Inductive Synthesis of Functional Programs: an Explanation Based Generalization Approach
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Program Synthesis with Grammars and Semantics in Genetic Programming
Program Synthesis with Grammars and Semantics in Genetic Programming Stefan Forstenlechner UCD student number: 14204817 The thesis is submitted to University College Dublin in fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY School of Business Head of School: Prof. Anthony Brabazon Research Supervisors: Prof. Michael O’Neill Dr. Miguel Nicolau External Examiner: Dr. John R. Woodward January 2019 Contents Contents i Abstract vii Statement of Original Authorship viii Acknowledgements ix List of Figures xi List of Tables xiv List of Algorithms xvii List of Abbreviations xviii Publications Arising xx I Introduction and Literature Review 1 1 Introduction 2 1.1 Aim of Thesis . .3 1.2 Research Questions . .4 1.3 Contributions . .7 1.3.1 Technical contributions . .8 1.4 Limitations . .8 1.5 Thesis Outline . .9 i CONTENTS 2 Related Work 12 2.1 Evolutionary Computation . 12 2.2 Genetic Programming . 14 2.2.1 Representation . 15 2.2.2 Initialization . 16 2.2.3 Fitness . 17 2.2.4 Selection . 17 2.2.5 Crossover . 19 2.2.6 Mutation . 19 2.2.7 GP Summary . 20 2.2.8 Grammars . 20 2.3 Program Synthesis . 23 2.3.1 Program Synthesis in Genetic Programming . 26 2.3.2 General Program Synthesis Benchmark Suite . 30 2.4 Semantics . 32 2.4.1 Semantic operators . 34 2.4.2 Geometric Semantic GP . 37 2.5 Conclusion . 38 II Experimental Research 40 3 General Grammar Design 41 3.1 Grammars for G3P . 41 3.2 Sorting Network . 42 3.3 Structure in Grammars . 43 3.4 Sorting Network Grammar Design . -
Approaches and Applications of Inductive Programming
Report from Dagstuhl Seminar 17382 Approaches and Applications of Inductive Programming Edited by Ute Schmid1, Stephen H. Muggleton2, and Rishabh Singh3 1 Universität Bamberg, DE, [email protected] 2 Imperial College London, GB, [email protected] 3 Microsoft Research – Redmond, US, [email protected] Abstract This report documents the program and the outcomes of Dagstuhl Seminar 17382 “Approaches and Applications of Inductive Programming”. After a short introduction to the state of the art to inductive programming research, an overview of the introductory tutorials, the talks, program demonstrations, and the outcomes of discussion groups is given. Seminar September 17–20, 2017 – http://www.dagstuhl.de/17382 1998 ACM Subject Classification I.2.2 Automatic Programming, Program Synthesis Keywords and phrases inductive program synthesis, inductive logic programming, probabilistic programming, end-user programming, human-like computing Digital Object Identifier 10.4230/DagRep.7.9.86 Edited in cooperation with Sebastian Seufert 1 Executive summary Ute Schmid License Creative Commons BY 3.0 Unported license © Ute Schmid Inductive programming (IP) addresses the automated or semi-automated generation of computer programs from incomplete information such as input-output examples, constraints, computation traces, demonstrations, or problem-solving experience [5]. The generated – typically declarative – program has the status of a hypothesis which has been generalized by induction. That is, inductive programming can be seen as a special approach to machine learning. In contrast to standard machine learning, only a small number of training examples is necessary. Furthermore, learned hypotheses are represented as logic or functional programs, that is, they are represented on symbol level and therefore are inspectable and comprehensible [17, 8, 18]. -
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Journal of Artificial Intelligence Research 1 (1993) 1-15 Submitted 6/91; published 9/91 Inductive logic programming at 30: a new introduction Andrew Cropper [email protected] University of Oxford Sebastijan Dumanˇci´c [email protected] KU Leuven Abstract Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to in- duce a hypothesis (a set of logical rules) that generalises given training examples. In contrast to most forms of machine learning, ILP can learn human-readable hypotheses from small amounts of data. As ILP approaches 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main ILP learning settings. We describe the main building blocks of an ILP system. We compare several ILP systems on several dimensions. We describe in detail four systems (Aleph, TILDE, ASPAL, and Metagol). We document some of the main application areas of ILP. Finally, we summarise the current limitations and outline promising directions for future research. 1. Introduction A remarkable feat of human intelligence is the ability to learn new knowledge. A key type of learning is induction: the process of forming general rules (hypotheses) from specific obser- vations (examples). For instance, suppose you draw 10 red balls out of a bag, then you might induce a hypothesis (a rule) that all the balls in the bag are red. Having induced this hypothesis, you can predict the colour of the next ball out of the bag. The goal of machine learning (ML) (Mitchell, 1997) is to automate induction. -
Bias Reformulation for One-Shot Function Induction
Bias reformulation for one-shot function induction Dianhuan Lin1 and Eyal Dechter1 and Kevin Ellis1 and Joshua B. Tenenbaum1 and Stephen H. Muggleton2 Abstract. In recent years predicate invention has been under- Input Output explored as a bias reformulation mechanism within Inductive Logic Task1 miKe dwIGHT Mike Dwight Programming due to difficulties in formulating efficient search mech- Task2 European Conference on ECAI anisms. However, recent papers on a new approach called Meta- Artificial Intelligence Interpretive Learning have demonstrated that both predicate inven- Task3 My name is John. John tion and learning recursive predicates can be efficiently implemented for various fragments of definite clause logic using a form of abduc- tion within a meta-interpreter. This paper explores the effect of bias reformulation produced by Meta-Interpretive Learning on a series Figure 1. Input-output pairs typifying string transformations in this paper of Program Induction tasks involving string transformations. These tasks have real-world applications in the use of spreadsheet tech- nology. The existing implementation of program induction in Mi- crosoft’s FlashFill (part of Excel 2013) already has strong perfor- problems are easy for us, but often difficult for automated systems, mance on this problem, and performs one-shot learning, in which a is that we bring to bear a wealth of knowledge about which kinds of simple transformation program is generated from a single example programs are more or less likely to reflect the intentions of the person instance and applied to the remainder of the column in a spreadsheet. who wrote the program or provided the example. However, no existing technique has been demonstrated to improve There are a number of difficulties associated with successfully learning performance over a series of tasks in the way humans do. -
On the Di Iculty of Benchmarking Inductive Program Synthesis Methods
On the Diiculty of Benchmarking Inductive Program Synthesis Methods Edward Pantridge omas Helmuth MassMutual Financial Group Washington and Lee University Amherst, Massachuses, USA Lexington, Virginia [email protected] [email protected] Nicholas Freitag McPhee Lee Spector University of Minnesota, Morris Hampshire College Morris, Minnesota 56267 Amherst, Massachuses, USA [email protected] [email protected] ABSTRACT ACM Reference format: A variety of inductive program synthesis (IPS) techniques have Edward Pantridge, omas Helmuth, Nicholas Freitag McPhee, and Lee Spector. 2017. On the Diculty of Benchmarking Inductive Program Syn- recently been developed, emerging from dierent areas of com- thesis Methods. In Proceedings of GECCO ’17 Companion, Berlin, Germany, puter science. However, these techniques have not been adequately July 15-19, 2017, 8 pages. compared on general program synthesis problems. In this paper we DOI: hp://dx.doi.org/10.1145/3067695.3082533 compare several methods on problems requiring solution programs to handle various data types, control structures, and numbers of outputs. e problem set also spans levels of abstraction; some 1 INTRODUCTION would ordinarily be approached using machine code or assembly Since the creation of Inductive Program Synthesis (IPS) in the language, while others would ordinarily be approached using high- 1970s [15], researchers have been striving to create systems capa- level languages. e presented comparisons are focused on the ble of generating programs competitively with human intelligence. possibility of success; that is, on whether the system can produce Modern IPS methods oen trace their roots to the elds of machine a program that passes all tests, for all training and unseen test- learning, logic programming, evolutionary computation and others. -
Learning Functional Programs with Function Invention and Reuse
Learning functional programs with function invention and reuse Andrei Diaconu University of Oxford arXiv:2011.08881v1 [cs.PL] 17 Nov 2020 Honour School of Computer Science Trinity 2020 Abstract Inductive programming (IP) is a field whose main goal is synthe- sising programs that respect a set of examples, given some form of background knowledge. This paper is concerned with a subfield of IP, inductive functional programming (IFP). We explore the idea of generating modular functional programs, and how those allow for function reuse, with the aim to reduce the size of the programs. We introduce two algorithms that attempt to solve the problem and explore type based pruning techniques in the context of modular programs. By experimenting with the imple- mentation of one of those algorithms, we show reuse is important (if not crucial) for a variety of problems and distinguished two broad classes of programs that will generally benefit from func- tion reuse. Contents 1 Introduction5 1.1 Inductive programming . .5 1.2 Motivation . .6 1.3 Contributions . .7 1.4 Structure of the report . .8 2 Background and related work 10 2.1 Background on IP . 10 2.2 Related work . 12 2.2.1 Metagol . 12 2.2.2 Magic Haskeller . 13 2.2.3 λ2 ............................. 13 2.3 Invention and reuse . 13 3 Problem description 15 3.1 Abstract description of the problem . 15 3.2 Invention and reuse . 19 4 Algorithms for the program synthesis problem 21 4.1 Preliminaries . 22 4.1.1 Target language and the type system . 22 4.1.2 Combinatorial search . -
Inductive Programming Meets the Real World
Inductive Programming Meets the Real World Sumit Gulwani José Hernández-Orallo Emanuel Kitzelmann Microsoft Corporation, Universitat Politècnica de Adam-Josef-Cüppers [email protected] València, Commercial College, [email protected] [email protected] Stephen H. Muggleton Ute Schmid Benjamin Zorn Imperial College London, UK. University of Bamberg, Microsoft Corporation, [email protected] Germany. [email protected] [email protected] Since most end users lack programming skills they often thesis, now called inductive functional programming (IFP), spend considerable time and effort performing tedious and and from inductive inference techniques using logic, nowa- repetitive tasks such as capitalizing a column of names man- days termed inductive logic programming (ILP). IFP ad- ually. Inductive Programming has a long research tradition dresses the synthesis of recursive functional programs gener- and recent developments demonstrate it can liberate users alized from regularities detected in (traces of) input/output from many tasks of this kind. examples [42, 20] using generate-and-test approaches based on evolutionary [35, 28, 36] or systematic [17, 29] search Key insights or data-driven analytical approaches [39, 6, 18, 11, 37, 24]. Its development is complementary to efforts in synthesizing • Supporting end-users to automate complex and programs from complete specifications using deductive and repetitive tasks using computers is a big challenge formal methods [8]. for which novel technological breakthroughs are de- ILP originated from research on induction in a logical manded. framework [40, 31] with influence from artificial intelligence, • The integration of inductive programing techniques machine learning and relational databases. It is a mature in software applications can support users by learning area with its own theory, implementations, and applications domain specific programs from observing interactions and recently celebrated the 20th anniversary [34] of its in- of the user with the system. -
Program Synthesis with Types
University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2015 Program Synthesis With Types Peter-Michael Santos Osera University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Computer Sciences Commons Recommended Citation Osera, Peter-Michael Santos, "Program Synthesis With Types" (2015). Publicly Accessible Penn Dissertations. 1926. https://repository.upenn.edu/edissertations/1926 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/1926 For more information, please contact [email protected]. Program Synthesis With Types Abstract Program synthesis, the automatic generation of programs from specification, promises to fundamentally change the way that we build software. By using synthesis tools, we can greatly speed up the time it takes to build complex software artifacts as well as construct programs that are automatically correct by virtue of the synthesis process. Studied since the 70s, researchers have applied techniques from many different sub-fields of computer science ot solve the program synthesis problem in a variety of domains and contexts. However, one domain that has been less explored than others is the domain of typed, functional programs. This is unfortunate because programs in richly-typed languages like OCaml and Haskell are known for ``writing themselves'' once the programmer gets the types correct. In light of this observation, can we use type theory to build more expressive and efficient type-directed synthesis systems for this domain of programs? This dissertation answers this question in the affirmative by building novel type- theoretic foundations for program synthesis. By using type theory as the basis of study for program synthesis, we are able to build core synthesis calculi for typed, functional programs, analyze the calculi's meta-theoretic properties, and extend these calculi to handle increasingly richer types and language features. -
Analytical Inductive Programming As a Cognitive Rule Acquisition Devise∗
AGI-2009 - Published by Atlantis Press, © the authors <1> Analytical Inductive Programming as a Cognitive Rule Acquisition Devise∗ Ute Schmid and Martin Hofmann and Emanuel Kitzelmann Faculty Information Systems and Applied Computer Science University of Bamberg, Germany {ute.schmid, martin.hofmann, emanuel.kitzelmann}@uni-bamberg.de Abstract desired one given enough time, analytical approaches One of the most admirable characteristic of the hu- have a more restricted language bias. The advantage of man cognitive system is its ability to extract gener- analytical inductive programming is that programs are alized rules covering regularities from example expe- synthesized very fast, that the programs are guaranteed rience presented by or experienced from the environ- to be correct for all input/output examples and fulfill ment. Humans’ problem solving, reasoning and verbal further characteristics such as guaranteed termination behavior often shows a high degree of systematicity and being minimal generalizations over the examples. and productivity which can best be characterized by a The main goal of inductive programming research is to competence level reflected by a set of recursive rules. provide assistance systems for programmers or to sup- While we assume that such rules are different for dif- port end-user programming (Flener & Partridge 2001). ferent domains, we believe that there exists a general mechanism to extract such rules from only positive ex- From a broader perspective, analytical inductive pro- amples from the environment. Our system Igor2 is an gramming provides algorithms for extracting general- analytical approach to inductive programming which ized sets of recursive rules from small sets of positive induces recursive rules by generalizing over regularities examples of some behavior. -
Program Synthesis
Program Synthesis Program Synthesis Sumit Gulwani Microsoft Research [email protected] Oleksandr Polozov University of Washington [email protected] Rishabh Singh Microsoft Research [email protected] Boston — Delft Foundations and Trends® in Programming Languages Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 United States Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is S. Gulwani, O. Polozov and R. Singh. Program Synthesis. Foundations and Trends® in Programming Languages, vol. 4, no. 1-2, pp. 1–119, 2017. ® This Foundations and Trends issue was typeset in LATEX using a class file designed by Neal Parikh. Printed on acid-free paper. ISBN: 978-1-68083-292-1 © 2017 S. Gulwani, O. Polozov and R. Singh All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for in- ternal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged. -
Template-Based Program Verification and Program Synthesis
Software Tools for Technology Transfer manuscript No. (will be inserted by the editor) Template-based Program Verification and Program Synthesis Saurabh Srivastava? and Sumit Gulwani?? and Jeffrey S. Foster??? University of California, Berkeley and Microsoft Research, Redmond and University of Maryland, College Park Received: date / Revised version: date Abstract. Program verification is the task of automat- the subsequent step of writing the program in C, C++, ically generating proofs for a program's compliance with Java etc. There is additional effort in ensuring that all a given specification. Program synthesis is the task of corner cases are covered, which is a tiresome and man- automatically generating a program that meets a given ual process. The dilligent programmer will also verify specification. Both program verification and program syn- that the final program is not only correct but also me- thesis can be viewed as search problems, for proofs and chanically verifiable, which usually requires them to add programs, respectively. annotations illustrating the correctness. For these search problems, we present approaches This makes programming a subtle task, and the ef- based on user-provided insights in the form of templates. fort involved in writing correct programs is so high that Templates are hints about the syntactic forms of the in- in practice we accept that programs can only be approx- variants and programs, and help guide the search for imately correct. While developers do realize the pres- solutions. We show how to reduce the template-based ence of corner cases, the difficulty inherent in enumer- search problem to satisfiability solving, which permits ating and reasoning about them, or using a verification the use of off-the-shelf solvers to efficiently explore the framework, ensures that developers typically leave most search space. -
A Visual Language for Composable Inductive Programming
A Visual Language for Composable Inductive Programming Edward McDaid FBCS Sarah McDaid PhD Chief Technology Officer Head of Digital Zoea Ltd Zoea Ltd Abstract We present Zoea Visual which is a visual programming language based on the Zoea composable inductive programming language. Zoea Visual allows users to create software directly from a specification that resembles a set of functional test cases. Programming with Zoea Visual involves the definition of a data flow model of test case inputs, optional intermediate values, and outputs. Data elements are represented visually and can be combined to create structures of any complexity. Data flows between elements provide additional information that allows the Zoea compiler to generate larger programs in less time. This paper includes an overview of the language. The benefits of the approach and some possible future enhancements are also discussed. 1. Introduction control structures or functions. Instead the developer simply provides a number of test cases This paper describes the visual programming showing examples of inputs and outputs as static language Zoea Visual. In order to understand the data. The Zoea compiler uses programming motivation and design of Zoea Visual it is first knowledge, pattern matching and abductive necessary to briefly recap the underlying Zoea reasoning [5] to automatically identify the required language. code [1]. Knowledge sources are organised as a Zoea is a simple declarative programming language distributed blackboard architecture [6] that allows a user to construct software directly from a The Zoea language is around 30% as complex as specification that resembles a set of functional test the simplest conventional programming languages cases [1].