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Why Dependent Types Matter
Why Dependent Types Matter Thorsten Altenkirch Conor McBride James McKinna The University of Nottingham The University of St Andrews {txa,ctm}@cs.nott.ac.uk [email protected] Abstract We exhibit the rationale behind the design of Epigram, a dependently typed programming language and interactive program development system, using refinements of a well known program—merge sort—as a running example. We discuss its relationship with other proposals to introduce aspects of dependent types into functional programming languages and sketch some topics for further work in this area. 1. Introduction Types matter. That’s what they’re for—to classify data with respect to criteria which matter: how they should be stored in memory, whether they can be safely passed as inputs to a given operation, even who is allowed to see them. Dependent types are types expressed in terms of data, explicitly relating their inhabitants to that data. As such, they enable you to express more of what matters about data. While conventional type systems allow us to validate our programs with respect to a fixed set of criteria, dependent types are much more flexible, they realize a continuum of precision from the basic assertions we are used to expect from types up to a complete specification of the program’s behaviour. It is the programmer’s choice to what degree he wants to exploit the expressiveness of such a powerful type discipline. While the price for formally certified software may be high, it is good to know that we can pay it in installments and that we are free to decide how far we want to go. -
LFCS Now and Then
LFCS Now and Then Gordon Plotkin LFCS@30 Edinburgh, April, 2016 Gordon Plotkin LFCS Now and Then Origins of LFCS Logic programming Gordon Plotkin LFCS Now and Then Hope Park Square Gordon Plotkin LFCS Now and Then Hope Park Square Gordon Plotkin LFCS Now and Then Metamathematics Unit Gordon Plotkin LFCS Now and Then The James Clerk Maxwell Building JCMB, KB Gordon Plotkin LFCS Now and Then 5 Readers who take a narrow view on the automation of inductive theorem proving might be surprised that we discuss the waterfall. It is impossible,however,tobuildagoodin- ductive theorem prover without considering how to transformtheinductionconclusioninto the hypothesis (or, alternatively, how to recognize that a legitimate induction hypothesis can dispatch a subgoal). So we take the expansive view and discuss not just the induction principle and its heuristic control, but also the waterfall architecture that is effectively an integral part of the success. Boyer and Moore had met in August 1971, a year before the induction work started, when Boyer took up the position of a post-doctoral research fellow at theMetamathe- matics Unit of the University of Edinburgh. Moore was at that time starting the second year of his PhD studies in “the Unit”. Ironically, they were both from Texas and they had both come to Edinburgh from MIT. Boyer’s PhD supervisor, W. W. Bledsoe,from The University of Texas at Austin, spent 1970–71 on sabbatical at MIT, and Boyer ac- companied him and completed his PhD work there. Moore got his bachelor’s degree at MIT (1966–70) before going to Edinburgh for his PhD. -
Growing the Artificial Intelligence Industry in the Uk
GROWING THE ARTIFICIAL INTELLIGENCE INDUSTRY IN THE UK Professor Dame Wendy Hall and Jérôme Pesenti Growing the Artificial Intelligence Industry in the UK FOREWORD We are grateful to the Business Secretary and Culture Secretary for asking us to conduct this Review of how to grow Artificial Intelligence in the UK, in terms of those developing it and deploying it. We believe that this is the right time for the UK to accelerate on AI, and ensure that our unique history of ground breaking research bears fruit in the social and economic benefits that the technology offers. We are at the threshold of an era when much of our productivity and prosperity will be derived from the systems and machines we create. We are accustomed now to technology developing fast, but that pace will increase and AI will drive much of that acceleration. The impacts on society and the economy will be profound, although the exact nature of those impacts is uncertain. We are convinced that because of the UK’s current and historical strengths in this area we are in a strong position to lead rather than follow in both the development of the technology and its deployment in all sectors of industry, education and government. We have a choice. The UK could stay among the world leaders in AI in the future, or allow other countries to dominate. We start from a good position in many respects but other leading countries are devoting significant resources to growing and deploying AI. The UK will need to act in key areas and to sustain action over a long period and across industry sectors, to retain its world leading status, and to grow our AI capability as well as deploying it much more widely. -
The History of Standard ML
The History of Standard ML DAVID MACQUEEN, University of Chicago, USA ROBERT HARPER, Carnegie Mellon University, USA JOHN REPPY, University of Chicago, USA Shepherd: Kim Bruce, Pomona College The ML family of strict functional languages, which includes F#, OCaml, and Standard ML, evolved from the Meta Language of the LCF theorem proving system developed by Robin Milner and his research group at the University of Edinburgh in the 1970s. This paper focuses on the history of Standard ML, which plays a central rôle in this family of languages, as it was the first to include the complete set of features that we now associate with the name “ML” (i.e., polymorphic type inference, datatypes with pattern matching, modules, exceptions, and mutable state). Standard ML, and the ML family of languages, have had enormous influence on the world of programming language design and theory. ML is the foremost exemplar of a functional programming language with strict evaluation (call-by-value) and static typing. The use of parametric polymorphism in its type system, together with the automatic inference of such types, has influenced a wide variety of modern languages (where polymorphism is often referred to as generics). It has popularized the idea of datatypes with associated case analysis by pattern matching. The module system of Standard ML extends the notion of type-level parameterization to large-scale programming with the notion of parametric modules, or functors. Standard ML also set a precedent by being a language whose design included a formal definition with an associated metatheory of mathematical proofs (such as soundness of the type system). -
A New Approach to Abstract Syntax with Variable Binding1
Formal Aspects of Computing (2002) 13: 341–363 c 2002 BCS A New Approach to Abstract Syntax with Variable Binding1 Murdoch J. Gabbay and Andrew M. Pitts Cambridge University Computer Laboratory, Cambridge, UK Keywords: Abstract syntax; Alpha-conversion; Permutation actions; Set theory; Structural induction Abstract. The permutation model of set theory with atoms (FM-sets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘name-abstraction’ and ‘fresh name’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variable-binding operations. In- ductively defined FM-sets involving the name-abstraction set former (together with Cartesian product and disjoint union) can correctly encode syntax modulo renaming of bound variables. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In par- ticular, there is an associated notion of structural recursion for defining syntax-manipulating functions (such as capture avoiding substitution, set of free variables, etc.) and a notion of proof by structural induction, both of which remain pleasingly close to informal practice in computer science. 1. Introduction This paper presents a simple variant of classical set theory that turns out to be very convenient for developing the metamathematics of formal systems involving variable-binding operations. The main message we wish to get across is that a relatively small change to classical set theory, involving the use of atoms (or urelements, as they are often referred to), can reap great benefits for this aspect of metamathematics. In particular we will see that in such a set theory it is possible to represent α-equivalence classes of abstract syntax trees as the elements of an inductively defined set, rather than just the quotient of such a set. -
Edit Summer 2009
SUMMER 09 THE ALUMNI MAGAZINE INCLUDING BILLET & GENERAL COUNCIL PAPERS The Origin of Genius Charles Darwin’s Edinburgh connection ALSO INSIDE Edinburgh’s innovative teaching leads the way Edit meets the winners of the Principal’s Medal The University of Edinburgh Forever a part of it Your links with Edinburgh don’t end when you leave the University – you’re an Edinburgh alumnus for life – so stay in touch and reap the benefits! The Alumni Card What will it do for you? Have you got your new-look Alumni Card • Receive 15% off hire of University • Enjoy free access to the University’s yet? As an alumnus you are eligible for the venues, accommodation and catering many libraries and their printed new card, which replaces the Edinburgh for weddings, parties, meetings and, collections – as well as 50% off Passport and allows discounted access of course, reunions! borrowing rights. to many of the University’s outstanding • Enjoy a 25% discount at the • Receive a 20% discount on all books facilities. The card also entitles you to University’s Centre for Sports and published by Edinburgh University a new range of discounts with partner Exercise – one of the Scotsman’s Press. organisations worldwide. Sign up at top five gyms in Scotland – which Get discounted rates with our partners www.ed.ac.uk/alumni. • offers you a wealth of fitness in the hotel and leisure industry all over classes, training, gym support, the world. We will be adding to our list climbing facilities, a circuit gym, of partners on a regular basis, so make playing fields, an outdoor activity sure you visit www.ed.ac.uk/alumni centre on Loch Tay and much more! for the latest offers. -
ICL Technical Journal Volume 5 Issue 3
TECHniCAl j o u m n i Volume 5 Issue 3 May 1987 Published by INTERNATIONAL COMPUTERS LIMITED at OXFORD UNIVERSITY PRESS iCL The ICL Technical Journal is published twice a year by TECHniCRl International Computers Limited at Oxford University jouRnfli Press. Editor J. Howlett ICL House, Putney, London SW15 ISW, UK Editorial Board J. Howlett (Editor) F.F. Land H.M. Cropper (F International) (London School of Economics & D.W. Davies, FRS Political Science) G.E. Felton K.H. Macdonald M.D. Godfrey M R. Miller C.H.L. Goodman (British Telecom Research (Standard Telephone Laboratories) Laboratories and Warwick J.M. Pinkerton University) E.C.P. Portman All correspondence and papers to be considered for publication should be addressed to the Editor. The views expressed in the papers are those of the authors and do not necessarily represent ICL policy. 1987 subscription rates: annual subscription £32 UK, £40 rest of world, US $72 N. America; single issues £17 UK, £22 rest of world, US $38 N. America. Orders with remittances should be sent to the Journals Subscriptions Department, Oxford University Press, Walton Street, Oxford 0X2 6DP, UK. This publication is copyright under the Berne Convention and the Interna tional Copyright Convention. All rights reserved. Apart from any copying under the UK Copyright Act 1956, part 1, section 7, whereby a single copy of an article may be supplied, under certain conditions, for the purposes of research or private study, by a library of a class prescribed by the UK Board of Trade Regulations (Statutory Instruments 1957, No. 868), no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means without the prior permission of the copyright owners. -
Symposium for Gordon Plotkin Edinburgh 07-08/09/2006 from Partial Lambda-Calculus to Monads
Symposium for Gordon Plotkin Edinburgh 07-08/09/2006 From Partial Lambda-calculus to Monads Eugenio Moggi [email protected] DISI, Univ. of Genova GDP symposium – p.1/11 AIM: recall influence of Plotkin (and others) on my PhD research (and beyond) Mainly overview of published work + personal comments and opinions Please interrupt to correct my account or to add your comments Main focus on Partial lambda-calculus [Mog88] 1984-1988 but work placed in broader context: partiality in: Logic, Algebra, Computability lambda-calculi as: PL [Lan66, Plo75], ML [Sco93, GMW79, Plo85] domain theory [FJM+96]: classical, axiomatic, synthetic Applications of monads [Mac71, Man76] for computational types (lifting and recursion) [Mog89, Mog91] 1988-. in pure functional languages (Haskell) – Wadler et al. for collection types (in databases) – Buneman et al. including recent contributions by Plotkin et al. [HPP02] GDP symposium – p.2/11 1984 reformulation of domain theory using partial continuous maps [Plo85] Previous relevant work (. -1983) 1982 more systematic study of categories of partial maps [Obt86, CO87] partiality in algebraic specifications: [Bur82] partiality in (intuitionistic) logic: LPE [Fou77, Sco79], LPT [Bee85] mismatch between lambda-calculus and programming languages [Plo75] λV CBV axioms (λx.t)v > t[x: =v] and (λx.vx) > v with v: : = x j λx.t values λp is derived from models like λV is derived from operational semantics λV ⊂ λc ⊂ λp are correct (but incomplete) for CBV (on untyped λ-terms) λc on (simply typed) λ-terms is inverse image of -
Bfm:978-3-642-97005-4/1.Pdf
W F. Clocksin C. S. Mellish Programming in Prolog Third, Revised and Extended Edition Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo William F. Clocksin Computer Laboratory, University of Cambridge Corn Exchange Street Cambridge CB2 3QG/Engiand Christopher S. Mellish Cognitive Studies Programme, University of Sussex Arts Building, Falmer Brighton BN1 9QN/Engiand ISBN-13: 978-3-540-17539-1 e-ISBN-13: 978-3-642-97005-4 DOl: 10.1007/978-3-642-97005-4 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1981, 1984, 1987 PREFACE TO THE THIRD EDITION We have added new material to Chapter 3 to give an account of up-to-date programming techniques using accumulators and difference structures. Chapter 8 contains some new information on syntax errors. Operator precedences are now compatible with the most widely-used implementations. We have made further reorganisations and improvements in presentation, and have corrected a number of minor errors. We thank the many people who brought typographical errors in the previous edition to our attention, and we thank A.R.C. -
AI and the Study of Mind Aaron Sloman School of Computer Science, the University of Birmingham, UK
Computer Conservation Society Meeting http://www.bcs.org/sg/ccs/events_se.html 11th October 2002 (Slightly re-formatted 10 Dec 2016) Science Museum, London Artificial Intelligence Recollections of the pioneers Early British AI AI and the study of mind Aaron Sloman School of Computer Science, The University of Birmingham, UK http://www.cs.bham.ac.uk/˜axs/ THIS PDF PRESENTATION IS ON-LINE AS “TALK 17” AT http://www.cs.bham.ac.uk/research/projects/cogaff/talks/ (Last changed December 11, 2016) CCS Slide 1 Oct 2002 ACKNOWLEDGEMENT This talk was prepared using free software, Linux, Latex, Acroread, Poplog, etc. Diagrams were created using tgif, freely available from http://bourbon.cs.umd.edu:8001/tgif I am especially grateful to the developers of Linux and all the gnu tools used in Linux CCS Slide 2 Oct 2002 The CCS Meeting The meeting at which this talk was presented was held on Friday 11th October at the Science Museum London. It was organised by the Computer Conservation Society, a co-operative venture between the British Computer Society, the Science Museum of London, and the Museum of Science and Industry in Manchester. http://www.bcs.org/sg/ccs/ It is dedicated to the conservation and restoration of early computers, preserving early computer software and other digital records of historical importance, and to recording the history of computing. It encourages research into, and awareness of, the importance of historic computers and early computer developments in Britain. The meeting started with a video presentation by Donald Michie, who is in Australia, followed by talks by Jim Doran (Essex University), Austin Tate (Edinburgh University) and Aaron Sloman (Birmingham University). -
Practical Implementation of a Dependently Typed Functional Programming Language
Practical Implementation of a Dependently Typed Functional Programming Language by Edwin C. Brady Submitted in conformity with the requirements for the degree of PhD Department of Computer Science University of Durham Copyright °c 2005 by Edwin C. Brady Abstract Practical Implementation of a Dependently Typed Functional Programming Language Edwin C. Brady Types express a program’s meaning, and checking types ensures that a program has the intended meaning. In a dependently typed programming language types are predicated on values, leading to the possibility of expressing invariants of a program’s behaviour in its type. Dependent types allow us to give more detailed meanings to programs, and hence be more confident of their correctness. This thesis considers the practical implementation of a dependently typed programming language, using the Epigram notation defined by McBride and McKinna. Epigram is a high level notation for dependently typed functional programming elaborating to a core type theory based on Luo’s UTT, using Dybjer’s inductive families and elimination rules to implement pattern matching. This gives us a rich framework for reasoning about programs. However, a na¨ıve implementation introduces several run-time overheads since the type sys- tem blurs the distinction between types and values; these overheads include the duplication of values, and the storage of redundant information and explicit proofs. A practical implementation of any programming language should be as efficient as pos- sible; in this thesis we see how the apparent efficiency problems of dependently typed pro- gramming can be overcome and that in many cases the richer type information allows us to apply optimisations which are not directly available in traditional languages. -
Michael John Caldwell Gordon (FRS 1994), 28 February 1948--22 August 2017
Michael John Caldwell Gordon (FRS 1994) 28 February 1948 { 22 August 2017 Lawrence C Paulson FRS Computer Laboratory, University of Cambridge [email protected] August 28, 2018 Abstract Michael Gordon was a pioneer in the field of interactive theorem proving and hardware verification. In the 1970s, he had the vision of formally verifying system designs, proving their correctness using mathematics and logic. He demonstrated his ideas on real-world com- puter designs. His students extended the work to such diverse areas as the verification of floating-point algorithms, the verification of proba- bilistic algorithms and the verified translation of source code to correct machine code. He was elected to the Royal Society in 1994, and he continued to produce outstanding research until retirement. His achievements include his work at Edinburgh University help- ing to create Edinburgh LCF, the first interactive theorem prover of its kind, and the ML family of functional programming languages. He adopted higher-order logic as a general formalism for verification, showing that it could specify hardware designs from the gate level right up to the processor level. It turned out to be an ideal formalism for many problems in computer science and mathematics. His tools and techniques have exerted a huge influence across the field of formal verification. 1 Early Life Mike Gordon was born in Ripon, Yorkshire to John Gordon and Daphne arXiv:1806.04002v2 [cs.GL] 26 Aug 2018 Mavis Gordon (n´eeMore). He had perhaps a lonely childhood: he was an only child, and his father committed suicide when Mike was eight years old.