HOL-Testgen Version 1.8 USER GUIDE
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Processing an Intermediate Representation Written in Lisp
Processing an Intermediate Representation Written in Lisp Ricardo Pena,˜ Santiago Saavedra, Jaime Sanchez-Hern´ andez´ Complutense University of Madrid, Spain∗ [email protected],[email protected],[email protected] In the context of designing the verification platform CAVI-ART, we arrived to the need of deciding a textual format for our intermediate representation of programs. After considering several options, we finally decided to use S-expressions for that textual representation, and Common Lisp for processing it in order to obtain the verification conditions. In this paper, we discuss the benefits of this decision. S-expressions are homoiconic, i.e. they can be both considered as data and as code. We exploit this duality, and extensively use the facilities of the Common Lisp environment to make different processing with these textual representations. In particular, using a common compilation scheme we show that program execution, and verification condition generation, can be seen as two instantiations of the same generic process. 1 Introduction Building a verification platform such as CAVI-ART [7] is a challenging endeavour from many points of view. Some of the tasks require intensive research which can make advance the state of the art, as it is for instance the case of automatic invariant synthesis. Some others are not so challenging, but require a lot of pondering and discussion before arriving at a decision, in order to ensure that all the requirements have been taken into account. A bad or a too quick decision may have a profound influence in the rest of the activities, by doing them either more difficult, or longer, or more inefficient. -
Rubicon: Bounded Verification of Web Applications
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by DSpace@MIT Rubicon: Bounded Verification of Web Applications Joseph P. Near, Daniel Jackson Computer Science and Artificial Intelligence Lab Massachusetts Institute of Technology Cambridge, MA, USA {jnear,dnj}@csail.mit.edu ABSTRACT ification language is an extension of the Ruby-based RSpec We present Rubicon, an application of lightweight formal domain-specific language for testing [7]; Rubicon adds the methods to web programming. Rubicon provides an embed- quantifiers of first-order logic, allowing programmers to re- ded domain-specific language for writing formal specifica- place RSpec tests over a set of mock objects with general tions of web applications and performs automatic bounded specifications over all objects. This compatibility with the checking that those specifications hold. Rubicon's language existing RSpec language makes it easy for programmers al- is based on the RSpec testing framework, and is designed to ready familiar with testing to write specifications, and to be both powerful and familiar to programmers experienced convert existing RSpec tests into specifications. in testing. Rubicon's analysis leverages the standard Ruby interpreter to perform symbolic execution, generating veri- Rubicon's automated analysis comprises two parts: first, fication conditions that Rubicon discharges using the Alloy Rubicon generates verification conditions based on specifica- Analyzer. We have tested Rubicon's scalability on five real- tions; second, Rubicon invokes a constraint solver to check world applications, and found a previously unknown secu- those conditions. The Rubicon library modifies the envi- rity bug in Fat Free CRM, a popular customer relationship ronment so that executing a specification performs symbolic management system. -
The Common HOL Platform
The Common HOL Platform Mark Adams Proof Technologies Ltd, UK Radboud University, Nijmegen, The Netherlands The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to be compatible with all HOL systems. So far, HOL Light and hol90 have been adapted for conformance, and HOL Zero was originally developed to conform. In this paper we provide motivation for a platform, give an overview of the Common HOL Platform’s theory and API components, and show how to adapt legacy systems. We also report on the platform’s successful application in the hand-translation of a few thousand lines of source code from HOL Light to HOL Zero. 1 Introduction The HOL family of theorem provers started in the 1980s with HOL88 [5], and has since grown to include many systems, most prominently HOL4 [16], HOL Light [8], ProofPower HOL [3] and Is- abelle/HOL [12]. These four main systems have developed their own advanced proof facilities and extensive theory libraries, and have been successfully employed in major projects in the verification of critical hardware and software [1, 11] and the formalisation of mathematics [7]. It would clearly be of benefit if these systems could “talk” to each other, specifically if theory, proofs and source code could be exchanged in a relatively seamless manner. This would reduce the considerable duplication of effort otherwise required for one system to benefit from the major projects and advanced capabilities developed on another. -
Interactive Theorem Proving (ITP) Course Web Version
Interactive Theorem Proving (ITP) Course Web Version Thomas Tuerk ([email protected]) Except where otherwise noted, this work is licened under Creative Commons Attribution-ShareAlike 4.0 International License version 3c35cc2 of Mon Nov 11 10:22:43 2019 Contents Part I Preface 3 Part II Introduction 6 Part III HOL 4 History and Architecture 16 Part IV HOL's Logic 24 Part V Basic HOL Usage 38 Part VI Forward Proofs 46 Part VII Backward Proofs 61 Part VIII Basic Tactics 83 Part IX Induction Proofs 110 Part X Basic Definitions 119 Part XI Good Definitions 163 Part XII Deep and Shallow Embeddings 184 Part XIII Rewriting 192 Part XIV Advanced Definition Principles 246 Part XV Maintainable Proofs 267 Part XVI Overview of HOL 4 289 Part XVII Other Interactive Theorem Provers 302 2 / 315 Part I Preface Except where otherwise noted, this work is licened under Creative Commons Attribution-ShareAlike 4.0 International License. Preface these slides originate from a course for advanced master students it was given by the PROSPER group at KTH in Stockholm in 2017 (see https://www.kth.se/social/group/interactive-theorem-) the course focused on how to use HOL 4 students taking the course were expected to I know functional programming, esp. SML I understand predicate logic I have some experience with pen and paper proofs the course consisted of 9 lectures, which each took 90 minutes there were 19 supervised practical sessions, which each took 2 h usually there was 1 lecture and 2 practical sessions each week students were expected to work about 10 h each -
Exploring Languages with Interpreters and Functional Programming Chapter 11
Exploring Languages with Interpreters and Functional Programming Chapter 11 H. Conrad Cunningham 24 January 2019 Contents 11 Software Testing Concepts 2 11.1 Chapter Introduction . .2 11.2 Software Requirements Specification . .2 11.3 What is Software Testing? . .3 11.4 Goals of Testing . .3 11.5 Dimensions of Testing . .3 11.5.1 Testing levels . .4 11.5.2 Testing methods . .6 11.5.2.1 Black-box testing . .6 11.5.2.2 White-box testing . .8 11.5.2.3 Gray-box testing . .9 11.5.2.4 Ad hoc testing . .9 11.5.3 Testing types . .9 11.5.4 Combining levels, methods, and types . 10 11.6 Aside: Test-Driven Development . 10 11.7 Principles for Test Automation . 12 11.8 What Next? . 15 11.9 Exercises . 15 11.10Acknowledgements . 15 11.11References . 16 11.12Terms and Concepts . 17 Copyright (C) 2018, H. Conrad Cunningham Professor of Computer and Information Science University of Mississippi 211 Weir Hall P.O. Box 1848 University, MS 38677 1 (662) 915-5358 Browser Advisory: The HTML version of this textbook requires a browser that supports the display of MathML. A good choice as of October 2018 is a recent version of Firefox from Mozilla. 2 11 Software Testing Concepts 11.1 Chapter Introduction The goal of this chapter is to survey the important concepts, terminology, and techniques of software testing in general. The next chapter illustrates these techniques by manually constructing test scripts for Haskell functions and modules. 11.2 Software Requirements Specification The purpose of a software development project is to meet particular needs and expectations of the project’s stakeholders. -
Beginner's Luck
Beginner’s Luck A Language for Property-Based Generators Leonidas Lampropoulos1 Diane Gallois-Wong2,3 Cat˘ alin˘ Hrit¸cu2 John Hughes4 Benjamin C. Pierce1 Li-yao Xia2,3 1University of Pennsylvania, USA 2INRIA Paris, France 3ENS Paris, France 4Chalmers University, Sweden Abstract An appealing feature of QuickCheck is that it offers a library Property-based random testing a` la QuickCheck requires build- of property combinators resembling standard logical operators. For ing efficient generators for well-distributed random data satisfying example, a property of the form p ==> q, built using the impli- complex logical predicates, but writing these generators can be dif- cation combinator ==>, will be tested automatically by generating ficult and error prone. We propose a domain-specific language in valuations (assignments of random values, of appropriate type, to which generators are conveniently expressed by decorating pred- the free variables of p and q), discarding those valuations that fail icates with lightweight annotations to control both the distribu- to satisfy p, and checking whether any of the ones that remain are tion of generated values and the amount of constraint solving that counterexamples to q. happens before each variable is instantiated. This language, called QuickCheck users soon learn that this default generate-and-test Luck, makes generators easier to write, read, and maintain. approach sometimes does not give satisfactory results. In particular, We give Luck a formal semantics and prove several fundamen- if the precondition p is satisfied by relatively few values of the ap- tal properties, including the soundness and completeness of random propriate type, then most of the random inputs that QuickCheck generation with respect to a standard predicate semantics. -
Quickcheck Tutorial
QuickCheck Tutorial Thomas Arts John Hughes Quviq AB Queues Erlang contains a queue data structure (see stdlib documentation) We want to test that these queues behave as expected What is “expected” behaviour? We have a mental model of queues that the software should conform to. Erlang Exchange 2008 © Quviq AB 2 Queue Mental model of a fifo queue …… first last …… Remove from head Insert at tail / rear Erlang Exchange 2008 © Quviq AB 3 Queue Traditional test cases could look like: We want to check for arbitrary elements that Q0 = queue:new(), if we add an element, Q1 = queue:cons(1,Q0), it's there. 1 = queue:last(Q1). Q0 = queue:new(), We want to check for Q1 = queue:cons(8,Q0), arbitrary queues that last added element is Q2 = queue:cons(0,Q1), "last" 0 = queue:last(Q2), Property is like an abstraction of a test case Erlang Exchange 2008 © Quviq AB 4 QuickCheck property We want to know that for any element, when we add it, it's there prop_itsthere() -> ?FORALL(I,int(), I == queue:last( queue:cons(I, queue:new()))). Erlang Exchange 2008 © Quviq AB 5 QuickCheck property We want to know that for any element, when we add it, it's there prop_itsthere() -> ?FORALL(I,int(), I == queue:last( queue:cons(I, queue:new()))). This is a property Test cases are generasted from such properties Erlang Exchange 2008 © Quviq AB 6 QuickCheck property We want to know that for any element, when we add it, it's there int() is a generator for random integers prop_itsthere() -> ?FORALL(I,int(), I == queue:last( queue:cons(I, I represents one queue:new()))). -
Branching Processes for Quickcheck Generators (Extended Version)
Branching Processes for QuickCheck Generators (extended version) Agustín Mista Alejandro Russo John Hughes Universidad Nacional de Rosario Chalmers University of Technology Chalmers University of Technology Rosario, Argentina Gothenburg, Sweden Gothenburg, Sweden [email protected] [email protected] [email protected] Abstract random test data generators or QuickCheck generators for short. In QuickCheck (or, more generally, random testing), it is chal- The generation of test cases is guided by the types involved in lenging to control random data generators’ distributions— the testing properties. It defines default generators for many specially when it comes to user-defined algebraic data types built-in types like booleans, integers, and lists. However, when (ADT). In this paper, we adapt results from an area of mathe- it comes to user-defined ADTs, developers are usually required matics known as branching processes, and show how they help to specify the generation process. The difficulty is, however, to analytically predict (at compile-time) the expected number that it might become intricate to define generators so that they of generated constructors, even in the presence of mutually result in a suitable distribution or enforce data invariants. recursive or composite ADTs. Using our probabilistic formu- The state-of-the-art tools to derive generators for user- las, we design heuristics capable of automatically adjusting defined ADTs can be classified based on the automation level probabilities in order to synthesize generators which distribu- as well as the sort of invariants enforced at the data genera- tions are aligned with users’ demands. We provide a Haskell tion phase. QuickCheck and SmallCheck [27] (a tool for writing implementation of our mechanism in a tool called generators that synthesize small test cases) use type-driven and perform case studies with real-world applications. -
Translating Scala Programs to Isabelle/HOL (System
Translating Scala Programs to Isabelle/HOL System Description Lars Hupel1 and Viktor Kuncak2 1 Technische Universität München 2 École Polytechnique Fédérale de Lausanne (EPFL) Abstract. We present a trustworthy connection between the Leon verification system and the Isabelle proof assistant. Leon is a system for verifying functional Scala programs. It uses a variety of automated theorem provers (ATPs) to check verification conditions (VCs) stemming from the input program. Isabelle, on the other hand, is an interactive theorem prover used to verify mathematical spec- ifications using its own input language Isabelle/Isar. Users specify (inductive) definitions and write proofs about them manually, albeit with the help of semi- automated tactics. The integration of these two systems allows us to exploit Is- abelle’s rich standard library and give greater confidence guarantees in the cor- rectness of analysed programs. Keywords: Isabelle, HOL, Scala, Leon, compiler 1 Introduction This system description presents a new tool that aims to connect two important worlds: the world of interactive proof assistant users who create a body of verified theorems, and the world of professional programmers who increasingly adopt functional programming to develop important applications. The Scala language (www.scala-lang.org) en- joys a prominent role today for its adoption in industry, a trend most recently driven by the Apache Spark data analysis framework (to which, e.g., IBM committed 3500 researchers recently [16]). We hope to introduce some of the many Scala users to formal methods by providing tools they can use directly on Scala code. Leon sys- tem (http://leon.epfl.ch) is a verification and synthesis system for a subset of Scala [2, 10]. -
Foundational Property-Based Testing
Foundational Property-Based Testing Zoe Paraskevopoulou1,2 Cat˘ alin˘ Hrit¸cu1 Maxime Den´ es` 1 Leonidas Lampropoulos3 Benjamin C. Pierce3 1Inria Paris-Rocquencourt 2ENS Cachan 3University of Pennsylvania Abstract Integrating property-based testing with a proof assistant creates an interesting opportunity: reusable or tricky testing code can be formally verified using the proof assistant itself. In this work we introduce a novel methodology for formally verified property-based testing and implement it as a foundational verification framework for QuickChick, a port of QuickCheck to Coq. Our frame- work enables one to verify that the executable testing code is testing the right Coq property. To make verification tractable, we provide a systematic way for reasoning about the set of outcomes a random data generator can produce with non-zero probability, while abstracting away from the actual probabilities. Our framework is firmly grounded in a fully verified implementation of QuickChick itself, using the same underlying verification methodology. We also apply this methodology to a complex case study on testing an information-flow control abstract machine, demonstrating that our verification methodology is modular and scalable and that it requires minimal changes to existing code. 1 Introduction Property-based testing (PBT) allows programmers to capture informal conjectures about their code as executable specifications and to thoroughly test these conjectures on a large number of inputs, usually randomly generated. When a counterexample is found it is shrunk to a minimal one, which is displayed to the programmer. The original Haskell QuickCheck [19], the first popular PBT tool, has inspired ports to every mainstream programming language and led to a growing body of continuing research [6,18,26,35,39] and industrial interest [2,33]. -
Specification Based Testing with Quickcheck
Specification Based Testing with QuickCheck (Tutorial Talk) John Hughes Chalmers University of Technology and QuviQ AB ABSTRACT QuickCheck is a tool which tests software against a formal specification, reporting discrepancies as minimal failing examples. QuickCheck uses properties specified by the developer both to generate test cases, and to identify failing tests. A property such as 8xs : list(int()): reverse(reverse(xs)) = xs is tested by generating random lists of integers, binding them to the variable xs, then evaluating the boolean expression under the quantifier and reporting a failure if the value is false. If a failing test case is found, QuickCheck “shrinks” it by searching for smaller, but similar test cases that also fail, terminating with a minimal example that cannot be shrunk further. In this example, if the developer accidentally wrote 8xs : list(int()): reverse(xs) = xs instead, then QuickCheck would report the list [0; 1] as the minimal failing case, containing as few list elements as possible, with the smallest absolute values possible. The approach is very practical: QuickCheck is implemented just a library in a host programming language; it needs only to execute the code under test, so requires no tools other than a compiler (in particular, no static analysis); the shrinking process “extracts the signal from the noise” of random testing, and usually results in very easy-to-debug failures. First developed in Haskell by Koen Claessen and myself, QuickCheck has been emulated in many programming languages, and in 2006 I founded QuviQ to develop and market an Erlang version. Of course, customers’ code is much more complex than the simple reverse function above, and requires much more complex properties to test it. -
Webdriver: Controlling Your Web Browser
WebDriver: Controlling your Web Browser Erlang User Conference 2013 Hans Svensson, Quviq AB [email protected] First, a confession... I have a confession to make... I have built a web system! In PHP! ... and it was painfully mundane to test It is all forgotten and forgiven... It was back in 2003! First DEMO DEMO A bit of history Proving program Erlang correctness Reality – a constant issue PhD Testing is studentPhD necessary A bit of history Proving program Erlang correctness Reality – a constant issue PhD Testing is studentPhD necessary • We like to write our properties in QuickCheck • How can we control ‘a browser’ from Erlang? • Doing it all from scratch seems hard, unnecessary, stupid, ... Selenium “Selenium automates browsers. That's it. What you do with that power is entirely up to you. Primarily it is for automating web applications for testing purposes, but is certainly not limited to just that. Boring web-based administration tasks can (and should!) also be automated as well.” Selenium • Basically you can create and run scripts • Supported by a wide range of browsers and operating systems • Run tests in: Chrome, IE, Opera, Firefox, and partial support also for other browsers. • Runs on: Windows, OS X, Linux, Solaris, and others. • Script recording using Selenium IDE (Firefox plugin). • Language support for: C#, Java, Python, Ruby, and partial support for Perl and PHP. • Widely used to create Unit-tests and regression testing suites for web services. Selenium 2 - WebDriver • In version 2, Selenium introduced the WebDriver API • Via WebDriver it is possible to drive the browser natively • The browser can be local or remote – possible to use a grid test • It is a compact Object Oriented API • Supports Chrome, Firefox, HtmlUnit, Opera, IE, and IPhone and Android • Languages implementing driver: C#, Java, Python, and Ruby.