Generalizers: New Metaobjects for Generalized Dispatch

Total Page:16

File Type:pdf, Size:1020Kb

Generalizers: New Metaobjects for Generalized Dispatch Generalizers: New Metaobjects for Generalized Dispatch Christophe Rhodes Jan Moringen David Lichteblau Department of Computing Universität Bielefeld ZenRobotics Ltd Goldsmiths, University of Technische Fakultät Vilhonkatu 5 A London 33594 Bielefeld FI-00100 Helsinki London SE14 6NW [email protected] [email protected] [email protected] bielefeld.de ABSTRACT first two chapters covered programmer interface concepts This paper introduces a new metaobject, the general- and the functions in the programmer interface [17, Chapter izer, which complements the existing specializer metaobject. 28] and were largely incorporated into the final standard; With the help of examples, we show that this metaobject al- the third chapter, covering a Metaobject Protocol (MOP) lows for the efficient implementation of complex non-class- for CLOS, was not. based dispatch within the framework of existing metaob- Nevertheless, the CLOS MOP continued to be developed, ject protocols. We present our modifications to the generic and the version documented in [8] has proven to be a rea- function invocation protocol from the Art of the Metaob- sonably robust design. While many implementations have ject Protocol; in combination with previous work, this pro- derived their implementations of CLOS from either the Clos- duces a fully-functional extension of the existing mechanism ette illustrative implementation in [8], or the Portable Com- for method selection and combination, including support for mon Loops implementation of CLOS from Xerox Parc, there method combination completely independent from method have been largely from-scratch reimplementations of CLOS selection. We discuss our implementation, within the SBCL (in CLISP1 and CCL2, at least) incorporating substantial implementation of Common Lisp, and in that context com- fractions of the Metaobject Protocol as described. pare the performance of the new protocol with the standard one, demonstrating that the new protocol can be tolerably efficient. AMOP space Report-No.: http://eprints.gold.ac.uk/id/eprint/9924 sparse slots Categories and Subject Descriptors D.1 [Software]: Programming Techniques|Object-oriented Programming; D.3.3 [Programming Languages]: Lan- guage Constructs and Features • General Terms • Languages, Design Keywords generic functions, specialization-oriented programming, method CLOS selection, method combination message-not-understood• arXiv:1403.2765v2 [cs.PL] 22 Apr 2014 1. INTRODUCTION The revisions to the original Common Lisp language [16] in- cluded the detailed specification of an object system, known as the Common Lisp Object System (CLOS), which was eventually standardized as part of the ANSI Common Lisp standard [12]. The object system as presented to the stan- Figure 1: MOP Design Space dardization committee was formed of three chapters. The Although it has stood the test of time, the CLOS MOP is neither without issues (e.g. semantic problems with make-method-lambda [1]; useful functions such as compute- effective-slot-definition-initargs being missing from the standard) nor is it a complete framework for the metaprogrammer to implement all conceivable variations of object-oriented behaviour. While metaprogramming offers 1GNU CLISP, at http://www.clisp.org/ 2Clozure Common Lisp, at http://ccl.clozure.com/ some possibilities for customization of the object system be- specializer haviour, those possibilities cannot extend arbitrarily in all specializer-accepts-generalizer-p directions (conceptually, if a given object system is a point in design space, then a MOP for that object system allows s-a-g-p gen.-spec. generalizer exploration of a region of design space around that point; see figure 1). In the case of the CLOS MOP, there is still generalizer-of an expectation that functionality is implemented with meth- class-of ods on generic functions, acting on objects with slots; it is class argument not possible, for example, to transparently implement sup- subtypep port for \message not understood" as in the message-passing eql paradigm, because the analogue of messages (generic func- eql-specializer tions) need to be defined before they are used. eql-specializer-object Nevertheless, the MOP is flexible, and is used for a number of things, including: documentation generation (where in- Figure 2: Dispatch Comparison trospection in the MOP is used to extract information from a running system3); object-relational mapping4 and other approaches to object persistence [11]; alternative backing describing each protocol function in detail and, where ap- stores for slots (hash-tables [7] or symbols [3]); and pro- plicable, relating it to existing protocol functions within the grammatic construction of metaobjects, for example for in- CLOS MOP. We survey related work in more detail in sec- teroperability with other language runtimes' object systems. tion 4, touching on work on customized dispatch schemes in other environments. Finally, we draw our conclusions from One area of functionality where there is scope for customiza- this work, and indicate directions for further development, tion by the metaprogrammer is in the mechanics and seman- in section 5; reading that section before the others indicates tics of method applicability and dispatch. While in princi- substantial trust in the authors' work. ple AMOP allows customization of dispatch in various dif- ferent ways (the metaprogrammer can define methods on 2. EXAMPLES protocol functions such as compute-applicable-methods, In this section, we present a number of examples of dis- compute-applicable-methods-using-classes), for exam- patch implemented using our protocol, which we describe ple, in practice implementation support for this was weak in section 3. For reasons of space, the metaprogram code until relatively recently5. examples in this section do not include some of the neces- Another potential mechanism for customizing dispatch is im- sary support code to run; complete implementations of each plicit in the class structure defined by AMOP: standard spe- of these cases, along with the integration of this protocol cializer objects (instances of class and eql-specializer) into the SBCL implementation [13] of Common Lisp, are are generalized instances of the specializer protocol class, included in the authors' repository6. and in principle there are no restrictions on the metapro- A note on terminology: we will attempt to distinguish be- grammer constructing additional subclasses. Previous work tween the user of an individual case of generalized dispatch [10] has explored the potential for customizing generic func- (the \programmer"), the implementor of a particular case tion dispatch using extended specializers, but there the of generalized dispatch (the \metaprogrammer"), and the metaprogrammer must override the entirety of the generic authors as the designers and implementors of our general- function invocation protocol (from compute-discriminating- ized dispatch protocol (the\metametaprogrammer", or more function on down), leading to toy implementations and du- likely \we"). plicated effort. This paper introduces a protocol for efficient and controlled 2.1 CONS specializers handling of new subclasses of specializer. In particular, One motivation for the use of generalized dispatch is in an it introduces the generalizer protocol class, which gener- extensible code walker: a new special form can be han- alizes the return value of class-of in method applicability dled simply by writing an additional method on the walking computation, and allows the metaprogrammer to hook into generic function, seamlessly interoperating with all existing cacheing schemes to avoid needless recomputation of effec- methods. In this use-case, dispatch is performed on the tive methods for sufficiently similar generic function argu- first element of lists. Semantically, we allow the program- ments (See Figure 2). mer to specialize any argument of methods with a new kind The remaining sections in this paper can be read in any of specializer, cons-specializer, which is applicable if and order. We give some motivating examples in section 2, in- only if the corresponding object is a cons whose car is eql cluding reimplementations of examples from previous work, to the symbol associated with the cons-specializer; these as well as examples which are poorly supported by previ- specializers are more specific than the cons class, but less ous protocols. We describe the protocol itself in section 3, specific than an eql-specializer on any given cons. The programmer code using these specializers is unchanged 3 as in many of the systems surveyed at from [10]; the benefits of the protocol described here are: https://sites.google.com/site/sabraonthehill/ that the separation of concerns is complete { method se- lisp-document-generation-apps lection is independent of method combination { and that 4e.g. CLSQL, at http://clsql.b9.com/ 5the Closer to MOP project, at http://common-lisp.net/ 6the tag els2014-submission in http://christophe. project/closer/, attempts to harmonize the different im- rhodes.io/git/specializable.git corresponds to the plementations of the metaobject protocol in Common Lisp. code repository at the point of submitting this paper. the protocol allows for efficient implementation where pos- (walk form env (cons form call-stack)))))) sible, even when method selection is customized. In an ap- (defmethod walk plication such as walking source code, we would expect to ((expr (cons let)) env call-stack) encounter special forms (distinguished by particular atoms (flet ((let-binding
Recommended publications
  • Bit Nove Signal Interface Processor
    www.audison.eu bit Nove Signal Interface Processor POWER SUPPLY CONNECTION Voltage 10.8 ÷ 15 VDC From / To Personal Computer 1 x Micro USB Operating power supply voltage 7.5 ÷ 14.4 VDC To Audison DRC AB / DRC MP 1 x AC Link Idling current 0.53 A Optical 2 sel Optical In 2 wire control +12 V enable Switched off without DRC 1 mA Mem D sel Memory D wire control GND enable Switched off with DRC 4.5 mA CROSSOVER Remote IN voltage 4 ÷ 15 VDC (1mA) Filter type Full / Hi pass / Low Pass / Band Pass Remote OUT voltage 10 ÷ 15 VDC (130 mA) Linkwitz @ 12/24 dB - Butterworth @ Filter mode and slope ART (Automatic Remote Turn ON) 2 ÷ 7 VDC 6/12/18/24 dB Crossover Frequency 68 steps @ 20 ÷ 20k Hz SIGNAL STAGE Phase control 0° / 180° Distortion - THD @ 1 kHz, 1 VRMS Output 0.005% EQUALIZER (20 ÷ 20K Hz) Bandwidth @ -3 dB 10 Hz ÷ 22 kHz S/N ratio @ A weighted Analog Input Equalizer Automatic De-Equalization N.9 Parametrics Equalizers: ±12 dB;10 pole; Master Input 102 dBA Output Equalizer 20 ÷ 20k Hz AUX Input 101.5 dBA OPTICAL IN1 / IN2 Inputs 110 dBA TIME ALIGNMENT Channel Separation @ 1 kHz 85 dBA Distance 0 ÷ 510 cm / 0 ÷ 200.8 inches Input sensitivity Pre Master 1.2 ÷ 8 VRMS Delay 0 ÷ 15 ms Input sensitivity Speaker Master 3 ÷ 20 VRMS Step 0,08 ms; 2,8 cm / 1.1 inch Input sensitivity AUX Master 0.3 ÷ 5 VRMS Fine SET 0,02 ms; 0,7 cm / 0.27 inch Input impedance Pre In / Speaker In / AUX 15 kΩ / 12 Ω / 15 kΩ GENERAL REQUIREMENTS Max Output Level (RMS) @ 0.1% THD 4 V PC connections USB 1.1 / 2.0 / 3.0 Compatible Microsoft Windows (32/64 bit): Vista, INPUT STAGE Software/PC requirements Windows 7, Windows 8, Windows 10 Low level (Pre) Ch1 ÷ Ch6; AUX L/R Video Resolution with screen resize min.
    [Show full text]
  • The Pros of Cons: Programming with Pairs and Lists
    The Pros of cons: Programming with Pairs and Lists CS251 Programming Languages Spring 2016, Lyn Turbak Department of Computer Science Wellesley College Racket Values • booleans: #t, #f • numbers: – integers: 42, 0, -273 – raonals: 2/3, -251/17 – floang point (including scien3fic notaon): 98.6, -6.125, 3.141592653589793, 6.023e23 – complex: 3+2i, 17-23i, 4.5-1.4142i Note: some are exact, the rest are inexact. See docs. • strings: "cat", "CS251", "αβγ", "To be\nor not\nto be" • characters: #\a, #\A, #\5, #\space, #\tab, #\newline • anonymous func3ons: (lambda (a b) (+ a (* b c))) What about compound data? 5-2 cons Glues Two Values into a Pair A new kind of value: • pairs (a.k.a. cons cells): (cons v1 v2) e.g., In Racket, - (cons 17 42) type Command-\ to get λ char - (cons 3.14159 #t) - (cons "CS251" (λ (x) (* 2 x)) - (cons (cons 3 4.5) (cons #f #\a)) Can glue any number of values into a cons tree! 5-3 Box-and-pointer diagrams for cons trees (cons v1 v2) v1 v2 Conven3on: put “small” values (numbers, booleans, characters) inside a box, and draw a pointers to “large” values (func3ons, strings, pairs) outside a box. (cons (cons 17 (cons "cat" #\a)) (cons #t (λ (x) (* 2 x)))) 17 #t #\a (λ (x) (* 2 x)) "cat" 5-4 Evaluaon Rules for cons Big step seman3cs: e1 ↓ v1 e2 ↓ v2 (cons) (cons e1 e2) ↓ (cons v1 v2) Small-step seman3cs: (cons e1 e2) ⇒* (cons v1 e2); first evaluate e1 to v1 step-by-step ⇒* (cons v1 v2); then evaluate e2 to v2 step-by-step 5-5 cons evaluaon example (cons (cons (+ 1 2) (< 3 4)) (cons (> 5 6) (* 7 8))) ⇒ (cons (cons 3 (< 3 4))
    [Show full text]
  • Signedness-Agnostic Program Analysis: Precise Integer Bounds for Low-Level Code
    Signedness-Agnostic Program Analysis: Precise Integer Bounds for Low-Level Code Jorge A. Navas, Peter Schachte, Harald Søndergaard, and Peter J. Stuckey Department of Computing and Information Systems, The University of Melbourne, Victoria 3010, Australia Abstract. Many compilers target common back-ends, thereby avoid- ing the need to implement the same analyses for many different source languages. This has led to interest in static analysis of LLVM code. In LLVM (and similar languages) most signedness information associated with variables has been compiled away. Current analyses of LLVM code tend to assume that either all values are signed or all are unsigned (except where the code specifies the signedness). We show how program analysis can simultaneously consider each bit-string to be both signed and un- signed, thus improving precision, and we implement the idea for the spe- cific case of integer bounds analysis. Experimental evaluation shows that this provides higher precision at little extra cost. Our approach turns out to be beneficial even when all signedness information is available, such as when analysing C or Java code. 1 Introduction The “Low Level Virtual Machine” LLVM is rapidly gaining popularity as a target for compilers for a range of programming languages. As a result, the literature on static analysis of LLVM code is growing (for example, see [2, 7, 9, 11, 12]). LLVM IR (Intermediate Representation) carefully specifies the bit- width of all integer values, but in most cases does not specify whether values are signed or unsigned. This is because, for most operations, two’s complement arithmetic (treating the inputs as signed numbers) produces the same bit-vectors as unsigned arithmetic.
    [Show full text]
  • The Use of UML for Software Requirements Expression and Management
    The Use of UML for Software Requirements Expression and Management Alex Murray Ken Clark Jet Propulsion Laboratory Jet Propulsion Laboratory California Institute of Technology California Institute of Technology Pasadena, CA 91109 Pasadena, CA 91109 818-354-0111 818-393-6258 [email protected] [email protected] Abstract— It is common practice to write English-language 1. INTRODUCTION ”shall” statements to embody detailed software requirements in aerospace software applications. This paper explores the This work is being performed as part of the engineering of use of the UML language as a replacement for the English the flight software for the Laser Ranging Interferometer (LRI) language for this purpose. Among the advantages offered by the of the Gravity Recovery and Climate Experiment (GRACE) Unified Modeling Language (UML) is a high degree of clarity Follow-On (F-O) mission. However, rather than use the real and precision in the expression of domain concepts as well as project’s model to illustrate our approach in this paper, we architecture and design. Can this quality of UML be exploited have developed a separate, ”toy” model for use here, because for the definition of software requirements? this makes it easier to avoid getting bogged down in project details, and instead to focus on the technical approach to While expressing logical behavior, interface characteristics, requirements expression and management that is the subject timeliness constraints, and other constraints on software using UML is commonly done and relatively straight-forward, achiev- of this paper. ing the additional aspects of the expression and management of software requirements that stakeholders expect, especially There is one exception to this choice: we will describe our traceability, is far less so.
    [Show full text]
  • Metaclasses: Generative C++
    Metaclasses: Generative C++ Document Number: P0707 R3 Date: 2018-02-11 Reply-to: Herb Sutter ([email protected]) Audience: SG7, EWG Contents 1 Overview .............................................................................................................................................................2 2 Language: Metaclasses .......................................................................................................................................7 3 Library: Example metaclasses .......................................................................................................................... 18 4 Applying metaclasses: Qt moc and C++/WinRT .............................................................................................. 35 5 Alternatives for sourcedefinition transform syntax .................................................................................... 41 6 Alternatives for applying the transform .......................................................................................................... 43 7 FAQs ................................................................................................................................................................. 46 8 Revision history ............................................................................................................................................... 51 Major changes in R3: Switched to function-style declaration syntax per SG7 direction in Albuquerque (old: $class M new: constexpr void M(meta::type target,
    [Show full text]
  • Meta-Class Features for Large-Scale Object Categorization on a Budget
    Meta-Class Features for Large-Scale Object Categorization on a Budget Alessandro Bergamo Lorenzo Torresani Dartmouth College Hanover, NH, U.S.A. faleb, [email protected] Abstract cation accuracy over a predefined set of classes, and without consideration of the computational costs of the recognition. In this paper we introduce a novel image descriptor en- We believe that these two assumptions do not meet the abling accurate object categorization even with linear mod- requirements of modern applications of large-scale object els. Akin to the popular attribute descriptors, our feature categorization. For example, test-recognition efficiency is a vector comprises the outputs of a set of classifiers evaluated fundamental requirement to be able to scale object classi- on the image. However, unlike traditional attributes which fication to Web photo repositories, such as Flickr, which represent hand-selected object classes and predefined vi- are growing at rates of several millions new photos per sual properties, our features are learned automatically and day. Furthermore, while a fixed set of object classifiers can correspond to “abstract” categories, which we name meta- be used to annotate pictures with a set of predefined tags, classes. Each meta-class is a super-category obtained by the interactive nature of searching and browsing large im- grouping a set of object classes such that, collectively, they age collections calls for the ability to allow users to define are easy to distinguish from other sets of categories. By us- their own personal query categories to be recognized and ing “learnability” of the meta-classes as criterion for fea- retrieved from the database, ideally in real-time.
    [Show full text]
  • Bit, Byte, and Binary
    Bit, Byte, and Binary Number of Number of values 2 raised to the power Number of bytes Unit bits 1 2 1 Bit 0 / 1 2 4 2 3 8 3 4 16 4 Nibble Hexadecimal unit 5 32 5 6 64 6 7 128 7 8 256 8 1 Byte One character 9 512 9 10 1024 10 16 65,536 16 2 Number of bytes 2 raised to the power Unit 1 Byte One character 1024 10 KiloByte (Kb) Small text 1,048,576 20 MegaByte (Mb) A book 1,073,741,824 30 GigaByte (Gb) An large encyclopedia 1,099,511,627,776 40 TeraByte bit: Short for binary digit, the smallest unit of information on a machine. John Tukey, a leading statistician and adviser to five presidents first used the term in 1946. A single bit can hold only one of two values: 0 or 1. More meaningful information is obtained by combining consecutive bits into larger units. For example, a byte is composed of 8 consecutive bits. Computers are sometimes classified by the number of bits they can process at one time or by the number of bits they use to represent addresses. These two values are not always the same, which leads to confusion. For example, classifying a computer as a 32-bit machine might mean that its data registers are 32 bits wide or that it uses 32 bits to identify each address in memory. Whereas larger registers make a computer faster, using more bits for addresses enables a machine to support larger programs.
    [Show full text]
  • 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.
    [Show full text]
  • A Metaobject Protocol for Fault-Tolerant CORBA Applications
    A Metaobject Protocol for Fault-Tolerant CORBA Applications Marc-Olivier Killijian*, Jean-Charles Fabre*, Juan-Carlos Ruiz-Garcia*, Shigeru Chiba** *LAAS-CNRS, 7 Avenue du Colonel Roche **Institute of Information Science and 31077 Toulouse cedex, France Electronics, University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305-8573, Japan Abstract The corner stone of a fault-tolerant reflective The use of metalevel architectures for the architecture is the MOP. We thus propose a special implementation of fault-tolerant systems is today very purpose MOP to address the problems of general-purpose appealing. Nevertheless, all such fault-tolerant systems ones. We show that compile-time reflection is a good have used a general-purpose metaobject protocol (MOP) approach for developing a specialized runtime MOP. or are based on restricted reflective features of some The definition and the implementation of an object-oriented language. According to our past appropriate runtime metaobject protocol for implementing experience, we define in this paper a suitable metaobject fault tolerance into CORBA applications is the main protocol, called FT-MOP for building fault-tolerant contribution of the work reported in this paper. This systems. We explain how to realize a specialized runtime MOP, called FT-MOP (Fault Tolerance - MetaObject MOP using compile-time reflection. This MOP is CORBA Protocol), is sufficiently general to be used for other aims compliant: it enables the execution and the state evolution (mobility, adaptability, migration, security). FT-MOP of CORBA objects to be controlled and enables the fault provides a mean to attach dynamically fault tolerance tolerance metalevel to be developed as CORBA software. strategies to CORBA objects as CORBA metaobjects, enabling thus these strategies to be implemented as 1 .
    [Show full text]
  • Floating Point Arithmetic
    Systems Architecture Lecture 14: Floating Point Arithmetic Jeremy R. Johnson Anatole D. Ruslanov William M. Mongan Some or all figures from Computer Organization and Design: The Hardware/Software Approach, Third Edition, by David Patterson and John Hennessy, are copyrighted material (COPYRIGHT 2004 MORGAN KAUFMANN PUBLISHERS, INC. ALL RIGHTS RESERVED). Lec 14 Systems Architecture 1 Introduction • Objective: To provide hardware support for floating point arithmetic. To understand how to represent floating point numbers in the computer and how to perform arithmetic with them. Also to learn how to use floating point arithmetic in MIPS. • Approximate arithmetic – Finite Range – Limited Precision • Topics – IEEE format for single and double precision floating point numbers – Floating point addition and multiplication – Support for floating point computation in MIPS Lec 14 Systems Architecture 2 Distribution of Floating Point Numbers e = -1 e = 0 e = 1 • 3 bit mantissa 1.00 X 2^(-1) = 1/2 1.00 X 2^0 = 1 1.00 X 2^1 = 2 1.01 X 2^(-1) = 5/8 1.01 X 2^0 = 5/4 1.01 X 2^1 = 5/2 • exponent {-1,0,1} 1.10 X 2^(-1) = 3/4 1.10 X 2^0 = 3/2 1.10 X 2^1= 3 1.11 X 2^(-1) = 7/8 1.11 X 2^0 = 7/4 1.11 X 2^1 = 7/2 0 1 2 3 Lec 14 Systems Architecture 3 Floating Point • An IEEE floating point representation consists of – A Sign Bit (no surprise) – An Exponent (“times 2 to the what?”) – Mantissa (“Significand”), which is assumed to be 1.xxxxx (thus, one bit of the mantissa is implied as 1) – This is called a normalized representation • So a mantissa = 0 really is interpreted to be 1.0, and a mantissa of all 1111 is interpreted to be 1.1111 • Special cases are used to represent denormalized mantissas (true mantissa = 0), NaN, etc., as will be discussed.
    [Show full text]
  • OMG Meta Object Facility (MOF) Core Specification
    Date : October 2019 OMG Meta Object Facility (MOF) Core Specification Version 2.5.1 OMG Document Number: formal/2019-10-01 Standard document URL: https://www.omg.org/spec/MOF/2.5.1 Normative Machine-Readable Files: https://www.omg.org/spec/MOF/20131001/MOF.xmi Informative Machine-Readable Files: https://www.omg.org/spec/MOF/20131001/CMOFConstraints.ocl https://www.omg.org/spec/MOF/20131001/EMOFConstraints.ocl Copyright © 2003, Adaptive Copyright © 2003, Ceira Technologies, Inc. Copyright © 2003, Compuware Corporation Copyright © 2003, Data Access Technologies, Inc. Copyright © 2003, DSTC Copyright © 2003, Gentleware Copyright © 2003, Hewlett-Packard Copyright © 2003, International Business Machines Copyright © 2003, IONA Copyright © 2003, MetaMatrix Copyright © 2015, Object Management Group Copyright © 2003, Softeam Copyright © 2003, SUN Copyright © 2003, Telelogic AB Copyright © 2003, Unisys USE OF SPECIFICATION - TERMS, CONDITIONS & NOTICES The material in this document details an Object Management Group specification in accordance with the terms, conditions and notices set forth below. This document does not represent a commitment to implement any portion of this specification in any company's products. The information contained in this document is subject to change without notice. LICENSES The companies listed above have granted to the Object Management Group, Inc. (OMG) a nonexclusive, royalty-free, paid up, worldwide license to copy and distribute this document and to modify this document and distribute copies of the modified version. Each of the copyright holders listed above has agreed that no person shall be deemed to have infringed the copyright in the included material of any such copyright holder by reason of having used the specification set forth herein or having conformed any computer software to the specification.
    [Show full text]
  • Chapter 15 Functional Programming
    Topics Chapter 15 Numbers n Natural numbers n Haskell numbers Functional Programming Lists n List notation n Lists as a data type n List operations Chapter 15: Functional Programming 2 Numbers Natural Numbers The natural numbers are the numbers 0, 1, Haskell provides a sophisticated 2, and so on, used for counting. hierarchy of type classes for describing various kinds of numbers. Introduced by the declaration data Nat = Zero | Succ Nat Although (some) numbers are provided n The constructor Succ (short for ‘successor’) as primitives data types, it is has type Nat à Nat. theoretically possible to introduce them n Example: as an element of Nat the number 7 through suitable data type declarations. would be represented by Succ(Succ(Succ(Succ(Succ(Succ(Succ Zero)))))) Chapter 15: Functional Programming 3 Chapter 15: Functional Programming 4 Natural Numbers Natural Numbers Every natural number is represented by a Multiplication ca be defined by unique value of Nat. (x) :: Nat à Nat à Nat m x Zero = Zero On the other hand, not every value of Nat m x Succ n = (m x n) + m represents a well-defined natural number. n Example: ^, Succ ^, Succ(Succ ^) Nat can be a member of the type class Eq Addition ca be defined by instance Eq Nat where Zero == Zero = True (+) :: Nat à Nat à Nat Zero == Succ n = False m + Zero = m Succ m == Zero = False m + Succ n = Succ(m + n) Succ m == Succ n = (m == n) Chapter 15: Functional Programming 5 Chapter 15: Functional Programming 6 1 Natural Numbers Haskell Numbers Nat can be a member of the type class Ord instance
    [Show full text]