Coherent Behavior from Incoherent Knowledge Sources in the Automatic Synthesis of Numerical Computer Programs

A fundamental problem in artificial intelligence is obtaining coherent behavior in rule-based problem solving systems. A good quantitative measure of coherence is time behavior; a system that never, in retrospect, applied a rule needlessly is certainly coherent; a system suffering from combinatorial blowup is certainly behaving incoherently. This report describes a rule-based problem solving system for automatically writing and improving numerical computer programs from specifications. The specifications are in terms of "constraints" among inputs and outputs. The system has solved program synthesis problems involving systems of equations, determining that methods of successive approximation converge, transforming recursion to iteration, and manipulating power series (using differing organizations, control structures, and argument-passing techniques).

Abstract specialization and its application to program parallelization

Program specialization optimizes programs for known valúes of the input. It is often the case that the set of possible input valúes is unknown, or this set is infinite. However, a form of specialization can still be performed in such cases by means of abstract interpretation, specialization then being with respect to abstract valúes (substitutions), rather than concrete ones. This paper reports on the application of abstract múltiple specialization to automatic program parallelization in the &-Prolog compiler. Abstract executability, the main concept underlying abstract specialization, is formalized, the design of the specialization system presented, and a non-trivial example of specialization in automatic parallelization is given.

FRAMEWORK SYNTHESIS FOR SYMBOLIC EXECUTION OF EVENT-DRIVEN FRAMEWORKS

Symbolic execution is a powerful program analysis technique, but it is very challenging to apply to programs built using event-driven frameworks, such as Android. The main reason is that the framework code itself is too complex to symbolically execute. The standard solution is to manually create a framework model that is simpler and more amenable to symbolic execution. However, developing and maintaining such a model by hand is difficult and error-prone. We claim that we can leverage program synthesis to introduce a high-degree of automation to the process of framework modeling. To support this thesis, we present three pieces of work. First, we introduced SymDroid, a symbolic executor for Android. While Android apps are written in Java, they are compiled to Dalvik bytecode format. Instead of analyzing an app’s Java source, which may not be available, or decompiling from Dalvik back to Java, which requires significant engineering effort and introduces yet another source of potential bugs in an analysis, SymDroid works directly on Dalvik bytecode. Second, we introduced Pasket, a new system that takes a first step toward automatically generating Java framework models to support symbolic execution. Pasket takes as input the framework API and tutorial programs that exercise the framework. From these artifacts and Pasket's internal knowledge of design patterns, Pasket synthesizes an executable framework model by instantiating design patterns, such that the behavior of a synthesized model on the tutorial programs matches that of the original framework. Lastly, in order to scale program synthesis to framework models, we devised adaptive concretization, a novel program synthesis algorithm that combines the best of the two major synthesis strategies: symbolic search, i.e., using SAT or SMT solvers, and explicit search, e.g., stochastic enumeration of possible solutions. Adaptive concretization parallelizes multiple sub-synthesis problems by partially concretizing highly influential unknowns in the original synthesis problem. Thanks to adaptive concretization, Pasket can generate a large-scale model, e.g., thousands lines of code. In addition, we have used an Android model synthesized by Pasket and found that the model is sufficient to allow SymDroid to execute a range of apps.

Automatic Inference of Graph Models for Complex Networks with Genetic Programming

Complex networks can arise naturally and spontaneously from all things that act as a part of a larger system. From the patterns of socialization between people to the way biological systems organize themselves, complex networks are ubiquitous, but are currently poorly understood. A number of algorithms, designed by humans, have been proposed to describe the organizational behaviour of real-world networks. Consequently, breakthroughs in genetics, medicine, epidemiology, neuroscience, telecommunications and the social sciences have recently resulted. The algorithms, called graph models, represent significant human effort. Deriving accurate graph models is non-trivial, time-intensive, challenging and may only yield useful results for very specific phenomena. An automated approach can greatly reduce the human effort required and if effective, provide a valuable tool for understanding the large decentralized systems of interrelated things around us. To the best of the author's knowledge this thesis proposes the first method for the automatic inference of graph models for complex networks with varied properties, with and without community structure. Furthermore, to the best of the author's knowledge it is the first application of genetic programming for the automatic inference of graph models. The system and methodology was tested against benchmark data, and was shown to be capable of reproducing close approximations to well-known algorithms designed by humans. Furthermore, when used to infer a model for real biological data the resulting model was more representative than models currently used in the literature.

Evolving Distributed Algorithms with Genetic Programming

Distributed systems are one of the most vital components of the economy. The most prominent example is probably the internet, a constituent element of our knowledge society. During the recent years, the number of novel network types has steadily increased. Amongst others, sensor networks, distributed systems composed of tiny computational devices with scarce resources, have emerged. The further development and heterogeneous connection of such systems imposes new requirements on the software development process. Mobile and wireless networks, for instance, have to organize themselves autonomously and must be able to react to changes in the environment and to failing nodes alike. Researching new approaches for the design of distributed algorithms may lead to methods with which these requirements can be met efficiently. In this thesis, one such method is developed, tested, and discussed in respect of its practical utility. Our new design approach for distributed algorithms is based on Genetic Programming, a member of the family of evolutionary algorithms. Evolutionary algorithms are metaheuristic optimization methods which copy principles from natural evolution. They use a population of solution candidates which they try to refine step by step in order to attain optimal values for predefined objective functions. The synthesis of an algorithm with our approach starts with an analysis step in which the wanted global behavior of the distributed system is specified. From this specification, objective functions are derived which steer a Genetic Programming process where the solution candidates are distributed programs. The objective functions rate how close these programs approximate the goal behavior in multiple randomized network simulations. The evolutionary process step by step selects the most promising solution candidates and modifies and combines them with mutation and crossover operators. This way, a description of the global behavior of a distributed system is translated automatically to programs which, if executed locally on the nodes of the system, exhibit this behavior. In our work, we test six different ways for representing distributed programs, comprising adaptations and extensions of well-known Genetic Programming methods (SGP, eSGP, and LGP), one bio-inspired approach (Fraglets), and two new program representations called Rule-based Genetic Programming (RBGP, eRBGP) designed by us. We breed programs in these representations for three well-known example problems in distributed systems: election algorithms, the distributed mutual exclusion at a critical section, and the distributed computation of the greatest common divisor of a set of numbers. Synthesizing distributed programs the evolutionary way does not necessarily lead to the envisaged results. In a detailed analysis, we discuss the problematic features which make this form of Genetic Programming particularly hard. The two Rule-based Genetic Programming approaches have been developed especially in order to mitigate these difficulties. In our experiments, at least one of them (eRBGP) turned out to be a very efficient approach and in most cases, was superior to the other representations.

Protocols between programs and proofs

In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting “correct” programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors, but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.

Modular extensions for modular (Logic) languages

We address the problem of developing mechanisms for easily implementing modular extensions to modular (logic) languages. By(language) extensions we refer to different groups of syntactic definitions and translation rules that extend a language. Our use of the concept of modularity in this context is twofold. We would like these extensions to be modular, in the sense above, i.e., we should be able to develop different extensions mostly separately. At the same time, the sources and targets for the extensions are modular languages, i.e., such extensions may take as input sepárate pieces of code and also produce sepárate pieces of code. Dealing with this double requirement involves interesting challenges to ensure that modularity is not broken: first, combinations of extensions (as if they were a single extensión) must be given a precise meaning. Also, the sepárate translation of múltiple sources (as if they were a single source) must be feasible. We present a detailed description of a code expansion-based framework that proposes novel solutions for these problems. We argüe that the approach, while implemented for Ciao, can be adapted for other Prolog-based systems and languages.

A flexible (C)LP-based approach to the analysis of object-oriented programs

Static analyses of object-oriented programs usually rely on intermediate representations that respect the original semantics while having a more uniform and basic syntax. Most of the work involving object-oriented languages and abstract interpretation usually omits the description of that language or just refers to the Control Flow Graph(CFG) it represents. However, this lack of formalization on one hand results in an absence of assurances regarding the correctness of the transformation and on the other it typically strongly couples the analysis to the source language. In this work we present a framework for analysis of object-oriented languages in which in a first phase we transform the input program into a representation based on Horn clauses. This allows on one hand proving the transformation correct attending to a simple condition and on the other being able to apply an existing analyzer for (constraint) logic programming to automatically derive a safe approximation of the semantics of the original program. The approach is flexible in the sense that the first phase decouples the analyzer from most languagedependent features, and correct because the set of Horn clauses returned by the transformation phase safely approximates the standard semantics of the input program. The resulting analysis is also reasonably scalable due to the use of mature, modular (C)LP-based analyzers. The overall approach allows us to report results for medium-sized programs.

Towards description and optimization of abstract machines in an extension of prolog

Competitive abstract machines for Prolog are usually large, intricate, and incorpórate sophisticated optimizations. This makes them difñcult to code, optimize, and, especially, maintain and extend. This is partly due to the fact that efñciency considerations make it necessary to use low-level languages in their implementation. Writing the abstract machine (and ancillary code) in a higher-level language can help harness this inherent complexity. In this paper we show how the semantics of basic components of an efficient virtual machine for Prolog can be described using (a variant of) Prolog which retains much of its semantics. These descriptions are then compiled to C and assembled to build a complete bytecode emulator. Thanks to the high level of the language used and its closeness to Prolog the abstract machine descriptions can be manipulated using standard Prolog compilation and optimization techniques with relative ease. We also show how, by applying program transformations selectively, we obtain abstract machine implementations whose performance can match and even exceed that of highly-tuned, hand-crafted emulators.

Removing superfluous versions in polyvariant specialization of prolog programs.

Polyvariant specialization allows generating múltiple versions of a procedure, which can then be separately optimized for different uses. Since allowing a high degree of polyvariance often results in more optimized code, polyvariant specializers, such as most partial evaluators, can genérate a large number of versions. This can produce unnecessarily large residual programs. Also, large programs can be slower due to cache miss effects. A possible solution to this problem is to introduce a minimization step which identifies sets of equivalent versions, and replace all occurrences of such versions by a single one. In this work we present a unifying view of the problem of superfluous polyvariance. It includes both partial deduction and abstract múltiple specialization. As regards partial deduction, we extend existing approaches in several ways. First, previous work has dealt with puré logic programs and a very limited class of builtins. Herein we propose an extensión to traditional characteristic trees which can be used in the presence of calis to external predicates. This includes all builtins, librarles, other user modules, etc. Second, we propose the possibility of collapsing versions which are not strictly equivalent. This allows trading time for space and can be useful in the context of embedded and pervasive systems. This is done by residualizing certain computations for external predicates which would otherwise be performed at specialization time. Third, we provide an experimental evaluation of the potential gains achievable using minimization which leads to interesting conclusions.

Experiments in context-sensitive analysis of modular programs

Several models for context-sensitive analysis of modular programs have been proposed, each with different characteristics and representing different trade-offs. The advantage of these context-sensitive analyses is that they provide information which is potentially more accurate than that provided by context-free analyses. Such information can then be applied to validating/debugging the program and/or to specializing the program in order to obtain important performance improvements. Some very preliminary experimental results have also been reported for some of these models which provided initial evidence on their potential. However, further experimentation, which is needed in order to understand the many issues left open and to show that the proposed modes scale and are usable in the context of large, real-life modular programs, was left as future work. The aim of this paper is two-fold. On one hand we provide an empirical comparison of the different models proposed in previous work, as well as experimental data on the different choices left open in those designs. On the other hand we explore the scalability of these models by using larger modular programs as benchmarks. The results have been obtained from a realistic implementation of the models, integrated in a production-quality compiler (CiaoPP/Ciao). Our experimental results shed light on the practical implications of the different design choices and of the models themselves. We also show that contextsensitive analysis of modular programs is indeed feasible in practice, and that in certain critical cases it provides better performance results than those achievable by analyzing the whole program at once, specially in terms of memory consumption and when reanalyzing after making changes to a program, as is often the case during program development.

Efficient local unfolding with ancestor stacks for full prolog

The integration of powerful partial evaluation methods into practical compilers for logic programs is still far from reality. This is related both to 1) efficiency issues and to 2) the complications of dealing with practical programs. Regarding efnciency, the most successful unfolding rules used nowadays are based on structural orders applied over (covering) ancestors, i.e., a subsequence of the atoms selected during a derivation. Unfortunately, maintaining the structure of the ancestor relation during unfolding introduces significant overhead. We propose an efficient, practical local unfolding rule based on the notion of covering ancestors which can be used in combination with any structural order and allows a stack-based implementation without losing any opportunities for specialization. Regarding the second issue, we propose assertion-based techniques which allow our approach to deal with real programs that include (Prolog) built-ins and external predicates in a very extensible manner. Finally, we report on our implementation of these techniques in a practical partial evaluator, embedded in a state of the art compiler which uses global analysis extensively (the Ciao compiler and, specifically, its preprocessor CiaoPP). The performance analysis of the resulting system shows that our techniques, in addition to dealing with practical programs, are also significantly more efficient in time and somewhat more efficient in memory than traditional tree-based implementations.

Determinacy analysis for logic programs using mode and type information

We propose an analysis for detecting procedures and goals that are deterministic (i.e. that produce at most one solution), or predicates whose clause tests are mutually exclusive (which implies that at most one of their clauses will succeed) even if they are not deterministic (because they cali other predicates that can produce more than one solution). Applications of such determinacy information include detecting programming errors, performing certain high-level program transformations for improving search efñciency, optimizing low level code generation and parallel execution, and estimating tighter upper bounds on the computational costs of goals and data sizes, which can be used for program debugging, resource consumption and granularity control, etc. We have implemented the analysis and integrated it in the CiaoPP system, which also infers automatically the mode and type information that our analysis takes as input. Experiments performed on this implementation show that the analysis is fairly accurate and efncient.