Recursive Types Research Articles

An operational domain-theoretic treatment of recursive types

We develop an operational domain theory for treating recursive types with respect to contextual equivalence. The principal approach we take deviates from classical domain theory in that we do not produce the recursive types using the usual inverse limits constructions – we get them for free by working directly with the operational semantics. By extending type expressions to functors between some ‘syntactic’ categories, we establish algebraic compactness. To do this, we rely on an operational version of the minimal invariance property, for which we give a purely operational proof.

A graph-based generic type system for object-oriented programs

We present a graph-basedmodel of a generic type system for an OO language. The type system supports the features of recursive types, generics and interfaces, which are commonly found in modern OO languages such as Java. In the classical graph theory, we define type graphs, instantiation graphs and conjunction graphs that naturally illustrate the relations among types, generics and interfaces within complex OO programs. The model employs a combination of nominal and anonymous nodes to represent respectively types that are identified by names and structures, and defines graph-based relations and operations on types including equivalence, subtyping, conjunction and instantiation. Algorithms based on the graph structures are designed for the implementation of the type system. We believe that this type system is important for the development of a graph-based logical foundation of a formal method for verification of and reasoning about OO programs.

Semi-cubically hyponormal weighted shifts with recursive type

In this paper, we discuss the semi-cubic hyponormality of recursively generated weighted shifts with weight α(x) : √ x,( √ a, √ b, √ c) ∧ to give a new bridge between cubically hyponormal and quadratically hyponormal weighted shifts. Using weight sequences with first two equal weights, we show that two notions of quadratic hyponormality and semi-cubic hyponormality are different one from another. Moreover, we characterize the semi-cubic hyponormality of weighted shifts.

Blind Adaptive Interference Suppression Based on Set-Membership Constrained Constant-Modulus Algorithms With Dynamic Bounds

This work presents blind constrained constant modulus (CCM) adaptive algorithms based on the set-membership filtering (SMF) concept and incorporates dynamic bounds for interference suppression applications. We develop stochastic gradient and recursive least squares type algorithms based on the CCM design criterion in accordance with the specifications of the SMF concept. We also propose a blind framework that includes channel and amplitude estimators that take into account parameter estimation dependency, multiple access interference (MAI) and inter-symbol interference (ISI) to address the important issue of bound specification in multiuser communications. A convergence and tracking analysis of the proposed algorithms is carried out along with the development of analytical expressions to predict their performance. Simulations for a number of scenarios of interest with a DS-CDMA system show that the proposed algorithms outperform previously reported techniques with a smaller number of parameter updates and a reduced risk of overbounding or underbounding.

Design and Determination of Optimum Coefficients of IIR Digital Highpass Filter using Analog to Digital Mapping Technique

Digital Signal Processing (DSP) , there two types of filters are used to perform the filtering operations and they are the Infinite Impulse Response (IIR) filter and the Finite Impulse Response (FIR) filter. The present output sample of an IIR filter depends on the present input samples, past input samples and past output samples, i.e IIR filter is of recursive type. Now to design the Digital IIR filter, the coefficients are essentially required. There are a numbers of techniques available for designing the IIR filter. In this paper, the design and determination of the IIR filter coefficients are introduced using computer based approach. The program based on the algorithm proposed in this paper is simulated in Matlab which provides with the satisfactory results.

Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions

We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree-level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero.

Syntactic soundness proof of a type-and-capability system with hidden state

AbstractThis paper presents a formal definition and machine-checked soundness proof for a very expressive type-and-capability system, that is, a low-level type system that keeps precise track of ownership and side effects. The programming language has first-class functions and references. The type system's features include the following: universal, existential, and recursive types; subtyping; a distinction between affine and unrestricted data; support for strong updates; support for naming values and heap fragments via singleton and group regions; a distinction between ordinary values (which exist at runtime) and capabilities (which do not); support for dynamic reorganizations of the ownership hierarchy by disassembling and reassembling capabilities; and support for temporarily or permanently hiding a capability via frame and anti-frame rules. One contribution of the paper is the definition of the type-and-capability system itself. We present the system as modularly as possible. In particular, at the core of the system, the treatment of affinity, in the style of dual intuitionistic linear logic, is formulated in terms of an arbitrarymonotonic separation algebra, a novel axiomatization of resources, ownership, and the manner in which they evolve with time. Only the peripheral layers of the system are aware that we are dealing with a specific monotonic separation algebra, whose resources are references and regions. This semi-abstract organization should facilitate further extensions of the system with new forms of resources. The other main contribution is a machine-checked proof of type soundness. The proof is carried out in the Wright and Felleisen's syntactic style. This offers an evidence that this relatively simple-minded proof technique can scale up to systems of this complexity, and constitutes a viable alternative to more sophisticated semantic proof techniques. We do not claim that the syntactic technique is superior: We simply illustrate how it is used and highlight its strengths and shortcomings.

First steps in synthetic guarded domain theory: step-indexing in the topos of trees

We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms, predicates, and types. In particular, we show how to solve recursive type equations involving dependent types. We propose that the internal logic of S provides the right setting for the synthetic construction of abstract versions of step-indexed models of programming languages and program logics. As an example, we show how to construct a model of a programming language with higher-order store and recursive types entirely inside the internal logic of S. Moreover, we give an axiomatic categorical treatment of models of synthetic guarded domain theory and prove that, for any complete Heyting algebra A with a well-founded basis, the topos of sheaves over A forms a model of synthetic guarded domain theory, generalizing the results for S.

Elmo's Sister's Ball: The Problem of Acquiring Nominal Recursion

Recursion is the ability to iterate syntactic constituents inside constituents. Experimental and corpus literature indicates that comprehending recursive structures is difficult for children. Since recursion is a fundamental property of language, the result of the application of core minimal tools (merge, label, and select), why does it present an acquisition challenge? We propose that while Merge itself is universal, its application is determined by selection, which is extensively parameterized. We investigate whether children's difficulties can be defined in terms of the complexity of the selectional demands involved. This investigation leads to three empirical questions: i. How does NP recursion compare to NP coordination in acquisition? ii. Do children acquire each level of recursion independently or is recursion triggered automatically once the initial selectional requirements are acquired? iii. Are there differences in the acquisition of different types of nominal recursion? We compare the selectional requirements of English genitives, PPs, and NP coordination. Our syntactic analysis suggests that genitive recursion has more complex selectional demands than PP recursion. We designed a study eliciting production of two level embedded prepositional and genitive NPs. Preschool-aged English-speaking children (n = 46) and adults (n = 11) participated in an elicitation study. Children were comparable to adults in their ability to produce three coordinated NPs, but had substantial difficulty linking three NPs using recursion. First- and second-level embedding were clearly distinct steps in development. These findings have implications for the independence of phrasal and selectional development in children and for our understanding of structural complexity in child language and in theory.

Automatic amortised analysis of dynamic memory allocation for lazy functional programs

This paper describes the first successful attempt, of which we are aware, to define an automatic, type-based static analysis of resource bounds for lazy functional programs. Our analysis uses the automatic amortisation approach developed by Hofmann and Jost, which was previously restricted to eager evaluation. In this paper, we extend this work to a lazy setting by capturing the costs of unevaluated expressions in type annotations and by amortising the payment of these costs using a notion of lazy potential . We present our analysis as a proof system for predicting heap allocations of a minimal functional language (including higher-order functions and recursive data types) and define a formal cost model based on Launchbury's natural semantics for lazy evaluation. We prove the soundness of our analysis with respect to the cost model. Our approach is illustrated by a number of representative and non-trivial examples that have been analysed using a prototype implementation of our analysis.

Application of Real-Time Wavelet Threshold Filtering in FOG Attitude Measurement System

A wavelet method is introduced to compensate stochastic errors of FOG attitude measurement system, analysing and comparing threshold and threshold function principle, a new threshold function combining with soft and hard threshold was designed. Adopting data moving window realizes recursive computation and real-time data update and solves filtering signal’s boundary problem with symmetric periodic extension method, and achieves real-time wavelet threshold filter. Experimental results show the feasibility of the real time wavelet threshold method in FOG signal de-noising, the real-time wavelet de-noising algorithm with new threshold function has the advantages of single algorithm. which improves the precision and stability of the FOG.

A data dependence test based on the projection of paths over shape graphs

We propose a data dependence detection test based on a new conflict analysis algorithm for C codes which make intensive use of recursive data structures dynamically allocated in the heap. This algorithm requires two pieces of information from the code section under analysis (a loop or a recursive function): (i) abstract shape graphs that represent the state of the heap at the code section; and (ii) path expressions that collect the traversing information for each statement. Our algorithm projects the path expressions on the shape graphs and checks over the graphs to ascertain whether one of the sites reached by a write statement matches one of the sites reached by another statement on a different loop iteration (or on a different call instance in a recursive function), in which case a conflict between the two statements is reported. Although our algorithm presents exponential complexity, we have found that in practice the parameters that dominate the computational cost have very low values, and to the best of our knowledge, all the other related studies involve higher costs. In fact, our experimental results show reductions in the data dependence analysis times of one or two orders of magnitude in some of the studied benchmarks when compared to a previous data dependence algorithm. Thanks to the information on uncovered data dependences, we have manually parallelized these codes, achieving speedups of 2.19 to 3.99 in four cores.

3-5 再帰型イントラ予測における走査方向の切り替えに関する検討(第3部門画像符号化)

3-5 再帰型イントラ予測における走査方向の切り替えに関する検討(第3部門画像符号化)

The impact of higher-order state and control effects on local relational reasoning

AbstractReasoning about program equivalence is one of the oldest problems in semantics. In recent years, useful techniques have been developed, based on bisimulations and logical relations, for reasoning about equivalence in the setting of increasingly realistic languages—languages nearly as complex as ML or Haskell. Much of the recent work in this direction has considered the interesting representation independence principles enabled by the use of local state, but it is also important to understand the principles that powerful features like higher-order state and control effects disable. This latter topic has been broached extensively within the framework of game semantics, resulting in what Abramsky dubbed the “semantic cube”: fully abstract game-semantic characterizations of various axes in the design space of ML-like languages. But when it comes to reasoning about many actual examples, game semantics does not yet supply a useful technique for proving equivalences.In this paper, we marry the aspirations of the semantic cube to the powerful proof method of step-indexed Kripke logical relations. Building on recent work of Ahmed et al. (2009), we define the first fully abstract logical relation for an ML-like language with recursive types, abstract types, general references and call/cc. We then show how, under orthogonal restrictions to the expressive power of our language—namely, the restriction to first-order state and/or the removal of call/cc—we can enhance the proving power of our possible-worlds model in correspondingly orthogonal ways, and we demonstrate this proving power on a range of interesting examples. Central to our story is the use of state transition systems to model the way in which properties of local state evolve over time.

Reservoir Characterization Using a Streamline-Assisted Ensemble Kalman Filter with Covariance Localization

Ensemble Kalman filter (EnKF) is a recursive data process algorithm that uses continuous updating. It has been proven that EnKF is an efficient method for data assimilation, uncertainty assessment, and large scale problems in many engineering fields. However, there are two common limitations-filter divergence and overshooting/undershooting. These are due to reduction of cross-covariance between model parameters and measurements. We propose a streamline-assisted ensemble Kalman filter (SL EnKF) that uses covariance localization according to the types of well and measurement data. This method enables selective updates of permeability, therefore, providing more reliable permeability field estimations than the standard EnKF without overshooting/undershooting or filter divergence. In addition, it gives efficient uncertainty evaluations by considering the performances of each ensemble member.

Recognition of logically related regions based heap abstraction

Abstract This paper presents a novel set of algorithms for heap abstraction, identifying logically related regions of the heap. The targeted regions include objects that are part of the same component structure (recursive data structure). The result of the technique outlined in this paper has the form of a compact normal form (an abstract model) that boosts the efficiency of the static analysis via speeding its convergence. The result of heap abstraction, together with some properties of data structures, can be used to enable program optimizations like static deallocation, pool allocation, region-based garbage collection, and object co-location. More precisely, this paper proposes algorithms for abstracting heap components with the layout of a singly linked list, a binary tree, a cycle, and a directed acyclic graph. The termination and correctness of these algorithms are studied in the paper. Towards presenting the algorithms the paper also presents concrete and abstract models for heap representations.

Speculative separation for privatization and reductions

Automatic parallelization is a promising strategy to improve application performance in the multicore era. However, common programming practices such as the reuse of data structures introduce artificial constraints that obstruct automatic parallelization. Privatization relieves these constraints by replicating data structures, thus enabling scalable parallelization. Prior privatization schemes are limited to arrays and scalar variables because they are sensitive to the layout of dynamic data structures. This work presents Privateer, the first fully automatic privatization system to handle dynamic and recursive data structures, even in languages with unrestricted pointers. To reduce sensitivity to memory layout, Privateer speculatively separates memory objects. Privateer's lightweight runtime system validates speculative separation and speculative privatization to ensure correct parallel execution. Privateer enables automatic parallelization of general-purpose C/C++ applications, yielding a geomean whole-program speedup of 11.4x over best sequential execution on 24 cores, while non-speculative parallelization yields only 0.93x.

English

Digital images provide a new way to represent pictures and scenes that only film and a darkroom could supply before. This new way to capture and store images opens a door to malicious individuals wishing to forge or otherwise manipulate original authentic images. Since digital photography is improving and becoming more widely used technology, a need exists to provide countermeasures against mali- cious forgers. The old adage don't believe everything you hear is becoming don't believe everything you see. Photo is considered as evidence in all digital era. Image Forensic area provide right value to authenticated original images. We proposed two algorithm to overcome such challenging problem in the forensic world. Much time and effort has gone into analyzing uncompressed images but current techniques return dismal success in detecting one of the most common digital image formats, JPEG. In this paper we presented here attempts to tailor methods toward the JPEG format as well as incorporate all image formats where possible. The proposed method is analogous to a recursive type process, with the sub-processing resembling a divide and conquer approach. Block Based Processing is useful because the calculations performed are influenced by only the information present in that particular block. A JPEG image can either be color or grayscale. For grayscale Images we propose direction filter technique and color images JPEG block analysis technique.

Fundamentals of session types

We present a reconstruction of session types in a linear pi calculus where types are qualified as linear or unrestricted. Linearly qualified communication channels are guaranteed to occur in exactly one thread, possibly multiple times; unrestricted (or shared) channels may appear in an unbounded number of threads. In our language each channel is characterized by two distinct variables, one used for reading, the other for writing; scope restriction binds together two variables, thus establishing the correspondence between the two ends of the same channel. This mechanism allows a precise control of resources via a conventional linear type system. Furthermore, the uniform treatment of linear and shared channels leads to a surprisingly simply theory which, in addition, extends typability when compared to traditional systems for session types. We build the language gradually, starting from simple input/output, then adding recursive types, replication and finally choice. We also present an algorithmic type checking system.

A relational realizability model for higher-order stateful ADTs

We present a realizability model for reasoning about contextual equivalence of higher-order programs with impredicative polymorphism, recursive types, and higher-order mutable state.The model combines the virtues of two recent earlier models: (1) Ahmed, Dreyer, and Rossberg’s step-indexed logical relations model, which was designed to facilitate proofs of representation independence for “state-dependent” ADTs and (2) Birkedal, Støvring, and Thamsborg’s realizability logical relations model, which was designed to facilitate abstract proofs without tedious step-index arithmetic. The resulting model can be used to give abstract proofs of representation independence for “state-dependent” ADTs.