Declare a Variable As Two Types C
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First Class Overloading Via Insersection Type Parameters⋆
First Class Overloading via Insersection Type Parameters? Elton Cardoso2, Carlos Camar~ao1, and Lucilia Figueiredo2 1 Universidade Federal de Minas Gerais, [email protected] 2 Universidade Federal de Ouro Preto [email protected], [email protected] Abstract The Hindley-Milner type system imposes the restriction that function parameters must have monomorphic types. Lifting this restric- tion and providing system F “first class" polymorphism is clearly desir- able, but comes with the difficulty that inference of types for system F is undecidable. More practical type systems incorporating types of higher- rank have recently been proposed, that rely on system F but require type annotations for the definition of functions with polymorphic type parameters. However, these type annotations inevitably disallow some possible uses of higher-rank functions. To avoid this problem and to pro- mote code reuse, we explore using intersection types for specifying the types of function parameters that are used polymorphically inside the function body, allowing a flexible use of such functions, on applications to both polymorphic or overloaded arguments. 1 Introduction The Hindley-Milner type system [9] (HM) has been successfuly used as the basis for type systems of modern functional programming languages, such as Haskell [23] and ML [20]. This is due to its remarkable properties that a compiler can in- fer the principal type for any language expression, without any help from the programmer, and the type inference algorithm [5] is relatively simple. This is achieved, however, by imposing some restrictions, a major one being that func- tion parameters must have monomorphic types. For example, the following definition is not allowed in the HM type system: foo g = (g [True,False], g ['a','b','c']) Since parameter g is used with distinct types in the function's body (being applied to both a list of booleans and a list of characters), its type cannot be monomorphic, and this definition of foo cannot thus be typed in HM. -
Disjoint Polymorphism
Disjoint Polymorphism João Alpuim, Bruno C. d. S. Oliveira, and Zhiyuan Shi The University of Hong Kong {alpuim,bruno,zyshi}@cs.hku.hk Abstract. The combination of intersection types, a merge operator and parametric polymorphism enables important applications for program- ming. However, such combination makes it hard to achieve the desirable property of a coherent semantics: all valid reductions for the same expres- sion should have the same value. Recent work proposed disjoint inter- sections types as a means to ensure coherence in a simply typed setting. However, the addition of parametric polymorphism was not studied. This paper presents Fi: a calculus with disjoint intersection types, a vari- ant of parametric polymorphism and a merge operator. Fi is both type- safe and coherent. The key difficulty in adding polymorphism is that, when a type variable occurs in an intersection type, it is not statically known whether the instantiated type will be disjoint to other compo- nents of the intersection. To address this problem we propose disjoint polymorphism: a constrained form of parametric polymorphism, which allows disjointness constraints for type variables. With disjoint polymor- phism the calculus remains very flexible in terms of programs that can be written, while retaining coherence. 1 Introduction Intersection types [20,43] are a popular language feature for modern languages, such as Microsoft’s TypeScript [4], Redhat’s Ceylon [1], Facebook’s Flow [3] and Scala [37]. In those languages a typical use of intersection types, which has been known for a long time [19], is to model the subtyping aspects of OO-style multiple inheritance. -
Polymorphic Intersection Type Assignment for Rewrite Systems with Abstraction and -Rule Extended Abstract
Polymorphic Intersection Type Assignment for Rewrite Systems with Abstraction and -rule Extended Abstract Steffen van Bakel , Franco Barbanera , and Maribel Fernandez´ Department of Computing, Imperial College, 180 Queen’s Gate, London SW7 2BZ. [email protected] Dipartimento di Matematica, Universita` degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italia. [email protected] LIENS (CNRS URA 8548), Ecole Normale Superieure,´ 45, rue d’Ulm, 75005 Paris, France. [email protected] Abstract. We define two type assignment systems for first-order rewriting ex- tended with application, -abstraction, and -reduction (TRS ). The types used in these systems are a combination of ( -free) intersection and polymorphic types. The first system is the general one, for which we prove a subject reduction theorem and show that all typeable terms are strongly normalisable. The second is a decidable subsystem of the first, by restricting types to Rank 2. For this sys- tem we define, using an extended notion of unification, a notion of principal type, and show that type assignment is decidable. Introduction The combination of -calculus (LC) and term rewriting systems (TRS) has attracted attention not only from the area of programming language design, but also from the rapidly evolving field of theorem provers. It is well-known by now that type disciplines provide an environment in which rewrite rules and -reduction can be combined with- out loss of their useful properties. This is supported by a number of results for a broad range of type systems [11, 12, 20, 7, 8, 5]. In this paper we study the combination of LC and TRS as a basis for the design of a programming language. -
Truffle/C Interpreter
JOHANNES KEPLER UNIVERSITAT¨ LINZ JKU Faculty of Engineering and Natural Sciences Truffle/C Interpreter Master’s Thesis submitted in partial fulfillment of the requirements for the academic degree Diplom-Ingenieur in the Master’s Program Computer Science Submitted by Manuel Rigger, BSc. At the Institut f¨urSystemsoftware Advisor o.Univ.-Prof. Dipl.-Ing. Dr.Dr.h.c. Hanspeter M¨ossenb¨ock Co-advisor Dipl.-Ing. Lukas Stadler Dipl.-Ing. Dr. Thomas W¨urthinger Xiamen, April 2014 Contents I Contents 1 Introduction 3 1.1 Motivation . .3 1.2 Goals and Scope . .4 1.3 From C to Java . .4 1.4 Structure of the Thesis . .6 2 State of the Art 9 2.1 Graal . .9 2.2 Truffle . 10 2.2.1 Rewriting and Specialization . 10 2.2.2 Truffle DSL . 11 2.2.3 Control Flow . 12 2.2.4 Profiling and Inlining . 12 2.2.5 Partial Evaluation and Compilation . 12 2.3 Clang . 13 3 Architecture 14 3.1 From Clang to Java . 15 3.2 Node Construction . 16 3.3 Runtime . 16 4 The Truffle/C File 17 4.1 Truffle/C File Format Goals . 17 4.2 Truffle/C File Format 1 . 19 4.2.1 Constant Pool . 19 4.2.2 Function Table . 20 4.2.3 Functions and Attributes . 20 4.3 Truffle/C File Considerations and Comparison . 21 4.3.1 Java Class File and Truffle/C File . 21 4.3.2 ELF and Truffle/C File . 22 4.4 Clang Modification Truffle/C File . 23 Contents II 5 Truffle/C Data Types 25 5.1 Data Type Hierarchy: Boxing, Upcasts and Downcasts . -
Rank 2 Type Systems and Recursive De Nitions
Rank 2 typ e systems and recursive de nitions Technical Memorandum MIT/LCS/TM{531 Trevor Jim Lab oratory for Computer Science Massachusetts Institute of Technology August 1995; revised Novemb er 1995 Abstract We demonstrate an equivalence b etween the rank 2 fragments of the p olymorphic lamb da calculus System F and the intersection typ e dis- cipline: exactly the same terms are typable in each system. An imme- diate consequence is that typability in the rank 2 intersection system is DEXPTIME-complete. Weintro duce a rank 2 system combining intersections and p olymorphism, and prove that it typ es exactly the same terms as the other rank 2 systems. The combined system sug- gests a new rule for typing recursive de nitions. The result is a rank 2 typ e system with decidable typ e inference that can typ e some inter- esting examples of p olymorphic recursion. Finally,we discuss some applications of the typ e system in data representation optimizations suchasunboxing and overloading. Keywords: Rank 2 typ es, intersection typ es, p olymorphic recursion, boxing/unboxing, overloading. 1 Intro duction In the past decade, Milner's typ e inference algorithm for ML has b ecome phenomenally successful. As the basis of p opular programming languages like Standard ML and Haskell, Milner's algorithm is the preferred metho d of typ e inference among language implementors. And in the theoretical 545 Technology Square, Cambridge, MA 02139, [email protected]. Supp orted by NSF grants CCR{9113196 and CCR{9417382, and ONR Contract N00014{92{J{1310. -
A Facet-Oriented Modelling
A Facet-oriented modelling JUAN DE LARA, Universidad Autónoma de Madrid (Spain) ESTHER GUERRA, Universidad Autónoma de Madrid (Spain) JÖRG KIENZLE, McGill University (Canada) Models are the central assets in model-driven engineering (MDE), as they are actively used in all phases of software development. Models are built using metamodel-based languages, and so, objects in models are typed by a metamodel class. This typing is static, established at creation time, and cannot be changed later. Therefore, objects in MDE are closed and fixed with respect to the class they conform to, the fields they have, and the wellformedness constraints they must comply with. This hampers many MDE activities, like the reuse of model-related artefacts such as transformations, the opportunistic or dynamic combination of metamodels, or the dynamic reconfiguration of models. To alleviate this rigidity, we propose making model objects open so that they can acquire or drop so-called facets. These contribute with a type, fields and constraints to the objects holding them. Facets are defined by regular metamodels, hence being a lightweight extension of standard metamodelling. Facet metamodels may declare usage interfaces, as well as laws that govern the assignment of facets to objects (or classes). This paper describes our proposal, reporting on a theory, analysis techniques and an implementation. The benefits of the approach are validated on the basis of five case studies dealing with annotation models, transformation reuse, multi-view modelling, multi-level modelling and language product lines. Categories and Subject Descriptors: [Software and its engineering]: Model-driven software engineering; Domain specific languages; Design languages; Software design engineering Additional Key Words and Phrases: Metamodelling, Flexible Modelling, Role-Based Modelling, METADEPTH ACM Reference Format: Juan de Lara, Esther Guerra, Jörg Kienzle. -
Approximations, Fibrations and Intersection Type Systems
Approximations, Fibrations and Intersection Type Systems Damiano Mazza*, Luc Pellissier† & Pierre Vial‡ June 16, 2017 Introduction The discovery of linear logic [7] has introduced the notionof linearity in computer science and proof theory. A remarkable fact of linear logic lies in its approximation theorem, stating that an arbitrary proof (not necessarily linear, that is, using its premisses any number of times) can be approximated arbitrarily well by a linear proof. This notion of approximation has then been explored in different directions [4, 10,14]. Approximations are known to be related to relational models, which in turn are related to intersection types [2, 12, 13]. In this work, we investigate approximations in the “type-systems as functors” perspective pioneered by [11]. After recasting fundamental properties of type systems, such as subject reduction and expansion in this framework, we give an intersection type system framework for linear logic, whose derivations are simply-typed approximations. Any calculus that translates meaningfully to linear logic is then endowed by a intersection type system, computed by pulling back one of these intersection type systems for linear logic, and which inherit its properties. All standard intersection type systems (idempotent, such as in [6, 1] or not, such as in [3]) for call-by-name and call-by-value λ-calculus, characterizing weak, strong, and head normalization, fit in this picture, thus justifying the equation: Simply-typed approximations = intersection types derivations. We moreover obtain new type systems, by considering other translations and reductions. 1 What is a type system? The starting point of this research is the work of [11]. -
DATA and C a Sample Program
03 0672326965 CH03 10/19/04 1:53 PM Page 49 CHAPTER 3 DATA AND C You will learn about the following in this chapter: • Keywords: • The distinctions between integer int, short, long, unsigned, char, types and floating-point types float, double, _Bool, _Complex, • Writing constants and declaring _Imaginary variables of those types • Operator: • How to use the printf() and sizeof scanf() functions to read and • Function: write values of different types scanf() • The basic data types that C uses rograms work with data. You feed numbers, letters, and words to the computer, and you expect it to do something with the data. For example, you might want the com- puter to calculate an interest payment or display a sorted list of vintners. In this chap- ter,P you do more than just read about data; you practice manipulating data, which is much more fun. This chapter explores the two great families of data types: integer and floating point. C offers several varieties of these types. This chapter tells you what the types are, how to declare them, and how and when to use them. Also, you discover the differences between constants and variables, and as a bonus, your first interactive program is coming up shortly. A Sample Program Once again, you begin with a sample program. As before, you’ll find some unfamiliar wrinkles that we’ll soon iron out for you. The program’s general intent should be clear, so try compiling and running the source code shown in Listing 3.1. To save time, you can omit typing the com- ments. -
Deconfined Intersection Types in Java
Deconfined Intersection Types in Java Dedicated to Maurizio Gabbrielli on the Occasion of His 60th Birthday Mariangiola Dezani-Ciancaglini Computer Science Department, University of Torino, Italy [email protected] Paola Giannini Department of Advanced Science and Technology, University of Eastern Piedmont, Alessandria, Italy [email protected] Betti Venneri Department of Statistics, Computer Science, Applications, University of Firenze, Italy betti.venneri@unifi.it Abstract We show how Java intersection types can be freed from their confinement in type casts, in such a way that the proposed Java extension is safe and fully compatible with the current language. To this aim, we exploit two calculi which formalise the simple Java core and the extended language, respectively. Namely, the second calculus extends the first one by allowing an intersection type to be used anywhere in place of a nominal type. We define a translation algorithm, compiling programs of the extended language into programs of the former calculus. The key point is the interaction between λ-expressions and intersection types, that adds safe expressiveness while being the crucial matter in the translation. We prove that the translation preserves typing and semantics. Thus, typed programs in the proposed extension are translated to typed Java programs. Moreover, semantics of translated programs coincides with the one of the source programs. 2012 ACM Subject Classification Theory of computation → Type structures; Theory of computation → Semantics and reasoning Keywords and phrases Intersection Types, Featherweight Java, Lambda Expressions Digital Object Identifier 10.4230/OASIcs.Gabbrielli.2020.3 Acknowledgements We are very pleased to dedicate this work to Maurizio, whose notable contri- butions to the theory of programming languages are well known and appreciated by the scientific community. -
C Programming Tutorial
C Programming Tutorial C PROGRAMMING TUTORIAL Simply Easy Learning by tutorialspoint.com tutorialspoint.com i COPYRIGHT & DISCLAIMER NOTICE All the content and graphics on this tutorial are the property of tutorialspoint.com. Any content from tutorialspoint.com or this tutorial may not be redistributed or reproduced in any way, shape, or form without the written permission of tutorialspoint.com. Failure to do so is a violation of copyright laws. This tutorial may contain inaccuracies or errors and tutorialspoint provides no guarantee regarding the accuracy of the site or its contents including this tutorial. If you discover that the tutorialspoint.com site or this tutorial content contains some errors, please contact us at [email protected] ii Table of Contents C Language Overview .............................................................. 1 Facts about C ............................................................................................... 1 Why to use C ? ............................................................................................. 2 C Programs .................................................................................................. 2 C Environment Setup ............................................................... 3 Text Editor ................................................................................................... 3 The C Compiler ............................................................................................ 3 Installation on Unix/Linux ............................................................................ -
Declared Type Vs Object Type
Declared Type Vs Object Type andEnforceable patronising and Silvio keeperless fimbriate Sax her laths evangelizations so essentially apotheosise that Jameson matrimonially rebroadcasts or hischants skatings. filthily, Flaggy is Lyle irrigationCytherean? treble Homomorphic shudderingly. Judas delaminating apishly and contingently, she demagnetized her Interface type attributes to type declared vs object They are building blocks for declaring types. Multiple constructors can be defined in a class. This use of patterns encourages consistency and reduces complexity for servers and clients. Object classes facilitate rapid development because they lessen the semantic gap between the code and the users. None along with checking that it has the right type. This answer has been undeleted. Useful in special relativity. Generic methods are methods that introduce their own type parameters. The package is not complete and contains no explicit imports. In short, link to only your code and be specific about what you want feedback on. Embedded reports whether the variable is an embedded field. Type for the results of type inference. Functions belong to the object type. Examples of instances of this type. Press J to jump to the feed. These are usually field types and names that will be associated with state variables at program run time; these state variables either belong to the class or specific instances of the class. The rational is similar to the justification for allowing multiple superclasses, that the Internet is so dynamic and flexible that dynamic changes to the hierarchy are required to manage this volatility. What is the output of the following program? Error: You must enter a valid Integer without commas. -
Typing the Numeric Tower
Typing the Numeric Tower Vincent St-Amour1, Sam Tobin-Hochstadt1, Matthew Flatt2, and Matthias Felleisen1 1 Northeastern University {stamourv,samth,matthias}@ccs.neu.edu 2 University of Utah [email protected] Abstract. In the past, the creators of numerical programs had to choose between simple expression of mathematical formulas and static type checking. While the Lisp family and its dynamically typed relatives support the straightforward ex- pression via a rich numeric tower, existing statically typed languages force pro- grammers to pollute textbook formulas with explicit coercions or unwieldy nota- tion. In this paper, we demonstrate how the type system of Typed Racket accom- modates both a textbook programming style and expressive static checking. The type system provides a hierarchy of numeric types that can be freely mixed as well as precise specifications of sign, representation, and range information—all while supporting generic operations. In addition, the type system provides infor- mation to the compiler so that it can perform standard numeric optimizations. 1 Designing the Numeric Tower From the classic two-line factorial program to financial applications to scientific com- putation to graphics software, programs rely on numbers and numeric computations. Because of this spectrum of numeric applications, programmers wish to use a wide vari- ety of numbers: the inductively defined natural numbers, fixed-width integers, floating- point numbers, complex numbers, etc. Supporting this variety demands careful attention to the design of programming languages that manipulate numbers. Most languages have taken one of two approaches to numbers. Many untyped lan- guages, drawing on the tradition of Lisp and Smalltalk, provide a hierarchy of numbers whose various levels can be freely used together, known as the numeric tower.