Singular and Plural Functions for Functional Logic Programming

Functional logic programming (FLP) languages use non-terminating and non-confluent constructor systems (CS's) as programs in order to define non-strict non-determi-nistic functions. Two semantic alternatives have been usually considered for parameter passing with this kind of functions: call-time choice and run-time choice. While the former is the standard choice of modern FLP languages, the latter lacks some properties---mainly compositionality---that have prevented its use in practical FLP systems. Traditionally it has been considered that call-time choice induces a singular denotational semantics, while run-time choice induces a plural semantics. We have discovered that this latter identification is wrong when pattern matching is involved, and thus we propose two novel compositional plural semantics for CS's that are different from run-time choice. We study the basic properties of our plural semantics---compositionality, polarity, monotonicity for substitutions, and a restricted form of the bubbling property for constructor systems---and the relation between them and to previous proposals, concluding that these semantics form a hierarchy in the sense of set inclusion of the set of computed values. We have also identified a class of programs characterized by a syntactic criterion for which the proposed plural semantics behave the same, and a program transformation that can be used to simulate one of them by term rewriting. At the practical level, we study how to use the expressive capabilities of these semantics for improving the declarative flavour of programs. We also propose a language which combines call-time choice and our plural semantics, that we have implemented in Maude. The resulting interpreter is employed to test several significant examples showing the capabilities of the combined semantics. To appear in Theory and Practice of Logic Programming (TPLP)Comment: 53 pages, 5 figure

Effectful Programming in Declarative Languages with an Emphasis on Non-Determinism: Applications and Formal Reasoning

This thesis investigates effectful declarative programming with an emphasis on non-determinism as an effect. On the one hand, we are interested in developing applications using non-determinism as underlying implementation idea. We discuss two applications using the functional logic programming language Curry. The key idea of these implementations is to exploit the interplay of non-determinism and non-strictness that Curry employs. The first application investigates sorting algorithms parametrised over a comparison function. By applying a non-deterministic predicate to these sorting functions, we gain a permutation enumeration function. We compare the implementation in Curry with an implementation in Haskell that uses a monadic interface to model non-determinism. The other application that we discuss in this work is a library for probabilistic programming. Instead of modelling distributions as list of event and probability pairs, we model distributions using Curry's built-in non-determinism. In both cases we observe that the combination of non-determinism and non-strictness has advantages over an implementation using lists to model non-determinism. On the other hand, we present an idea to apply formal reasoning on effectful declarative programming languages. In order to start with simple effects, we focus on modelling a functional subset first. That is, the effects of interest are totality and partiality. We then observe that the general scheme to model these two effects can be generalised to capture a wide range of effects. Obviously, the next step is to apply the idea to model non-determinism. More precisely, we implement a model for the non-determinism of Curry: non-strict non-determinism with call-time choice. Therefore, we finally discuss why the current representation models call-by-name rather than Curry's call-by-need semantics and give an outlook on ideas to tackle this problem.Diese Arbeit beschäftigt sich mit der deklarativen Programmierung mit Effekten und legt dabei besonderen Fokus auf Nichtdeterminismus als Effekt. Einerseits möchten wir Anwendungen entwickeln, deren zugrundeliegende Implementierungsidee auf Nichtdeterminismus basiert. Wir stellen dazu zwei beispielhafte Anwendungen vor, die in der funktional logischen Programmiersprache Curry implementiert sind. Die Kernidee dieser Implementierungen ist dabei die Kombination von Nichtstriktheit und Nichtdeterminismus, die Curry unterliegen, gewinnbringend auszunutzen. Für die erste Anwendung untersuchen wir Sortierfunktionen, die über eine Vergleichsfunktion parametrisiert sind, und wenden diese Funktionen auf ein nichtdeterministisches Prädikat an. Dabei entsteht eine Funktion, die Permutationen der Eingabeliste berechnet. Wir vergleichen unsere Implementierung in Curry mit einer Implementierung in Haskell, die den Nichtdeterminismus monadisch modelliert. Als zweite Anwendung werden wir über eine Bibliothek zur probabilistischen Programmierung diskutieren. Statt der üblichen Modellierung von Wahrscheinlichkeitsverteilungen als Liste von Paaren von Ereignis- und korrespondierenden Wahrscheinlichkeitswerten modellieren wir diese Verteilungen mithilfe von Currys nativem Nichtdeterminismus. Beide Implementierungen haben durch die Kombination von Nichtdeterminismus und Nichtstriktheit Vorteile gegenüber einer Implementierung, die den Nichtdeterminismus durch Listen repräsentiert. Andererseits möchten wir eine Möglichkeit schaffen, über die Programme, die wir in effektbehafteten deklarativen Programmiersprachen entwickelt haben, in einem formalen Rahmen zu argumentieren. Dabei fangen wir mit der Teilmenge der rein funktionalen Effekte an, das heißt, wir interessieren uns zunächst für totale und partielle Programme. Die zugrundeliegende Idee zur Modellierung dieser zwei Effekte kann dann auch für weitere Effekte genutzt werden. Als natürlichen nächsten Schritt betrachten wir den Effekt, der bei der Sprache Curry zusätzlich hinzukommt: nicht-strikter Nichtdeterminismus mit call-time choice Semantik. Dabei geben wir eine Übersicht darüber, warum die aktuelle Repräsentation call-by-name modelliert, sowie erste Ideen, wie die für Curry erforderliche call-by-need Semantik modelliert werden könnte

Purely Functional Lazy Non-deterministic Programming

Functional logic programming and probabilistic programming have demonstrated the broad benefits of combining laziness (non-strict evaluation with sharing of the results) with non-determinism. Yet these benefits are seldom enjoyed in functional programming, because the existing features for non-strictness, sharing, and nondeterminism in functional languages are tricky to combine. We present a practical way to write purely functional lazy non-deterministic programs that are efficient and perspicuous. We achieve this goal by embedding the programs into existing languages (such as Haskell, SML, and OCaml) with high-quality implementations, by making choices lazily and representing data with non-deterministic components, by working with custom monadic data types and search strategies, and by providing equational laws for the programmer to reason about their code

順方向プログラムと逆方向動作例からのwell-behaved な双方向プログラムの合成

Tohoku University住井英二

Search Techniques for Code Generation

This dissertation explores techniques that synthesize and generate program fragments and test inputs. The main goal of these techniques is to improve and support automation in program synthesis and test input generation. This is important because performing those processes manually is often tedious, time consuming and error prone. The main challenge that these techniques face is exploring the search space in efficient and scalable ways. In the first part of the dissertation, we present tools InSynth and PolySynth that interactively synthesize code fragments. They take as input a partial program and automatically extract type information, the desired type, and set of visible declarations. They use this input to synthesize ranked list of expressions with the desired type. Finally, they present the expressions to a developer in similar manner to code completions in modern IDEs. InSynth is the first tool that uses a complete algorithm to generate expressions with first class functions and higher order functions. We present the theoretical foundation of the InSynth problem, that is based on type inhabitation, and the type-based backward search algorithm that solves it. PolySynth uses type-driven, resolution based algorithm that considers polymorphic types (generics) to generate expressions. Furthermore, the uniqueness of both tools comes from the fact that their algorithms operate using corpus statistics. The statistics are used to steer the algorithms and the search space exploration towards the most relevant solutions. In the second part of the dissertation we present the tool anyCode that uses natural language input to synthesize expressions. As input it accepts English words or Java program language constructs. This allows a developer to encode her intuition about the desired expression using words or the expression that approximates the desired structure. Thanks to this flexibility, anyCode can also repair broken expressions. It uses a pipeline of natural language and related-word tools to analyze the input. This helps anyCode to identify the set of the most relevant components and to reduce the size of search space. To further reduce the size of search space and to create the most relevant expressions, anyCode uses two statistical models: unigram and probabilistic context free grammar. Finally, in the last part of the dissertation we present UDITA, a Java-like language with support for non-determinism, which allows a user to describe test generation programs. Test generation programs are run on a top of Java PathFinder (JPF), a popular explicit-state model checker, that has a built-in backtracking mechanism and supports non-determinism. Using UDITA programs, JPF generates test inputs. The first benefit of UDITA is that non-determinism empowers a user to describe many test inputs as easily as describing a single test input. The second benefit is that it gives a user more flexibility allowing her to describe test generation programs by arbitrarily combining filters and generators. UDITA reduces the size of search space using an algorithm that reduces the number of generated complex isomorphic structures and that delays non-deterministic choices

Génération automatique de tests unitaires avec Praspel, un langage de spécification pour PHP

The works presented in this memoir are about the validation of PHPprograms through a new specification language, along with its tools. These works follow three axes: specification language, automatic test data generation and automatic unit test generation. The first contribution is Praspel, a new specification language for PHP, based on the Design by Contract. Praspel specifies data with realistic domains, which are new structures allowing to validate and generate data. Based on a contract, we are able to perform Contract-based Testing, i.e.using contracts to automatically generate unit tests. The second contribution isabout test data generation. For booleans, integers and floating point numbers, auniform random generation is used. For arrays, a dedicated constraint solver has been implemented and used. For strings, a grammar description language along with an LL(⋆) compiler compiler and several algorithms for data generation are used. Finally, the object generation is supported. The third contribution defines contract coverage criteria. These latters provide test objectives. All these contributions are implemented and experimented into tools distributed to the PHP community.Les travaux présentés dans ce mémoire portent sur la validation de programmes PHP à travers un nouveau langage de spécification, accompagné de ses outils. Ces travaux s’articulent selon trois axes : langage de spécification, génération automatique de données de test et génération automatique de tests unitaires.La première contribution est Praspel, un nouveau langage de spécification pour PHP, basé sur la programmation par contrat. Praspel spécifie les données avec des domaines réalistes, qui sont des nouvelles structures permettant de valider etgénérer des données. À partir d’un contrat écrit en Praspel, nous pouvons faire du Contract-based Testing, c’est à dire exploiter les contrats pour générer automatiquement des tests unitaires. La deuxième contribution concerne la génération de données de test. Pour les booléens, les entiers et les réels, une génération aléatoire uniforme est employée. Pour les tableaux, un solveur de contraintes a été implémenté et utilisé. Pour les chaînes de caractères, un langage de description de grammaires avec un compilateur de compilateurs LL(⋆) et plusieurs algorithmes de génération de données sont employés. Enfin, la génération d’objets est traitée.La troisième contribution définit des critères de couverture sur les contrats.Ces derniers fournissent des objectifs de test. Toutes ces contributions ont été implémentées et expérimentées dans des outils distribués à la communauté PHP