Practical, Pluggable Types for a Dynamic Language

Most languages fall into one of two camps: either they adopt a unique, static type system, or they abandon static type-checks for run-time checks. Pluggable types blur this division by (i) making static type systems optional, and (ii) supporting a choice of type systems for reasoning about different kinds of static properties. Dynamic languages can then benefit from static-checking without sacrificing dynamic features or committing to a unique, static type system. But the overhead of adopting pluggable types can be very high, especially if all existing code must be decorated with type annotations before any type-checking can be performed. We propose a practical and pragmatic approach to introduce pluggable type systems to dynamic languages. First of all, only annotated code is type-checked. Second, limited type inference is performed on unannotated code to reduce the number of reported errors. Finally, external annotations can be used to type third-party code. We present Typeplug, a Smalltalk implementation of our framework, and report on experience applying the framework to three different pluggable type systems.

Programming with global analysis

Global data-flow analysis of (constraint) logic programs, which is generally based on abstract interpretation [7], is reaching a comparatively high level of maturity. A natural question is whether it is time for its routine incorporation in standard compilers, something which, beyond a few experimental systems, has not happened to date. Such incorporation arguably makes good sense only if: • the range of applications of global analysis is large enough to justify the additional complication in the compiler, and • global analysis technology can deal with all the features of "practical" languages (e.g., the ISO-Prolog built-ins) and "scales up" for large programs. We present a tutorial overview of a number of concepts and techniques directly related to the issues above, with special emphasis on the first one. In particular, we concéntrate on novel uses of global analysis during program development and debugging, rather than on the more traditional application área of program optimization. The idea of using abstract interpretation for validation and diagnosis has been studied in the context of imperative programming [2] and also of logic programming. The latter work includes issues such as using approximations to reduce the burden posed on programmers by declarative debuggers [6, 3] and automatically generating and checking assertions [4, 5] (which includes the more traditional type checking of strongly typed languages, such as Gódel or Mercury [1, 8, 9]) We also review some solutions for scalability including modular analysis, incremental analysis, and widening. Finally, we discuss solutions for dealing with meta-predicates, side-effects, delay declarations, constraints, dynamic predicates, and other such features which may appear in practical languages. In the discussion we will draw both from the literature and from our experience and that of others in the development and use of the CIAO system analyzer. In order to emphasize the practical aspects of the solutions discussed, the presentation of several concepts will be illustrated by examples run on the CIAO system, which makes extensive use of global analysis and assertions.

Mecanización de semántica de lenguajes de programación: teoría, implementación y desarrollo.

El presente proyecto se enmarca en el área de métodos formales para computación; el objetivo de los métodos formales es asegurar, a través de herramientas lógicas y matemáticas, que sistemas computacionales satisfacen ciertas propiedades. El campo de semántica de lenguajes de programación trata justamente de construir modelos matemáticos que den cuenta de las diferentes características de cada lenguaje (estado mutable, mecanismos de paso de parámetros, órdenes de ejecución, etc.); permitiendo razonar de una manera abstracta, en vez de lidiar con las peculiaridades de implementaciones o las vaguezas de descripciones informales. Como las pruebas formales de corrección son demasiado intrincadas, es muy conveniente realizar estos desarrollos teóricos con la ayuda de asistentes de prueba. Este proceso de formalizar y corrobar aspectos semánticos a través de un asistente se denomina mecanización de semántica. Este proyecto – articulado en tres líneas: semántica de teoría de tipos, implementación de un lenguaje con tipos dependientes y semántica de lenguajes imperativos con alto orden - se propone realizar avances en el estudio semántico de lenguajes de programación, mecanizar dichos resultados, e implementar un lenguaje con tipos dependientes con la intención de que se convierta, en un mediano plazo, en un asistente de pruebas. En la línea de semántica de teoría de tipos los objetivos son: (a) extender el método de normalización por evaluación para construcciones no contempladas aun en la literatura, (b) probar la adecuación de la implementación en Haskell de dicho método de normalización, y (c) construir nuevos modelos categóricos de teoría de tipos. El objetivo de la segunda línea es el diseño e implementación de un lenguaje con tipos dependientes con la intención de que el mismo se convierta en un asistente de pruebas. Una novedad de esta implementación es que el algoritmo de chequeo de tipos es correcto y completo respecto al sistema formal, gracias a resultados ya obtenidos; además la implementación en Haskell del algoritmo de normalización (fundamental para el type-checking) también tendrá su prueba de corrección. El foco de la tercera línea está en el estudio de lenguajes de programación que combinan aspectos imperativos (estado mutable) con características de lenguajes funcionales (procedimientos y funciones). Por un lado se avanzará en la mecanización de pruebas de corrección de compiladores para lenguajes Algollike. El segundo aspecto de esta línea será la definición de semánticas operacional y denotacional del lenguaje de programación Lua y la posterior caracterización del mismo a partir de ellas. Para lograr dichos objetivos hemos dividido las tareas en actividades con metas graduales y que constituyen en sí mismas aportes al estado del arte de cada una de las líneas. La importancia académica de este proyecto radica en los avances teóricos que se propone en la línea de semántica de teoría de tipos, en las contribución para la construcción de pruebas mecanizadas de corrección de compiladores, en el aporte que constituye la definición de una semántica formal para el lenguaje Lua, y en el desarrollo de un lenguaje con tipos dependientes cuyos algoritmos más importantes están respaldados por pruebas de corrección. Además, a nivel local, este proyecto permitirá incorporar cuatro integrantes al grupo de “Semántica de la programación”.

Integrating runtime assertions with dynamic types: Structuring a derivation from an incomputable specification

An inherent incomputability in the specification of a functional language extension that combines assertions with dynamic type checking is isolated in an explicit derivation from mathematical specifications. The combination of types and assertions (into "dynamic assertion-types" - DATs) is a significant issue since, because the two are congruent means for program correctness, benefit arises from their better integration in contrast to the harm resulting from their unnecessary separation. However, projecting the "set membership" view of assertion-checking into dynamic types results in some incomputable combinations. Refinement of the specification of DAT checking into an implementation by rigorous application of mathematical identities becomes feasible through the addition of a "best-approximate" pseudo-equality that isolates the incomputable component of the specification. This formal treatment leads to an improved, more maintainable outcome with further development potential.

Practical secure information flow in programming languages

If we classify variables in a program into various security levels, then a secure information flow analysis aims to verify statically that information in a program can flow only in ways consistent with the specified security levels. One well-studied approach is to formulate the rules of the secure information flow analysis as a type system. A major trend of recent research focuses on how to accommodate various sophisticated modern language features. However, this approach often leads to overly complicated and restrictive type systems, making them unfit for practical use. Also, problems essential to practical use, such as type inference and error reporting, have received little attention. This dissertation identified and solved major theoretical and practical hurdles to the application of secure information flow. ^ We adopted a minimalist approach to designing our language to ensure a simple lenient type system. We started out with a small simple imperative language and only added features that we deemed most important for practical use. One language feature we addressed is arrays. Due to the various leaking channels associated with array operations, arrays have received complicated and restrictive typing rules in other secure languages. We presented a novel approach for lenient array operations, which lead to simple and lenient typing of arrays. ^ Type inference is necessary because usually a user is only concerned with the security types for input/output variables of a program and would like to have all types for auxiliary variables inferred automatically. We presented a type inference algorithm B and proved its soundness and completeness. Moreover, algorithm B stays close to the program and the type system and therefore facilitates informative error reporting that is generated in a cascading fashion. Algorithm B and error reporting have been implemented and tested. ^ Lastly, we presented a novel framework for developing applications that ensure user information privacy. In this framework, core computations are defined as code modules that involve input/output data from multiple parties. Incrementally, secure flow policies are refined based on feedback from the type checking/inference. Core computations only interact with code modules from involved parties through well-defined interfaces. All code modules are digitally signed to ensure their authenticity and integrity. ^

Static analysis for checking data format compatibility of programs

Large software systems are developed by composing multiple programs. If the programs manip-ulate and exchange complex data, such as network packets or files, it is essential to establish that they follow compatible data formats. Most of the complexity of data formats is associated with the headers. In this paper, we address compatibility of programs operating over headers of network packets, files, images, etc. As format specifications are rarely available, we infer the format associated with headers by a program as a set of guarded layouts. In terms of these formats, we define and check compatibility of (a) producer-consumer programs and (b) different versions of producer (or consumer) programs. A compatible producer-consumer pair is free of type mismatches and logical incompatibilities such as the consumer rejecting valid outputs gen-erated by the producer. A backward compatible producer (resp. consumer) is guaranteed to be compatible with consumers (resp. producers) that were compatible with its older version. With our prototype tool, we identified 5 known bugs and 1 potential bug in (a) sender-receiver modules of Linux network drivers of 3 vendors and (b) different versions of a TIFF image library.

Type-alpha DPLs

This paper introduces Denotational Proof Languages (DPLs). DPLs are languages for presenting, discovering, and checking formal proofs. In particular, in this paper we discus type-alpha DPLs---a simple class of DPLs for which termination is guaranteed and proof checking can be performed in time linear in the size of the proof. Type-alpha DPLs allow for lucid proof presentation and for efficient proof checking, but not for proof search. Type-omega DPLs allow for search as well as simple presentation and checking, but termination is no longer guaranteed and proof checking may diverge. We do not study type-omega DPLs here. We start by listing some common characteristics of DPLs. We then illustrate with a particularly simple example: a toy type-alpha DPL called PAR, for deducing parities. We present the abstract syntax of PAR, followed by two different kinds of formal semantics: evaluation and denotational. We then relate the two semantics and show how proof checking becomes tantamount to evaluation. We proceed to develop the proof theory of PAR, formulating and studying certain key notions such as observational equivalence that pervade all DPLs. We then present NDL, a type-alpha DPL for classical zero-order natural deduction. Our presentation of NDL mirrors that of PAR, showing how every basic concept that was introduced in PAR resurfaces in NDL. We present sample proofs of several well-known tautologies of propositional logic that demonstrate our thesis that DPL proofs are readable, writable, and concise. Next we contrast DPLs to typed logics based on the Curry-Howard isomorphism, and discuss the distinction between pure and augmented DPLs. Finally we consider the issue of implementing DPLs, presenting an implementation of PAR in SML and one in Athena, and end with some concluding remarks.

Type-omega DPLs

Type-omega DPLs (Denotational Proof Languages) are languages for proof presentation and search that offer strong soundness guarantees. LCF-type systems such as HOL offer similar guarantees, but their soundness relies heavily on static type systems. By contrast, DPLs ensure soundness dynamically, through their evaluation semantics; no type system is necessary. This is possible owing to a novel two-tier syntax that separates deductions from computations, and to the abstraction of assumption bases, which is factored into the semantics of the language and allows for sound evaluation. Every type-omega DPL properly contains a type-alpha DPL, which can be used to present proofs in a lucid and detailed form, exclusively in terms of primitive inference rules. Derived inference rules are expressed as user-defined methods, which are "proof recipes" that take arguments and dynamically perform appropriate deductions. Methods arise naturally via parametric abstraction over type-alpha proofs. In that light, the evaluation of a method call can be viewed as a computation that carries out a type-alpha deduction. The type-alpha proof "unwound" by such a method call is called the "certificate" of the call. Certificates can be checked by exceptionally simple type-alpha interpreters, and thus they are useful whenever we wish to minimize our trusted base. Methods are statically closed over lexical environments, but dynamically scoped over assumption bases. They can take other methods as arguments, they can iterate, and they can branch conditionally. These capabilities, in tandem with the bifurcated syntax of type-omega DPLs and their dynamic assumption-base semantics, allow the user to define methods in a style that is disciplined enough to ensure soundness yet fluid enough to permit succinct and perspicuous expression of arbitrarily sophisticated derived inference rules. We demonstrate every major feature of type-omega DPLs by defining and studying NDL-omega, a higher-order, lexically scoped, call-by-value type-omega DPL for classical zero-order natural deduction---a simple choice that allows us to focus on type-omega syntax and semantics rather than on the subtleties of the underlying logic. We start by illustrating how type-alpha DPLs naturally lead to type-omega DPLs by way of abstraction; present the formal syntax and semantics of NDL-omega; prove several results about it, including soundness; give numerous examples of methods; point out connections to the lambda-phi calculus, a very general framework for type-omega DPLs; introduce a notion of computational and deductive cost; define several instrumented interpreters for computing such costs and for generating certificates; explore the use of type-omega DPLs as general programming languages; show that DPLs do not have to be type-less by formulating a static Hindley-Milner polymorphic type system for NDL-omega; discuss some idiosyncrasies of type-omega DPLs such as the potential divergence of proof checking; and compare type-omega DPLs to other approaches to proof presentation and discovery. Finally, a complete implementation of NDL-omega in SML-NJ is given for users who want to run the examples and experiment with the language.

On Szegö’s Type Theorems

This study is to look the effect of change in the ordering of the Fourier system on Szegö’s classical observations of asymptotic distribution of eigenvalues of finite Toeplitz forms.This is done by checking proofs and Szegö’s properties in the new set up.The Fourier system is unconditional [19], any arbitrary ordering of the Fourier system forms a basis for the Hilbert space L2 [-Π, Π].Here study about the classical Szegö’s theorem.Szegö’s type theorem for operators in L2(R+) and check its validity for certain multiplication operators.Since the trigonometric basis is not available in L2(R+) or in L2(R) .This study discussed about the classes of orderings of Haar System in L2 (R+) and in L2(R) in which Szegö’s Type TheoreT Am is valid for certain multiplication operators.It is divided into two sections. In the first section there is an ordering to Haar system in L2(R+) and prove that with respect to this ordering, Szegö’s Type theorem holds for general class of multiplication operators Tƒ with multiplier ƒ ε L2(R+), subject to some conditions on ƒ.Finally in second section more general classes of ordering of Haar system in L2(R+) and in L2(R) are identified in such a way that for certain classes of multiplication operators the asymptotic distribution of eigenvalues exists.

Model checking Z specifications using SAL

The Symbolic Analysis Laboratory (SAL) is a suite of tools for analysis of state transition systems. Tools supported include a simulator and four temporal logic model checkers. The common input language to these tools was originally developed with translation from other languages, both programming and specification languages, in mind. It is, therefore, a rich language supporting a range of type definitions and expressions. In this paper, we investigate the translation of Z specifications into the SAL language as a means of providing model checking support for Z. This is facilitated by a library of SAL definitions encoding the Z mathematical toolkit.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes : (Part 10) The infrared and Raman characteristics of phthalocyanine in heteroleptic bis(phthalocyaninato) rare earth complexes with decreased molecular symmetry

The infrared (IR) spectroscopic data for a series of eleven heteroleptic bis(phthalocyaninato) rare earth complexes MIII(Pc)[Pc(α-OC5H11)4] (M = Sm–Lu, Y) [H2Pc = unsubstituted phthalocyanine, H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected with 2 cm−1 resolution. Raman spectroscopic properties in the range of 500–1800 cm−1 for these double-decker molecules have also been comparatively studied using laser excitation sources emitting at 632.8 and 785 nm. Both the IR and Raman spectra for M(Pc)[Pc(α-OC5H11)4] are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues due to the decreased molecular symmetry of these double-decker compounds, namely C4. For this series, the IR Pc√− marker band appears as an intense absorption at 1309–1317 cm−1, attributed to the pyrrole stretching. With laser excitation at 632.8 nm, Raman vibrations derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. In contrast, when excited with laser radiation of 785 nm, the ring radial vibrations of isoindole moieties and dihedral plane deformations between 500 and 1000 cm−1 for M(Pc)[Pc(α-OC5H11)4] intensify to become the strongest scatterings. Both techniques reveal that the frequencies of pyrrole stretching, isoindole breathing, isoindole stretchings, aza stretchings and coupling of pyrrole and aza stretchings depend on the rare earth ionic size, shifting to higher energy along with the lanthanide contraction due to the increased ring-ring interaction across the series. The assignments of the vibrational bands for these compounds have been made and discussed in relation to other unsubstituted and substituted bis(phthalocyaninato) rare earth analogues, such as M(Pc)2 and M(OOPc)2 [H2OOPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine].