Advanced Type Systems
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ECSS-E-TM-40-07 Volume 2A 25 January 2011
ECSS-E-TM-40-07 Volume 2A 25 January 2011 Space engineering Simulation modelling platform - Volume 2: Metamodel ECSS Secretariat ESA-ESTEC Requirements & Standards Division Noordwijk, The Netherlands ECSS‐E‐TM‐40‐07 Volume 2A 25 January 2011 Foreword This document is one of the series of ECSS Technical Memoranda. Its Technical Memorandum status indicates that it is a non‐normative document providing useful information to the space systems developers’ community on a specific subject. It is made available to record and present non‐normative data, which are not relevant for a Standard or a Handbook. Note that these data are non‐normative even if expressed in the language normally used for requirements. Therefore, a Technical Memorandum is not considered by ECSS as suitable for direct use in Invitation To Tender (ITT) or business agreements for space systems development. Disclaimer ECSS does not provide any warranty whatsoever, whether expressed, implied, or statutory, including, but not limited to, any warranty of merchantability or fitness for a particular purpose or any warranty that the contents of the item are error‐free. In no respect shall ECSS incur any liability for any damages, including, but not limited to, direct, indirect, special, or consequential damages arising out of, resulting from, or in any way connected to the use of this document, whether or not based upon warranty, business agreement, tort, or otherwise; whether or not injury was sustained by persons or property or otherwise; and whether or not loss was sustained from, or arose out of, the results of, the item, or any services that may be provided by ECSS. -
Design and Implementation of Generics for the .NET Common Language Runtime
Design and Implementation of Generics for the .NET Common Language Runtime Andrew Kennedy Don Syme Microsoft Research, Cambridge, U.K. fakeÒÒ¸d×ÝÑeg@ÑicÖÓ×ÓfغcÓÑ Abstract cally through an interface definition language, or IDL) that is nec- essary for language interoperation. The Microsoft .NET Common Language Runtime provides a This paper describes the design and implementation of support shared type system, intermediate language and dynamic execution for parametric polymorphism in the CLR. In its initial release, the environment for the implementation and inter-operation of multiple CLR has no support for polymorphism, an omission shared by the source languages. In this paper we extend it with direct support for JVM. Of course, it is always possible to “compile away” polymor- parametric polymorphism (also known as generics), describing the phism by translation, as has been demonstrated in a number of ex- design through examples written in an extended version of the C# tensions to Java [14, 4, 6, 13, 2, 16] that require no change to the programming language, and explaining aspects of implementation JVM, and in compilers for polymorphic languages that target the by reference to a prototype extension to the runtime. JVM or CLR (MLj [3], Haskell, Eiffel, Mercury). However, such Our design is very expressive, supporting parameterized types, systems inevitably suffer drawbacks of some kind, whether through polymorphic static, instance and virtual methods, “F-bounded” source language restrictions (disallowing primitive type instanti- type parameters, instantiation at pointer and value types, polymor- ations to enable a simple erasure-based translation, as in GJ and phic recursion, and exact run-time types. -
Parametric Polymorphism Parametric Polymorphism
Parametric Polymorphism Parametric Polymorphism • is a way to make a language more expressive, while still maintaining full static type-safety (every Haskell expression has a type, and types are all checked at compile-time; programs with type errors will not even compile) • using parametric polymorphism, a function or a data type can be written generically so that it can handle values identically without depending on their type • such functions and data types are called generic functions and generic datatypes Polymorphism in Haskell • Two kinds of polymorphism in Haskell – parametric and ad hoc (coming later!) • Both kinds involve type variables, standing for arbitrary types. • Easy to spot because they start with lower case letters • Usually we just use one letter on its own, e.g. a, b, c • When we use a polymorphic function we will usually do so at a specific type, called an instance. The process is called instantiation. Identity function Consider the identity function: id x = x Prelude> :t id id :: a -> a It does not do anything with the input other than returning it, therefore it places no constraints on the input's type. Prelude> :t id id :: a -> a Prelude> id 3 3 Prelude> id "hello" "hello" Prelude> id 'c' 'c' Polymorphic datatypes • The identity function is the simplest possible polymorphic function but not very interesting • Most useful polymorphic functions involve polymorphic types • Notation – write the name(s) of the type variable(s) used to the left of the = symbol Maybe data Maybe a = Nothing | Just a • a is the type variable • When we instantiate a to something, e.g. -
Bidirectional Typing
Bidirectional Typing JANA DUNFIELD, Queen’s University, Canada NEEL KRISHNASWAMI, University of Cambridge, United Kingdom Bidirectional typing combines two modes of typing: type checking, which checks that a program satisfies a known type, and type synthesis, which determines a type from the program. Using checking enables bidirectional typing to support features for which inference is undecidable; using synthesis enables bidirectional typing to avoid the large annotation burden of explicitly typed languages. In addition, bidirectional typing improves error locality. We highlight the design principles that underlie bidirectional type systems, survey the development of bidirectional typing from the prehistoric period before Pierce and Turner’s local type inference to the present day, and provide guidance for future investigations. ACM Reference Format: Jana Dunfield and Neel Krishnaswami. 2020. Bidirectional Typing. 1, 1 (November 2020), 37 pages. https: //doi.org/10.1145/nnnnnnn.nnnnnnn 1 INTRODUCTION Type systems serve many purposes. They allow programming languages to reject nonsensical programs. They allow programmers to express their intent, and to use a type checker to verify that their programs are consistent with that intent. Type systems can also be used to automatically insert implicit operations, and even to guide program synthesis. Automated deduction and logic programming give us a useful lens through which to view type systems: modes [Warren 1977]. When we implement a typing judgment, say Γ ` 4 : 퐴, is each of the meta-variables (Γ, 4, 퐴) an input, or an output? If the typing context Γ, the term 4 and the type 퐴 are inputs, we are implementing type checking. If the type 퐴 is an output, we are implementing type inference. -
CSE 307: Principles of Programming Languages Classes and Inheritance
OOP Introduction Type & Subtype Inheritance Overloading and Overriding CSE 307: Principles of Programming Languages Classes and Inheritance R. Sekar 1 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Topics 1. OOP Introduction 3. Inheritance 2. Type & Subtype 4. Overloading and Overriding 2 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Section 1 OOP Introduction 3 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding OOP (Object Oriented Programming) So far the languages that we encountered treat data and computation separately. In OOP, the data and computation are combined into an “object”. 4 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Benefits of OOP more convenient: collects related information together, rather than distributing it. Example: C++ iostream class collects all I/O related operations together into one central place. Contrast with C I/O library, which consists of many distinct functions such as getchar, printf, scanf, sscanf, etc. centralizes and regulates access to data. If there is an error that corrupts object data, we need to look for the error only within its class Contrast with C programs, where access/modification code is distributed throughout the program 5 / 52 OOP Introduction Type & Subtype Inheritance Overloading and Overriding Benefits of OOP (Continued) Promotes reuse. by separating interface from implementation. We can replace the implementation of an object without changing client code. Contrast with C, where the implementation of a data structure such as a linked list is integrated into the client code by permitting extension of new objects via inheritance. Inheritance allows a new class to reuse the features of an existing class. -
INF 102 CONCEPTS of PROG. LANGS Type Systems
INF 102 CONCEPTS OF PROG. LANGS Type Systems Instructors: James Jones Copyright © Instructors. What is a Data Type? • A type is a collection of computational entities that share some common property • Programming languages are designed to help programmers organize computational constructs and use them correctly. Many programming languages organize data and computations into collections called types. • Some examples of types are: o the type Int of integers o the type (Int→Int) of functions from integers to integers Why do we need them? • Consider “untyped” universes: • Bit string in computer memory • λ-expressions in λ calculus • Sets in set theory • “untyped” = there’s only 1 type • Types arise naturally to categorize objects according to patterns of use • E.g. all integer numbers have same set of applicable operations Use of Types • Identifying and preventing meaningless errors in the program o Compile-time checking o Run-time checking • Program Organization and documentation o Separate types for separate concepts o Indicates intended use declared identifiers • Supports Optimization o Short integers require fewer bits o Access record component by known offset Type Errors • A type error occurs when a computational entity, such as a function or a data value, is used in a manner that is inconsistent with the concept it represents • Languages represent values as sequences of bits. A "type error" occurs when a bit sequence written for one type is used as a bit sequence for another type • A simple example can be assigning a string to an integer -
Programming with Gadts
Chapter 8 Programming with GADTs ML-style variants and records make it possible to define many different data types, including many of the types we encoded in System F휔 in Chapter 2.4.1: booleans, sums, lists, trees, and so on. However, types defined this way can lead to an error-prone programming style. For example, the OCaml standard library includes functions List .hd and List . tl for accessing the head and tail of a list: val hd : ’ a l i s t → ’ a val t l : ’ a l i s t → ’ a l i s t Since the types of hd and tl do not express the requirement that the argu- ment lists be non-empty, the functions can be called with invalid arguments, leading to run-time errors: # List.hd [];; Exception: Failure ”hd”. In this chapter we introduce generalized algebraic data types (GADTs), which support richer types for data and functions, avoiding many of the errors that arise with partial functions like hd. As we shall see, GADTs offer a num- ber of benefits over simple ML-style types, including the ability to describe the shape of data more precisely, more informative applications of the propositions- as-types correspondence, and opportunities for the compiler to generate more efficient code. 8.1 Generalising algebraic data types Towards the end of Chapter 2 we considered some different approaches to defin- ing binary branching tree types. Under the following definition a tree is either empty, or consists of an element of type ’a and a pair of trees: type ’ a t r e e = Empty : ’ a t r e e | Tree : ’a tree * ’a * ’a tree → ’ a t r e e 59 60 CHAPTER 8. -
Parametric Polymorphism (Generics) 30 April 2018 Lecturer: Andrew Myers
CS 4120/5120 Lecture 36 Parametric Polymorphism (Generics) 30 April 2018 Lecturer: Andrew Myers Parametric polymorphism, also known as generics, is a programming language feature with implications for compiler design. The word polymorphism in general means that a value or other entity that can have more than one type. We have already talked about subtype polymorphism, in which a value of one type can act like another (super)type. Subtyping places constraints on how we implemented objects. In parametric polymorphism, the ability for something to have more than one “shape” is by introducing a type parameter. A typical motivation for parametric polymorphism is to support generic collection libraries such as the Java Collection Framework. Prior to the introduction of parametric polymorphism, all that code could know about the contents of a Set or Map was that it contained Objects. This led to code that was clumsy and not type-safe. With parametric polymorphism, we can apply a parameterized type such as Map to particular types: a Map String, Point maps Strings to Points. We can also parameterize procedures (functions, methods) withh respect to types.i Using Xi-like syntax, we might write a is_member method that can look up elements in a map: contains K, V (c: Map K, V , k: K): Value { ... } Map K, V h m i h i ...h i p: Point = contains String, Point (m, "Hello") h i Although Map is sometimes called a parameterized type or a generic type , it isn’t really a type; it is a type-level function that maps a pair of types to a new type. -
Polymorphism
Polymorphism A closer look at types.... Chap 8 polymorphism º comes from Greek meaning ‘many forms’ In programming: Def: A function or operator is polymorphic if it has at least two possible types. Polymorphism i) OverloaDing Def: An overloaDeD function name or operator is one that has at least two Definitions, all of Different types. Example: In Java the ‘+’ operator is overloaDeD. String s = “abc” + “def”; +: String * String ® String int i = 3 + 5; +: int * int ® int Polymorphism Example: Java allows user DefineD polymorphism with overloaDeD function names. bool f (char a, char b) { return a == b; f : char * char ® bool } bool f (int a, int b) { f : int * int ® bool return a == b; } Note: ML Does not allow function overloaDing Polymorphism ii) Parameter Coercion Def: An implicit type conversion is calleD a coercion. Coercions usually exploit the type-subtype relationship because a wiDening type conversion from subtype to supertype is always DeemeD safe ® a compiler can insert these automatically ® type coercions. Example: type coercion in Java Double x; x = 2; the value 2 is coerceD from int to Double by the compiler Polymorphism Parameter coercion is an implicit type conversion on parameters. Parameter coercion makes writing programs easier – one function can be applieD to many subtypes. Example: Java voiD f (Double a) { ... } int Ì double float Ì double short Ì double all legal types that can be passeD to function ‘f’. byte Ì double char Ì double Note: ML Does not perform type coercion (ML has no notion of subtype). Polymorphism iii) Parametric Polymorphism Def: A function exhibits parametric polymorphism if it has a type that contains one or more type variables. -
Scala by Example (2009)
Scala By Example DRAFT January 13, 2009 Martin Odersky PROGRAMMING METHODS LABORATORY EPFL SWITZERLAND Contents 1 Introduction1 2 A First Example3 3 Programming with Actors and Messages7 4 Expressions and Simple Functions 11 4.1 Expressions And Simple Functions...................... 11 4.2 Parameters.................................... 12 4.3 Conditional Expressions............................ 15 4.4 Example: Square Roots by Newton’s Method................ 15 4.5 Nested Functions................................ 16 4.6 Tail Recursion.................................. 18 5 First-Class Functions 21 5.1 Anonymous Functions............................. 22 5.2 Currying..................................... 23 5.3 Example: Finding Fixed Points of Functions................ 25 5.4 Summary..................................... 28 5.5 Language Elements Seen So Far....................... 28 6 Classes and Objects 31 7 Case Classes and Pattern Matching 43 7.1 Case Classes and Case Objects........................ 46 7.2 Pattern Matching................................ 47 8 Generic Types and Methods 51 8.1 Type Parameter Bounds............................ 53 8.2 Variance Annotations.............................. 56 iv CONTENTS 8.3 Lower Bounds.................................. 58 8.4 Least Types.................................... 58 8.5 Tuples....................................... 60 8.6 Functions.................................... 61 9 Lists 63 9.1 Using Lists.................................... 63 9.2 Definition of class List I: First Order Methods.............. -
An Ontology-Based Semantic Foundation for Organizational Structure Modeling in the ARIS Method
An Ontology-Based Semantic Foundation for Organizational Structure Modeling in the ARIS Method Paulo Sérgio Santos Jr., João Paulo A. Almeida, Giancarlo Guizzardi Ontology & Conceptual Modeling Research Group (NEMO) Computer Science Department, Federal University of Espírito Santo (UFES) Vitória, ES, Brazil [email protected]; [email protected]; [email protected] Abstract—This paper focuses on the issue of ontological Although present in most enterprise architecture interpretation for the ARIS organization modeling language frameworks, a semantic foundation for organizational with the following contributions: (i) providing real-world modeling elements is still lacking [1]. This is a significant semantics to the primitives of the language by using the UFO challenge from the perspective of modelers who must select foundational ontology as a semantic domain; (ii) the and manipulate modeling elements to describe an Enterprise identification of inappropriate elements of the language, using Architecture and from the perspective of stakeholders who a systematic ontology-based analysis approach; and (iii) will be exposed to models for validation and decision recommendations for improvements of the language to resolve making. In other words, a clear semantic account of the the issues identified. concepts underlying Enterprise Modeling languages is Keywords: semantics for enterprise models; organizational required for Enterprise Models to be used as a basis for the structure; ontological interpretation; ARIS; UFO (Unified management, design and evolution of an Enterprise Foundation Ontology) Architecture. In this paper we are particularly interested in the I. INTRODUCTION modeling of this architectural domain in the widely- The need to understand and manage the evolution of employed ARIS Method (ARchitecture for integrated complex organizations and its information systems has given Information Systems). -
Obstacl: a Language with Objects, Subtyping, and Classes
OBSTACL: A LANGUAGE WITH OBJECTS, SUBTYPING, AND CLASSES A DISSERTATION SUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCE AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY By Amit Jayant Patel December 2001 c Copyright 2002 by Amit Jayant Patel All Rights Reserved ii I certify that I have read this dissertation and that in my opin- ion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. John Mitchell (Principal Adviser) I certify that I have read this dissertation and that in my opin- ion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Kathleen Fisher I certify that I have read this dissertation and that in my opin- ion it is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David Dill Approved for the University Committee on Graduate Studies: iii Abstract Widely used object-oriented programming languages such as C++ and Java support soft- ware engineering practices but do not have a clean theoretical foundation. On the other hand, most research languages with well-developed foundations are not designed to support software engineering practices. This thesis bridges the gap by presenting OBSTACL, an object-oriented extension of ML with a sound theoretical basis and features that lend themselves to efficient implementation. OBSTACL supports modular programming techniques with objects, classes, structural subtyping, and a modular object construction system. OBSTACL's parameterized inheritance mechanism can be used to express both single inheritance and most common uses of multiple inheritance.