DOCSLIB.ORG

Shared Data Types for OSRA and TASTE Using Modern C++

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Shared Data Types for OSRA and TASTE Using Modern C++ Shared Data Types for OSRA and TASTE using Modern C++ Jan Sommer Andreas Gerndt Daniel Lüdtke Institute for Software Technology Institute for Software Technology Institute for Software Technology DLR (German Aerospace Center) DLR (German Aerospace Center) DLR (German Aerospace Center) Lilienthalplatz 7, 38108 Braunschweig Lilienthalplatz 7, 38108 Braunschweig Lilienthalplatz 7, 38108 Braunschweig [email protected] Universität Bremen [email protected] Bibliothekstraße 5, 28359 Bremen [email protected] Abstract—The European Space Agency (ESA) currently pro­ on­board software. At the same time, it leaves the concrete vides two tools for the modeling of on­board software: The Assert implementation of the code generators to the entity using Set of Tools for Engineering (TASTE) and the On­Board Software OSRA. TASTE, on the other hand, provides a more generic Reference Architecture (OSRA). For data type modeling, TASTE uses the standardized Ab­ framework, includes code generators for the C and Ada lan­ stract Syntax Notation One (ASN.1), while OSRA provides an guages, and has been also applied in robotics applications [3]. internal eCore­based data type representation. Unfortunately, the Unfortunately, the interworking between the two frameworks interworking between the two frameworks lacks a mechanism to lacks a mechanism to exchange data easily without duplicating exchange data easily without duplicating the data type informa­ the data type information. Our goal is to eliminate this tion. In this work, we present our approach for the exchange of problem and use the same data type descriptions across both data types and data values between software developed with frameworks and also have a compatible binary representation both tools. We show our additions to the OSRA infrastructure for the data types to allow seamless data exchange between enabling the exchange of data types between OSRA and TASTE applications developed using TASTE or OSRA. based on the same data type descriptions in ASN.1. This includes In this paper, we first have a short comparison between the complementing the OSRA editor with the ability to read and write ASN.1 data type descriptions and to specify the data type existing data type definition methods in OSRA and TASTE encodings in TASTE’s ASN.1 Control Notation. in Section II. In the following section, we present how we Our previous implementation of the ASN.1 data types in Mod­ integrated support for ASN.1 and ACN to the OSRA model ern C++ has been extended with a prototypical implementation editor. In Section IV, we give a short overview of the data type for the serialization of the data types compatible with TASTE’s system we developed previously [4] and which will be the ACN encoded types. As for the data types themselves, C++ metaprogramming foundation for the encoding infrastructure. Section V presents techniques have been used for the encoder. This allows us to some of the concepts and implementation details behind our keep the code generators simple and maintainable. Some early new ACN encoding prototype. In Section VI we discuss the results on the exchange of data between OSRA, enabled with current state of our prototype and its achieved results. Finally our prototype generator, and the TASTE framework with its own ASN.1 compiler are presented and discussed. we give our conclusions and ideas about the future direction of our work in Section VII. I. INTRODUCTION The demand for more complex on­board functionalities for II. DATA TYPE DEFINITION IN OSRA AND TASTE future spacecraft continues to rise, increasing the burden on In complex software projects, data is exchanged by a often small software teams. To handle such a complexity, plethora of software modules, potentially developed by dif­ model­driven methodologies can help to capture the overall ferent software teams. To ensure safe data exchange inside a architecture and design of the software. In a later step, they single as well as across many different modules, essentially also allow auto­generating source code and documentation three basic problems need to be solved: First, there has to be a artifacts from the model, thereby relieving software developers common source defining the data types, ideally with the option from monotonous tasks. to define constraints. Secondly, there needs to be some way In order to support model­based software development, to determine whether a value is valid or not. Finally, a shared the European Space Agency (ESA) provides The Assert Set understanding about how to encode values of these data types of Tools for Engineering (TASTE) [1] and the On­Board for exchange across modules or even devices is necessary. Software Reference Architecture (OSRA) [2]. Both share TASTE solves the first problem by describing its data types some common design concepts like separation of concerns, through the programming language agnostic Abstract Syntax component­based modeling and graphical tooling for the de­ Notation One (ASN.1) notation. The second one is addressed sign tasks. OSRA targets mostly the design of spacecraft by generating test routines for validity checks during runtime. The last problem is solved by implementing encoding rules <<Float>> <<unsigned Integer>> <<Structured>> of ASN.1 or by using a custom description for the encoding MyFloat MyInteger MyStruct of data types using TASTE’s own ASN.1 Control Notation fieldBool:MyBoolean (ACN). <<Constrained MyFloat>> fieldEnum:Color ConstraintFloat <<signed Integer>> OSRA provides mainly its metamodel, the Space Compo­ SignedInteger maxBound := 5.0 <<Array Color>> nent Model (SCM), and a corresponding editor which also ColorArray nbOfElements := 20 provides a modeling workflow for the user. Of the three <<Constrained MyInteger>> ConstraintInt <<Alias MyInteger>> mentioned problems, OSRA currently solves only the first UnsignedInteger minBound := 0 <<Boolean>> problem through its graphical data type editor. We only present maxBound := 10 MyBoolean a short summary of OSRA’s type modeling system here. A more in­depth analysis was carried out by us in [4]. <<Union : >> <<Enumeration>> MyUnion Color <<Constant ConstraintInt>> The data type part of the OSRA metamodel has a complex fieldBool : MyBoolean blue constant class hierarchy with several layers of abstract classes, which fieldInt : ConstraintInt red value := 6 are used in other parts of the metamodel to refer to generic fielEnum : Color green types. It provides common numerical metatypes for integer and Fig. 1. Example of OSRA data types modeled in the SCM editor with simple numerical types, constrainted numerical types, a structured type and an array floating point numbers and also allows to constrain the value type. space of those types. Other supported elementary metatypes include representations for boolean types, enumerations, and fixed point values. The OSRA metamodel also allows the for that purpose. Within the frame of the TASTE project, modeling of several kinds of array and string types as well ESA already evaluated different programming language in­ as common structured and union types. dependent data type notations and decided to use ASN.1 [1]. For every type definition, it is also possible to instantiate a TASTE only selected a subset of ASN.1 which provides a constant of that type, which will be available for further use reasonable feature set for space applications where type sizes in the model. and value sets must be known at compile­time. This reduced Additionally, there are two special metatypes available: the feature set also means less complexity in the necessary ASN.1 AliasType that allows to declare a new type with the same grammar. By adopting this approach for OSRA as well, only features as a reference type, but with a new name; and the OSRA needs to be complemented with an additional ASN.1 ExternalType that allows to register data types which have infrastructure. No changes are necessary for TASTE. not been defined through the OSRA model itself. For the latter, Within the ESA funded PaTaS activity [6], an intial ASN.1 the OSRA model cannot determine any properties but relies grammar implementation in Xtext was already started. It on the external model to check validity. It only knows the became a starting point to add an ASN.1 editor to OSRA. registered types’ names which is enough to use them like Like OSRA, Xtext is also based on the Eclipse Modeling native types throughout the model (for example for interface Framework. Therefore, the ASN.1 grammar can be tightly in­ definitions). tegrated with OSRA. The bi­directional implementation works The OSRA editor provides a graphical interface to define as follows: For all data types, which were created with the concrete types and constants from the described metatypes. graphical model editor of OSRA, a corresponding type in Fig. 1 shows an example of such a data type diagram, which ASN.1 textual notation is generated using Xtend code genera­ looks similar to data type diagrams in UML [5]. tors [7]. For all data types which have been manually written For every type or constant defined in such a way, a and for which an ASN.1 representation exists, a corresponding corresponding element is added to the underlying eCore model ExternalType is registered in the OSRA model. In this way, including all the range properties and base type references. all types are available in the OSRA model and can be used in, e.g., interface modeling. All types have also a representation in III. INTRODUCING OSRA TO ASN.1 AND ACN ASN.1, which means they can be shared with external tools, Although graphical modeling of data types is intuitive, it can such as TASTE. This work was carried out as part of [4] become difficult to understand and maintain when complex and allowed the exchange of data types between OSRA and structured types and type hierarchies have to be modeled. TASTE. Furthermore, the data types are, by default, only available in The upper part of Fig.
Load more

Recommended publications
  • Type-Safe Composition of Object Modules*
    International Conference on Computer Systems and Education I ISc Bangalore Typ esafe Comp osition of Ob ject Mo dules Guruduth Banavar Gary Lindstrom Douglas Orr Department of Computer Science University of Utah Salt LakeCity Utah USA Abstract Intro duction It is widely agreed that strong typing in We describ e a facility that enables routine creases the reliability and eciency of soft typ echecking during the linkage of exter ware However compilers for statically typ ed nal declarations and denitions of separately languages suchasC and C in tradi compiled programs in ANSI C The primary tional nonintegrated programming environ advantage of our serverstyle typ echecked ments guarantee complete typ esafety only linkage facility is the ability to program the within a compilation unit but not across comp osition of ob ject mo dules via a suite of suchunits Longstanding and widely avail strongly typ ed mo dule combination op era able linkers comp ose separately compiled tors Such programmability enables one to units bymatching symb ols purely byname easily incorp orate programmerdened data equivalence with no regard to their typ es format conversion stubs at linktime In ad Such common denominator linkers accom dition our linkage facility is able to automat mo date ob ject mo dules from various source ically generate safe co ercion stubs for com languages by simply ignoring the static se patible encapsulated data mantics of the language Moreover com monly used ob ject le formats are not de signed to incorp orate source language typ e
    [Show full text]
  • 5. Data Types
    IEEE FOR THE FUNCTIONAL VERIFICATION LANGUAGE e Std 1647-2011 5. Data types The e language has a number of predefined data types, including the integer and Boolean scalar types common to most programming languages. In addition, new scalar data types (enumerated types) that are appropriate for programming, modeling hardware, and interfacing with hardware simulators can be created. The e language also provides a powerful mechanism for defining OO hierarchical data structures (structs) and ordered collections of elements of the same type (lists). The following subclauses provide a basic explanation of e data types. 5.1 e data types Most e expressions have an explicit data type, as follows: — Scalar types — Scalar subtypes — Enumerated scalar types — Casting of enumerated types in comparisons — Struct types — Struct subtypes — Referencing fields in when constructs — List types — The set type — The string type — The real type — The external_pointer type — The “untyped” pseudo type Certain expressions, such as HDL objects, have no explicit data type. See 5.2 for information on how these expressions are handled. 5.1.1 Scalar types Scalar types in e are one of the following: numeric, Boolean, or enumerated. Table 17 shows the predefined numeric and Boolean types. Both signed and unsigned integers can be of any size and, thus, of any range. See 5.1.2 for information on how to specify the size and range of a scalar field or variable explicitly. See also Clause 4. 5.1.2 Scalar subtypes A scalar subtype can be named and created by using a scalar modifier to specify the range or bit width of a scalar type.
    [Show full text]
  • 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/.
    [Show full text]
  • Type Conversion ,Type Casting, Operator Precedence and Associativity in C
    Type Conversion ,Type Casting, Operator Precedence and Associativity in C Gaurav Kr. suman 4/30/20 MAT09 The type conversion in C is basically converting one type of data type to other to perform some operation. The conversion is done only between those datatypes wherein the conversion is possible There are two types of type conversion: This type of conversion is usually performed by the compiler when necessary without any commands by the user. Thus it is also called "Automatic Type Conversion". • Done by the compiler on its own, without any external trigger from the user. • Generally takes place when in an expression more than one data type is present. In such condition type conversion (type promotion) takes place to avoid lose of data. • All the data types of the variables are upgraded to the data type of the variable with largest data type. Now, let’s focus on some examples to further understand about type conversions in C. Example 1 int a = 20; double b = 20.5; a + b; Here, first operand is int type and other is of type double. So, as per rule, the variable a will be converted to double. Therefore, the final answer is double a + b = 40.500000. Example 2 char ch='a'; int a =13; a+c; Here, first operand is char type and other is of type int. So, as per rule , the char variable will be converted to int type during the operation and the final answer will be of type int. We know the ASCII value for ch is 97.
    [Show full text]
  • Object Oriented Pogramming with C++
    OBJECT ORIENTED POGRAMMING WITH C++ 1. What is type conversion? Type Conversion is the process of converting one predefined type into another type. When variables of one type are mixed with variables of another type, a type conversion will occur. C++ facilitates the type conversion into the following two forms: Implicit Type Conversion: An implicit type conversion is a conversion performed by the compiler without programmer's intervention. It is applied whenever different data types are intermixed in an expression, so as not to lose information short x=6000; int y; y=x; // data type short variable x is converted to int and is assigned to the integer variable y. Explicit Type Conversion: The explicit conversion of an operand to a specific type is called type casting. An explicit type conversion is user-defined that forces an expression to be of specific type. Syntax: (type) expression #include <iostream.h> void main( ) { int a; float b, c; cout << "Enter the value of a:"; cin >> a; cout << "Enter the value of b:"; cin >> b; c = float(a)+b; cout << "The value of c is:" << c; getch(); } In the above program “a” is declared as integer and “b” and “c” are declared as float. In the type conversion statement namely c = float (a) +b; The variable a of type integer is converted into float type and so the value 10 is converted as 10.0 and then is added with the float variable b with value 12.5 giving a resultant float variable c with value as 22.5 2. Why C++ is called OOP language? M.VIJAY .
    [Show full text]
  • VHDL Type Conversion | Bitweenie
    VHDL Type Conversion | BitWeenie http://www.bitweenie.com/listings/vhdl-type-conversion/ Home About Electrical Engineer Jobs Request Topic Resources Home » VHDL Type Conversion VHDL Type Conversion Posted by Shannon Hilbert in Verilog / VHDL on 2-10-13 Any given VHDL FPGA design may have multiple VHDL types being used. The most common VHDL types used in synthesizable VHDL code are std_logic, std_logic_vector, signed, unsigned, and integer. Because VHDL is a strongly-typed language, most often differing types cannot be used in the same expression. In cases where you can directly combine two types into one expression, you are really leaving it up to the compiler or synthesis tool to determine how the expression should behave, which is a dangerous thing to do. This article will discuss the following concepts: 1. Type casting and conversion functions. 2. The importance of using the appropriate type. 3. Common uses and examples. VHDL Type Cast and Conversion Functions The picture below illustrates how to convert between the most common VHDL types. Type casting is used to move between the std_logic_vector type and the signed and unsigned types. 1 --signal definitions 2 signal slv : std_logic_vector(7 downto 0); 3 signal s : signed(7 downto 0); 4 signal us : unsigned(7 downto 0); 5 6 --FROM std_logic_vector TO signed/unsigned 1 de 5 07/10/2015 14:58 VHDL Type Conversion | BitWeenie http://www.bitweenie.com/listings/vhdl-type-conversion/ 7 sgn <= signed(slv); 8 usgn <= unsigned(slv); 9 10-- FROM signed/unsigned TO std_logic_vector 11svl <= std_logic_vector(sgn); 12svl <= std_logic_vector(usgn); Functions are used to move between signed and unsigned types and the integer type.
    [Show full text]
  • N1592 Explicit Conversion Operators
    Document Number: SC22/WG21/N1592=04-0032 Date: 2004-2-13 Author: Lois Goldthwaite Email: [email protected] Explicit Conversion Operators This paper proposes a small change in C++ grammar to permit the function-specifier 'explicit' to be applied to the definition of a user-defined conversion operator. The semantic effect is to inhibit automatic conversions in situations where they may not have been intended. The Problem One of the design principles of C++ is that the language does not enforce a different syntax for user-defined types and built-in primitive types. A variable of either category can be passed by value (assuming the programmer has not intentionally disabled this), and a variable of any type can be passed by reference. The compiler will perform automatic promotions and conversions, if necessary, when numeric types are used as function parameters or when differing types are combined with an operator (int to long, signed to unsigned, float to double, etc.). Similarly, the programmer can write conversion functions for user-defined types, so that the conversions will take place transparently. This is a feature, and A Good Thing, as it decreases the number of overloaded functions which would otherwise be needed (D&E 3.6.1). In Modern C++ Design, Alexandrescu says, "User-defined conversions in C++ have an interesting history. Back in the 1980s, when user-defined conversions were introduced, most programmers considered them a great invention. User-defined conversions promised a more unified type system, expressive semantics, and the ability to define new types that were indistinguishable from built-in ones.
    [Show full text]
  • 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.
    [Show full text]
  • Primitive Data, Variables, and Expressions; Simple Conditional Execution
    Unit 2, Part 1 Primitive Data, Variables, and Expressions; Simple Conditional Execution Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Overview of the Programming Process Analysis/Specification Design Implementation Testing/Debugging Example Problem: Adding Up Your Change • Let's say that we have a bunch of coins of various types, and we want to figure out how much money we have. • Let’s begin the process of developing a program that does this. Step 1: Analysis and Specification • Analyze the problem (making sure that you understand it), and specify the problem requirements clearly and unambiguously. • Describe exactly what the program will do, without worrying about how it will do it. Step 2: Design • Determine the necessary algorithms (and possibly other aspects of the program) and sketch out a design for them. • This is where we figure out how the program will solve the problem. • Algorithms are often designed using pseudocode. • more informal than an actual programming language • allows us to avoid worrying about the syntax of the language • example for our change-adder problem: get the number of quarters get the number of dimes get the number of nickels get the number of pennies compute the total value of the coins output the total value Step 3: Implementation • Translate your design into the programming language. pseudocode code • We need to learn more Java before we can do this! • Here's a portion or fragment of a Java program for computing the value of a particular collection of coins: quarters = 10; dimes = 3; nickels = 7; pennies = 6; cents = 25*quarters + 10*dimes + 5*nickels + pennies; System.out.println("Your total in cents is:"); System.out.println(cents); • In a moment, we'll use this fragment to examine some of the fundamental building blocks of a Java program.
    [Show full text]
  • Operator Overloading, Friend Functions/Classes
    Chapter 8 Operator Overloading, Friends, and References Learning Objectives Basic Operator Overloading Unary operators As member functions Friends and Automatic Type Conversion Friend functions, friend classes Constructors for automatic type conversion References and More Overloading << and >> Operators: = , ++, -- Operator Overloading Introduction Operators +, -, %, ==, etc. Really just functions! Simply ‘called’ with different syntax: x + 7 ‘+’ is binary operator with x & 7 as operands We ‘like’ this notation as humans Think of it as: +(x, 7) ‘+’ is the function name x, 7 are the arguments Function ‘+’ returns ‘sum’ of it’s arguments Operator Overloading Perspective Built-in operators e.g.: +, -, = , %, ==, /, * Already work for C++ built-in types In standard ‘binary’ notation We can overload them! To work with OUR types! To add ‘Chair types’, or ‘Money types’ As appropriate for our needs In ‘notation’ we’re comfortable with Always overload with similar ‘actions’! Overloading Basics Overloading operators VERY similar to overloading functions Operator itself is ‘name’ of function Example Declaration: const Money operator +( const Money& amount1, const Money& amount2); Overloads + for operands of type Money Uses constant reference parameters for efficiency Returned value is type Money Allows addition of ‘Money’ objects Overloaded ‘+’ Given previous example: Note: overloaded ‘+’ NOT member function Definition is ‘more involved’ than simple ‘add’ Requires issues of money type addition Must handle
    [Show full text]
  • Type Conversion Type Conversion
    1.3b Type Conversion Type Conversion When we write expressions involved data that involves two different data types , such as multiplying an integer and floating – point number, we need to perform a type conversion…. Two type of conversions mainly Implicit type conversion Explicit type conversion Implicit Type Conversion When the types of the two operands in a binary expression are different,C automatically converts one type to another which is known as Implicit Type Conversion. Some of the simple conversions are : Conversion Rank Conversions in Assignment Expressions Promotion Demotion Conversion in other Binary Expressions Conversion Rank In C , we assign a rank to the integral and floating point arithmetic types Real 9.long double 10.double 11.float Conversion Rank Integer 6.long long 5.long 4. int 3. short Character 2. Char Boolean 1. Bool Conversions in Assignment Expressions A simple assignment involves an assignment operator and two operands Depending on the difference in the rank, C tries to either promote or demote the right expression to make it the same rank as the left variable. Promotion occurs if the right expression has lower rank Demotion occurs if the right expression has a higher rank Promotion The rank of the left expression is elevated to the rank of the left variable The value of the expression is the value of the right expression after the promotion bool b = true; char c = ‘A’; int i = 1234; long double d = 3458.0004 c = b; //Value of c is SOH i = c; //Value of i is 65 d = b; //Value of d is 1.0 d = i; //Value of d is 1234.0 Demotion If the size of the variable at the left side can accommodate the value of the expression, there is no problem An integral or real value can be assigned to a Boolean Type.
    [Show full text]
  • Chapter 6 Data Types
    Chapter 6 Data Types • Introduction • Type Nomenclature • Primitive Types • Type constructors – Ordinal Types – Structured Types • Type Checking • Type conversion CSCI325 Chapter 6 Dr Ahmed Rafea 1 Introduction Evolution of Data Types: FORTRAN I (1956) - INTEGER, REAL, arrays … Ada (1983) - User can create a unique type for every category of variables in the problem space and have the system enforce the types Def: A descriptor is the collection of the attributes of a variable Def: A data type is a set of values, together with a set of operations on those values having certain properties CSCI325 Chapter 6 Dr Ahmed Rafea 2 Type Nomenclature C Types Basic Derived Void Numeric Pointer Array Function struct union Integral Floating Float (signed) enum Double (unsigned) Long double char Int Short int Long int CSCI325 Chapter 6 Dr Ahmed Rafea 3 Primitive Data Types Integer - 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 Floating Point - Model real numbers, but only as approximations - Languages for scientific use support at least two floating-point types; sometimes more - Usually exactly like the hardware, but not always; Decimal - For business applications (money) - Store a fixed number of decimal digits (coded) - Advantage: accuracy - Disadvantages: limited range, wastes memory Boolean - Could be implemented as bits, but often as bytes - Advantage: readability CSCI325 Chapter 6 Dr Ahmed Rafea 4 Ordinal Types (user defined) An ordinal type is one in which the range of possible values can be easily associated with the set of positive integers 1.
    [Show full text]