Simple Algebraic Data Types for C
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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 -
Programming the Capabilities of the PC Have Changed Greatly Since the Introduction of Electronic Computers
1 www.onlineeducation.bharatsevaksamaj.net www.bssskillmission.in INTRODUCTION TO PROGRAMMING LANGUAGE Topic Objective: At the end of this topic the student will be able to understand: History of Computer Programming C++ Definition/Overview: Overview: A personal computer (PC) is any general-purpose computer whose original sales price, size, and capabilities make it useful for individuals, and which is intended to be operated directly by an end user, with no intervening computer operator. Today a PC may be a desktop computer, a laptop computer or a tablet computer. The most common operating systems are Microsoft Windows, Mac OS X and Linux, while the most common microprocessors are x86-compatible CPUs, ARM architecture CPUs and PowerPC CPUs. Software applications for personal computers include word processing, spreadsheets, databases, games, and myriad of personal productivity and special-purpose software. Modern personal computers often have high-speed or dial-up connections to the Internet, allowing access to the World Wide Web and a wide range of other resources. Key Points: 1. History of ComputeWWW.BSSVE.INr Programming The capabilities of the PC have changed greatly since the introduction of electronic computers. By the early 1970s, people in academic or research institutions had the opportunity for single-person use of a computer system in interactive mode for extended durations, although these systems would still have been too expensive to be owned by a single person. The introduction of the microprocessor, a single chip with all the circuitry that formerly occupied large cabinets, led to the proliferation of personal computers after about 1975. Early personal computers - generally called microcomputers - were sold often in Electronic kit form and in limited volumes, and were of interest mostly to hobbyists and technicians. -
Certification of a Tool Chain for Deductive Program Verification Paolo Herms
Certification of a Tool Chain for Deductive Program Verification Paolo Herms To cite this version: Paolo Herms. Certification of a Tool Chain for Deductive Program Verification. Other [cs.OH]. Université Paris Sud - Paris XI, 2013. English. NNT : 2013PA112006. tel-00789543 HAL Id: tel-00789543 https://tel.archives-ouvertes.fr/tel-00789543 Submitted on 18 Feb 2013 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. UNIVERSITÉ DE PARIS-SUD École doctorale d’Informatique THÈSE présentée pour obtenir le Grade de Docteur en Sciences de l’Université Paris-Sud Discipline : Informatique PAR Paolo HERMS −! − SUJET : Certification of a Tool Chain for Deductive Program Verification soutenue le 14 janvier 2013 devant la commission d’examen MM. Roberto Di Cosmo Président du Jury Xavier Leroy Rapporteur Gilles Barthe Rapporteur Emmanuel Ledinot Examinateur Burkhart Wolff Examinateur Claude Marché Directeur de Thèse Benjamin Monate Co-directeur de Thèse Jean-François Monin Invité Résumé Cette thèse s’inscrit dans le domaine de la vérification du logiciel. Le but de la vérification du logiciel est d’assurer qu’une implémentation, un programme, répond aux exigences, satis- fait sa spécification. Cela est particulièrement important pour le logiciel critique, tel que des systèmes de contrôle d’avions, trains ou centrales électriques, où un mauvais fonctionnement pendant l’opération aurait des conséquences catastrophiques. -
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). -
Comparative Studies of Programming Languages; Course Lecture Notes
Comparative Studies of Programming Languages, COMP6411 Lecture Notes, Revision 1.9 Joey Paquet Serguei A. Mokhov (Eds.) August 5, 2010 arXiv:1007.2123v6 [cs.PL] 4 Aug 2010 2 Preface Lecture notes for the Comparative Studies of Programming Languages course, COMP6411, taught at the Department of Computer Science and Software Engineering, Faculty of Engineering and Computer Science, Concordia University, Montreal, QC, Canada. These notes include a compiled book of primarily related articles from the Wikipedia, the Free Encyclopedia [24], as well as Comparative Programming Languages book [7] and other resources, including our own. The original notes were compiled by Dr. Paquet [14] 3 4 Contents 1 Brief History and Genealogy of Programming Languages 7 1.1 Introduction . 7 1.1.1 Subreferences . 7 1.2 History . 7 1.2.1 Pre-computer era . 7 1.2.2 Subreferences . 8 1.2.3 Early computer era . 8 1.2.4 Subreferences . 8 1.2.5 Modern/Structured programming languages . 9 1.3 References . 19 2 Programming Paradigms 21 2.1 Introduction . 21 2.2 History . 21 2.2.1 Low-level: binary, assembly . 21 2.2.2 Procedural programming . 22 2.2.3 Object-oriented programming . 23 2.2.4 Declarative programming . 27 3 Program Evaluation 33 3.1 Program analysis and translation phases . 33 3.1.1 Front end . 33 3.1.2 Back end . 34 3.2 Compilation vs. interpretation . 34 3.2.1 Compilation . 34 3.2.2 Interpretation . 36 3.2.3 Subreferences . 37 3.3 Type System . 38 3.3.1 Type checking . 38 3.4 Memory management . -
“Scrap Your Boilerplate” Reloaded
“Scrap Your Boilerplate” Reloaded Ralf Hinze1, Andres L¨oh1, and Bruno C. d. S. Oliveira2 1 Institut f¨urInformatik III, Universit¨atBonn R¨omerstraße164, 53117 Bonn, Germany {ralf,loeh}@informatik.uni-bonn.de 2 Oxford University Computing Laboratory Wolfson Building, Parks Road, Oxford OX1 3QD, UK [email protected] Abstract. The paper “Scrap your boilerplate” (SYB) introduces a com- binator library for generic programming that offers generic traversals and queries. Classically, support for generic programming consists of two es- sential ingredients: a way to write (type-)overloaded functions, and in- dependently, a way to access the structure of data types. SYB seems to lack the second. As a consequence, it is difficult to compare with other approaches such as PolyP or Generic Haskell. In this paper we reveal the structural view that SYB builds upon. This allows us to define the combinators as generic functions in the classical sense. We explain the SYB approach in this changed setting from ground up, and use the un- derstanding gained to relate it to other generic programming approaches. Furthermore, we show that the SYB view is applicable to a very large class of data types, including generalized algebraic data types. 1 Introduction The paper “Scrap your boilerplate” (SYB) [1] introduces a combinator library for generic programming that offers generic traversals and queries. Classically, support for generic programming consists of two essential ingredients: a way to write (type-)overloaded functions, and independently, a way to access the structure of data types. SYB seems to lacks the second, because it is entirely based on combinators. -
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). -
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. -
Algebraic Data Types
Composite Data Types as Algebra, Logic Recursive Types Algebraic Data Types Christine Rizkallah CSE, UNSW (and data61) Term 3 2019 1 Classes Tuples Structs Unions Records Composite Data Types as Algebra, Logic Recursive Types Composite Data Types Most of the types we have seen so far are basic types, in the sense that they represent built-in machine data representations. Real programming languages feature ways to compose types together to produce new types, such as: 2 Classes Unions Composite Data Types as Algebra, Logic Recursive Types Composite Data Types Most of the types we have seen so far are basic types, in the sense that they represent built-in machine data representations. Real programming languages feature ways to compose types together to produce new types, such as: Tuples Structs Records 3 Unions Composite Data Types as Algebra, Logic Recursive Types Composite Data Types Most of the types we have seen so far are basic types, in the sense that they represent built-in machine data representations. Real programming languages feature ways to compose types together to produce new types, such as: Classes Tuples Structs Records 4 Composite Data Types as Algebra, Logic Recursive Types Composite Data Types Most of the types we have seen so far are basic types, in the sense that they represent built-in machine data representations. Real programming languages feature ways to compose types together to produce new types, such as: Classes Tuples Structs Unions Records 5 Composite Data Types as Algebra, Logic Recursive Types Combining values conjunctively We want to store two things in one value. -
Csci 555: Functional Programming Functional Programming in Scala Functional Data Structures
CSci 555: Functional Programming Functional Programming in Scala Functional Data Structures H. Conrad Cunningham 6 March 2019 Contents 3 Functional Data Structures 2 3.1 Introduction . .2 3.2 A List algebraic data type . .2 3.2.1 Algebraic data types . .2 3.2.2 ADT confusion . .3 3.2.3 Using a Scala trait . .3 3.2.3.1 Aside on Haskell . .4 3.2.4 Polymorphism . .4 3.2.5 Variance . .5 3.2.5.1 Covariance and contravariance . .5 3.2.5.2 Function subtypes . .6 3.2.6 Defining functions in companion object . .7 3.2.7 Function to sum a list . .7 3.2.8 Function to multiply a list . .9 3.2.9 Function to remove adjacent duplicates . .9 3.2.10 Variadic function apply ................... 11 3.3 Data sharing . 11 3.3.1 Function to take tail of list . 12 3.3.2 Function to drop from beginning of list . 13 3.3.3 Function to append lists . 14 3.4 Other list functions . 15 3.4.1 Tail recursive function reverse . 15 3.4.2 Higher-order function dropWhile . 17 3.4.3 Curried function dropWhile . 17 3.5 Generalizing to Higher Order Functions . 18 3.5.1 Fold Right . 18 3.5.2 Fold Left . 22 3.5.3 Map . 23 1 3.5.4 Filter . 25 3.5.5 Flat Map . 26 3.6 Classic algorithms on lists . 27 3.6.1 Insertion sort and bounded generics . 27 3.6.2 Merge sort . 29 3.7 Lists in the Scala standard library .