DOCSLIB.ORG

Lists in Lisp and Scheme

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lists in Lisp and Scheme Lists in Lisp and Scheme Lisp Lists • Lists are Lisp’s fundamental data structures, • Lists in Lisp and its descendants are very but there are others Lists in Lisp simple linked lists – Arrays, characters, strings, etc. – Represented as a linear chain of nodes – Common Lisp has moved on from being • Each node has a (pointer to) a value (car of merely a LISt Processor and Scheme list) and a pointer to the next node (cdr of list) • However, to understand Lisp and Scheme – Last node’s cdr pointer is to null you must understand lists • Lists are immutable in Scheme – common functions on them • Typical access pattern is to traverse the list a – how to build other useful data structures from its head processing each node with them In the beginning was the cons (or pair) Pairs Box and pointer notation • What cons really does is combines two objects into a a Common notation: two-part object called a cons in Lisp and a pair in use diagonal line in • Lists in Lisp and Scheme are defined as (a) cdr part of a cons Scheme cell for a pointer to • Conceptually, a cons is a pair of pointers -- the first is pairs null a a null the car, and the second is the cdr • Any non empty list can be considered as a • Conses provide a convenient representation for pairs A one element list (a) of any type pair of the first element and the rest of • the list The two halves of a cons can point to any kind of (a b c) object, including conses • We use one half of a cons cell to point to • This is the mechanism for building lists the first element of the list, and the other • (pair? ‘(1 2) ) => #t a b c to point to the rest of the list (which is a null either another cons or nil) A list of three elements (a b c) 1 What sort of list is this? Z Pair? Equality • Each time you call (define L1 (cons 'a null)) • The function pair? returns true if its cons, Scheme L1 allocates a new (A) argument is a cons cell (define L2 (cons 'a null))) a d cons cell from • The equivalent function in CL is consp memory with room L2 • So list? could be defined: for two pointers (A) (eq? L1 L2) (define (list? x) (or (null? x) (pair? x))) • If we call cons twice #f with the same args, b c • Since everything that is not a pair is an (equal? L1 L2) we get two values #t Z is a list with three > (define Z (list ‘a (list ‘b ‘c) ‘d)) atom, the predicate atom could be defined: elements: (i) the atom a, > Z that look the same, (and (eq? (car L1)(car L2)) (ii) a list of two elements, (a (b c) d) (define (atom? x) (not (pair? x))) but are distinct (eq? (cdr L1)(cdr L2))) b & c and (iii) the atom d. > (car (cdr z)) objects #t ?? Equal? Equal? Use trace to see how it works • Do two lists have the same elements? (define (myequal? x y) > (require racket/trace) >(myequal? (c) (c)) • Scheme provides a predicate equal? that is like > (trace myequal?) > (myequal? c c) Java’s equal method ; this is how equal? could be defined > ( myequal ? '(a b c) '(a b c)) < #t • eq? returns true iff its arguments are the same (cond ((and (number? x) (number? y))(= x y)) >(myequal? (a b c) (a b c)) >(myequal? () ()) > (myequal? a a) <#t object, and ((and (string? x) (string? y)) (string=? x y)) < #t #t • equal?, more or less, returns true if its ((not (pair? x)) (eq? x y)) >(myequal? (b c) (b c)) arguments would print the same. ((not (pair? y)) #f) > (myequal? b b) > (equal? L1 L2) ((myequal? (car x) (car y)) < #t #t (myequal? (cdr x) (cdr y))) • Trace is a debugging package showing what args a user- • Note: (eq? x y) implies (equal? x y) defined function is called with and what it returns (#t #f))) • The require function loads the package if needed 2 Does Lisp have pointers? Variables point to their values Does Scheme have pointers? • A secret to understanding Lisp is to realize that > (define x ‘(a b)) environment • variables have values in the same way that lists The location in memory associated with the > x VAR VALUE have elements variable x does not contain the list itself, but a (a b) … a b pointer to it. • As pairs have pointers to their elements, > (define y x) • variables have pointers to their values x When we assign the same value to y, Scheme y copies the pointer, not the list. • Scheme maintains a data structure … (a b) • Therefore, what would the value of representing the mapping of variables to their y > (eq? x y) current values. … be, #t or #f? Variables point to their values Variables point to their values Length is a simple function on Lists > (define x ‘(a b)) environment > (define x ‘(a b)) environment • The built-in function length takes a list and > x VAR VALUE > x VAR VALUE returns the number of its top-level elements (a b) … a b (a b) … a b • Here’s how we could implement it > (define y x) x > (define y x) x (define (length L) y y (if (null? L) 0 (+ 1 (length (cdr L)))) (a b) … (a b) … 1 2 • As typical in dynamically typed languages y > (set! y ‘(1 2)) y (e.g., Python), we do minimal type checking … > y … – The underlying interpreter does it for us (1 2) – Get run-time error if we apply length to a non-list 3 Building Lists Copy-list Append • append returns the • >(append ‘(a b) ‘(c d)) list-copy takes a list and returns a copy of it • List-copy is a Lisp built-in (as copy-list) that concatenation of any number of lists (a b c d) • The new list has the same elements, but could be defined in Scheme as: > (append ‘((a)(b)) ‘(((c)))) contained in new pairs • Append copies its (define (list-copy s) arguments except ((a) (b) ((c))) > (set! x ‘(a b c)) (if (pair? s) the last > (append ‘(a b) ‘(c d) ‘(e)) (a b c d e) (a b c) (cons (list-copy (car s)) –If not, it would have > (set! y (list-copy x)) to modify the lists >(append ‘(a b) ‘()) (list-copy (cdr s))) (a b) (a b c) –Such side effects s)) are undesirable in >(append ‘(a b)) • Spend a few minutes to draw a box diagram • Given a non-atomic s-expression, it makes and functional (a b) of x and y to show where the pointers point returns a complete copy (e.g., not just the top- languages >(append) level spine) () Append Visualizing Append Visualizing Append > (load "append2.ss") > (require racket/trace) > (load "append2.ss") environment • The two argument version of append could be > (define L1 '(1 2)) > (trace append2) > (define L1 '(1 2)) VAR VALUE > (append2 L1 L2) defined like this > (define L2 '(a b)) > (define L2 '(a b)) a b >(append2 (1 2) (a b)) … (define (append2 s1 s2) > (define L3 (append2 L1 L2)) > (define L3 > L3 > (append2 (2) (a b)) (append2 L1 L2)) L2 (if (null? s1) (1 2 a b) > >(append2 () (a b)) > L3 s2 > L1 < <(a b) (1 2 a b) L1 < (2 a b) (cons (car s1) (1 2) > L1 1 2 <(1 2 a b) L3 > L2 (1 2) (append2 (cdr s1) s2)))) (1 2 a b) (a b) > L2 … • Notice how it ends up copying the top level list (a b) Append does not modify its arguments. It makes structure of its first argument > (eq? (cdr (cdr L3) L2) Append2 copies the top level of its copies of all of the lists save the last. #f first list argument, L1 4 List access functions List-ref and list-tail Defining Scheme’s list-ref & list-tail > (define L '(a b c d)) > (list-tail L 0) (define (mylist-ref l n) • To find the element at a given position in a list > (list-ref L 2) (a b c d) (cond ((< n 0) (error...)) use the function list-ref (nth in CL) c > (list-tail L 2) ((not (pair? l)) (error...)) > (list-ref ‘(a b c) 0) > (list-ref L 0) (c d) ((= n 0) (car l)) a a > (list-tail L 4) (#t (mylist-ref (cdr l) (- n 1))))) • To find the nth cdr, use list-tail (nthcdr in CL) > (list-ref L -1) () (define (mylist-tail l n) list-ref: expects type <non-negative > (list-tail L 5) > (list-tail ‘(a b c) 2) exact integer> as 2nd arg, given: -1; (cond ((< n 0) (error...)) other arguments were: (a b c d) list-tail: index 5 too large for list: (a b (c) c d) ((not (pair? l)) (error...)) > (list-ref L 4) • Both functions are zero indexed ((= n 0) l) list-ref: index 4 too large for list: (a b c d) (#t (mylist-tail (cdr l) (- n 1))))) Accessing lists Member Recall: defining member • Scheme’s last returns the last element in a list • Member returns true, but instead of simply (define (member X L) > (define (last l) returning t, its returns the part of the list (if (null? (cdr l)) beginning with the object it was looking for. (cond ((null? L) #f) (car l) > (member ‘b ‘(a b c)) ((equal? X (car L)) L) (last (cdr l)))) (b c) (#t (member X (cdr L))))) (last ‘(a b c)) • member compares objects using equal? c • Note: in CL, last returns the last cons cell (aka pair) • There are versions that use eq? and eqv? • We also have: first, second, third, and CxR, where x is And that take an arbitrary function a string of up to four as or ds.
Load more

Recommended publications
  • CSC 242: Artificial Intelligence
    CSC 242: Artificial Intelligence Course website: www.cs.rochester.edu/u/kyros/courses/csc242 Instructor: Kyros Kutulakos Office: 623 CSB Extension: x5-5860 Email: [email protected] Hours: TR 3:30-4:30 (or by appointment) TA: Joel Tetreault Email: [email protected] Hours: M 1:00-2:00 Recitations: TBA Textbooks: Russell & Norvig, Artificial Intelligence Wilensky, Common LISPcraft Another very good LISP textbook: Winston & Horn, LISP (Addison-Wesley) Common Lisp • LISP is one of the most common “AI programming languages” • LISP (=LISt Processing) is a language whose main power is in manipulating lists of symbols: (a b c (d e f (g h))) arithmetic operations are also included (sqrt (+ (* 3 3) (* 4 4))) • Lisp is a general-purpose, interpreter-based language • All computation consists of expression evaluations: lisp-prompt>(sqrt (+ (* 3 3) (* 4 4))) lisp-prompt> 25 • Since data are list structures and programs are list structures, we can manipulate programs just like data • Lisp is the second-oldest high-level programming language (after Fortran) Getting Started • Command-line invocation unix-prompt>cl system responds with loading & initialization messages followed by a Lisp prompt USER(1): whenever you have balanced parentheses & hit return, the value of the expression (or an error message) are returned USER(1): (+ 1 2) 3 saying “hello” USER(2): ‘hello HELLO USER(3): “Hello” “Hello” • Exiting Lisp: USER(2):(exit) unix-prompt> Getting Started (cont.) • Reading a file f that is in the same directory from which you are running Lisp:
    [Show full text]
  • Redis in Action
    IN ACTION Josiah L. Carlson FOREWORD BY Salvatore Sanfilippo MANNING Redis in Action Redis in Action JOSIAH L. CARLSON MANNING Shelter Island For online information and ordering of this and other Manning books, please visit www.manning.com. The publisher offers discounts on this book when ordered in quantity. For more information, please contact Special Sales Department Manning Publications Co. 20 Baldwin Road PO Box 261 Shelter Island, NY 11964 Email: [email protected] ©2013 by Manning Publications Co. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by means electronic, mechanical, photocopying, or otherwise, without prior written permission of the publisher. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in the book, and Manning Publications was aware of a trademark claim, the designations have been printed in initial caps or all caps. Recognizing the importance of preserving what has been written, it is Manning’s policy to have the books we publish printed on acid-free paper, and we exert our best efforts to that end. Recognizing also our responsibility to conserve the resources of our planet, Manning books are printed on paper that is at least 15 percent recycled and processed without the use of elemental chlorine. Manning Publications Co. Development editor: Elizabeth Lexleigh 20 Baldwin Road Technical proofreaders: James Philips, Kevin Chang, PO Box 261 and Nicholas Lindgren Shelter Island, NY 11964 Java translator: Eric Van Dewoestine Copyeditor: Benjamin Berg Proofreader: Katie Tennant Typesetter: Gordan Salinovic Cover designer: Marija Tudor ISBN 9781935182054 Printed in the United States of America 1 2 3 4 5 6 7 8 9 10 – MAL – 18 17 16 15 14 13 To my dear wife, See Luan, and to our baby girl, Mikela brief contents PART 1 GETTING STARTED .
    [Show full text]
  • A History of Clojure
    A History of Clojure RICH HICKEY, Cognitect, Inc., USA Shepherd: Mira Mezini, Technische Universität Darmstadt, Germany Clojure was designed to be a general-purpose, practical functional language, suitable for use by professionals wherever its host language, e.g., Java, would be. Initially designed in 2005 and released in 2007, Clojure is a dialect of Lisp, but is not a direct descendant of any prior Lisp. It complements programming with pure functions of immutable data with concurrency-safe state management constructs that support writing correct multithreaded programs without the complexity of mutex locks. Clojure is intentionally hosted, in that it compiles to and runs on the runtime of another language, such as the JVM. This is more than an implementation strategy; numerous features ensure that programs written in Clojure can leverage and interoperate with the libraries of the host language directly and efficiently. In spite of combining two (at the time) rather unpopular ideas, functional programming and Lisp, Clojure has since seen adoption in industries as diverse as finance, climate science, retail, databases, analytics, publishing, healthcare, advertising and genomics, and by consultancies and startups worldwide, much to the career-altering surprise of its author. Most of the ideas in Clojure were not novel, but their combination puts Clojure in a unique spot in language design (functional, hosted, Lisp). This paper recounts the motivation behind the initial development of Clojure and the rationale for various design decisions and language constructs. It then covers its evolution subsequent to release and adoption. CCS Concepts: • Software and its engineering ! General programming languages; • Social and pro- fessional topics ! History of programming languages.
    [Show full text]
  • Lisp and Scheme I
    4/10/2012 Versions of LISP Why Study Lisp? • LISP is an acronym for LISt Processing language • It’s a simple, elegant yet powerful language • Lisp (b. 1958) is an old language with many variants • You will learn a lot about PLs from studying it – Fortran is only older language still in wide use • We’ll look at how to implement a Scheme Lisp and – Lisp is alive and well today interpreter in Scheme and Python • Most modern versions are based on Common Lisp • Scheme is one of the major variants • Many features, once unique to Lisp, are now in – We’ll use Scheme, not Lisp, in this class “mainstream” PLs: python, javascript, perl … Scheme I – Scheme is used for CS 101 in some universities • It will expand your notion of what a PL can be • The essentials haven’t changed much • Lisp is considered hip and esoteric among computer scientists LISP Features • S-expression as the universal data type – either at atom (e.g., number, symbol) or a list of atoms or sublists • Functional Programming Style – computation done by applying functions to arguments, functions are first class objects, minimal use of side-effects • Uniform Representation of Data & Code – (A B C D) can be interpreted as data (i.e., a list of four elements) or code (calling function ‘A’ to the three parameters B, C, and D) • Reliance on Recursion – iteration is provided too, but We lost the documentation on quantum mechanics. You'll have to decode recursion is considered more natural and elegant the regexes yourself. • Garbage Collection – frees programmer’s explicit memory management How Programming Language Fanboys See Each Others’ Languages 1 4/10/2012 What’s Functional Programming? Pure Lisp and Common Lisp Scheme • The FP paradigm: computation is applying • Lisp has a small and elegant conceptual core • Scheme is a dialect of Lisp that is favored by functions to data that has not changed much in almost 50 years.
    [Show full text]
  • Lists in Lisp and Scheme
    Lists in Lisp and Scheme • Lists are Lisp’s fundamental data structures • However, it is not the only data structure Lists in Lisp – There are arrays, characters, strings, etc. – Common Lisp has moved on from being merely a LISt Processor and Scheme • However, to understand Lisp and Scheme you must understand lists – common funcAons on them – how to build other useful data structures with them In the beginning was the cons (or pair) Pairs nil • What cons really does is combines two objects into a a two-part object called a cons in Lisp and a pair in • Lists in Lisp and Scheme are defined as Scheme • Conceptually, a cons is a pair of pointers -- the first is pairs the car, and the second is the cdr • Any non empty list can be considered as a • Conses provide a convenient representaAon for pairs pair of the first element and the rest of of any type • The two halves of a cons can point to any kind of the list object, including conses • We use one half of the cons to point to • This is the mechanism for building lists the first element of the list, and the other • (pair? ‘(1 2) ) => #t to point to the rest of the list (which is a nil either another cons or nil) 1 Box nota:on Z What sort of list is this? null Where null = ‘( ) null a a d A one element list (a) null null b c a b c > (set! z (list ‘a (list ‘b ‘c) ‘d)) (car (cdr z)) A list of 3 elements (a b c) (A (B C) D) ?? Pair? Equality • Each Ame you call cons, Scheme allocates a new memory with room for two pointers • The funcAon pair? returns true if its • If we call cons twice with the
    [Show full text]
  • Pairs and Lists (V1.0) Week 5
    CS61A, Spring 2006, Wei Tu (Based on Chung’s Notes) 1 CS61A Pairs and Lists (v1.0) Week 5 Pair Up! Introducing - the only data structure you’ll ever need in 61A - pairs. A pair is a data structure that contains two things - the ”things” can be atomic values or even another pair. For example, you can represent a point as (x . y), and a date as (July . 1). Note the Scheme representation of a pair; the pair is enclosed in parentheses, and separated by a single period. Note also that there’s an operator called pair? that tests whether something is a pair or not. For example, (pair? (cons 3 4)) is #t, while (pair? 10) is #f. You’ve read about cons, car, and cdr: • cons - takes in two parameters and constructs a pair out of them. So (cons 3 4) returns (3 . 4) • car - takes in a pair and returns the first part of the pair. So (car (cons 3 4)) will return 3. • cdr - takes in a pair and returns the second part of the pair. So (cdr (cons 3 4)) will return 4. These, believe it or not, will be all we’ll ever need to build complex data structures in this course. QUESTIONS: What do the following evaluate to? (define u (cons 2 3)) (define w (cons 5 6)) (define x (cons u w)) (define y (cons w x)) (define z (cons 3 y)) 1. u, w, x, y, z (write out how Scheme would print them and box and pointer diagram). CS61A, Spring 2006, Wei Tu (Based on Chung’s Notes) 2 2.
    [Show full text]
  • A Lisp Machine with Very Compact Programs
    Session 25 Hardware and Software for Artificial Intelligence A LISP MACHINE WITH VERY COMPACT PROGRAMS L. Peter Deutsch Xerox corporation, Palo Alto Research center (PARC) Palo Alto, California 94304 Abstract Data Types This paper presents a machine designed for LISP has many data types (e.g. list, compact representation and rapid execution symbolic atom, integer) but no declarations. of LISP programs. The machine language is a The usual implementation of languages with factor of 2 to 5 more compact than this property affixes a tag to each datum to S-expressions or conventional compiled code, indicate its type, in LISP, however, the , and the.compiler is extremely simple. The vast majority of data are pointers to lists encoding scheme is potentially applicable to or atoms, and it would be wasteful to leave data as well as program. The machine also room for a full word plus tag (the space provides for user-defined data structures. needed for an integer datum, for example) in every place where a datum can appear such as Introduction the CAR and CDR of list cells. Consequently, in BBN-LISP every datum is a Pew existing computers permit convenient or pointer; integers, strings, etc. are all efficient implementation of dynamic storage referenced indirectly. Storage is allocated in quanta, and each quantum holds data of allocation, recursive procedures, or only one type, so what type of object a operations on data whose type is represented given pointer references is just a function explicitly at run time rather than of the object's address, i.e. the pointer determined at compile time.
    [Show full text]
  • Mattox's Quick Introduction to Scheme
    Mattox’s Quick Introduction to Scheme or, What Do People See in This Language, Anyway? c November, 2000 Mattox Beckman 1 Introduction The purpose of this document is to give the reader an introduction to both the Scheme programming language and some of the techniques and reasoning used in functional programming. The goal is that the reader will be comfortable using Scheme and be able to write programs in functional style. The reader is assumed to be a CS321 student: someone who has written some large programs in C++ or Java, and is at any rate familiar with imperative or object oriented languages; but who is not familiar with functional programming. You will get a lot more out of this if you have a Dr. Scheme window open, try out the examples, and make up some of your own as you go along. The outline of this paper is as follows: Section 2 briefly discusses four major language paradigms. Section 3 introduces lists and list operations. 2 Language Paradigms There are four major language paradigms in use today, which have different definitions as to what constitutes a program. • Imperative: Languages like C, Fortran are called imperative, meaning “command”, because a program is thought of as being a list of commands for the computer to execute. • Functional: Languages like SML, Haskell, Lisp, and Scheme are common examples. These language involve “programming with functions.” A program is considered an expression to be evaluated. • Object Oriented: Languages like Smalltalk, in which a program is a collection of objects which com- municate with each other.
    [Show full text]
  • Functional Programming Pure Functional Languages
    Functional Programming • Pure functional PLs • S-expressions – cons, car, cdr • Defining functions • read-eval-print loop of Lisp interpreter • Examples of recursive functions – Shallow, deep • Equality testing 1 Functional-10, CS5314, Sp16 © BGRyder Pure Functional Languages • Referential transparency – value of an expression is independent of context where the function application occurs – means that all variables in a function body must be local to that function; why? • There is no concept of assignment – variables are bound to values only through parameter associations – no side effects 2 Functional-10, CS5314, Sp16 © BGRyder 1 Pure Functional Languages • Control flow accomplished through function application (and recursion) – a program is a set of function definitions and their application to arguments • Implicit storage management – copy semantics, needs garbage collection • Functions are 1st class values! – can be returned as value of an expression or function application – can be passed as an argument – can be put into a data structure and saved • Unnamed functions exist as values 3 Functional-10, CS5314, Sp16 © BGRyder Pure Functional Languages • Lisp designed for symbolic computing – simple syntax – data and programs have same syntactic form • S-expression – function application written in prefix form (e1 e2 e3 … ek) means • Evaluate e1 to a function value • Evaluate each of e2,…,ek to values • Apply the function to these values (+ 1 3) evaluates to 4 4 Functional-10, CS5314, Sp16 © BGRyder 2 History Lisp Scheme Common Lisp
    [Show full text]
  • Introduction to Cognitive Robotics
    Introduction to Cognitive Robotics Module 8: An Introduction to Functional Programming with Lisp Lecture 1: Common Lisp - REPL, lists, structures, equality, conditionals, CONS, CAR, CDR, dotted and assoc-list www.cognitiverobotics.net An Introduction to Functional Programming with Lisp 1 1 Introduction to Cognitive Robotics Aside: Programming Paradigms An Introduction to Functional Programming with Lisp 1 2 Introduction to Cognitive Robotics Note: This is an oversimplification Programming Paradigms Imperative Declarative Object- Procedural Functional Logic Oriented An Introduction to Functional Programming with Lisp 1 3 Introduction to Cognitive Robotics Programming Paradigms Imperative Declarative e.g. C Object- Procedural Functional Logic Oriented First do this and next do that Focus on how An Introduction to Functional Programming with Lisp 1 4 Introduction to Cognitive Robotics Programming Paradigms Imperative Declarative e.g. C++, Java Object- Procedural Functional Logic Oriented Send messages between objects to accomplish some task Focus on how An Introduction to Functional Programming with Lisp 1 5 Introduction to Cognitive Robotics Programming Paradigms Imperative Declarative e.g. Lisp Object- Procedural Functional Logic Oriented Evaluate an expression and use the resulting value for something Focus on what An Introduction to Functional Programming with Lisp 1 6 Introduction to Cognitive Robotics Programming Paradigms Imperative Declarative e.g. Prolog Object- Procedural Functional Logic Oriented Answer a question using logical
    [Show full text]
  • Lists in Lisp and Scheme • Lists Are Lisp’S Fundamental Data Structures, Lists in Lisp but There Are Others – Arrays, Characters, Strings, Etc
    Lists in Lisp and Scheme • Lists are Lisp’s fundamental data structures, Lists in Lisp but there are others – Arrays, characters, strings, etc. – Common Lisp has moved on from being and Scheme merely a LISt Processor • However, to understand Lisp and Scheme you must understand lists – common func?ons on them a – how to build other useful data structures with them Lisp Lists In the beginning was the cons (or pair) • What cons really does is combines two obJects into a • Lists in Lisp and its descendants are very two-part obJect called a cons in Lisp and a pair in Scheme simple linked lists • Conceptually, a cons is a pair of pointers -- the first is – Represented as a linear chain of nodes the car, and the second is the cdr • Each node has a (pointer to) a value (car of • Conses provide a convenient representaon for pairs list) and a pointer to the next node (cdr of list) of any type • The two halves of a cons can point to any kind of – Last node ‘s cdr pointer is to null obJect, including conses • Lists are immutable in Scheme • This is the mechanism for building lists • Typical access paern is to traverse the list • (pair? ‘(1 2) ) => #t from its head processing each node a null 1 Pairs Box and pointer notaon a Common notation: use diagonal line in • Lists in Lisp and Scheme are defined as (a) cdr part of a cons cell pairs for a pointer to null a a null • Any non empty list can be considered as a pair of the first element and the rest of A one element list (a) the list (a b c) • We use one half of a cons cell to point to the first element
    [Show full text]
  • Hilbert's Program Revisited
    1 1 Hilbert’s Program Revisited Volume I Base case: -computation 휔 Dr Stephen Gaito PerceptiSys Ltd April 7, 2019 Perish then Publish Press. 1 1 2 2 This document was prepared using ConTEXt and LuaTEX on April 7, 2019. Unless explicitly stated otherwise, all content contained in this document which is not software code is Copyright © 2019 PerceptiSys Ltd (Stephen Gaito) and is licensed for release under the Creative Commons Attribution-ShareAlike 4.0 International License (CC-BY-SA 4.0 License). You may obtain a copy of the License at http://creativecommons.org/licenses/by-sa/4.0/ Unless required by applicable law or agreed to in writing, all non-code content distributed under the above CC-BY-SA 4.0 License is distributed on an ‘AS IS’ BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the CC-BY-SA 4.0 License whose URL is listed above for the specific language governing permissions and limitations under the License. Again, unless explicitly stated otherwise, all content contained in this document which is software code is Copyright © 2019 PerceptiSys Ltd (Stephen Gaito) and is licensed under the Apache License, Version 2.0 (the "License"); you may not use this code except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed un- der the Apache 4.0 License is distributed on an ‘AS IS’ BASIS, WITHOUT WAR- RANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    [Show full text]