Generic Programming with Dependent Types
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A Polymorphic Type System for Extensible Records and Variants
A Polymorphic Typ e System for Extensible Records and Variants Benedict R. Gaster and Mark P. Jones Technical rep ort NOTTCS-TR-96-3, November 1996 Department of Computer Science, University of Nottingham, University Park, Nottingham NG7 2RD, England. fbrg,[email protected] Abstract b oard, and another indicating a mouse click at a par- ticular p oint on the screen: Records and variants provide exible ways to construct Event = Char + Point : datatyp es, but the restrictions imp osed by practical typ e systems can prevent them from b eing used in ex- These de nitions are adequate, but they are not par- ible ways. These limitations are often the result of con- ticularly easy to work with in practice. For example, it cerns ab out eciency or typ e inference, or of the di- is easy to confuse datatyp e comp onents when they are culty in providing accurate typ es for key op erations. accessed by their p osition within a pro duct or sum, and This pap er describ es a new typ e system that reme- programs written in this way can b e hard to maintain. dies these problems: it supp orts extensible records and To avoid these problems, many programming lan- variants, with a full complement of p olymorphic op era- guages allow the comp onents of pro ducts, and the al- tions on each; and it o ers an e ective type inference al- ternatives of sums, to b e identi ed using names drawn gorithm and a simple compilation metho d. -
Multi-Level Constraints
Multi-Level Constraints Tony Clark1 and Ulrich Frank2 1 Aston University, UK, [email protected] 2 University of Duisburg-Essen, DE, [email protected] Abstract. Meta-modelling and domain-specific modelling languages are supported by multi-level modelling which liberates model-based engi- neering from the traditional two-level type-instance language architec- ture. Proponents of this approach claim that multi-level modelling in- creases the quality of the resulting systems by introducing a second ab- straction dimension and thereby allowing both intra-level abstraction via sub-typing and inter-level abstraction via meta-types. Modelling ap- proaches include constraint languages that are used to express model semantics. Traditional languages, such as OCL, support intra-level con- straints, but not inter-level constraints. This paper motivates the need for multi-level constraints, shows how to implement such a language in a reflexive language architecture and applies multi-level constraints to an example multi-level model. 1 Introduction Conceptual models aim to bridge the gap between natural languages that are required to design and use a system and implementation languages. To this end, general-purpose modelling languages (GPML) like the UML consist of concepts that represent semantic primitives such as class, attribute, etc., that, on the one hand correspond to concepts of foundational ontologies, e.g., [4], and on the other hand can be nicely mapped to corresponding elements of object-oriented programming languages. Since GPML can be used to model a wide range of systems, they promise at- tractive economies of scale. At the same time, their use suffers from the fact that they offer generic concepts only. -
Union Types for Semistructured Data
Edinburgh Research Explorer Union Types for Semistructured Data Citation for published version: Buneman, P & Pierce, B 1999, Union Types for Semistructured Data. in Union Types for Semistructured Data: 7th International Workshop on Database Programming Languages, DBPL’99 Kinloch Rannoch, UK, September 1–3,1999 Revised Papers. Lecture Notes in Computer Science, vol. 1949, Springer-Verlag GmbH, pp. 184-207. https://doi.org/10.1007/3-540-44543-9_12 Digital Object Identifier (DOI): 10.1007/3-540-44543-9_12 Link: Link to publication record in Edinburgh Research Explorer Document Version: Peer reviewed version Published In: Union Types for Semistructured Data General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 27. Sep. 2021 Union Typ es for Semistructured Data Peter Buneman Benjamin Pierce University of Pennsylvania Dept of Computer Information Science South rd Street Philadelphia PA USA fpeterbcpiercegcisupenn edu Technical -
Djangoshop Release 0.11.2
djangoSHOP Release 0.11.2 Oct 27, 2017 Contents 1 Software Architecture 1 2 Unique Features of django-SHOP5 3 Upgrading 7 4 Tutorial 9 5 Reference 33 6 How To’s 125 7 Development and Community 131 8 To be written 149 9 License 155 Python Module Index 157 i ii CHAPTER 1 Software Architecture The django-SHOP framework is, as its name implies, a framework and not a software which runs out of the box. Instead, an e-commerce site built upon django-SHOP, always consists of this framework, a bunch of other Django apps and the merchant’s own implementation. While this may seem more complicate than a ready-to-use solution, it gives the programmer enormous advantages during the implementation: Not everything can be “explained” to a software system using graphical user interfaces. After reaching a certain point of complexity, it normally is easier to pour those requirements into executable code, rather than to expect yet another set of configuration buttons. When evaluating django-SHOP with other e-commerce solutions, I therefore suggest to do the following litmus test: Consider a product which shall be sold world-wide. Depending on the country’s origin of the request, use the native language and the local currency. Due to export restrictions, some products can not be sold everywhere. Moreover, in some countries the value added tax is part of the product’s price, and must be stated separately on the invoice, while in other countries, products are advertised using net prices, and tax is added later on the invoice. -
Presentation on Ocaml Internals
OCaml Internals Implementation of an ML descendant Theophile Ranquet Ecole Pour l’Informatique et les Techniques Avancées SRS 2014 [email protected] November 14, 2013 2 of 113 Table of Contents Variants and subtyping System F Variants Type oddities worth noting Polymorphic variants Cyclic types Subtyping Weak types Implementation details α ! β Compilers Functional programming Values Why functional programming ? Allocation and garbage Combinatory logic : SKI collection The Curry-Howard Compiling correspondence Type inference OCaml and recursion 3 of 113 Variants A tagged union (also called variant, disjoint union, sum type, or algebraic data type) holds a value which may be one of several types, but only one at a time. This is very similar to the logical disjunction, in intuitionistic logic (by the Curry-Howard correspondance). 4 of 113 Variants are very convenient to represent data structures, and implement algorithms on these : 1 d a t a t y p e tree= Leaf 2 | Node of(int ∗ t r e e ∗ t r e e) 3 4 Node(5, Node(1,Leaf,Leaf), Node(3, Leaf, Node(4, Leaf, Leaf))) 5 1 3 4 1 fun countNodes(Leaf)=0 2 | countNodes(Node(int,left,right)) = 3 1 + countNodes(left)+ countNodes(right) 5 of 113 1 t y p e basic_color= 2 | Black| Red| Green| Yellow 3 | Blue| Magenta| Cyan| White 4 t y p e weight= Regular| Bold 5 t y p e color= 6 | Basic of basic_color ∗ w e i g h t 7 | RGB of int ∗ i n t ∗ i n t 8 | Gray of int 9 1 l e t color_to_int= function 2 | Basic(basic_color,weight) −> 3 l e t base= match weight with Bold −> 8 | Regular −> 0 in 4 base+ basic_color_to_int basic_color 5 | RGB(r,g,b) −> 16 +b+g ∗ 6 +r ∗ 36 6 | Grayi −> 232 +i 7 6 of 113 The limit of variants Say we want to handle a color representation with an alpha channel, but just for color_to_int (this implies we do not want to redefine our color type, this would be a hassle elsewhere). -
Generic Programming
Generic Programming July 21, 1998 A Dagstuhl Seminar on the topic of Generic Programming was held April 27– May 1, 1998, with forty seven participants from ten countries. During the meeting there were thirty seven lectures, a panel session, and several problem sessions. The outcomes of the meeting include • A collection of abstracts of the lectures, made publicly available via this booklet and a web site at http://www-ca.informatik.uni-tuebingen.de/dagstuhl/gpdag.html. • Plans for a proceedings volume of papers submitted after the seminar that present (possibly extended) discussions of the topics covered in the lectures, problem sessions, and the panel session. • A list of generic programming projects and open problems, which will be maintained publicly on the World Wide Web at http://www-ca.informatik.uni-tuebingen.de/people/musser/gp/pop/index.html http://www.cs.rpi.edu/˜musser/gp/pop/index.html. 1 Contents 1 Motivation 3 2 Standards Panel 4 3 Lectures 4 3.1 Foundations and Methodology Comparisons ........ 4 Fundamentals of Generic Programming.................. 4 Jim Dehnert and Alex Stepanov Automatic Program Specialization by Partial Evaluation........ 4 Robert Gl¨uck Evaluating Generic Programming in Practice............... 6 Mehdi Jazayeri Polytypic Programming........................... 6 Johan Jeuring Recasting Algorithms As Objects: AnAlternativetoIterators . 7 Murali Sitaraman Using Genericity to Improve OO Designs................. 8 Karsten Weihe Inheritance, Genericity, and Class Hierarchies.............. 8 Wolf Zimmermann 3.2 Programming Methodology ................... 9 Hierarchical Iterators and Algorithms................... 9 Matt Austern Generic Programming in C++: Matrix Case Study........... 9 Krzysztof Czarnecki Generative Programming: Beyond Generic Programming........ 10 Ulrich Eisenecker Generic Programming Using Adaptive and Aspect-Oriented Programming . -
Practical Subtyping for System F with Sized (Co-)Induction Rodolphe Lepigre, Christophe Raffalli
Practical Subtyping for System F with Sized (Co-)Induction Rodolphe Lepigre, Christophe Raffalli To cite this version: Rodolphe Lepigre, Christophe Raffalli. Practical Subtyping for System F with Sized (Co-)Induction. 2017. hal-01289760v3 HAL Id: hal-01289760 https://hal.archives-ouvertes.fr/hal-01289760v3 Preprint submitted on 10 Jul 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives| 4.0 International License PRACTICAL SUBTYPING FOR SYSTEM F WITH SIZED (CO-)INDUCTION RODOLPHE LEPIGRE AND CHRISTOPHE RAFFALLI LAMA, UMR 5127 CNRS - Universit´eSavoie Mont Blanc e-mail address: frodolphe.lepigre j christophe.raff[email protected] Abstract. We present a rich type system with subtyping for an extension of System F. Our type constructors include sum and product types, universal and existential quanti- fiers, inductive and coinductive types. The latter two may carry annotations allowing the encoding of size invariants that are used to ensure the termination of recursive programs. For example, the termination of quicksort can be derived by showing that partitioning a list does not increase its size. The system deals with complex programs involving mixed induction and coinduction, or even mixed polymorphism and (co-)induction (as for Scott- encoded data types). -
Java for Scientific Computing, Pros and Cons
Journal of Universal Computer Science, vol. 4, no. 1 (1998), 11-15 submitted: 25/9/97, accepted: 1/11/97, appeared: 28/1/98 Springer Pub. Co. Java for Scienti c Computing, Pros and Cons Jurgen Wol v. Gudenb erg Institut fur Informatik, Universitat Wurzburg wol @informatik.uni-wuerzburg.de Abstract: In this article we brie y discuss the advantages and disadvantages of the language Java for scienti c computing. We concentrate on Java's typ e system, investi- gate its supp ort for hierarchical and generic programming and then discuss the features of its oating-p oint arithmetic. Having found the weak p oints of the language we pro- p ose workarounds using Java itself as long as p ossible. 1 Typ e System Java distinguishes b etween primitive and reference typ es. Whereas this distinc- tion seems to b e very natural and helpful { so the primitives which comprise all standard numerical data typ es have the usual value semantics and expression concept, and the reference semantics of the others allows to avoid p ointers at all{ it also causes some problems. For the reference typ es, i.e. arrays, classes and interfaces no op erators are available or may b e de ned and expressions can only b e built by metho d calls. Several variables may simultaneously denote the same ob ject. This is certainly strange in a numerical setting, but not to avoid, since classes have to b e used to intro duce higher data typ es. On the other hand, the simple hierarchy of classes with the ro ot Object clearly b elongs to the advantages of the language. -
Data Types and Variables
Color profile: Generic CMYK printer profile Composite Default screen Complete Reference / Visual Basic 2005: The Complete Reference / Petrusha / 226033-5 / Chapter 2 2 Data Types and Variables his chapter will begin by examining the intrinsic data types supported by Visual Basic and relating them to their corresponding types available in the .NET Framework’s Common TType System. It will then examine the ways in which variables are declared in Visual Basic and discuss variable scope, visibility, and lifetime. The chapter will conclude with a discussion of boxing and unboxing (that is, of converting between value types and reference types). Visual Basic Data Types At the center of any development or runtime environment, including Visual Basic and the .NET Common Language Runtime (CLR), is a type system. An individual type consists of the following two items: • A set of values. • A set of rules to convert every value not in the type into a value in the type. (For these rules, see Appendix F.) Of course, every value of another type cannot always be converted to a value of the type; one of the more common rules in this case is to throw an InvalidCastException, indicating that conversion is not possible. Scalar or primitive types are types that contain a single value. Visual Basic 2005 supports two basic kinds of scalar or primitive data types: structured data types and reference data types. All data types are inherited from either of two basic types in the .NET Framework Class Library. Reference types are derived from System.Object. Structured data types are derived from the System.ValueType class, which in turn is derived from the System.Object class. -
Categorical Models of Type Theory
Categorical models of type theory Michael Shulman February 28, 2012 1 / 43 Theories and models Example The theory of a group asserts an identity e, products x · y and inverses x−1 for any x; y, and equalities x · (y · z) = (x · y) · z and x · e = x = e · x and x · x−1 = e. I A model of this theory (in sets) is a particularparticular group, like Z or S3. I A model in spaces is a topological group. I A model in manifolds is a Lie group. I ... 3 / 43 Group objects in categories Definition A group object in a category with finite products is an object G with morphisms e : 1 ! G, m : G × G ! G, and i : G ! G, such that the following diagrams commute. m×1 (e;1) (1;e) G × G × G / G × G / G × G o G F G FF xx 1×m m FF xx FF m xx 1 F x 1 / F# x{ x G × G m G G ! / e / G 1 GO ∆ m G × G / G × G 1×i 4 / 43 Categorical semantics Categorical semantics is a general procedure to go from 1. the theory of a group to 2. the notion of group object in a category. A group object in a category is a model of the theory of a group. Then, anything we can prove formally in the theory of a group will be valid for group objects in any category. 5 / 43 Doctrines For each kind of type theory there is a corresponding kind of structured category in which we consider models. -
Static Typing Where Possible, Dynamic Typing When Needed: the End of the Cold War Between Programming Languages
Intended for submission to the Revival of Dynamic Languages Static Typing Where Possible, Dynamic Typing When Needed: The End of the Cold War Between Programming Languages Erik Meijer and Peter Drayton Microsoft Corporation Abstract Advocates of dynamically typed languages argue that static typing is too rigid, and that the softness of dynamically lan- This paper argues that we should seek the golden middle way guages makes them ideally suited for prototyping systems with between dynamically and statically typed languages. changing or unknown requirements, or that interact with other systems that change unpredictably (data and application in- tegration). Of course, dynamically typed languages are indis- 1 Introduction pensable for dealing with truly dynamic program behavior such as method interception, dynamic loading, mobile code, runtime <NOTE to="reader"> Please note that this paper is still very reflection, etc. much work in progress and as such the presentation is unpol- In the mother of all papers on scripting [16], John Ousterhout ished and possibly incoherent. Obviously many citations to argues that statically typed systems programming languages related and relevant work are missing. We did however do our make code less reusable, more verbose, not more safe, and less best to make it provocative. </NOTE> expressive than dynamically typed scripting languages. This Advocates of static typing argue that the advantages of static argument is parroted literally by many proponents of dynami- typing include earlier detection of programming mistakes (e.g. cally typed scripting languages. We argue that this is a fallacy preventing adding an integer to a boolean), better documenta- and falls into the same category as arguing that the essence of tion in the form of type signatures (e.g. -
Software II: Principles of Programming Languages
Software II: Principles of Programming Languages Lecture 6 – Data Types Some Basic Definitions • A data type defines a collection of data objects and a set of predefined operations on those objects • A descriptor is the collection of the attributes of a variable • An object represents an instance of a user- defined (abstract data) type • One design issue for all data types: What operations are defined and how are they specified? Primitive Data Types • Almost all programming languages provide a set of primitive data types • Primitive data types: Those not defined in terms of other data types • Some primitive data types are merely reflections of the hardware • Others require only a little non-hardware support for their implementation The Integer Data Type • Almost always an exact reflection of the hardware so the mapping is trivial • There may be as many as eight different integer types in a language • Java’s signed integer sizes: byte , short , int , long The Floating Point Data Type • Model real numbers, but only as approximations • Languages for scientific use support at least two floating-point types (e.g., float and double ; sometimes more • Usually exactly like the hardware, but not always • IEEE Floating-Point Standard 754 Complex Data Type • Some languages support a complex type, e.g., C99, Fortran, and Python • Each value consists of two floats, the real part and the imaginary part • Literal form real component – (in Fortran: (7, 3) imaginary – (in Python): (7 + 3j) component The Decimal Data Type • For business applications (money)