, we discuss the extension of our type checking to multiple dispatch and side effects. This paper synthesizes several practical results, their proofs, and algorithms.

Information flow inference for free

This paper shows how to systematically extend an arbitrary type system with dependency information, and how soundness and non-interference proofs for the new system may rely upon, rather than duplicate, the soundness proof of the original system. This allows enriching virtually any of the type systems known today with information flow analysis, while requiring only a minimal proof effort.Our approach is based on an untyped operational semantics for a labelled calculus akin to core ML. Thus, it is simple, and should be applicable to other computing paradigms, such as object or process calculi.The paper also discusses access control, and shows it may be viewed as entirely independent of information flow control. Letting the two mechanisms coexist, without interacting, yields a simple and expressive type system, which allows, in particular, "selective" declassification.

The duality of computation

We present the &amp;mu; -calculus, a syntax for &amp;lambda;-calculus + control operators exhibiting symmetries such as program/context and call-by-name/call-by-value. This calculus is derived from implicational Gentzen's sequent calculus LK , a key classical logical system in proof theory. Under the Curry-Howard correspondence between proofs and programs, we can see LK , or more precisely a formulation called LK &amp;mu; , as a syntax-directed system of simple types for &amp;mu; -calculus. For &amp;mu; -calculus, choosing a call-by-name or call-by-value discipline for reduction amounts to choosing one of the two possible symmetric orientations of a critical pair. Our analysis leads us to revisit the question of what is a natural syntax for call-by-value functional computation. We define a translation of &amp;lambda;&amp;mu;-calculus into &amp;mu; -calculus and two dual translations back to &amp;lambda;-calculus, and we recover known CPS translations by composing these translations.

Focus adjustment-free imaging over a long range

Focus adjustment-free imaging over a long range is demonstrated, both theoretically and experimentally, by using a simple telescopic system of the Galilean type that has an eyepiece with specified spherical aberration. Computer simulation results show that such a telescopic system with a 5 cm aperture can form clear images of a target over a range from 60 to ∼400 m, without focusing adjustment. The imaging results of an experiment carried out using such a telescopic system confirm that clear images can indeed be obtained in this range without focusing adjustment, verifying the usefulness of the new technique.

Secrecy in Programming-Language Semantics

These notes discuss secrecy properties of programs from the perspective of programming-language theory. They present and compare some simple type systems for establishing secrecy properties. They also distinguish descriptive and prescriptive statements of secrecy properties.