Proceedings of the ACM SIGPLAN Workshop on Approaches and Applications of Inductive Programming (AAIP 2009)

Inductive programming is concerned with the automated construction of declarative, often functional, recursive programs from incomplete specifications such as input/output examples. The inferred program must be correct with respect to the provided examples in a generalising sense: it should be neither equivalent to them, nor inconsistent. Inductive programming algorithms are guided explicitly or implicitly by a language bias (the class of programs that can be induced) and a search bias (determining which generalised program is constructed first). Induction strategies are either generate-and-test or example-driven. In generate-and-test approaches, hypotheses about candidate programs are generated independently from the given specifications. Program candidates are tested against the given specification and one or more of the best evaluated candidates are developed further. In analytical approaches, candidate programs are constructed in an example-driven way. While generate-and-test approaches can -- in principle -- construct any kind of program, analytical approaches have a more limited scope. On the other hand, efficiency of induction is much higher in analytical approaches. Inductive programming is still mainly a topic of basic research, exploring how the intellectual ability of humans to infer generalised recursive procedures from incomplete evidence can be captured in the form of synthesis methods. Intended applications are mainly in the domain of programming assistance -- either to relieve professional programmers from routine tasks or to enable non-programmers to some limited form of end-user programming. Furthermore, in the future, inductive programming techniques might be applied to further areas such as supporting the inference of lemmata in theorem proving or learning grammar rules. Inductive automated program construction has been originally addressed by researchers in artificial intelligence and machine learning. During the last years, some work on exploiting induction techniques has been started also in the functional programming community. Therefore, the third workshop on |Approaches and Applications of Inductive Programming| took place for the first time in conjunction with the ACM SIGPLAN International Conference on Functional Programming (ICFP 2009). The first and second workshop were associated with the International Conference on Machine Learning (ICML 2005) and the European Conference on Machine Learning (ECML 2007). AAIP´09 aimed to bring together researchers from the functional programming and the artificial intelligence communities, working in the field of inductive functional programming, and advance fruitful interactions between these communities with respect to programming techniques for inductive programming algorithms, the identification of challenge problems and potential applications. For everybody interested in inductive programming we recommend to visit the website: www.inductive-programming.org

Ein kombinierter analytischer und suchbasierter Ansatz zur induktiven Synthese funktionaler Programme

This thesis is concerned with the inductive synthesis of recursive declarative programs and in particular with the analytical inductive synthesis of functional programs. Program synthesis addresses the problem of (semi-)automatically generating computer programs from specifications. In inductive program synthesis, recursive programs are constructed by generalizing over incomplete specifications such as finite sets of input/output examples (I/O examples). Classical methods for induction of functional programs are analytical, that is, a recursive function definition is derived by detecting and generalizing recurrent patterns between the given I/O examples. Most recent methods, on the other side, are generate-and-test based, that is, they repeatedly generate programs independently from the provided I/O examples until a program is found that correctly computes the examples. Analytical methods are much faster than generate-and-test methods, because they do not rely on search in a program space. Therefore, however, the schemas that generatable programs conform to, must be much more restricted. This thesis at first provides a comprehensive overview of current approaches and methods to inductive program synthesis. Then we present a new algorithm to the inductive synthesis of functional programs that generalizes the analytical approach and combines it with search in a program space. Thereby, the strong restrictions of analytical methods can be resolved for the most part. At the same time, applying analytical techniques allows for pruning large parts of the problem space so that solutions can often be found faster than with generate-and-test methods. By means of several experiments with an implementation of the described algorithm, we demonstrate its capabilities.Diese Arbeit befasst sich mit der induktiven Synthese rekursiver deklarativer Programme und speziell mit der analytischen induktiven Synthese funktionaler Programme. Die Programmsynthese beschäftigt sich mit der (semi-)automatischen Konstruktion von Computer-Programmen aus Spezifikationen. In der induktiven Programmsynthese werden rekursive Programme durch das Generalisieren über unvollständige Spezifikationen, wie zum Beispiel endliche Mengen von Eingabe/Ausgabe Beispielen (E/A-Beispielen), generiert. Klassische Methoden der induktiven Synthese funktionaler Programme sind analytisch; eine rekursive Funktionsdefinition wird generiert, indem rekurrente Strukturen zwischen den einzelnen E/A-Beispielen gefunden und generalisiert werden. Die meisten aktuellen Ansätze basieren hingegen auf erzeugen und testen, das heißt, es werden unabhängig von den bereitgestellten E/A-Beispielen solange Programme einer Klasse generiert, bis schließlich ein Programm gefunden wurde das alle Beispiele korrekt berechnet. Analytische Methoden sind sehr viel schneller, weil sie nicht auf Suche in einem Programmraum beruhen. Allerdings müssen dafür auch die Schemata, denen die generierbaren Programme gehorchen, sehr viel beschränkter sein. Diese Arbeit bietet zunächst einen umfassenden Überblick über bestehende Ansätze und Methoden der induktiven Programmsynthese. Anschließend wird ein neuer Algorithmus zur induktiven Synthese funktionaler Programme beschrieben, der den analytischen Ansatz generalisiert und mit Suche in einem Programmraum kombiniert. Dadurch lassen sich die starken Restriktionen des analytischen Ansatzes zu großen Teilen überwinden. Gleichzeitig erlaubt der Einsatz analytischer Techniken das Beschneiden großer Teile des Problemraums, so dass Lösungsprogramme oft schneller gefunden werden können als mit Methoden, die auf erzeugen und testen beruhen. Mittels einer Reihe von Experimenten mit einer Implementation des beschriebenen Algorithmus' werden seine Möglichkeiten gezeigt