Refinement Kinds
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Typescript Language Specification
TypeScript Language Specification Version 1.8 January, 2016 Microsoft is making this Specification available under the Open Web Foundation Final Specification Agreement Version 1.0 ("OWF 1.0") as of October 1, 2012. The OWF 1.0 is available at http://www.openwebfoundation.org/legal/the-owf-1-0-agreements/owfa-1-0. TypeScript is a trademark of Microsoft Corporation. Table of Contents 1 Introduction ................................................................................................................................................................................... 1 1.1 Ambient Declarations ..................................................................................................................................................... 3 1.2 Function Types .................................................................................................................................................................. 3 1.3 Object Types ...................................................................................................................................................................... 4 1.4 Structural Subtyping ....................................................................................................................................................... 6 1.5 Contextual Typing ............................................................................................................................................................ 7 1.6 Classes ................................................................................................................................................................................. -
Gradual Liquid Type Inference
Gradual Liquid Type Inference NIKI VAZOU, IMDEA, Spain ÉRIC TANTER, University of Chile, Chile DAVID VAN HORN, University of Maryland, USA Refinement types allow for lightweight program verification by enriching types with logical predicates. Liquid typing provides a decidable refinement inference mechanism that is convenient but subject to two major issues: (1) inference is global and requires top-level annotations, making it unsuitable for inference of modular code components and prohibiting its applicability to library code, and (2) inference failure results in obscure error messages. These difficulties seriously hamper the migration of existing code to use refinements. This paper shows that gradual liquid type inferenceśa novel combination of liquid inference and gradual refinement typesśaddresses both issues. Gradual refinement types, which support imprecise predicates that are optimistically interpreted, can be used in argument positions to constrain liquid inference so that the global inference process effectively infers modular specifications usable for library components. Dually, when gradual refinements appear as the result of inference, they signal an inconsistency in the use of static refinements. Because liquid refinements are drawn from a finite set of predicates, in gradual liquid type inference wecan enumerate the safe concretizations of each imprecise refinement, i.e., the static refinements that justify why a program is gradually well-typed. This enumeration is useful for static liquid type error explanation, since the safe concretizations exhibit all the potential inconsistencies that lead to static type errors. We develop the theory of gradual liquid type inference and explore its pragmatics in the setting of Liquid 132 Haskell. To demonstrate the utility of our approach, we develop an interactive tool, GuiLT, for gradual liquid type inference in Liquid Haskell that both infers modular types and explores safe concretizations of gradual refinements. -
A System of Constructor Classes: Overloading and Implicit Higher-Order Polymorphism
A system of constructor classes: overloading and implicit higher-order polymorphism Mark P. Jones Yale University, Department of Computer Science, P.O. Box 2158 Yale Station, New Haven, CT 06520-2158. [email protected] Abstract range of other data types, as illustrated by the following examples: This paper describes a flexible type system which combines overloading and higher-order polymorphism in an implicitly data Tree a = Leaf a | Tree a :ˆ: Tree a typed language using a system of constructor classes – a mapTree :: (a → b) → (Tree a → Tree b) natural generalization of type classes in Haskell. mapTree f (Leaf x) = Leaf (f x) We present a wide range of examples which demonstrate mapTree f (l :ˆ: r) = mapTree f l :ˆ: mapTree f r the usefulness of such a system. In particular, we show how data Opt a = Just a | Nothing constructor classes can be used to support the use of monads mapOpt :: (a → b) → (Opt a → Opt b) in a functional language. mapOpt f (Just x) = Just (f x) The underlying type system permits higher-order polymor- mapOpt f Nothing = Nothing phism but retains many of many of the attractive features that have made the use of Hindley/Milner type systems so Each of these functions has a similar type to that of the popular. In particular, there is an effective algorithm which original map and also satisfies the functor laws given above. can be used to calculate principal types without the need for With this in mind, it seems a shame that we have to use explicit type or kind annotations. -
Irrelevance, Heterogeneous Equality, and Call-By-Value Dependent Type Systems
Irrelevance, Heterogeneous Equality, and Call-by-value Dependent Type Systems Vilhelm Sjoberg¨ Chris Casinghino Ki Yung Ahn University of Pennsylvania University of Pennsylvania Portland State University [email protected] [email protected] [email protected] Nathan Collins Harley D. Eades III Peng Fu Portland State University University of Iowa University of Iowa [email protected] [email protected] [email protected] Garrin Kimmell Tim Sheard Aaron Stump University of Iowa Portland State University University of Iowa [email protected] [email protected] [email protected] Stephanie Weirich University of Pennsylvania [email protected] We present a full-spectrum dependently typed core language which includes both nontermination and computational irrelevance (a.k.a. erasure), a combination which has not been studied before. The two features interact: to protect type safety we must be careful to only erase terminating expressions. Our language design is strongly influenced by the choice of CBV evaluation, and by our novel treatment of propositional equality which has a heterogeneous, completely erased elimination form. 1 Introduction The Trellys project is a collaborative effort to design a new dependently typed programming language. Our goal is to bridge the gap between ordinary functional programming and program verification with dependent types. Programmers should be able to port their existing functional programs to Trellys with minor modifications, and then gradually add more expressive types as appropriate. This goal has implications for our design. First, and most importantly, we must consider nonter- mination and other effects. Unlike Coq and Agda, functional programming languages like OCaml and Haskell allow general recursive functions, so to accept functional programs ‘as-is’ we must be able to turn off the termination checker. -
Python Programming
Python Programming Wikibooks.org June 22, 2012 On the 28th of April 2012 the contents of the English as well as German Wikibooks and Wikipedia projects were licensed under Creative Commons Attribution-ShareAlike 3.0 Unported license. An URI to this license is given in the list of figures on page 149. If this document is a derived work from the contents of one of these projects and the content was still licensed by the project under this license at the time of derivation this document has to be licensed under the same, a similar or a compatible license, as stated in section 4b of the license. The list of contributors is included in chapter Contributors on page 143. The licenses GPL, LGPL and GFDL are included in chapter Licenses on page 153, since this book and/or parts of it may or may not be licensed under one or more of these licenses, and thus require inclusion of these licenses. The licenses of the figures are given in the list of figures on page 149. This PDF was generated by the LATEX typesetting software. The LATEX source code is included as an attachment (source.7z.txt) in this PDF file. To extract the source from the PDF file, we recommend the use of http://www.pdflabs.com/tools/pdftk-the-pdf-toolkit/ utility or clicking the paper clip attachment symbol on the lower left of your PDF Viewer, selecting Save Attachment. After extracting it from the PDF file you have to rename it to source.7z. To uncompress the resulting archive we recommend the use of http://www.7-zip.org/. -
Relatively Complete Refinement Type System for Verification of Higher-Order Non-Deterministic Programs
Relatively Complete Refinement Type System for Verification of Higher-Order Non-deterministic Programs HIROSHI UNNO, University of Tsukuba, Japan YUKI SATAKE, University of Tsukuba, Japan TACHIO TERAUCHI, Waseda University, Japan This paper considers verification of non-deterministic higher-order functional programs. Our contribution is a novel type system in which the types are used to express and verify (conditional) safety, termination, non-safety, and non-termination properties in the presence of 8-9 branching behavior due to non-determinism. 88 For instance, the judgement ` e : u:int ϕ(u) says that every evaluation of e either diverges or reduces 98 to some integer u satisfying ϕ(u), whereas ` e : u:int ψ (u) says that there exists an evaluation of e that either diverges or reduces to some integer u satisfying ψ (u). Note that the former is a safety property whereas the latter is a counterexample to a (conditional) termination property. Following the recent work on type-based verification methods for deterministic higher-order functional programs, we formalize theideaon the foundation of dependent refinement types, thereby allowing the type system to express and verify rich properties involving program values, branching behaviors, and the combination thereof. Our type system is able to seamlessly combine deductions of both universal and existential facts within a unified framework, paving the way for an exciting opportunity for new type-based verification methods that combine both universal and existential reasoning. For example, our system can prove the existence of a path violating some safety property from a proof of termination that uses a well-foundedness termination 12 argument. -
Refinement Types for ML
Refinement Types for ML Tim Freeman Frank Pfenning [email protected] [email protected] School of Computer Science School of Computer Science Carnegie Mellon University Carnegie Mellon University Pittsburgh, Pennsylvania 15213-3890 Pittsburgh, Pennsylvania 15213-3890 Abstract tended to the full Standard ML language. To see the opportunity to improve ML’s type system, We describe a refinement of ML’s type system allow- consider the following function which returns the last ing the specification of recursively defined subtypes of cons cell in a list: user-defined datatypes. The resulting system of refine- ment types preserves desirable properties of ML such as datatype α list = nil | cons of α * α list decidability of type inference, while at the same time fun lastcons (last as cons(hd,nil)) = last allowing more errors to be detected at compile-time. | lastcons (cons(hd,tl)) = lastcons tl The type system combines abstract interpretation with We know that this function will be undefined when ideas from the intersection type discipline, but remains called on an empty list, so we would like to obtain a closely tied to ML in that refinement types are given type error at compile-time when lastcons is called with only to programs which are already well-typed in ML. an argument of nil. Using refinement types this can be achieved, thus preventing runtime errors which could be 1 Introduction caught at compile-time. Similarly, we would like to be able to write code such as Standard ML [MTH90] is a practical programming lan- case lastcons y of guage with higher-order functions, polymorphic types, cons(x,nil) => print x and a well-developed module system. -
UC San Diego UC San Diego Previously Published Works
UC San Diego UC San Diego Previously Published Works Title Liquid information flow control Permalink https://escholarship.org/uc/item/0t20j69d Journal Proceedings of the ACM on Programming Languages, 4(ICFP) ISSN 2475-1421 Authors Polikarpova, Nadia Stefan, Deian Yang, Jean et al. Publication Date 2020-08-02 DOI 10.1145/3408987 Peer reviewed eScholarship.org Powered by the California Digital Library University of California Type-Driven Repair for Information Flow Security Nadia Polikarpova Jean Yang Shachar Itzhaky Massachusetts Institute of Technology Carnegie Mellon University Armando Solar-Lezama [email protected] [email protected] Massachusetts Institute of Technology shachari,[email protected] Abstract We present LIFTY, a language that uses type-driven program repair to enforce information flow policies. In LIFTY, the programmer Policies specifies a policy by annotating the source of sensitive data with a refinement type, and the system automatically inserts access checks Program Program Verify necessary to enforce this policy across the code. This is a significant with Repair with Program improvement over current practice, where programmers manually holes checks implement access checks, and any missing check can cause an information leak. To support this programming model, we have developed (1) an encoding of information flow security in terms of decidable refine- ment types that enables fully automatic verification and (2) a pro- gram repair algorithm that localizes unsafe accesses to sensitive data and replaces them with provably secure alternatives. We for- ✓ ✗ malize the encoding and prove its noninterference guarantee. Our experience using LIFTY to implement a conference management Specification Core program Program hole system shows that it decreases policy burden and is able to effi- ciently synthesize all necessary access checks, including those re- Policy check Tool component quired to prevent a set of reported real-world information leaks. -
Umltmprofile for Schedulability, Performance, and Time Specification
UMLTM Profile for Schedulability, Performance, and Time Specification September 2003 Version 1.0 formal/03-09-01 An Adopted Specification of the Object Management Group, Inc. Copyright © 2001, ARTiSAN Software Tools, Inc. Copyright © 2001, I-Logix, Ind. Copyright © 2003, Object Management Group Copyright © 2001, Rational Software Corp. Copyright © 2001, Telelogic AB Copyright © 2001, TimeSys Corporation Copyright © 2001, Tri-Pacific Software USE OF SPECIFICATION - TERMS, CONDITIONS & NOTICES The material in this document details an Object Management Group specification in accordance with the terms, conditions and notices set forth below. This document does not represent a commitment to implement any portion of this specification in any company's products. The information contained in this document is subject to change without notice. LICENSES The companies listed above have granted to the Object Management Group, Inc. (OMG) a nonexclusive, royalty-free, paid up, worldwide license to copy and distribute this document and to modify this document and distribute copies of the modified version. Each of the copyright holders listed above has agreed that no person shall be deemed to have infringed the copyright in the included material of any such copyright holder by reason of having used the specification set forth herein or having conformed any computer software to the specification. Subject to all of the terms and conditions below, the owners of the copyright in this specification hereby grant you a fully- paid up, non-exclusive, nontransferable, -
Lecture Slides
Outline Meta-Classes Guy Wiener Introduction AOP Classes Generation 1 Introduction Meta-Classes in Python Logging 2 Meta-Classes in Python Delegation Meta-Classes vs. Traditional OOP 3 Meta-Classes vs. Traditional OOP Outline Meta-Classes Guy Wiener Introduction AOP Classes Generation 1 Introduction Meta-Classes in Python Logging 2 Meta-Classes in Python Delegation Meta-Classes vs. Traditional OOP 3 Meta-Classes vs. Traditional OOP What is Meta-Programming? Meta-Classes Definition Guy Wiener Meta-Program A program that: Introduction AOP Classes One of its inputs is a program Generation (possibly itself) Meta-Classes in Python Its output is a program Logging Delegation Meta-Classes vs. Traditional OOP Meta-Programs Nowadays Meta-Classes Guy Wiener Introduction AOP Classes Generation Compilers Meta-Classes in Python Code Generators Logging Delegation Model-Driven Development Meta-Classes vs. Traditional Templates OOP Syntactic macros (Lisp-like) Meta-Classes The Problem With Static Programming Meta-Classes Guy Wiener Introduction AOP Classes Generation Meta-Classes How to share features between classes and class hierarchies? in Python Logging Share static attributes Delegation Meta-Classes Force classes to adhere to the same protocol vs. Traditional OOP Share code between similar methods Meta-Classes Meta-Classes Guy Wiener Introduction AOP Classes Definition Generation Meta-Classes in Python Meta-Class A class that creates classes Logging Delegation Objects that are instances of the same class Meta-Classes share the same behavior vs. Traditional OOP Classes that are instances of the same meta-class share the same behavior Meta-Classes Meta-Classes Guy Wiener Introduction AOP Classes Definition Generation Meta-Classes in Python Meta-Class A class that creates classes Logging Delegation Objects that are instances of the same class Meta-Classes share the same behavior vs. -
Why Dependent Types Matter
Why Dependent Types Matter Thorsten Altenkirch Conor McBride James McKinna The University of Nottingham The University of St Andrews {txa,ctm}@cs.nott.ac.uk [email protected] Abstract We exhibit the rationale behind the design of Epigram, a dependently typed programming language and interactive program development system, using refinements of a well known program—merge sort—as a running example. We discuss its relationship with other proposals to introduce aspects of dependent types into functional programming languages and sketch some topics for further work in this area. 1. Introduction Types matter. That’s what they’re for—to classify data with respect to criteria which matter: how they should be stored in memory, whether they can be safely passed as inputs to a given operation, even who is allowed to see them. Dependent types are types expressed in terms of data, explicitly relating their inhabitants to that data. As such, they enable you to express more of what matters about data. While conventional type systems allow us to validate our programs with respect to a fixed set of criteria, dependent types are much more flexible, they realize a continuum of precision from the basic assertions we are used to expect from types up to a complete specification of the program’s behaviour. It is the programmer’s choice to what degree he wants to exploit the expressiveness of such a powerful type discipline. While the price for formally certified software may be high, it is good to know that we can pay it in installments and that we are free to decide how far we want to go. -
Refinement Session Types
MENG INDIVIDUAL PROJECT IMPERIAL COLLEGE LONDON DEPARTMENT OF COMPUTING Refinement Session Types Supervisor: Prof. Nobuko Yoshida Author: Fangyi Zhou Second Marker: Dr. Iain Phillips 16th June 2019 Abstract We present an end-to-end framework to statically verify multiparty concurrent and distributed protocols with refinements, where refinements are in the form of logical constraints. We combine the theory of multiparty session types and refinement types and provide a type system approach for lightweight static verification. We formalise a variant of the l-calculus, extended with refinement types, and prove their type safety properties. Based on the formalisation, we implement a refinement type system extension for the F# language. We design a functional approach to generate APIs with refinement types from a multiparty protocol in F#. We generate handler-styled APIs, which statically guarantee the linear usage of channels. With our refinement type system extension, we can check whether the implementation is correct with respect to the refinements. We evaluate the expressiveness of our system using three case studies of refined protocols. Acknowledgements I would like to thank Prof. Nobuko Yoshida, Dr. Francisco Ferreira, Dr. Rumyana Neykova and Dr. Raymond Hu for their advice, support and help during the project. Without them I would not be able to complete this project. I would like to thank Prof. Paul Kelly, Prof. Philippa Gardner and Prof. Sophia Drossopoulou, whose courses enlightened me to explore the area of programming languages. Without them I would not be motivated to discover more in this area. I would like to thank Prof. Paul Kelly again, this time for being my personal tutor.