Abstract Data Types Research Articles

Semantic Code Refactoring for Abstract Data Types

Modifications to the data representation of an abstract data type (ADT) can require significant semantic refactoring of the code. Motivated by this observation, this paper presents a new method to automate semantic code refactoring tasks. Our method takes as input the original ADT implementation, a new data representation, and a so-called relational representation invariant (relating the old and new data representations), and automatically generates a new ADT implementation that is semantically equivalent to the original version. Our method is based on counterexample-guided inductive synthesis (CEGIS) but leverages three key ideas that allow it to handle real-world refactoring tasks. First, our approach reduces the underlying relational synthesis problem to a set of (simpler) programming-by-example problems, one for each method in the ADT. Second, it leverages symbolic reasoning techniques, based on logical abduction, to deduce code snippets that should occur in the refactored version. Finally, it utilizes a notion of partial equivalence to make inductive synthesis much more effective in this setting. We have implemented the proposed approach in a new tool called Revamp ‍ for automatically refactoring Java classes and evaluated it on 30 Java class mined from Github. Our evaluation shows that Revamp can correctly refactor the entire ADT in 97% of the cases and that it can successfully re-implement 144 out of the 146 methods that require modifications.

Tree-Shaped Formats of Address Programming Language


 
 
 In the Address Programming Language (1955), the concept of indirect addressing of higher ranks (Pointers) was introduced, which allows the arbitrary connection of the computer’s RAM cells. This connection is based on standard sequences of the cell addresses in RAM and addressing sequences, which is determined by the programmer with indirect addressing. Two types of sequences allow programmers to determine an arbitrary connection of RAM cells with the arbitrary content: data, addresses, subroutines, program labels, etc. Therefore, the formed connections of cells can relate to each other. The result of connecting cells with the arbitrary content and any structure is called tree-shaped formats. Tree-shaped formats allow programmers to combine data into complex data structures that are like abstract data types. For tree-shaped formats, the concept of “review scheme” is defined, which is like the concept of “bypassing” trees. Programmers can define multiple overview diagrams for the one tree-shaped format. Programmers can create tree-shaped formats over the connected cells to define the desired overview schemes for these connected cells. The work gives a modern interpretation of the concept of tree-shaped formats in Address Programming. Tree-shaped formats are based on “stroke-operation” (pointer dereference), which was hardware implemented in the command system of computer “Kyiv”. Group operations of modernization of computer “Kyiv” addresses accelerate the processing of tree-shaped formats and are designed as organized cycles, like those in high-level imperative programming languages. The commands of computer “Kyiv”, due to operations with indirect addressing, have more capabilities than the first high-level programming language – Plankalkül. Machine commands of the computer “Kyiv” allow direct access to the i-th element of the “list” by its serial number in the same way as such access is obtained to the i-th element of the array by its index. Given examples of singly linked lists show the features of tree-shaped formats and their differences from abstract data types. The article opens a new branch of theoretical research, the purpose of which is to analyze the expe- diency of partial inclusion of Address Programming in modern programming languages.
 
 

Continuous Abstract Data Types for Verified Computation

AbstractWe devise imperative programming languages for verified real number computation where real numbers are provided as abstract data types such that the users of the languages can express real number computation by considering real numbers as abstract mathematical entities. Unlike other common approaches toward real number computation, based on an algebraic model that lacks implementability or transcendental computation, or finite-precision approximation such as using double precision computation that lacks a formal foundation, our languages are devised based on computable analysis, a foundation of rigorous computation over continuous data. Consequently, the users of the language can easily program real number computation and reason about the behaviours of their programs, relying on their mathematical knowledge of real numbers without worrying about artificial roundoff errors. As the languages are imperative, we adopt precondition–postcondition-style program specification and Hoare-style program verification methodologies. Consequently, the users of the language can easily program a computation over real numbers, specify the expected behaviour of the program, including termination, and prove the correctness of the specification. Furthermore, we suggest extending the languages with other interesting continuous data, such as matrices, continuous real functions, et cetera.Abstract taken directly from the thesis.E-mail: sewonpark17@gmail.comURL: https://sewonpark.com/thesis

A Rogue Dream: Automatically Generating Meaningful Content For Games

Procedural content generation is often seen simply as a means to generate stuff, elaborating on or rearranging abstract data types that describe levels or modular pieces of gameplay. Generating content which is situated in an understanding of the real-world is a much harder task; it requires access to large amounts of knowledge, and a good technique for parsing and using that knowledge. In this paper we describe A Rogue Dream, a game prototype which can generate new visual content and change its design based on an input word from the player at the start of the game. We describe the game and the tools it makes use of to do this, and use the game to discuss ways in which such techniques might enable unique kinds of gameplay or new directions for intelligent design tools.

Algebraic Specification for Input-Output in Abstract Data Types

Data Types (ADT) are used when creating software systems, in the systems design. Usually we use algebraic specification to specify the operations in a data type. The use of data types is a methodology or style of working which yields improved design when followed. In this paper we study the addition of input-output operations to the algebraic specification of operations over a data type. The motivation is that input-output operations are used in actual implementations. A specification with input-output is more complete than one without it. We need input-output operations in our programs. This justifies the addition of such operations to the specification. We consider the definition of input-output operations in functional programming in particular in Haskell. Our input-output specifications are not exactly equal to Haskell programs although some of them are likely. We specify input-output operations in a form likely to the specification of the other operations. The result is the algebraic specification of the input-output operations for many frequently used data types. The language considered is sufficiently expressive to model all these operations. The technique is illustrated by means of a variety of examples. We started from sequences, continued with sets and finish with dictionaries. The specifications we present in this paper can be used as specifications of methods of ADT definitions in object oriented programing.

The Transrational Numbers as an Abstract Data Type

In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to its opposite, and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.

Most General Algebraic Specifications for an Abstract Datatype of Rational Numbers

The notion of a most general algebraic specification of an arithmetical datatype of characteristic zero is introduced.Three examples of such specifications are given. A preference is formulated for a specification by means of infinitely many equations which can be presented via a finite number of so-called schematic equations phrased in terms of an infinite signature. On the basis of the latter specification three topics are discussed: (i) fracterm decomposition operators and the numerator paradox, (ii) foundational specifications of arithmetical datatypes, and (iii) poly-infix operations.

ECG signals filtering and analysis using the Compact Genetic Algorithm Based on Abstract Data Types in GPU/CUDA

This paper presents the process of adaptive filtering of cardiovascular disease signals from the processing and cleaning of ECG signals developed by the Compact Genetic Algorithm Based on Abstract Data Types (CGAADT), implemented in MATLAB using GPU/CUDA architecture from the examples of the base of MIT-BIH data. The results show that CGAADT can improve the filtering, cleaning, detection and diagnosis of arrhythmias using a single algorithm (CGAADT) in the adoption of a representation for the population with fixed size of chromosomes, pre-established by fragmentation of the GPU base when implemented in high performance systems, aiming to improve the health systems offered to patients with cardiovascular problems.

Improved time bounds for linearizable implementations of abstract data types

Linearizability is a well-known consistency condition for shared objects in concurrent systems. We focus on the problem of implementing linearizable objects of arbitrary data types in message-passing systems with bounded, but uncertain, message delay and bounded, but non-zero, clock skew. We present an algorithm that exploits axiomatic properties of different operations to reduce the running time of each operation below that obtainable with previously known algorithms. We also prove lower bounds on the time complexity of various kinds of operations, specified by the axioms they satisfy, resulting in reduced gaps in some cases and tight bounds in others.

Reducing the Amount of Hard Drive Memory Used For Storing Elements of Abstract Data Types

Reducing the Amount of Hard Drive Memory Used For Storing Elements of Abstract Data Types

Sound, complete, and tractable linearizability monitoring for concurrent collections

While many program properties like the validity of assertions and in-bounds array accesses admit nearly-trivial monitoring algorithms, the standard correctness criterion for concurrent data structures does not. Given an implementation of an arbitrary abstract data type, checking whether the operations invoked in one single concurrent execution are linearizable, i.e., indistinguishable from an execution where the same operations are invoked atomically, requires exponential time in the number of operations. In this work we identify a class of collection abstract data types which admit polynomial-time linearizability monitors. Collections capture the majority of concurrent data structures available in practice, including stacks, queues, sets, and maps. Although monitoring executions of arbitrary abstract data types requires enumerating exponentially-many possible linearizations, collections enjoy combinatorial properties which avoid the enumeration. We leverage these properties to reduce linearizability to Horn satisfiability. As far as we know, ours is the first sound, complete, and tractable algorithm for monitoring linearizability for types beyond single-value registers.

A Transactional Correctness Tool for Abstract Data Types

Transactional memory simplifies multiprocessor programming by providing the guarantee that a sequential block of code in the form of a transaction will exhibit atomicity and isolation. Transactional data structures offer the same guarantee to concurrent data structures by enabling the atomic execution of a composition of operations. The concurrency control of transactional memory systems preserves atomicity and isolation by detecting read/write conflicts among multiple concurrent transactions. State-of-the-art transactional data structures improve on this concurrency control protocol by providing explicit transaction-level synchronization for only non-commutative operations. Since read/write conflicts are handled by thread-level concurrency control, the correctness of transactional data structures cannot be evaluated according to the read/write histories. This presents a challenge for existing correctness verification techniques for transactional memory, because correctness is determined according to the transitions taken by the transactions in the presence of read/write conflicts. In this article, we present Transactional Correctness tool for Abstract Data Types (TxC-ADT), the first tool that can check the correctness of transactional data structures. TxC-ADT elevates the standard definitions of transactional correctness to be in terms of an abstract data type, an essential aspect for checking correctness of transactions that synchronize only for high-level semantic conflicts. To accommodate a diverse assortment of transactional correctness conditions, we present a technique for defining correctness as a happens-before relation. Defining a correctness condition in this manner enables an automated approach in which correctness is evaluated by generating and analyzing a transactional happens-before graph during model checking. A transactional happens-before graph is maintained on a per-thread basis, making our approach applicable to transactional correctness conditions that do not enforce a total order on a transactional execution. We demonstrate the practical applications of TxC-ADT by checking Lock Free Transactional Transformation and Transactional Data Structure Libraries for serializability, strict serializability, opacity, and causal consistency.

Using Coq to write fast and correct Haskell

Correctness and performance are often at odds in the field of systems engineering, either because correct programs are too costly to write or impractical to execute, or because well-performing code involves so many tricks of the trade that formal analysis is unable to isolate the main properties of the algorithm. As a prime example of this tension, Coq is an established proof environment that allows writing correct, dependently-typed code, but it has been criticized for exorbitant development times, forcing the developer to choose between optimal code or tractable proofs. On the other side of the divide, Haskell has proven itself to be a capable, well-typed programming environment, yet easy-to-read, straightforward code must all too often be replaced by highly optimized variants that obscure the author's original intention. This paper builds on the existing Fiat refinement framework to bridge this divide, demonstrating how to derive a correct-by-construction implementation that meets (or exceeds) the performance characteristics of highly optimized Haskell, starting from a high-level Coq specification. To achieve this goal, we extend Fiat with a stateful notion of refinement of abstract data types and add support for extracting stateful code via a free monad equipped with an algebra of heap-manipulating operations. As a case study, we reimplement a subset of the popular bytestring library, with little to no loss of performance, while retaining a high guarantee of program correctness.

Efficient Data Streaming Multiway Aggregation through Concurrent Algorithmic Designs and New Abstract Data Types

Data streaming relies on continuous queries to process unbounded streams of data in a real-time fashion. It is commonly demanding in computation capacity, given that the relevant applications involve very large volumes of data. Data structures act as articulation points and maintain the state of data streaming operators, potentially supporting high parallelism and balancing the work among them. Prompted by this fact, in this work we study and analyze parallelization needs of these articulation points, focusing on the problem of streaming multiway aggregation, where large data volumes are received from multiple input streams. The analysis of the parallelization needs, as well as of the use and limitations of existing aggregate designs and their data structures, leads us to identify needs for appropriate shared objects that can achieve low-latency and high-throughput multiway aggregation. We present the requirements of such objects as abstract data types and we provide efficient lock-free linearizable algorithmic implementations of them, along with new multiway aggregate algorithmic designs that leverage them, supporting both deterministic order-sensitive and order-insensitive aggregate functions. Furthermore, we point out future directions that open through these contributions. The article includes an extensive experimental study, based on a variety of continuous aggregation queries on two large datasets extracted from SoundCloud, a music social network, and from a Smart Grid network. In all the experiments, the proposed data structures and the enhanced aggregate operators improved the processing performance significantly, up to one order of magnitude, in terms of both throughput and latency, over the commonly used techniques based on queues.

Automatic Scalable Atomicity via Semantic Locking

In this article, we consider concurrent programs in which the shared state consists of instances of linearizable abstract data types (ADTs). We present an automated approach to concurrency control that addresses a common need: the need to atomically execute a code fragment, which may contain multiple ADT operations on multiple ADT instances. We present a synthesis algorithm that automatically enforces atomicity of given code fragments (in a client program) by inserting pessimistic synchronization that guarantees atomicity and deadlock-freedom (without using any rollback mechanism). Our algorithm takes a commutativity specification as an extra input. This specification indicates for every pair of ADT operations the conditions under which the operations commute. Our algorithm enables greater parallelism by permitting commuting operations to execute concurrently. We have implemented the synthesis algorithm in a Java compiler and applied it to several Java programs. Our results show that our approach produces efficient and scalable synchronization.

A relational model of types-and-effects in higher-order concurrent separation logic

Recently we have seen a renewed interest in programming languages that tame the complexity of state and concurrency through refined type systems with more fine-grained control over effects. In addition to simplifying reasoning and eliminating whole classes of bugs, statically tracking effects opens the door to advanced compiler optimizations. In this paper we present a relational model of a type-and-effect system for a higher-order, concurrent program- ming language. The model precisely captures the semantic invariants expressed by the effect annotations. We demonstrate that these invariants are strong enough to prove advanced program transformations, including automatic parallelization of expressions with suitably disjoint effects. The model also supports refinement proofs between abstract data types implementations with different internal data representations, including proofs that fine-grained concurrent algorithms refine their coarse-grained counterparts. This is the first model for such an expressive language that supports both effect-based optimizations and data abstraction. The logical relation is defined in Iris, a state-of-the-art higher-order concurrent separation logic. This greatly simplifies proving well-definedness of the logical relation and also provides us with a powerful logic for reasoning in the model.

Proof checking and logic programming

Abstract In a world where trusting software systems is increasingly important, formal methods and formal proof can help provide some basis for trust. Proof checking can help to reduce the size of the trusted base since we do not need to trust an entire theorem prover: instead, we only need to trust a (smaller and simpler) proof checker. Many approaches to building proof checkers require embedding within them a full programming language. In most modern proof checkers and theorem provers, that programming language is a functional programming language, often a variant of ML. In fact, aspects of ML (e.g., strong typing, abstract datatypes, and higher-order programming) were designed to make ML a trustworthy “meta-language” for checking proofs. While there is considerable overlap between logic programming and proof checking (e.g., both benefit from unification, backtracking search, efficient term structures, etc.), the discipline of logic programming has, in fact, played a minor role in the history of proof checking. I will argue that logic programming can have a major role in the future of this important topic.

Large-scale system development using Abstract Data Types and refinement

We present a formal modelling approach using Abstract Data Types (ADTs) for large-scale system development in Event-B. The novelty of our approach is the combination of refinement and instantiation techniques to manage the complexity of systems under development. With ADTs, we model system components on an abstract level, specifying just their necessary properties, and we postpone the introduction of their concrete definitions to later development steps. As the ADTs are incrementally instantiated and become more concrete, behavioural details of systems are expanded via refinement in a manner consistent with the ADTs' transformation. We evaluate this approach using a large-scale case study in train control systems. The results show that our approach helps reduce system details during early development stages and leads to simpler and more automated proofs.

A Formal Architectural Description Language based on Symbolic Transition Systems and Modal Logic

Component Based Software Engineering has now emerged as a discipline for system development. After years of battle between component platforms, the need for means to abstract away from specific implementation details is now recognized. This paves the way for model driven approaches (such as MDE) but also for the more older Architectural Description Language (ADL) paradigm. In this paper we present KADL, an ADL based on the Korrigan formal language which supports the following features: integration of fully formal behaviours and data types, expressive component composition mechanisms through the use of modal logic, specification readability through graphical notations, and dedicated architectural analysis techniques. Key Words: Architectural Description Language, Component Based Software Engineering, Mixed Formal Specifications, Symbolic Transition Systems, Abstract Data Types, Modal Logic Glue, Graphical Notations, Verification.

Declarative encodings of acyclicity properties

Abstract Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this article, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.