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CHARYBDIS: A LISP PROGRAM TO DISPLAY MATHEMATICAL EXPRESSIONS ON TYPEWRITER-LIKE DEVICES

IP.com Disclosure Number: IPCOM000128822D
Original Publication Date: 1967-Aug-01
Included in the Prior Art Database: 2005-Sep-19
Document File: 10 page(s) / 38K

Publishing Venue

Software Patent Institute

Related People

Millen, J.K.: AUTHOR [+3]

Abstract

Charybdis is a LISP program that accepts, as input, mathematical expressions written in LISP prefix notation, and displays them in familiar two-dimensional form on devices with a small fixed character set. It is a simply organized, modular program whose structure is based on the recursive structure of mathematical expressions. Changes and additions to the repertory of Charybdis can be made easily and independently of one another by LISP programmers familiar win little more than its conceptual basis. [ Page VI omitted ] TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS ..... viii SECTION I INTRODUCTION ..... 1 SECTION II DESCRIPTION OF THE DISPLAYS ..... 3 THE CHARACTER SET AND ITS LIMITATIONS ..... 3 LINE OVERFLOW ..... 8 SPECIAL SYMBOLISM ..... 10 OTHER DISPLAYS .....10 SECTION III PROGRAM STRUCTURE .....14 INTRODUCTION .....14 CHARYBDIS .....14 PROGRAM STRUCTURE ..... 15 CONCEPTUAL BASIS .....16 THE EXAMPLE .....19 SECTION IV SUMMARY .....22 REFERENCES .....23 LIST OF ILLUSTRATIONS Figure No. Page 1 Some Displays (a) Continued Fraction ..... 3 (b) MATHLAB: Differentiation Result ..... 4 (c) MATHLAB: Integration Result ..... 5 2 Parentheses (a) Single Line ..... 7 (b) Stacked ..... 7 3 Splitting Across Lines (a) A Differential Equation ..... 9 (b) Its Solution ..... 9 4 Extended Summation ..... 11 5 Other Displays (a) Matrix ..... 12 (b) Binary Trees ..... 13 6 Block Diagram of Charybdis ..... 15 7 Illustration of Terms ..... 18

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

CHARYBDIS: A LISP PROGRAM TO DISPLAY MATHEMATICAL EXPRESSIONS ON TYPEWRITER- LIKE DEVICES

J. K. Millen

AUGUST 1967

THE: MITRE CORPORATION

BOX 208
BEDFORD, MASSACHUSETTS

This document has been released for public dissemination.

Project 9515

ACKNOWLEDGMENTS

This project was sponsored by The MITRE Corporation's Dependent Research Program.

It was also supported, in part, through access to its computer facilities, by Project MAC, an M. I.
T. Research Program sponsored by the Advanced Research Projects Agency, Department of Defense, under Office of Naval Research Contract No. NONR-4102(01).

The author wishes to thank C. Engelman for his many helpful comments and suggestions.

[ Page IV omitted ]

ABSTRACT

Charybdis is a LISP program that accepts, as input, mathematical expressions written in LISP prefix notation, and displays them in familiar two-dimensional form on devices with a small fixed character set. It is a simply organized, modular program whose structure is based on the recursive structure of mathematical expressions. Changes and additions to the repertory of Charybdis can be made easily and independently of one another by LISP programmers familiar win little more than its conceptual basis.

[ Page VI omitted ]

TABLE OF CONTENTS Page

LIST OF ILLUSTRATIONS ..... viii
SECTION I INTRODUCTION ..... 1
SECTION II DESCRIPTION OF THE DISPLAYS ..... 3

     THE CHARACTER SET AND ITS LIMITATIONS ..... 3
LINE OVERFLOW ..... 8
SPECIAL SYMBOLISM ..... 10
OTHER DISPLAYS .....10
SECTION III PROGRAM STRUCTURE .....14

INTRODUCTION .....14

Mitre Corporation Page 1 Aug 01, 1967

Page 2 of 10

CHARYBDIS: A LISP PROGRAM TO DISPLAY MATHEMATICAL EXPRESSIONS ON TYPEWRITER-LIKE DEVICES

         CHARYBDIS .....14
PROGRAM STRUCTURE ..... 15
CONCEPTUAL BASIS .....16
THE EXAMPLE .....19
SECTION IV SUMMARY .....22
REFERENCES .....23
LIST OF ILLUSTRATIONS

Figure No. Page 1 Some Displays

(a) Continued Fraction ..... 3
(b) MATHLAB: Differentiation Result ..... 4
(c) MATHLAB: Integration Result ..... 5
2 Parentheses

(a) Single Line ..... 7
(b) Stacked ..... 7
3 Splitting Across Lines

(a) A Differential Equation ..... 9
(b) Its Solution ..... 9
Extended Summation ..... 11
5 Other Displays

(a) Matrix ..... 12
(b) Binary Trees ..... 13
6 Block Diagram of Charybdis ..... 15
7 Illustration of Terms ..... 18

SECTION I INTRODUCTION

Charybdis (from CHARacter-composed sYmBolic DISplay) is a LISP program to display mathematical expressions on typewriter-like devices (line printers, teletypes, and scopes which display lines of characters, as well as typewriters). It was written as part of the output interface for MATHLAB ] , which uses LISP for two reasons which apply to Charybdis. First is the fact that the data expressions in LISP are lists, i. e., tree structures, composed ultimately of atomic symbols, which include variables, numbers, and, in particular, characters. Second, but at least as important, is the power of recursion.

Th...