Verified Lustre Normalization with Node Subsampling

In this paper a , we present a dynamic semantics for the Java Virtual Machine Language (JVML).The semantics is specified in an operational style according to the syntactic structure of JVML programs.In order to ascribe meanings to threading, the semantics is made small-step and is structured in two layers: The first layer consists of judgements that capture the semantics of sequential JVML programs in isolation.The second layer consists of judgements that capture the parallel execution of JVML threads.The semantics presented in this paper is a faithful and formal transcription of JVML specification as described in [1].Besides, we provide full account details for the most technical and tricky aspects of JVML such as multi-threading, synchronization, method invocations, exception handling, object creation, object's fields manipulation, stack manipulation, local variable access, modifiers, etc.The presented semantics is, to the best of our knowledge, the first dynamic semantics of JVML that provides semantics for that many features within the same framework.

Falafel, a functional programming language with first-class arrays, is being developed at the University of Saskatchewan. It is an experimental vehicle for work in language definition and implementation. This paper discusses some of the fundamental design decisions that underlie the language and its implementations. Falafel has drawn ideas from array-based programming languages (APL [Iverson] and Nial [Jenkins]_[More]), functional programming languages (Miranda™ [Turner] and Haskell [Haskell]), and dataflow programming languages (Id [Nikhil]_and Sisal [Sisal]). This paper discusses the nature of Falafel’s value space, the structure of arrays, the role of strong polymorphic typing, the use of lazy evaluation, and a means of partial definition of arrays. A full definition of Falafel is to be published separately.

The work described in this paper began with a desire to include some linguistic concept of a resource manager within a dataflow language we have been designing [AGP76]. In doing so, we discovered that dataflow monitors (resource managers) provide a natural way of thinking about resources and especially their scheduling. Dataflow semantics are based upon a program composed of asynchronous operators interconnected by lines along which data tokens (messages) flow, such that when all of the input tokens for a given operator have arrived then that operator may fire (execute) by absorbing the input tokens, computing, and producing an output token as its result. These operations closely match one's intuitive model of resource managers (operators) passing signals (tokens) to one another for the purpose of synchronizing and scheduling resource usage. Previously though, dataflow languages [D73, K73, W75] have dealt only with the expression of highly asynchronous yet determinate computations; however, resource management characteristically involves indeterminate computation. The introduction here of dataflow monitors and an explicit nondeterministic merge operator for dataflow streams makes dataflow very well suited for expressing interprocess communication and operations on resources.

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle – the refined extension principle – which is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though based on stable models, complies with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.

We present a proof of correctness in Matita for an optimising assembler for the MCS-51 microcontroller. The efficient expansion of pseudoinstructions, namely jumps, into machine instructions is complex. We isolate the decision making over how jumps should be expanded from the expansion process itself as much as possible using ‘policies’, making the proof of correctness for the assembler more straightforward.Our proof strategy contains a tracking facility for ‘good addresses’ and only programs that use good addresses have their semantics preserved under assembly, as we observe that it is impossible for an assembler to preserve the semantics of every assembly program. Our strategy offers increased flexibility over the traditional approach to proving the correctness of assemblers, wherein addresses in assembly are kept opaque and immutable. In particular, we may experiment with allowing the benign manipulation of addresses.KeywordsVerified softwareCerCo (Certified Complexity)MCS-51 microcontrollerMatita proof assistant

This paper extends the algorithms for implementing the working set concept for data-flow machines proposed in [7] in order to cope with dynamic data-flow programs which include branches, loops, and procedure calls. The algorithms for computing the D-, E-, and L-levels are revised and the performance for static data-flow programs is reevaluated. Algorithms to manage branches, loops, and function calls are developed. The effectiveness of these algorithms is shown through computer simulation.

This paper proves correctness of Nöcker's method of strictness analysis, implemented in the Clean compiler, which is an effective way for strictness analysis in lazy functional languages based on their operational semantics. We improve upon the work Clark, Hankin and Hunt did on the correctness of the abstract reduction rules in two aspects. Our correctness proof is based on a functional core language and a contextual semantics, thus proving a wider range of strictness-based optimizations as correct, and our method fully considers the cycle detection rules, which contribute to the strength of Nöcker's strictness analysis. Our algorithm SAL is a reformulation of Nöcker's strictness analysis algorithm in a functional core language LR. This is a higher order call-by-need lambda calculus with case , constructors, letrec , and seq , which is extended during strictness analysis by set constants like Top or Inf , denoting sets of expressions, which indicate different evaluation demands. It is also possible to define new set constants by recursive equations with a greatest fixpoint semantics. The operational semantics of LR is a small-step semantics. Equality of expressions is defined by a contextual semantics that observes termination of expressions. Basically, SAL is a nontermination checker. The proof of its correctness and hence of Nöcker's strictness analysis is based mainly on an exact analysis of the lengths of evaluations, i.e., normal-order reduction sequences to WHNF. The main measure being the number of “essential” reductions in evaluations. Our tools and results provide new insights into call-by-need lambda calculi, the role of sharing in functional programming languages, and into strictness analysis in general. The correctness result provides a foundation for Nöcker's strictness analysis in Clean, and also for its use in Haskell.

A correct proof is given for the following assertions about the two-dimensional sloshing problem. The fundamental eigenvalue is simple and the corresponding stream function may be chosen to be non-negative in the closure of the water domain. New proof is based on stricter assumptions about the water domain; namely, it must satisfy John’s condition.

In this paper we explore the idea that the code that constitutes a program actually forms a higher-level, program specific language. The symbols of the language are the abstractions of the program, and the grammar of the language is the set of (generally unwritten) rules about the allowable combinations of those abstractions. As such, a program is both a language definition, and the only use of that language. This specificity means that reading a never-before encountered program involves learning a new natural language, and that porting code from one program to another requires translation from one natural language into another. We suggest that the complexity and depth of the program language is affected by the gap between the program semantics (what the program is meant to do) and the code semantics (the way in which the machine runs). We believe that in seeing that programs are languages, we gain new insight into our own experience as programmers, and are able to gain new perspective on the intense complexity of code and its creation.

In this paper, two approaches are used to construct the dynamic semantics of computer programs: the first is the representation of mathematical models of computational processes generated by a computer program in the form of a discrete transformer; the second is the representation of the mathematical model of a computer program in terms of functional grammars. The study focuses on the computational process generated by a computer program. Application of the discrete transducers concept to describe computational processes allows us to obtain a mathematical model or dynamic semantics of a program, which is a composition of two discrete systems B and C. In this case, component A is a control component (a model of the program block diagram), and component B is a model of the program memory. The decomposition of a program into two components B and B is convenient when studying the process of modelling a computational process. This is due to the fact that the prospects of searching for invariants in critical nodes of a programme for mathematical proof of correctness of a computer programme are opened. The comparative analysis of the two approaches leads to the theorem on the regularity of the representation of a function generated by a programme within the framework of functional grammar.

A fundamental challenge in automated reasoning about programming assignments at scale is clustering student submissions based on their underlying algorithms. State-of-the-art clustering techniques are sensitive to control structure variations, cannot cluster buggy solutions with similar correct solutions, and either require expensive pair-wise program analyses or training efforts. We propose a novel technique that can cluster small imperative programs based on their algorithmic essence: (A) how the input space is partitioned into equivalence classes and (B) how the problem is uniquely addressed within individual equivalence classes. We capture these algorithmic aspects as two quantitative semantic program features that are merged into a program's vector representation. Programs are then clustered using their vector representations. The computation of our first semantic feature leverages model counting to identify the number of inputs belonging to an input equivalence class. The computation of our second semantic feature abstracts the program's data flow by tracking the number of occurrences of a unique pair of consecutive values of a variable during its lifetime. The comprehensive evaluation of our tool SemCluster on benchmarks drawn from solutions to small programming assignments shows that SemCluster (1) generates far fewer clusters than other clustering techniques, (2) precisely identifies distinct solution strategies, and (3) boosts the performance of clustering-based program repair, all within a reasonable amount of time.

I report on an experience using the Coq proof assistant to develop a program verification tool with a machine-checkable proof of full correctness. The verifier is able to prove memory safety of x86 machine code programs compiled from code that uses algebraic datatypes. The tool's soundness theorem is expressed in terms of the bit-level semantics of x86 programs, so its correctness depends on very few assumptions. I take advantage of Coq's support for programming with dependent types and modules in the structure of my development. The approach is based on developing a library of reusable functors for transforming a verifier at one level of abstraction into a verifier at a lower level. Using this library, it's possible to prototype a verifier based on a new type system with a minimal amount of work, while obtaining a very strong soundness theorem about the final product.

Software composition connects separately defined software artifacts. Such connection may be in program structure (such as inheritance), data flow (such as message passing) and/or control flow (such as function calls or loop control).

This chapter introduces inductively defined sets and simple inductive data types such as natural numbers, words, lists and trees with emphasis on definition patterns. For these sets and data types, recursive equations in Backus-Naur form are introduced and it is shown how, e.g., propositional formulae and simple while programs can be specified in this format. Next it is explained how functions can be defined inductively on such sets and data types. Examples include the factorial function, Harmonic numbers, Fibonacci numbers, addition and multiplication on natural numbers and functions that compute the length of a word or list and the height of a tree. In contrast, recursive functions are defined in a way that does not necessarily lead to terminating evaluations. Recursive procedures are also described, with examples presented of various sorting algorithms and the Towers of Hanoi puzzle.

The PSG programming system generator developed at the Technical University of Darmstadt produces interactive, language-specific programming environments from formal language definitions. All language-dependent parts of the environment are generated from an entirely nonprocedural specification of the language's syntax, context conditions, and dynamic semantics. The generated environment consists of a language-based editor, supporting systematic program development by named program fragments, an interpreter, and a fragment library system. The major component of the environment is a full-screen editor, which allows both structure and text editing. In structure mode the editor guarantees prevention of both syntactic and semantic errors, whereas in textual mode it guarantees their immediate recognition. PSG editors employ a novel algorithm for incremental semantic analysis which is based on unification. The algorithm will immediately detect semantic errors even in incomplete program fragments. The dynamic semantics of the language are defined in denotational style using a functional language based on the lambda calculus. Program fragments are compiled to terms of the functional language which are executed by an interpreter. The PSG generator has been used to produce environments for Pascal, ALGOL 60, MODULA-2, and the formal language definition language itself.