DOCSLIB.ORG

A Modular Monadic Action Semantics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Modular Monadic Action Semantics The following paper was originally published in the Proceedings of the Conference on Domain-Specific Languages Santa Barbara, California, October 1997 A Modular Monadic Action Semantics Keith Wansbrough and John Hamer University of Auckland For more information about USENIX Association contact: 1. Phone: 510 528-8649 2. FAX: 510 548-5738 3. Email: [email protected] 4. WWW URL:http://www.usenix.org A Modular Monadic Action Semantics Keith Wansbrough John Hamer Department of Computer Science University of Auckland Auckland, New Zealand g fkeith-w,j-hamer @cs.auckland.ac.nz Abstract clearly and precisely defined; modular enough to change A domain-specific language (DSL) is a framework incrementally; and amenable to formal reasoning. Differ- which is designed to precisely meet the needs of a particu- ent tools exist that address these varied requirements, but lar application. Domain-specific languages exist for a vari- few make any attempt to address them all. Compiler gener- ety of reasons. As productivity tools, they are used to make ators provide efficient implementations, but they typically application prototyping and development faster and more have weak formal properties. We do not consider such sys- robust in the presence of evolving requirements. Further- tems further in this paper. Semantic formalisms, such as more, by bridging the “semantic gap” between an applica- denotational semantics and structural operational seman- tion domain and program code, DSLs increase the oppor- tics, have richly developed theories but are difficult to use tunity to apply formal methods in proving properties of an and lack modularity. application. The conceptual distance between the high-level language In this paper, we contribute a synthesis of two existing and established semantic formalisms is huge. Writing such systems that address the problem of providing sound se- specifications is a tedious and difficult task. Natural con- mantic descriptions of realistic programming languages: cepts in the high-level language must be accurately simu- action semantics and modular monadic semantics. The lated by constructs built from the small range of primitives resulting synthesis, modular monadic action semantics, is in the semantic formalism. The probability of introducing compatible with action semantics yet adds true modularity errors is large, and the maintainability of the specification and allows domain specific specifications to be made at a is poor. variety of levels. Three attempts at solving the problem of providing sound semantic descriptions of realistic programming lan- 1 Introduction guages are presented here. The first is action seman- tics [Mos92], a highly readable notation with formal foun- “I’d rather write programs to write programs than dations in Peter Mosses’s unified algebra and Plotkin’s write programs.” (Programming proverb). structural operational semantics [Plo83]. This system has proven quite popular, and has been used to specify a num- A domain-specific language (DSL) is a framework ber of existing and evolving languages. which is designed to precisely meet the needs of a particu- The second is Hudak, Liang and Jones’ modular lar application. Domain-specific languages exist for a vari- monadic semantics [LH96]. Modular monadic semantics ety of reasons. As productivity tools, they are used to make is a structured form of denotational semantics, embedded application prototyping and development faster and more in the Haskell language. As a relatively new system it is robust in the presence of evolving requirements. Further- yet to gain widespread use, but it has a number of highly more, by bridging the “semantic gap” between an applica- attractive features, foremost its excellent modularity prop- tion domain and program code, DSLs increase the oppor- erties. tunity to apply formal methods in proving properties of an These two systems can be seen as competing for the application. same market (Figure 1(c) and (d)): both are attempts to Designing and implementing a domain specific language reduce the conceptual distance that must be bridged when is, however, problematic. Putting aside the requirement formally specifying a high-level language (compare with for an efficient implementation, the language needs to be: Figure 1(a) and (b)). Both appear to do so successfully; This work was supported in part by a scholarship from the University they are, however, different DSLs and are based in differ- of Auckland. ent semantic formalisms. HLL HLL HLL HLL HLL The primary aim of action semantics is to al- low useful semantic descriptions of realistic pro- mo d. gramming languages. [Mos92, p. xv] mo d. mo d. AS MMS AS It aims at being simultaneously formal and readable, and mo d. mono. mono. achieves this goal admirably. An action semantic descrip- MMS tion is entirely formal, yet it can be intuitively understood mo d. mono. to a surprising degree by someone with no prior knowledge mo d. -calculus SOS -calculus SOS SOS of the system. However, action semantics has two significant limita- b c d e a tions. Firstly, it is incomplete. Not all programming lan- guage concepts can be represented directly within action Figure 1: Formal specification techniques. semantics—only those which Mosses has chosen to build into the system. There is no provision for the extension of action semantics. Secondly, action semantics theory has The third approach arises our observation that action not progressed very far: it is difficult to use an action se- semantics and modular monadic semantics have much to mantics of a language to prove properties of that language offer each other. Action semantics provides a friendly or of programs written within it. syntax to the language specifier, and encapsulates a sub- stantial but fixed range of language concepts. Modular Despite these disadvantages, action semantics has monadic semantics, on the other hand, provides a rather proven quite popular and rather successful. A num- less friendly syntax, but with complete flexibility and ex- ber of compiler generators based on action semantics tensibility afforded by its internal modularity. By combin- exist [Ørb94, BMW92, Pal92], along with at least one ing these two systems, we obtain a tiered system containing tool [vDM96] for assistance in developing new action se- two domain-specific semantic notations, featuring all the mantic descriptions. Action semantic descriptions exist for key features of action semantics along with the underlying a number of real languages [Mos96a, x7.1], and others are flexibility and extensibility of modular monadic semantics being developed. An action semantics for an intermedi- (Figure 1(e)). This system we call modular monadic action ate language for compilers, ANDF-FS [NT94, HT94], is semantics (MMAS). currently in use in the ‘real world’, by the Open Software The user of modular monadic action semantics specifies Foundation. Work is progressing in a number of directions. the high-level language using the rich set of primitives pro- In the following sections the essential features of ac- vided by action semantics. If the language requires a con- tion semantics are briefly summarised. More detail can be cept that is not present in action semantics, the specifier found in Mosses’ book [Mos92], or his tutorial [Mos96b]. simply drops down one level, and uses the underlying mod- ular monadic semantics to specify the new feature. If this is not sufficient, the modular monadic layer itself may be 2.1 Structure of action semantics modified or extended as required. All this takes place in a An action semantic description (ASD) of a language spec- highly modular fashion, with little or no change to existing ifies the semantics of the language by means of actions, parts of the specification. Furthermore, theories developed representing computations. The action corresponding to a at each layer can also be developed in a modular fashion. given program phrase is built up from primitive actions and New features can be introduced without undermining the action combinators. Data referred to by the actions may be validity of existing proofs. accessed by means of yielders, and new types of data may In the remainder of this paper we describe action seman- be readily defined in an algebraic fashion. tics, modular monadic semantics, and modular monadic Action semantics divides program behaviour into a num- action semantics in more detail, and we investigate some ber of facets, corresponding to the types of information of the applications of MMAS. We conclude with a look dealt with. The basic facet refers to control flow. The func- at some related work, some concluding comments, and tional facet refers to transient information, i.e., data passed directions for future work. Full details on modular between successive actions. The declarative facet refers to monadic action semantics can be found in Wansbrough’s scoped information, i.e., bindings of tokens to data. The thesis [Wan97]. imperative facet refers to stable information, i.e., the stor- age of data in cells. Finally, the communicative facet refers 2 Action semantics to permanent information, i.e., the communication of data between distributed actions. Two further facets, the reflec- Action semantics [Mos92, Mos96a] is a notation devel- tive and directive facets, refer to reflection and indirection. oped over some years by Mosses at Aarhus University. As Action semantics has these seven computational concepts Mosses puts it, built in, and they can be used directly by specifications. The primitive actions, yielders and data of action seman- 2.2 Semantics tics are separated into these categories, and are intended to Action semantics is intended to be a formal notation, and act on only one facet at a time. This automatically lends a in order to achieve this its own semantics must be precisely degree of modularity to an action semantic description: ac- and formally defined. Mosses chose to do this by providing tions involving only, say, basic and functional behaviour a low-level definition of action semantics as a structural (such as expression evaluation) need not concern them- operational semantics (SOS) [Plo81, Plo83], using a slight selves with behaviour in other facets (such as the declar- variation on Plotkin’s original approach.
Load more

Recommended publications
  • Uncovering Dynamic Semantic Networks in the Brain Using Novel Approaches for EEG/MEG Connectome Reconstruction
    Uncovering Dynamic Semantic Networks in the Brain Using Novel Approaches for EEG/MEG Connectome Reconstruction SEYEDEHREZVAN FARAHIBOZORG SELWYN COLLEGE MRC COGNITION AND BRAIN SCIENCES UNIT SCHOOL OF CLINICAL MEDICINE UNIVERSITY OF CAMBRIDGE This dissertation is submitted for the degree of Doctor of Philosophy February 2018 Uncovering Dynamic Semantic Networks in the Brain Using Novel Approaches for EEG/MEG Connectome Reconstruction Seyedehrezvan Farahibozorg The current thesis addresses some of the unresolved predictions of recent models of the semantic brain system, such as the hub-and-spokes model. In particular, we tackle different aspects of the hypothesis that a widespread network of interacting heteromodal (hub(s)) and unimodal (spokes) cortices underlie semantic cognition. For this purpose, we use connectivity analyses, measures of graph theory and permutation-based statistics with source reconstructed Electro- /MagnetoEncephaloGraphy (EEG/MEG) data in order to track dynamic modulations of activity and connectivity within the semantic networks while a concept unfolds in the brain. Moreover, in order to obtain more accurate connectivity estimates of the semantic networks, we propose novel methods for some of the challenges associated with EEG/MEG connectivity analysis in source space. We utilised data-driven analyses of EEG/MEG recordings of visual word recognition paradigms and found that: 1) Bilateral Anterior Temporal Lobes (ATLs) acted as potential processor hubs for higher- level abstract representation of concepts. This was reflected in modulations of activity by multiple contrasts of semantic variables; 2) ATL and Angular Gyrus (AG) acted as potential integrator hubs for integration of information produced in distributed semantic areas. This was observed using Dynamic Causal Modelling of connectivity among the main left-hemispheric candidate hubs and modulations of functional connectivity of ATL and AG to semantic spokes by word concreteness.
    [Show full text]
  • Head-Order Techniques and Other Pragmatics of Lambda Calculus Graph Reduction
    HEAD-ORDER TECHNIQUES AND OTHER PRAGMATICS OF LAMBDA CALCULUS GRAPH REDUCTION Nikos B. Troullinos DISSERTATION.COM Boca Raton Head-Order Techniques and Other Pragmatics of Lambda Calculus Graph Reduction Copyright © 1993 Nikos B. Troullinos All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from the publisher. Dissertation.com Boca Raton, Florida USA • 2011 ISBN-10: 1-61233-757-0 ISBN-13: 978-1-61233-757-9 Cover image © Michael Travers/Cutcaster.com Abstract In this dissertation Lambda Calculus reduction is studied as a means of improving the support for declarative computing. We consider systems having reduction semantics; i.e., systems in which computations consist of equivalence-preserving transformations between expressions. The approach becomes possible by reducing expressions beyond weak normal form, allowing expression-level output values, and avoiding compilation-centered transformations. In particular, we develop reduction algorithms which, although not optimal, are highly efficient. A minimal linear notation for lambda expressions and for certain runtime structures is introduced for explaining operational features. This notation is related to recent theories which formalize the notion of substitution. Our main reduction technique is Berkling’s Head Order Reduction (HOR), a delayed substitution algorithm which emphasizes the extended left spine. HOR uses the de Bruijn representation for variables and a mechanism for artificially binding relatively free variables. HOR produces a lazy variant of the head normal form, the natural midway point of reduction. It is shown that beta reduction in the scope of relative free variables is not hard.
    [Show full text]
  • What Does Semantic Tiling of the Cortex Tell Us About Semantics? MARK ⁎ Lawrence W
    Neuropsychologia 105 (2017) 18–38 Contents lists available at ScienceDirect Neuropsychologia journal homepage: www.elsevier.com/locate/neuropsychologia What does semantic tiling of the cortex tell us about semantics? MARK ⁎ Lawrence W. Barsalou University of Glasgow, UK ARTICLE INFO ABSTRACT Keywords: Recent use of voxel-wise modeling in cognitive neuroscience suggests that semantic maps tile the cortex. Semantics Although this impressive research establishes distributed cortical areas active during the conceptual processing Conceptual processing that underlies semantics, it tells us little about the nature of this processing. While mapping concepts between Neural encoding and decoding Marr's computational and implementation levels to support neural encoding and decoding, this approach ignores Multi-voxel pattern analysis Marr's algorithmic level, central for understanding the mechanisms that implement cognition, in general, and Explanatory levels conceptual processing, in particular. Following decades of research in cognitive science and neuroscience, what Cognitive mechanisms do we know so far about the representation and processing mechanisms that implement conceptual abilities? Most basically, much is known about the mechanisms associated with: (1) feature and frame representations, (2) grounded, abstract, and linguistic representations, (3) knowledge-based inference, (4) concept composition, and (5) conceptual flexibility. Rather than explaining these fundamental representation and processing mechanisms, semantic tiles simply provide a trace of their activity over a relatively short time period within a specific learning context. Establishing the mechanisms that implement conceptual processing in the brain will require more than mapping it to cortical (and sub-cortical) activity, with process models from cognitive science likely to play central roles in specifying the intervening mechanisms.
    [Show full text]
  • Former Associate Professor of Linguistics) [email protected] Working Version 16.2
    Cognitax Tool Grammar: Re-factoring the Generative Program A pervasive action dimension for linguistic description, theory and models 12 Lawrence R. Smith (Former Associate Professor of Linguistics) [email protected] Working Version 16.2 This is a preliminary and frequently changing dynamic document responsive to reader critique and is likely not the latest version available by contacting the author. (Note the title has changed.3) The later version always supersedes the earlier and typically may include major revisions. Comments and challenges are welcome for future versions. The extended version under development is freely available on request from the author. 1 We are indebted for the incisive comments of readers who suggested constructive improvements even as the ideas presented here were sometimes at considerable variance with their own current working frameworks. We owe special thanks to the following for comments on either parts or the whole of this work: John Hewson, Paul Postal, Vit Bubenik, Pieter Seurens and Willem de Reuse. 2We had considered an alternative title for this paper since it seeks to explain malformation: “A Review of Verbal Misbehavior” 3 From version 12.9 ‘Cognitax’ replaces ‘Pragmatax’ to clarify that Tool Grammar is distinct from pragmatics, as well as separate work that may refer to grammatical tools. Both were absent from the title in an earlier version. 1 Operative Motivating Hypotheses of Tool Grammar 1. There exists an empirically evident necessity for representation of linguistic structural action intent which has been generally overlooked in the theory of language, including centralized configurational syntax in the generative program. 2. Linguistic structural action intent extends the basic Chomskyan focus on linguistic creativity (unbounded generation from finite means) to a new level of representation useful for explaining and constraining the inventive means by which the species- specific features of human language are effected.
    [Show full text]
  • An Agile Approach to Language Modelling and Development
    ISSE manuscript No. (will be inserted by the editor) An Agile Approach to Language Modelling and Development Adrian Johnstone · Peter D. Mosses · Elizabeth Scott Received: ??? / Accepted: ??? Abstract We have developed novel techniques for 1 Introduction component-based specification of programming languages. In our approach, the semantics of each fundamental We are developing a component-based approach to language programming construct is specified independently, using an modelling. Our models are formal specifications of syntax inherently modular framework such that no reformulation and semantics. is needed when constructs are combined. A language Language designers already use formal specifications specification consists of an unrestricted context-free for syntax; we claim that formal semantics can be useful grammar for the syntax of programs, together with an and worthwhile for them too, provided that the following analysis of each language construct in terms of fundamental features are combined in a single, coherent framework: constructs. An open-ended collection of fundamental – a substantial collection of specification components that constructs is currently being developed. can be used without change; When supported by appropriate tools, our techniques – accessible formalisms and notation; allow a more agile approach to the design, modelling, – tool support for developing and checking specifications; and implementation of programming and domain-specific – tools for generating (at least prototype) implementations languages. In particular, our approach encourages lan- from tentative language specifications; guage designers to proceed incrementally, using prototype – successful case studies involving major languages; and implementations generated from specifications to test – an online repository providing access to all specifica- tentative designs. The components of our specifications tions.
    [Show full text]
  • Chapter 1 Introduction
    Chapter Intro duction A language is a systematic means of communicating ideas or feelings among people by the use of conventionalized signs In contrast a programming lan guage can be thought of as a syntactic formalism which provides ameans for the communication of computations among p eople and abstract machines Elements of a programming language are often called programs They are formed according to formal rules which dene the relations between the var ious comp onents of the language Examples of programming languages are conventional languages likePascal or C and also the more the oretical languages such as the calculus or CCS A programming language can b e interpreted on the basis of our intuitive con cept of computation However an informal and vague interpretation of a pro gramming language may cause inconsistency and ambiguity As a consequence dierent implementations maybegiven for the same language p ossibly leading to dierent sets of computations for the same program Had the language in terpretation b een dened in a formal way the implementation could b e proved or disproved correct There are dierent reasons why a formal interpretation of a programming language is desirable to give programmers unambiguous and p erhaps informative answers ab out the language in order to write correct programs to give implementers a precise denition of the language and to develop an abstract but intuitive mo del of the language in order to reason ab out programs and to aid program development from sp ecications Mathematics often emphasizes
    [Show full text]
  • Basic Action Theory Basic Research in Computer Science
    BRICS BRICS RS-95-25 S. B. Lassen: Basic Action Theory Basic Research in Computer Science Basic Action Theory Søren B. Lassen BRICS Report Series RS-95-25 ISSN 0909-0878 May 1995 Copyright c 1995, BRICS, Department of Computer Science University of Aarhus. All rights reserved. Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS Department of Computer Science University of Aarhus Ny Munkegade, building 540 DK - 8000 Aarhus C Denmark Telephone: +45 8942 3360 Telefax: +45 8942 3255 Internet: [email protected] BRICS publications are in general accessible through WWW and anonymous FTP: http://www.brics.dk/ ftp ftp.brics.dk (cd pub/BRICS) Basic Action Theory ∗ S. B. Lassen BRICS† Department of Computer Science University of Aarhus email: [email protected] URL: http://www.daimi.aau.dk/~thales Abstract Action semantics is a semantic description framework with very good pragmatic properties but until now a rather weak theory for reasoning about programs. A strong action theory would have a great practical potential, as it would facilitate reasoning about the large class of programming languages that can be described in action semantics. This report develops the foundations for a richer action theory, by bringing together concepts and techniques from process theory and from work on operational reasoning about functional programs. Se- mantic preorders and equivalences in the action semantics setting are studied and useful operational techniques for establishing contextual equivalences are presented.
    [Show full text]
  • Formal Semantics of Programming Languages —Anoverview—
    Electronic Notes in Theoretical Computer Science 148 (2006) 41–73 www.elsevier.com/locate/entcs Formal Semantics of Programming Languages —AnOverview— Peter D. Mosses1 Department of Computer Science University of Wales Swansea Swansea, United Kingdom Abstract These notes give an overview of the main frameworks that have been developed for specifying the formal semantics of programming languages. Some of the pragmatic aspects of semantic de- scriptions are discussed, including modularity, and potential applicability to visual and modelling languages. References to the literature provide starting points for further study. Keywords: semantics, operational semantics, denotational semantics, SOS, MSOS, reduction semantics, abstract state machines, monadic semantics, axiomatic semantics, action semantics, programming languages, modelling languages, visual languages 1 Introduction £ A semantics for a programming language models the computational meaning of each program. The computational meaning of a program—i.e. what actually happens when a program is executed on some real computer—is far too complex to be de- scribed in its entirety. Instead, a semantics for a programming language pro- vides abstract entities that represent just the relevant features of all possible executions, and ignores details that have no relevance to the correctness of implementations. Usually, the only features deemed to be relevant are the relationship between input and output, and whether the execution terminates 1 Email: [email protected] 1571-0661/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.entcs.2005.12.012 42 P.D. Mosses / Electronic Notes in Theoretical Computer Science 148 (2006) 41–73 or not. Details specific to implementations, such as the actual machine ad- dresses where the values of variables are stored, the possibility of ‘garbage collection’, and the exact running time of the program, may all be ignored in the semantics.
    [Show full text]
  • Chapter 13 ACTION SEMANTICS
    Chapter 13 ACTION SEMANTICS he formal methods discussed in earlier chapters, particularly denotational semantics and structural operational semantics, have T been used extensively to provide accurate and unambiguous defini- tions of programming languages. Unlike informal definitions written in En- glish or some other natural language, formal definitional techniques can serve as a basis for proving properties of programming languages and the correctness of programs. Although most programmers rely on informal speci- fications of languages, these definitions are often vague, incomplete, and even erroneous. English does not lend itself to precise and unambiguous definitions. In spite of the arguments for relying on formal specifications of programming languages, programmers generally avoid them when learning, trying to un- derstand, or even implementing a programming language. They find formal definitions notationally dense, cryptic, and unlike the way they view the be- havior of programming languages. Furthermore, formal specifications are difficult to create accurately, to modify, and to extend. Formal definitions of large programming languages are overwhelming to both the language de- signer and the language user, and therefore remain mostly unread. Programmers understand programming languages in terms of basic concepts such as control flow, bindings, modifications of storage, and parameter pass- ing. Formal specifications often obscure these notions to the point that the reader must invest considerable time to determine whether a language fol- lows static or dynamic scoping and how parameters are actually passed. Sometimes the most fundamental concepts of the programming language are the hardest to understand in a formal definition. Action semantics, which attempts to answer these criticisms of formal meth- ods for language specification, has been developed over the past few years by Peter Mosses with the collaboration of David Watt.
    [Show full text]
  • Action Semantics
    Action Semantics Formal Syntax BNF — In common use Formal Specification of Programming Languages Formal Semantics Advantages: Denotational semantics • Unambiguous definitions Structural operational semantics • Basis for proving properties of programs and languages Axiomatic semantics • Mechanical generation of language Algebraic semantics processors Used only by specialists in prog. languages. Disadvantages: Action Semantics • Notationally dense • Developed by Peter Mosses and David Watt • Often cryptic • Based on ordinary computation concepts • Unlike the way programmers view languages • Difficult to create and modify accurately • English-like notation (readable) • Completely formal, but can be understood informally • Reflects the ordinary computational concepts of programming languages Chapter 13 1 Chapter 13 2 Specifying a Programming Language Introduction to Action Semantics An action specification breaks into two parts: Three kinds of first-order entities: • Data: Basic mathematical values Programming Language • Yielders: Expressions that evaluate to data Definition of the constructs of a using current information Upper level language in terms of action notation. • Actions: Dynamic, computational entities Action Notation that model operational behavior Specification of the meaning Lower level of action notation. Data and Sorts Meaning of Actions Data manipulated by a programming language • integers • cells • booleans • tuples Meaning of a language is defined by mapping program phrases to actions • maps whose performance describes the execution of the program phrases. Chapter 13 3 Chapter 13 4 Classification of Data Data Specification Data classified according to how far it tends to module be propagated during action performance. TruthValues exports sort TruthValue Transient operations Tuples of data given as the immediate results true : TruthValue of action performance. Use them or lose false : TruthValue them.
    [Show full text]
  • Formalisation and Execution of Linear Algebra: Theorems and Algorithms
    Formalisation and execution of Linear Algebra: theorems and algorithms Jose Divas´onMallagaray Dissertation submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy Supervisors: Dr. D. Jes´usMar´ıaAransay Azofra Dr. D. Julio Jes´usRubio Garc´ıa Departamento de Matem´aticas y Computaci´on Logro~no,June 2016 Examining Committee Dr. Francis Sergeraert (Universit´eGrenoble Alpes) Prof. Dr. Lawrence Charles Paulson (University of Cambridge) Dr. Laureano Lamb´an (Universidad de La Rioja) External Reviewers Dr. Johannes H¨olzl (Technische Universit¨atM¨unchen) Ass. Prof. Dr. Ren´eThiemann (Universit¨atInnsbruck) This work has been partially supported by the research grants FPI-UR-12, ATUR13/25, ATUR14/09, ATUR15/09 from Universidad de La Rioja, and by the project MTM2014-54151-P from Ministerio de Econom´ıay Competitividad (Gobierno de Espa~na). Abstract This thesis studies the formalisation and execution of Linear Algebra algorithms in Isabelle/HOL, an interactive theorem prover. The work is based on the HOL Multivariate Analysis library, whose matrix representation has been refined to datatypes that admit a representation in functional programming languages. This enables the generation of programs from such verified algorithms. In par- ticular, several well-known Linear Algebra algorithms have been formalised in- volving both the computation of matrix canonical forms and decompositions (such as the Gauss-Jordan algorithm, echelon form, Hermite normal form, and QR decomposition). The formalisation of these algorithms is also accompanied by the formal proofs of their particular applications such as calculation of the rank of a matrix, solution of systems of linear equations, orthogonal matrices, least squares approximations of systems of linear equations, and computation of determinants of matrices over B´ezoutdomains.
    [Show full text]
  • On Excusable and Inexcusable Failures Towards an Adequate Notion of Translation Correctness
    On Excusable and Inexcusable Failures Towards an Adequate Notion of Translation Correctness Markus M¨uller-Olm and Andreas Wolf ? 1 Fachbereich Informatik, LS V, Universit¨at Dortmund, 44221 Dortmund, Germany [email protected] 2 Institut f¨ur Informatik und Praktische Mathematik, Christian-Albrechts-Universit¨at, 24105 Kiel, Germany [email protected] Abstract. The classical concepts of partial and total correctness iden- tify all types of runtime errors and divergence. We argue that the as- sociated notions of translation correctness cannot cope adequately with practical questions like optimizations and finiteness of machines. As a step towards a solution we propose more fine-grained correctness no- tions, which are parameterized in sets of acceptable failure outcomes, and study a corresponding family of predicate transformers that gener- alize the well-known wp and wlp transformers. We also discuss the utility of the resulting setup for answering compiler correctness questions. Keywords: compiler, correctness, divergence, refinement, runtime-error, predicate transformer, verification 1 Introduction Compilers are ubiquitous in today’s computing environments. Their use ranges from the traditional translation of higher programming languages to conversions between data formats of a large variety. The rather inconspicuous use of compil- ers helps to get rid of architecture or system specific representations and allows thus to handle data or algorithms in a more convenient abstract form. There is a standard theory for the syntactic aspects of compiler construction which is well-understood and documented in a number of text books (e.g. [1, 24– 26]). It is applied easily in practice via automated tools like scanner and parser generators.
    [Show full text]