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\helv{\bold{\flushright{Andrew Consortium School of Computer Science Carnegie Mellon }}} \smaller{\flushright{August, 1994}}\majorheading{ } }\majorheading{The 1994 Visual Languages Comparison}\footnote{\ \begindata{fnote,541255704} \textdsversion{12} \enddata{fnote,541255704} \view{fnotev,541255704,87,0,0}(C) 1994 IEEE. Reprinted with permission, from Proceedings 1994 IEEE Symposium on Visual Languages, IEEE Computer Society Press, Los Alamitos, CA, October 4-7, 1994. St. Louis, Missouri, to appear. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the IEEE copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Institute of Electrical and Electronics Engineers. To copy otherwise, or to republish, requires a fee and specific permission.} \indent{Moderator: Wilfred J. Hansen, Director, Andrew Consortium, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213-3891 } \indent{Panelists: Brigham Bell, USWest; Greg A. McKaskle, National Instruments; Garth Smedley, Prograph; Dan Kimura, Washington University; Joerg Poswig, Universitaet Dortmund} \formatnote{ }\bigger{\onesmaller{\center{\bold{Abstract}}}}\italic{\bold{\bigger{\ \onesmaller{ }}} Diverse visual languages have been proposed, implemented, and published; but each is demonstrated on problems chosen by its authors. To make a fair comparison, the 1994 Visual Languages Comparison project proposed a set of three problems and solicited solutions to these problems in various visual languages. Submissions arrived for one graphic rewriting system--ChemTrains--and four data flow languages--LabVIEW, Prograph, Show and Tell, and VisaVis.} Visual programming has been a fruitful and provocative area of research with many diverse languages proposed and implemented. Since some of these are proposed for general programming, it is fair to ask how well they can be used for typical programming problems. To explore this issue a committee chose three problems and invited authors of visual languages to solve those problems in their languages. \formatnote{ }Submissions were received from ChemTrains, which is a graphic rewriting system, and four data flow languages: LabVIEW, Prograph, Show and Tell, and VisaVis. All submissions included solutions to the first problem; the other problems were more complex and received fewer solutions. \section{1. Prime number generator} \formatnote{ }The first problem was intended to test computation and iteration over a set of data: \quotation{Write a program to compute the number of primes in the first k integers, where k is a value elicited from the user at run-time.} The canonical solution to this problem is the Sieve of Erastothenes, which starts with a list of integers and crosses out those which are multiples of primes. After crossing out multiples of the \italic{i}\superscript{th} prime, the \italic{i+1}\superscript{th} prime is the next larger undeleted entry. This scheme requires no division and is usually faster than algorithms with division, but only the ChemTrains and LabVIEW solutions used this approach. \subsection{1.1 ChemTrains - Brigham Bell} \formatnote{ }ChemTrains is a visual production system (or rule-based) language, in which both the rules and the arena on which they operate are defined using pictures. These pictures are composed from four kinds of objects--text, boxes, ovals, and freehand sketches--interconnected by unidirectional or bidirectional links. Each rule consists of a pattern picture and a result picture. \formatnote{ }For execution, the pattern picture in each successive rules is checked against the arena. When the pattern picture matches a portion of the arena, that portion is modified as indicated by the differences between the pattern and the rule's result picture. The only attributes that are matched are objects, connections, and containment; no other geometric constraints--such as adjacency--are considered. For a further description of ChemTrains design and its rationale refer to [Bell, 1992a; Bell, 1993]. \formatnote{ }The ChemTrains prime number program requires eight rules: skip-non-prime, delete-non-prime, increment-multiple, increment-prime-finder, cleanup, condense, start-prime-filtering, make-integer-list. The first four filter out the non-prime numbers from an ordered list of integers. 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0107h8043e0g20 1008g08043eg02 0103h8043e0g20 1070g08041cg02 01020eg804081 g201020e00804 925202g | 1011g080418g02 010880g80!40g 201018g080420 g020104h804020 g201088g080422 g02010611g8041 83g2010611008 04f25202g | 1011g080408g02 01g80g804080g 201028g080420 g020108h804020 g201088g080422 g02010211g8040 81g2010201008 04825202g | 1011g080408g02 !01h8041c0g20 1048g08043cg02 010fh80!40g20 1070g080422g02 010211g804081 g2010!20080492 5202g | 1011g080408g02 0102h804020g20 1088g080402g02 010880g80!40g 201088g08041e g02010211g8040 81g2010204008 04624e02g | 1011g080408g02 0104h804020g20 10fcg080402g02 010880g804080 g201088g080402 g02010211g8040 81g2010208008 04h02g | 100eg080408g02 0108h804220g20 1008g080422g02 010880g804080 g201088g08!04 g02010211g8040 81g201021g0804 h02g | 10h080408g0201 0f80g8041c0g20 1008g08041cg02 0107h804080g20 1070g080418g02 01020eg804081 g201021f00804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201g 10g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201g 28g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201g 54g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201g aag8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 55g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h020102 aa!8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h020105 55408040h2010 h0804h0201i80 40h2010h0804h 0201i8040h2010 h0804h02g | 10h0804h02010f abe08040h2010 h0804h0201i80 40h2010h0804h 0201i8040h2010 h0804h02g | 10h0804h02!01 55g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 abg8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 55g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 abg8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 55g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 abg8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 55g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02!01 Gg8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0844h0211i 8440h2110h0844 h0211i8440h21 10h0844h0211i 8440h2110h0844 h02g | 10h0824h0209i 8240h2090h0824 h0209i8240h20 90h0824h0209i 8240h2090h0824 h02g | 10h0814h0205i 8140h2050h0814 h0205i8140h20 50h0814h0205i 8140h2050h0814 h02g | 10h0ffch03GiG c0h3ff0h0ffch 03GiGc0h3ff0h 0ffch03GiGc0h 3ff0h0ffch02g | 10h080ch0203i 80c0h2030h080c h0203i80c0h20 30h080ch0203i 80c0h2030h080c h02g | 10h0814h0205i 8140h2050h0814 h0205i8140h20 50h0814h0205i 8140h2050h0814 h02g | 10h0864h0219g 10g8640h2190h 0864h0219i8640 h2190h0864h02 19i8640h2190h 0864h02g | 10h0804h0201g 28g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201g 44g8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201g aag8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02"01 g8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h020102 aa!8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h020104 g408040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02010f abe08040h2010 h0804h0201i80 40h2010h0804h 0201i8040h2010 h0804h02g | 10h0804h02"01 g8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h02!01 abg8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02"01 g8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h02!01 abg8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02"01 g8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h02!01 abg8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h02"01 g8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h02!01 Gg8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 1001g0804h0201 i8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 1002800804h02 01i8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 1004400804h02 01i8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 1008200804h02 01i8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 1020!0804h0201 i8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 1040040804h02 01i8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10f01e0804h02 01i8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | "100804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 101ff00804h02 01i8040h2010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 1fHf807Hfe01I 807fHe01fHf807 Hfe01I807fHe0 1fHf807Hfe01I 807fHe01fHf807 Hfeg | \enddata{raster, 539406808} \view{rasterview,539406808,55,0,0} Pointer P ("Prime", \begindata{raster,539407064} 2 0 68266 68266 0 0 13 16 bits 539407064 13 16 02g | 05g | 0a80 | 1540 | 2aa0 | 5550 | aaa8 | f578 | 2aa0 | 3560 | 2aa0 | 3560 | 2aa0 | 3560 | 2aa0 | 3fe0 | \enddata{raster, 539407064} \view{rasterview,539407064,56,0,0}) points to a currently known prime number whose multiples are used to delete non-prime numbers. \ Pointer M ("Marker", \begindata{raster,539407240} 2 0 68266 68266 0 0 14 17 bits 539407240 14 17 h | 02g | 05g | 0880 | 1540 | !20 | 5550 | 8008 | f57c | !20 | 3560 | !20 | 3560 | !20 | 3560 | !20 | 3fe0 | \enddata{raster, 539407240} \view{rasterview,539407240,57,0,0}) travels between the P pointer and the end of the list, deleting multiples of P's integer. \ Pointer X ("indeX", \begindata{raster,539407464} 2 0 68266 68266 0 0 14 16 bits 539407464 14 16 02g | 05g | 0880 | 1040 | !20 | 4010 | 8008 | e03c | !20 | !20 | !20 | !20 | !20 | !20 | !20 | 3fe0 | \enddata{raster, 539407464} \view{rasterview,539407464,58,0,0}), marches upward from zero while M is advancing; when X reaches P, M has reached a multiple of P. \formatnote{ }Increment-prime-finder moves M and X each to the right by one cell: \begindata{raster,539407688} 2 0 68266 68266 0 0 454 150 bits 539407688 454 150 o01ZZLfc | o01zzl04 | o01zzl04 | o01zzl04 | o01zzl04 | o01zzl04 | 03e006g0620i01 04l02h04i62g04 zo04 | 021002g0620i01 m02l80g04zo04 | 0212221c05238b 30e0010c587173 8b30e2c701e2ec 598701c62c3c71 70zm04 | 0212!2205244c c9120104648984 4cc91322011304 66488082324489 80zm04 | 03e2!2204a3c8 89100104448104 48891222011204 44488082224489 zn04 | 0282223e04a448 89f00104448107 c889f222011204 444f80822244f9 zn04 | 02422220046448 89g0104448104 08890222011204 4448g82224481 zn04 | 02226222046448 89100104448904 48891222011204 44488082224489 zn04 | 0211a21c0423c8 88e20104447103 !88e22181e204 4447g82223c71 zn04 | o01n01zw04 | o01n01zw04 | o01zzl04 | o01zzl04 | o01zzl04 | o01zzl04 | o01ZZLfc | zzw | zzw | zzw | zzw | zzw | zzw | zzw | zzw | o3fg0c18i07e1 8006z01f8ie180 3f0cg30l | o31800c18i0630 g06z018ci6180 3180g30l | o318f1e!3c7ef8 0633878f199f9e w018c!78cc63c0 319c3c78ccfcf0 i | o31998c186670 ec06318cc6199c 33w018c"cc6180 318c6630cce198 i | o3f0f8c186660 cc07e18c061998 33w01f8ccc0cc 61803f0c6030cc c198i | o30198c187e60 cc06018c061998 3fw01e0fc78cc 6180300c6030cc c1f8i | o30198c18!60cc 06018c06199830 w01b0c00ccc61 80300c6030ccc1 80i | o30198c186660 cc06018cc61b98 33w0198!ccdc61 80300c6630dcc1 98i | o300f870e3c60 cc060187838f98 1ew018c!787c60 e0300c3c1c7cc0 f0i | zzw | zzw | zzw | zzw | zzw | zzw | ZZVfc | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80g01I8007Hfe j1fHf8gIc0l01 80zj04 | 80g01i8004h02 j10h08g80h40l 0180g07Hfeg1f Hf8j7fHe001I80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8104h02 j10h081080h40 l0180g04h02g10 h08j40h2001i80 g04 | 80g01i80c4h02 j1001g!0880h40 l0180g04h0204 10h08j40h2041 i80g04 | 80g01i8034h02 j100280080680 h40l0180g04h02 0310h08j40h20 31i80g04 | 80g01iGfch02j 1004400fG80h40 l0180g04h02gd0 h08j40h200dg10 g80g04 | 80g01i801ch02 j100aa0080180 h40l0180g04h03 Gf0h08j40h3fG g28g80g04 | 80g01i8064h02 j"10080680h40 l0180g04h02g70 h08j40h2007g44 g80g04 | 80g01i8184h02 j102aa8081880 h40l0180g04h02 0190h08j40h20 19gaag80g04 | 80g01i8004h02 j10400408g80h 40l0180g04h02 0610h08j40h20 61!01g80g04 | 80g01i8004h02 j10fabe08g80h 40l0180g04h02 g10h08j40h2001 02aa!80g04 | 80g01i8004h02 j"1008g80h40l 0180g04h02g10 h08j40h200104 g4080g04 | 80g01i8004h02 j101ab008g80h 40l0180g04h02 g10h08j40h2001 0fabe080g04 | 80g01i8004h02 j"1008g80h40l 0180g04h02g10 h08j40h20"01g 80g04 | 80g01i8004h02 j101ab008g80h 40l0180g04h02 g10h08j40h20!01 abg80g04 | 80g01i8004h02 j"1008g80h40l 0180g04h02g10 h08j40h20"01g 80g04 | 80g01i8004h02 j101ab008g80h 40l0180g04h02 g10h08j40h20!01 abg80g04 | 80g01i8004h02 j"1008g80h40l 0180g04h02g10 h08j40h20"01g 80g04 | 80g01i8004h02 j101ff008g80h 40l0180g04h02 g10h08j40h20!01 abg80g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h20"01g 80g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h20!01G g80g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01g10g8004 h02j10h08g80h 40l0180g04h02 g10h08j40h2001 i80g04 | 80g01g28g8004 h02j10h08g80h 40l0180g04h02 g1001g08j40h20 01i80g04 | 80g01g44g8004 h02j10h08g80h 40l0180g04h02 g10028008j40h 2001i80g04 | 80g01g82g8004 h02j10h08g80h 40l0180g04h02 g10044008j40h 2001i80g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g10 082008j40h2001 i80g04 | 80g0102g!8004 h02j10h08g80h 40l0180g04h02 g"1008j40h2001 i80g04 | 80g0104g408004 h02j10h08g80h 40l0180g04h02 g1020!08j40h20 01i80g04 | 80g010f01e080 04h02j10h08g80 h40l0180g04h02 g10400408j40h 2001i80g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g10 f01e08j40h2001 i80g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g"10 08j40h2001i80 g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g"10 08j40h2001i80 g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g"10 08j40h2001i80 g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g"10 08j40h2001i80 g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g"10 08j40h2001i80 g04 | 80g"01g8004h02 j10h08g80h40l 0180g04h02g"10 08j40h2001i80 g04 | 80g!01Gg8004h 02j10h08g80h40 l0180g04h02g"10 08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 1ff008j40h2001 i80g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01i8004h02 j10h08g80h40l 0180g04h02g10 h08j40h2001i80 g04 | 80g01I8007Hfe j1fHf8gIc0l01 80g04h02g10h08 j40h2001i80g04 | 80zo0180g07Hfe g1fHf8j7fHe001 I80g04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | 80zo0180zj04 | ZZVfc | zzw | \enddata{raster, 539407688} \view{rasterview,539407688,59,0,0} Eventually, pointer X, \begindata{raster,539407912} 2 0 68266 68266 0 0 14 16 bits 539407912 14 16 02g | 05g | 0880 | 1040 | !20 | 4010 | 8008 | e03c | !20 | !20 | !20 | !20 | !20 | !20 | !20 | 3fe0 | \enddata{raster, 539407912} \view{rasterview,539407912,60,0,0}, will arrive at the same cell as P, \begindata{raster,539408088} 2 0 68266 68266 0 0 13 16 bits 539408088 13 16 02g | 05g | 0a80 | 1540 | 2aa0 | 5550 | aaa8 | f578 | 2aa0 | 3560 | 2aa0 | 3560 | 2aa0 | 3560 | 2aa0 | 3fe0 | \enddata{raster, 539408088} \view{rasterview,539408088,61,0,0}. Then because of rule order, the second rule, delete-non-prime, will fire: \begindata{raster,539408312} 2 0 68266 68266 0 0 450 147 bits 539408312 450 147 o01ZZLc0 | o01zzl40 | o01zzl40 | o01zzl40 | o01zzl40 | o01zzl40 | 03e006g0620i01 g803001l02zu40 | 021002g0620i01 g801001zzh40 | 0212221c05238b 30e001078e10e3 870161c580f176 2cc380zr40 | 0212!2205244c c912010891!11 08819226408982 332440zr40 | 03e2!2204a3c8 8910010891!11 08811224408902 222440zr40 | 0282223e04a448 89f001089f11f1 0f811224408902 2227c0zr40 | 02422220046448 89g0108901101 08011224408902 2224zs40 | 02226222046448 8910010891!11 08811224408902 222440zr40 | 0211a21c0423c8 88e201078e10e0 c70111c440f102 222380zr40 | o01o80zv40 | o01o80zv40 | o01zzl40 | o01zzl40 | o01zzl40 | o01zzl40 | o01ZZLc0 | zzw | zzw | zzw | zzw | zzw | zzw | zzw | zzw | o3fg0c18i07e1 8006z01f8ie180 3f0cg30l | o31800c18i0630 g06z018ci6180 3180g30l | o318f1e!3c7ef8 0633878f199f9e w018c!78cc63c0 319c3c78ccfcf0 i | o31998c186670 ec06318cc6199c 33w018c"cc6180 318c6630cce198 i | o3f0f8c186660 cc07e18c061998 33w01f8ccc0cc 61803f0c6030cc c198i | o30198c187e60 cc06018c061998 3fw01e0fc78cc 6180300c6030cc c1f8i | o30198c18!60cc 06018c06199830 w01b0c00ccc61 80300c6030ccc1 80i | o30198c186660 cc06018cc61b98 33w0198!ccdc61 80300c6630dcc1 98i | o300f870e3c60 cc060187838f98 1ew018c!787c60 e0300c3c1c7cc0 f0i | zzw | zzw | zzw | zzw | zzw | zzw | ZZVc0 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80i7fHe0hIc0v 0180k03Ih0fHfc h3fHf0i40 | 80i40h20h80h40 h7fHe0p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i400eg20h80 h40h40h20p0180 k02g7001h08h04 h20h10i40 | 80i4011g20h80 h40h40h20p0180 k02g8801h08h04 h20h10i40 | 80i4011g20h80 h40h40h20p0180 k02g8801h08h04 h20h10i40 | 80i4011g20h80 h40h401cg20p01 80k02g8801h08 h04h2011g10i40 | 80i4011g20h80 h40h4012g20p01 80k02g8801h08 h04h200ag10i40 | 80i4011g20h80 h40h4024g20p01 80k02g8801h08 h04h2004g10i40 | 80i4011g20h80 h40h4024g20p01 80k02g8801h08 h04h2004g10i40 | 80i400eg20h80 h40h4048g20p01 80k02g7001h08 h04h200ag10i40 | 80i40h20h80h40 h4048g20p0180 k02h01h08h04h 2011g10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h8008 g40h40h20p0180 k02h01h08g4004 h20h10i40 | 80i40h20h8014 g40h40h20p0180 k02h01h08ga004 h20h10i40 | 80i40h20h802a g40h40h20p0180 k02h01h080150 04h20h10i40 | 80i40h20h8055 g40h40h20p0180 k02h01h0802a8 04h20h10i40 | 80i40h20h80aa 8040h40h20p01 80k02h01h0805 5404h20h10i40 | 80i40h20h8155 !40h40h20p0180 k02h01h080aaa 04h20h10i40 | 80i40h20h82aa a040h40h20p01 80k02h01h0815 5504h20h10i40 | 80i40h20h87d5 f040h40h20p01 80k02h01h083e af84h20h10i40 | 80i40h20h80aa 8040h40h20p01 80k02h01h0805 5404h20h10i40 | 80i40h20h80d5 8040h40h20p01 80k02h01h0806 ac04h20h10i40 | 80i40h20h80aa 8040h40h20p01 80k02h01h0805 5404h20h10i40 | 80i40h20h80d5 8040h40h20p01 80k02h01h0806 ac04h20h10i40 | 80i40h20h80aa 8040h40h20p01 80k02h01h0805 5404h20h10i40 | 80i40h20h80d5 8040h40h20p01 80k02h01h0806 ac04h20h10i40 | 80i40h20h80aa 8040h40h20p01 80k02h01h0805 5404h20h10i40 | 80i40h20h80G80 40h40h20p0180 k02h01h0807fc 04h20h10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h2002 g10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h2005 g10i40 | 80i40h20h80h40 h4002g20p0180 k02h01h08h04h 20088010i40 | 80i40h20h80h40 h4005g20p0180 k02h01h08h04h 20154010i40 | 80i40h20h80h40 h40088020p0180 k02h01h08h04h "2010i40 | 80i40h20h80h40 h40154020p0180 k02h01h08h04h 20555010i40 | 80i40h20h80h40 h40"20p0180k02 h01h08h04h2080 0810i40 | 80i40h20h80h40 h40555020p0180 k02h01h08h04h 21f57c10i40 | 80i40h20h80h40 h40800820p0180 k02h01h08h04h "2010i40 | 80i40h20h80h40 h41f57c20p0180 k02h01h08h04h 20356010i40 | 80i40h20h80h40 h40"20p0180k02 h01h08h04h"20 10i40 | 80i40h20h80h40 h40356020p0180 k02h01h08h04h 20356010i40 | 80i40h20h80h40 h40"20p0180k02 h01h08h04h"20 10i40 | 80i40h20h80h40 h40356020p0180 k02h01h08h04h 20356010i40 | 80i40h20h80h40 h40"20p0180k02 h01h08h04h"20 10i40 | 80i40h20h80h40 h40356020p0180 k02h01h08h04h 203fe010i40 | 80i40h20h80h40 h40"20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h403fe020p0180 k02h01h08h04h 20h10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 g1001h08h04h20 h10i40 | 80i40h20h80h40 h40h20p0180k02 g2801h08h04h20 h10i40 | 80i40h20h8004 g40h40h20p0180 k02g4401h08h04 h20h10i40 | 80i40h20h800a g40h40h20p0180 k02g8201h08h04 h20h10i40 | 80i40h20h8011 g40h40h20p0180 k02"01h08h04h 20h10i40 | 80i40h20h8020 8040h40h20p01 80k!02g81h08h 04h20h10i40 | 80i40h20h80"40 h40h20p0180k02 04g41h08h04h20 h10i40 | 80i40h20h!8020 40h40h20p0180 k020f01e1h08h 04h20h10i40 | 80i40h20h81g10 40h40h20p0180 k02"01h08h04h 20h10i40 | 80i40h20h83c0 7840h40h20p01 80k02"01h08h04 h20h10i40 | 80i40h20h80"40 h40h20p0180k02 "01h08h04h20h 10i40 | 80i40h20h80"40 h40h20p0180k02 "01h08h04h20h 10i40 | 80i40h20h80"40 h40h20p0180k02 "01h08h04h20h 10i40 | 80i40h20h80"40 h40h20p0180k02 "01h08h04h20h 10i40 | 80i40h20h80"40 h40h20p0180k02 "01h08h04h20h 10i40 | 80i40h20h80"40 h40h20p0180k02 01G01h08h04h20 h10i40 | 80i40h20h80"40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h807f c040h40h20p01 80k02h01h08h04 h20h10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i40h20h80h40 h40h20p0180k02 h01h08h04h20h 10i40 | 80i7fHe0hIc0h 40h20p0180k03 Ih0fHfch3fHf0 i40 | 80u7fHe0p0180 zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | 80zo0180zj40 | ZZVc0 | \enddata{raster, 539408312} \view{rasterview,539408312,62,0,0} The italicized \italic{n} is a ChemTrains "variable"; it will match any object, in this case an integer. Delete-non-prime moves X to zero and changes the integer over M to an "x". Subsequently, M and X will resume marching to the right under rule increment-prime-finder. \formatnote{ }The third rule, increment-multiple, fires when pointer M has reached the end of the list: \begindata{raster,539408536} 2 0 68266 68266 0 0 457 155 bits 539408536 457 155 o01ZZM80 | o01zzm80 | o01zzm80 | o01zzm80 | o01zzm80 | o01q204008zs80 | 03e006g0620i01 04l02i244008zs 80 | 021002g0620i01 m02i24g08zs80 | 0212221c05238b 30e0010c587173 8b30e2c7016621 2f4b88f0zr80 | 0212!2205244c c9120104648984 4cc91322019921 244cc998zr80 | 03e2!2204a3c8 89100104448104 48891222011121 24484908zr80 | 0282223e04a448 89f00104448107 c889f222011121 244849f8zr80 | 02422220046448 89g0104448104 08890222011121 244849zs80 | 02226222046448 89100104448904 48891222011121 244849zs80 | 0211a21c0423c8 88e20104447103 !88e221811133 244cc998zr80 | o01n01111d234b 88f0zr80 | o01r08zt80 | o01r08zt80 | o01zzm80 | o01zzm80 | o01zzm80 | o01ZZM80 | zzx | zzx | zzx | zzx | zzx | zzx | zzx | zzx | o3fg0c18i07e1 8006x03f0h01c3 g7e18g60o | o31800c18i0630 g06x0318ic3g63 h60o | o318f1e!3c7ef8 0633878f199f9e u0318f0f198c7 80633878f199f9 e0l | o31998c186670 ec06318cc6199c 33u0319!9998c3 g6318cc6199c3 30l | o3f0f8c186660 cc07e18c061998 33u03f1998198 c3g7e18c06199 8330l | o30198c187e60 cc06018c061998 3fu03c1f8f198 c3g6018c06199 83f0l | o30198c18!60cc 06018c06199830 u0361801998c3 g6018c0619983 m | o30198c186660 cc06018cc61b98 33u0331!99b8c3 g6018cc61b983 30l | o300f870e3c60 cc060187838f98 1eu0318!f0f8c1 c060187838f981 e0l | zzx | zzx | zzx | zzx | zzx | zzx | ZZW80 | 80zm30zn80 | 80zm30zn80 | 80zm30zn80 | 80zm30zn80 | 80zm30zn80 | 80zm30zn80 | 80zm30zn80 | 8007Hfei07Hfe g1fHf8q30gIc0 iIc003Ih07Hfe g1fHf8g80 | 8004h02i04h02 g10h08g01I8007 Hfeg30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 80040eg02i04h 02g10h08g01i80 04h02g30g81c0 g40i80h4002h01 h04h02g10g0408 g80 | 800411g02i04h 02g10h08g01i80 04g0102g30g82 20g40i80h4002 h01h04h02g10g 0408g80 | 800411g02i04h 02g10h08g01i80 04g0102g30g82 20g40i80h4002 h01h04h02g10c7 1c08g80 | 800411g02i04h 02g10h08g01i80 0431c702g30g82 20g40i80h4002 h01h04h02g1124 a408g80 | 800411g02i04h 02g10h08g01i80 04492902g30g82 20g40i80h4002 h01h04h02g11e4 a408g80 | 800411g02i04h 02g10h08g01i80 04792902g30g82 20g40i80h4002 h01h04h02g1104 a408g80 | 800411g02i04h 02g10h08g01i80 04412902g30g82 20g40i80h4002 h01h04h02g1124 a408g80 | 80040eg02i04h 02g10h08g01i80 04492902g30g81 c0g40i80h4002 h01h04h02g10c4 9c08g80 | 8004h02i04h02 g10h08g01i8004 312702g30g80h 40i80h4002h01 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04g20 02g10h08g01i80 04h02g30g80h40 i80h4002g2001 h04h02g10h08g 80 | 8004h02i04g50 02g10h08g01i80 04h02g30g80h40 i80h4002g5001 h04h02g10h08g 80 | 8004h02i04ga8 02g10h08g01i80 04h02g30g80h40 i80h4002ga801 h04h02g10h08g 80 | 8004h02i040154 02g10h08g01i80 04h02g30g80h40 i80h4002015401 h04h02g10h08g 80 | 8004h02i0402aa 02g10h08g01i80 04h02g30g80h40 i80h40!02aa01 h04h02g10h08g 80 | 8004h02i040555 02g10h08g01i80 04h02g30g80h40 i80h4002055501 h04h02g10h08g 80 | 8004h02i040aaa 82g10h08g01i80 04h02g30g80h40 i80h40020aaa81 h04h02g10h08g 80 | 8004h02i041f57 c2g10h08g01i80 04h02g30g80h40 i80h40021f57c1 h04h02g10h08g 80 | 8004h02i0402aa 02g10h08g01i80 04h02g30g80h40 i80h40!02aa01 h04h02g10h08g 80 | 8004h02i040356 02g10h08g01i80 04h02g30g80h40 i80h4002035601 h04h02g10h08g 80 | 8004h02i0402aa 02g10h08g01i80 04h02g30g80h40 i80h40!02aa01 h04h02g10h08g 80 | 8004h02i040356 02g10h08g01i80 04h02g30g80h40 i80h4002035601 h04h02g10h08g 80 | 8004h02i0402aa 02g10h08g01i80 04h02g30g80h40 i80h40!02aa01 h04h02g10h08g 80 | 8004h02i040356 02g10h08g01i80 04h02g30g80h40 i80h4002035601 h04h02g10h08g 80 | 8004h02i0402aa 02g10h08g01i80 04h02g30g80h40 i80h40!02aa01 h04h02g10h08g 80 | 8004h02i0403fe 02g10h08g01i80 04h02g30g80h40 i80h400203fe01 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 0410h08g01i80 04h02g30g80h40 i80h4082h01h04 h020410h08g80 | 8004h02i04h02 0310h08g01i81 04h02g30g80h40 i80h4062h01h04 h020310h08g80 | 8004h02i04h02 gd0h08g01i80c4 h02g30g80h40i 80h401ah01h04 h02gd0h08g80 | 8004h02i04h03 Gf0h08g01i8034 h02g30g80h40i 80h7ffeh01h04 h03Gf0h08g80 | 8004h02i04h02 g70h08g01iGfc h02g30g80h40i 80h400eh01h04 h02g70h08g80 | 8004h02i04h02 0190h08g01i80 1ch02g30g80h40 i80h4032g2001 h04h020190h08 g80 | 8004h02i04h02 0610h08g01i80 64h02g30g80h40 i80h40c2g5001 h04h020610h08 g80 | 8004h02i04h02 g10h08g01i8184 h02g30g80h40i 80h4002g8801h 04h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002015401 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h40"0201h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002055501 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h400208g81h 04h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h40021f57c1 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h40"0201h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002035601 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h40"0201h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002035601 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h40"0201h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002035601 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h40"0201h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h400203fe01 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g80h40i 80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01i8004 h02g30g8008g40 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01g08g 8004h02g30g80 14g40i80h4002 h01h04h02g10h 08g80 | 8004h02i04h02 g10h08g01g14g 8004h02g30g80 22g40i80h4002 h01h04h02g10h 08g80 | 8004h02i04h02 g10h08g01g22g 8004h02g30g80 41g40i80h4002 h01h04h02g10h 08g80 | 8004h02i04h02 g10h08g01g55g 8004h02g30g"80 40i80h4002h01 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01g"80 04h02g30g81g!40 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g!015540 8004h02g30g82 g2040i80h4002 h01h04h02g10h 08g80 | 8004h02i04h02 g10h08g0102g20 8004h02g30g87 80f040i80h4002 h01h04h02g10h 08g80 | 8004h02i04h02 g10h08g0107d5 f08004h02g30g "8040i80h4002 h01h04h02g10h 08g80 | 8004h02i04h02 g10h08g01g"80 04h02g30g"8040 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01gd5!80 04h02g30g"8040 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01g"80 04h02g30g"8040 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01gd5!80 04h02g30g"8040 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01g"80 04h02g30g"8040 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01gd5!80 04h02g30g"8040 i80h4002h01h04 h02g10h08g80 | 8004h02i04h02 g10h08g01g"80 04h02g30g80G80 40i80h4002h01 h04h02g10h08g 80 | 8004h02i04h02 g10h08g01gG!80 04h02g30g80h40 i80h4002h01h04 h02g10h08g80 | 8004h02g01g04 h02g10h08g01i 8004h02g30g80 h40i80h4002h01 h04h02g10h08g 80 | 8004h02g028004 h02g10h08g01i 8004h02g30g80 h40i80h4002h01 h04h02g10h08g 80 | 8007Hfeg044007 Hfeg1fHf8g01i 8004h02g30gIc0 iIc003Ih07Hfe g1fHf8g80 | 80k0820p01I80 07Hfeg30zn80 | 80k!10z30zn80 | 80k2008z30zn80 | 80k4004z30zn80 | 80kf01ez30zn80 | 80k!10z30zn80 | 80k!10z30zn80 | 80k!10z30zn80 | 80k!10z30zn80 | 80k!10z30zn80 | 80k!10z30zn80 | 80k!10z30zn80 | 80k1ff0z30zn80 | 80zm30zn80 | 80zm30zn80 | 80zm30zn80 | ZZW80 | \enddata{raster, 539408536} \view{rasterview,539408536,63,0,0} It moves P to the right, moves M to join P and moves X from wherever it is back to the zero cell. Usually the result will leave P pointing at a cell with an "x" instead of an integer, so the next rule to fire will be skip-non-prime which moves P and M to the right together until they are at the next cell with an integer. By construction, this is the next prime. \formatnote{ }At one point in the execution, the multiples of two have been deleted and the integer 9 is just about to be deleted as a multiple of three: \begindata{raster,539408712} 2 0 68266 68266 0 0 474 90 bits 539408712 474 90 zzz | zzz | 1fHf807Hfe01I 807fHe01fHf807 Hfe01I807fHe0 1fHf807Hfe01I 807fHe01fHf807 Hfeg | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 g!02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 g!02g | 100eg0804h0201 i8040h2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04638e02g | 1011g080408g02 0107h8043e0g20 10h08043eg0201 i8043e0g2010h 08041cg0201i80 4081g2010h0804 925202g | 1011g080418g02 010880g80!40g 2010h080420g02 01i804020g2010 h080422g0201i 804183g2010h08 04f25202g | 1011g080408g02 01g80g804080g 2010h080420g02 01i804020g2010 h080422g0201i 804081g2010h08 04825202g | 1011g080408g02 !01h8041c0g20 10088008043cg 0201g88g80!40 g201008800804 22g0201g88g80 4081g20100880 0804925202g | 1011g080408g02 0102h804020g20 1005g080402g02 01g50g80!40g20 1005g08041eg02 01g50g804081g 201005g080462 4e02g | 1011g080408g02 0104h804020g20 1002g080402g02 01g20g804080g 201002g080402 g0201g20g8040 81g201002g0804 h02g | 100eg080408g02 0108h804220g20 1002g080422g02 01g20g804080g 201002g08!04g 0201g20g804081 g201002g0804h 02g | 10h080408g0201 0f80g8041c0g20 1005g08041cg02 01g50g804080g 201005g080418 g0201g50g8040 81g201005g0804 h02g | 10h0804h0201i 8040h20100880 0804h0201g88g 8040h20100880 0804h0201g88g 8040h20100880 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 804004g2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 80400ag2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 804015g2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 80402a802010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 804055402010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 8040aaa02010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 804155502010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 8043eaf82010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 804055402010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 80406ac02010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 804055402010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 80406ac02010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 804055402010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 80406ac02010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 804055402010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 80407fc02010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0844h0211i 8440h2110h0844 h0211i8440h21 10h0844h0211i 8440h2110h0844 h02g | 10h0824h0209i 8240h2090h0824 h0209i8240h20 90h0824h0209i 8240h2090h0824 h02g | 10h0814h0205i 8140h2050h0814 h0205i8140h20 50h0814g400205 i8140h2050h08 14h02g | 10h0ffch03GiG c0h3ff0h0ffch 03GiGc0h3ff0h 0ffcga003GiGc0 h3ff0h0ffch02 g | 10h080ch0203i 80c0h2030h080c h0203i80c0h20 30h080c011002 03i80c0h2030h 080ch02g | 10h0814h0205i 8140h2050h0814 h0205i8140h20 50h081402a802 05i8140h2050h 0814h02g | 10h0864h0219i 8640h2190h0864 h0219i8640h21 90h0864!040219 i8640h2190h08 64h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h08040aaa02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804100102 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h08043eaf82 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h08"040201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h080406ac02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h08"040201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h080406ac02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h08"040201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h080406ac02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h08"040201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h080407fc02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 804004g2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 80400ag2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 804011g2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 804020802010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 804080!2010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 8041g102010h08 04h0201i8040h 2010h0804h0201 i8040h2010h08 04h02g | 10h0804h0201i 8043c0782010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 80"402010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 80407fc02010h 0804h0201i8040 h2010h0804h02 01i8040h2010h 0804h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 1fHf807Hfe01I 807fHe01fHf807 Hfe01I807fHe0 1fHf807Hfe01I 807fHe01fHf807 Hfeg | zzz | zzz | zzz | \enddata{raster, 539408712} \view{rasterview,539408712,64,0,0} Eventually, this final state is reached: \begindata{raster,539408888} 2 0 68266 68266 0 0 474 88 bits 539408888 474 88 zzz | zzz | zzz | 1fHf807Hfe01I 807fHe01fHf807 Hfe01I807fHe0 1fHf807Hfe01I 807fHe01fHf807 Hfeg | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 100eg0804h0201 i8040h2010f8g 08043eg020102 04g8040g102010 h0804h0201i80 40h2010h0804h 02g | 1011g080408g02 0107h8043e0g20 1080g080402g02 01060cg8040g10 2010h0804h0201 i8040h2010h08 04h02g | 1011g080418g02 010880g80!40g 201080g080402 g02010204g8043 1c702010h0804 h0201i8040h20 10h0804h02g | 1011g080408g02 01g80g804080g 2010f0g08!04g 02010204g8044 9290201088g08 0422g02010880 g804220g201088 g080422g02g | 1011g080408g02 !01h8041c0g20 1008g08!04g02 010204g804792 90201050g0804 14g020105h8041 40g201050g0804 14g02g | 1011g080408g02 0102h804020g20 1008g080408g02 010204g804412 90201020g0804 08g020102h8040 80g201020g0804 08g02g | 1011g080408g02 0104h804020g20 1088g080408g02 010204g804492 90201020g0804 08g020102h8040 80g201020g0804 08g02g | 100eg080408g02 0108h804220g20 1070g080408g02 010204g804312 70201050g0804 14g020105h8041 40g201050g0804 14g02g | 10h080408g0201 0f80g8041c0g20 10h0804h0201i 8040h201088g08 0422g02010880 g804220g201088 g080422g02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 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10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 10h0804h0201i 8040h2010h0804 h0201i8040h20 10h0804h0201i 8040h2010h0804 h02g | 1fHf807Hfe01I 807fHe01fHf807 Hfe01I807fHe0 1fHf807Hfe01I 807fHe01fHf807 Hfeg | \enddata{raster, 539408888} \view{rasterview,539408888,65,0,0} with all the primes shoved to the left by the condense rule. \formatnote{ }One advantage of this solution is that it produces a graphical--and potentially educational--simulation of the Sieve of Erastothenes. The solution illustrates the importance of rule order; for instance, "increment-prime-finder" must follow "delete-non-prime" or the program will not delete non-prime numbers. \subsection{1.2 LabVIEW - Greg A. McKaskle} LabVIEW is a data flow language with a large library of predefined functions and interaction images. Each data flow diagram has an associated front panel--a graphic representation which can accept input from the user and provide imagery as feedback. See [Daley, 1992], [Jagadeesh, 1993], [Kodosky, 1991]. \formatnote{ }The front panel shown for the primes problem, Figure 1a, shows SampleSize as a user set-able parameter and NumberOfPrimes as a computed value. These are displayed with standard widgets supplied with LabVIEW. The corresponding block diagram, Figure 1b, stretches from input of SampleSize on the left to output of Primes and NumberOfPrimes on the right. The left side of the diagram initializes a Boolean array to contain two false values (for 0 and 1) and SampleSize-minus-2 true values. Then a FOR loop is executed N times with SampleSize supplied as the value for N; if the \italic{i}\superscript{th} element is false, the number isn't prime and the box with the dark grey border is not executed. If the \italic{i}\superscript{th} element is true, it is prime; so all multiples of \italic{i}, starting at twice \italic{i}, are set to false by the computation within the innermost box. \formatnote{ }Arithmetic operations are shown in triangular blocks and array operations in rectangles with suggestive pictures. From left to right, these rectangles have the semantics of: \leftindent{generate an array of like values (twice) concatenate two arrays select the \italic{i}\superscript{th} element of an array store a value at a location in an array} \formatnote{ }The rightmost operator rectangle invokes an operation defined with another data flow diagram. It selects from an array of integers those corresponding to the true values in the Boolean array. The associated front panel is the lower half of Figure 1a: it displays a sequence of white or black disks for the Boolean values and a sequence of integers giving the primes. \subsection{1.3 Prograph - Garth Smedley} \formatnote{ }Prograph is a visual object-oriented data-flow language. Classes, attributes, and methods are created and modified through direct manipulation of icons on the screen. Prograph has an integrated development environment with an editor, interpreter, debugger and compiler. The interpreter supports creating, editing and browsing code, even while it is executing. Prograph offers class libraries, one of which implements the Macintosh graphical user interface. [Cox, 1989] \formatnote{ }The prime number computation takes advantage of Prograph's built-in list handling. 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80k01l02q20 | 80l80k02q20 | 80l80k02q20 | 80l40k01q20 | 80l20k01q20 | 80l20k01q20 | 80l10k01q20 | 80l08k01q20 | 80l08l80p20 | 80l04l80p20 | 80l02l80p20 | 80l07k01c0p20 | 80l0880j0220p 20 | 80l0880j0220p 20 | 80l0880j0220p 20 | 80l07k01c0p20 | 80hWfcj20 | 80g03c4/444fj 20 | 80g06/88888980 i20 | 80g07/11!1180 i20 | 80g06/22!2280 i20 | 80g04/44!4480 i20 | 80g04/88!8880 i20 | 80g07X80i20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | 80zj20 | ZKe0 | \enddata{raster, 539446840} \view{rasterview,539446840,67,0,0} "try candidate" has three inputs, the second of which is a list. The call on "try candidate" in the first pane shows that it is iterated, with the left output being supplied as the left input and the list recycling in the middle. The comparison of candidate+2 with \sansserif{\smaller{K}} determines when to terminate the loop. \ \formatnote{ }The call on "add it or not" determines whether to add the candidate to the list. This function is implemented with two panes, called "cases": \begindata{raster,539447016} 2 0 68266 68266 0 0 215 188 bits 539447016 215 188 ZLfe | 80zk02 | 80zk02 | 80zk02 | 80h1fGc0z02 | 80h2511201803 c0g"0630j03m02 | 80h2623203804 60g!06g30j03m 02 | 80h24452018!60 3c!3e06780f1b 07c3c780l02 | 80h24892018!60 46!660630199c 066663m02 | 80h25112018gc0 3e!6606301998 066663m02 | 80h2623201801 80"6606301998 066663m02 | 80h2445201803 g"660630199806 6663m02 | 80h2489201866 g"660630199806 6663m02 | 80h2511201867 e0"3e06180f18 0663c180l02 | 80h1fGc0z02 | 80zk02 | 80zk02 | 80zk02 | ZLfe | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80i01ZGe2 | 80i01/11$1122 | 80i01/22%22 | 80i01/44$4462 | 80i01/88$88a2 | 80i0191/11#11 62 | 80je2/22"2223 c2 | 80j3fZ02 | 80k1cr0380k02 | 80k22r0440k02 | 80k22r0440k02 | 80k22r0440k02 | 80k1cr0380k02 | 80k1cr03l02 | 80k1br06l02 | 80k28c0q0al02 | 80k2820q12l02 | 80l18q24l02 | 80l06x02 | 80l01x02 | 80h024202hc0w 02 | 80h"02h30o3202 g1880i02 | 8006338ece6730 g08o1002g2080 i02 | 80090a!521248 g06o1677067097 1905c002 | 80083a!527278 g0180n12820920 !a4a92002 | 80094a!529240 h40n12620920c4 a4a92002 | 80063a!4e7130 h30m0192120920 !a4512002 | 80n0cm0212e106 209498512002 | 80n02m04n02 | 80j!10h0180l08 n02 | 80j2010i60l10 n02 | 80j2010i10l20 n02 | 80j4020i0clc0 n02 | 80j4020i03k01 h04l02 | 80j8020j80j02 o02 | 80j8020j60j04 g396dd8c7j02 | 80i01g20j18j08 g25852528j02 | 80i01g20j04j10 g250525e6j02 | 80i02g20j03j20 g25052501j02 | 80i02g20kc0ic0 g390524cej02 | 80i04g20k20h01 h20m02 | 80i04g20k18h02 h20m02 | 80i08g20k06h04 h02m02 | 80i08g20k01h08 h02m02 | 80i10g20lc0g10 h02m02 | 80i10g20l20g20 h02m02 | 80i20g40l18gc0 h04m02 | 80i20g40l0601 i04m02 | 80i40n0102i04 m02 | 80i40oc4i08m02 | 80i80o38i08m02 | 80i80o18i08m02 | 80h01p26i08m02 | 80h01025ce32c lc180h10m02 | 80h!025294b0k 01g40h10m02 | 80h!025297a0k 02g30h10m02 | 80h0402529420 k04g0ch20m02 | 80h0401dce320 k08g02h20m02 | 80h08g1080l10 g0180g20m02 | 80h08g1080l20 h60g20m02 | 80h10oc0h10g40 m02 | 80h10n01i0cg40 m02 | 80h20n02i03g40 m02 | 80h4002h04j04 j!80m02 | 80h4002h04j08 j6080m02 | 80h80038c971c j10j1880m02 | 80h80025294a4 j60j0480m02 | 80g01g025294a4 j80j03n02 | 80g01g025294a4 i01k01c0m02 | 80g02g038c749c i02k0120m02 | 80g02n04k0218 m02 | 80g04n08k0206 m02 | 80g04i80j10k02 01m02 | 80g08h01k60k02 gc0l02 | 80g08h01k80k04 g30l02 | 80g10h01j01l04 g08l02 | 80g10h01j02l04 g06l02 | 80g20h01j04l08 g0180k02 | 80g20h0380h1c 0el08h40k02 | 80g40h0440h30 03l1ch38k02 | 80ge0h0920h36 dbl22h44k02 | 80G1fHf39fHf6 dbfck22h44k02 | 810110h3390h30 0302k22h44k02 | 83G1fHc09fHfc 0ff2k1ch38k02 | 84ge0h2190j0a iMfci02 | 8fJf39fJcfG80 01&4446i02 | 91(444630g4001 88l0ai02 | 91"88j08888a30 g400110l12i02 | 91!1110j!1112 30g400122l22i 02 | 91!2220j"2230 g400144gc6g06 h46i02 | 91"44g10g0c04 4446318c400188 gc6g06h0ai02 | 91"88i1208888a 30d840011039ef 38e7807c12i02 | 91!1110e5b763 02!1112307040 01220cc60db6df 7022i02 | 91!2220961494 84"2230704001 443cc63d86c060 46i02 | 91"4494149788 04444630d84001 886cc66db6c060 0ai02 | 91"88941494g08 888a318c400110 3c633ce6c06012 i02 | 91!1110e41493 08!111230g4001 22l22i02 | 91!222080i"22 30g4001fel7ei 02 | 91"4480i044446 30g4001m02i02 | 91(888a30g40g Mfci02 | 8fPcfG80j0380 l02 | 80j2720q0440l 02 | 80j2610q0440l 02 | 80j2408q0440l 02 | 80j2730q0380l 02 | 80j2720q02m02 | 80j1240q04m02 | 80j0880q08m02 | 80j07r10m02 | 80w20m02 | 80w40m02 | 80w80m02 | 80v01n02 | 80v01n02 | 80v02n02 | 80v04n02 | 80v08n02 | 80v10n02 | 80v20n02 | 80v40n02 | 80v80n02 | 80u01o02 | 80u02o02 | 80u02o02 | 80u04o02 | 80u08o02 | 80u10o02 | 80u20o02 | 80u40o02 | 80u80o02 | 80t01p02 | 80t02p02 | 80t07p02 | 80t0880o02 | 80t0880o02 | 80t0880o02 | 80t07p02 | 80k03Wf0g02 | 80k0f/11113cg 02 | 80k1a/222226g 02 | 80k1c/444446g 02 | 80k18/88888ag 02 | 80k/11!1112g02 | 80k12/22!22g02 | 80k1fWfeg02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | 80zk02 | ZLfe | \enddata{raster, 539447016} \view{rasterview,539447016,68,0,0}\formatnote{ }\ \begindata{raster,539447192} 2 0 68266 68266 0 0 178 104 bits 539447192 178 104 ZHc0 | 80zg40 | 80zg40 | 80zg40 | 80g03Gf8w40 | 80g04a2240780 78h!c0c6k60i40 | 80g04c46408c0 8ch!c006k60i40 | 80g0488a4gcc0c 0787c7c0cf01e3 60f878f0i40 | 80g049124gcc0c 08!ccc0c60333 80!cc60i40 | 80g04a2240180 1807!ccc0c603 33g!cc60i40 | 80g04c46403g30 0c!ccc0c60333 g!cc60i40 | 80g0488a406g60 0c!ccc0c60333 g!cc60i40 | 80g049124!0cc0 0c!ccc0c60333 g!cc60i40 | 80g04a2240fcc fc07!c7c0c301 e3gcc7830i40 | 80g03Gf8w40 | 80zg40 | 80zg40 | 80zg40 | ZHc0 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80Xf0h40 | 80/88!8890h40 | 8091/111110h40 | 80a2/222230h40 | 80c4/444450h40 | 80c8/8888b0h40 | 8071/1111e0h40 | 801fW80h40 | 80ke0m1cm40 | 80j0110m22m40 | 80j0110m22m40 | 80j0110m22m40 | 80ke0m1cm40 | 80s10m40 | 80s20m40 | 80s40m40 | 80s80m40 | 80r01n40 | 80r02n40 | 80r04n40 | 80i012101l08n 40 | 80i"01l1006!40 0310i40 | 80g0319c76733 98k1002g400410 i40 | 80g0485!290924 k2002cee0ce12 e320b840 | 80g041d!29393c k400250412414 94952440 | 80g04a5!294920 k80024c412418 94952440 | 80g031d!273898 j01g0242412414 948a2440 | 80q02g025c20c4 12930a2440 | 80q04o40 | 80q08o40 | 80q10o40 | 80q20o40 | 80q20o40 | 80q40i80k40 | 80q80o40 | 80p01h072dbb18 e0i40 | 80p02h04b0a4a5 j40 | 80p04h04a0a4bc c0i40 | 80p08h04a0a4a0 20i40 | 80p10h0720a499 c0i40 | 80p20h04m40 | 80p40h04m40 | 80p80p40 | 80p80p40 | 80o01q40 | 80o02q40 | 80o04q40 | 80o08q40 | 80o10q40 | 80o20q40 | 80o40q40 | 80o80q40 | 80n01r40 | 80n0380q40 | 80n0440q40 | 80n0440q40 | 80n0440q40 | 80n0380q40 | 80Wfci40 | 83c4/444fi40 | 86/88888980h40 | 87/11!1180h40 | 86/22!2280h40 | 84/44!4480h40 | 84/88!8880h40 | 87X80h40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | 80zg40 | ZHc0 | \enddata{raster, 539447192} \view{rasterview,539447192,69,0,125} The first of these iterates through the list of known primes with predicate "prime?" calling it once for each element of the list as indicated by "...". When the list is exhausted, the case attaches the candidate to the list of known primes. If the predicate fails, the \sansserif{\bold{x}} in the square--called a "next case control"--terminates the first case and initiates the second, which discards the candidate. The "prime?" block \begindata{raster,539447368} 2 0 68266 68266 0 0 276 201 bits 539447368 276 201 ZTf0 | 80zs10 | 80zs10 | 80zs10 | 80n7fGzi10 | 80n9444806006 h06h03c0s10 | 80n988c80e00e k0460s10 | 80n9114806186 01f1b67fc3c060 s10 | 80n9224806186 0199c6!6660c0 s10 | 80n9444806006 019986!666180 s10 | 80n988c806006 0199866667e180 s10 | 80n9114806006 019986!66u10 | 80n9224806186 019986!662180 s10 | 80n9444806186 01f1866663c180 s10 | 80n7fGi0180x10 | 80s0180x10 | 80zs10 | 80zs10 | ZTf0 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80l07X80m10 | 80l04/44!4480 m10 | 80l04/88!8880 m10 | 80l05/11!1180 m10 | 80l06/22!2280 m10 | 80l06/44444580 m10 | 80l03/88888fn 10 | 80mWfcn10 | 80n01c0k0380j 38q10 | 80n0220k0440j 44q10 | 80n0220k0440j 44q10 | 80n0220k0440j 44q10 | 80n01c0k0380j 38q10 | 80o80l80j70q10 | 80o80l40j88q10 | 80o40l20i0308 q10 | 80o40p0c08q10 | 80o40p1008q10 | 80z6004q10 | 80y018004g01h 04g80j10 | 80y06g04g01h04 01k10 | 80l024202k25ce 32c0g08g04g09 2789ce3380j10 | 80l"02k25294b h30g02g15!5524 49k10 | 80j06338ece67 30j25297ahc0g 02g1d755d2449 k10 | 80j090a!521248 j252942g01h02 g1145512449k10 | 80j083a!527278 j1dce32g06h02 g0d354d2431k10 | 80j094a!529240 j0108h18h01q10 | 80j063a!4e7130 j0108g0460h01 q10 | 80w0280h01q10 | 80w03i01q10 | 80o10m0480i80 3202g1880k10 | 80o10j20h!40i 801002g2080k10 | 80o08j20h4020 i801677067097 1905c0h10 | 80o08j38c971c0 10i8012820920 !a4a920h10 | 80o08j25294a40 10i8012620920 c4a4a920h10 | 80o08j25294a40 08i40!120920!a4 5120h10 | 80o08j25294a40 04i4012e10620 94985120h10 | 80o04j38c749c0 02i40p10 | 80o04n01i40p10 | 80o04o80h20p10 | 80o04k18i40h20 p10 | 80o04k20i20h20 p10 | 80o04kc0i10h20 g04n10 | 80o02j03j08h10 p10 | 80o02j0cj04h10 396dd8c7l10 | 80o02j10j02h10 25852528l10 | 80o02j60j02h10 250525e6l10 | 80o02i0180j01 h0825052501l10 | 80o02i02l80g08 390524cel10 | 80o01i0cl40g08 20o10 | 80o01i30l20g08 20o10 | 80o01ic0l10g04 p10 | 80o01h01m08g04 p10 | 80o01h06m04g04 p10 | 80p80g18m02g04 p10 | 80p80g20m01g02 p10 | 80p80gc0n8002 p10 | 80o01c007n01c0 07p10 | 80o02200880m02 200880o10 | 80o02200880m02 200880o10 | 80o02200880m02 200880o10 | 80o01c007n01c0 07p10 | 80n0fJc0lIfcG f8m10 | 80n14#4460k01 "44477ff4m10 | 80n1888h08a0k 018880g8b5554 m10 | 80n1110h1120k 0111g01133fe4 m10 | 80n1222h2220k 0122200223g04 m10 | 80n1444h4460k 0144400447g64 m10 | 80n1888183008 a0k018880c08b gc4m10 | 80n1110h1120k 01110181130184 m10 | 80n12227efc22 20k0122230223 3304m10 | 80n1444h4460k 01444184471e04 m10 | 80n1888183008 a0k018880c08b 0c04m10 | 80n1110h1120k 0111g0113g04m 10 | 80n1222h2220k 0122200223g04 m10 | 80n1ffeh7fe0k 01Ge007Gg04m10 | 80n10j20k01i03 g04m10 | 80n0fJc0lIfcG f8m10 | 80o01c0g70z10 | 80o0220g88z10 | 80o0220g88z10 | 80o0220g88z10 | 80o01c0g70z10 | 80p80g0f80y10 | 80p80h78y10 | 80p80h0780x10 | 80p80i7cx10 | 80p80i03c0w10 | 80p80j3ew10 | 80p80j01e0v10 | 80p80j0110v10 | 80o01k0110v10 | 80o01k0110v10 | 80o01le0v10 | 80o01j07Hf87f t10 | 80o01nG80s10 | 80o01m01c1c0s 10 | 80o01m0380e0s 10 | 80o01m07g70s10 | 80o01k01e00601 b0s10 | 80o01k03300603 30s10 | 80o01k0330!06 30s10 | 80o01k033006cc 30s10 | 80o01k03300678 30s10 | 80o01k033006!30 s10 | 80o01k01e007g 70s10 | 80o01m0380e0s 10 | 80o01m01c1c0s 10 | 80o01nG80s10 | 80o02n7ft10 | 80o02zi10 | 80o02zi10 | 80o02zi10 | 80o02zi10 | 80o02i0118i80 20g2007p10 | 80o02j20j20h08 80o10 | 80o02i0370b33b 19b8e658670880 o10 | 80o02i0120c4a4 84a52960280880 o10 | 80o02i012087a4 9ca52f40260880 o10 | 80o02i01208424 a4a52840210880 o10 | 80o02i01208324 9ca4e6402e07p 10 | 80o02zi10 | 80o02zi10 | 80o02zi10 | 80o02zi10 | 80o02zi10 | 80o04i0120i02 4202g20p10 | 80o04i0120i"02 r10 | 80o04i03b8ce06 338ece673067p 10 | 80o04i01252909 0a!52124828p10 | 80o04i0125e908 3a!52727826p10 | 80o04i0125!09 4a!52924021p10 | 80o04ja4c9063a !4e71302ep10 | 80o04zi10 | 80o04zi10 | 80o04zi10 | 80o04zi10 | 80o04zi10 | 80o04k40g20u10 | 80o04k40w10 | 80o04i038ce1cb 6ec6t10 | 80o04i0252412c !29t10 | 80o04i02524128 292ft10 | 80o04i02524128 2928t10 | 80o08i024c21c8 2926t10 | 80o08k01w10 | 80o08k01w10 | 80o08zi10 | 80o08zi10 | 80o08zi10 | 80o08zi10 | 80o08zi10 | 80o08zi10 | 80o1czi10 | 80o22zi10 | 80o22zi10 | 80o22zi10 | 80o1czi10 | 80j1fW80p10 | 80j78/8889e0p 10 | 80jd1/111130p 10 | 80je2/222230p 10 | 80jc4/444450p 10 | 80j/88!8890p10 | 80j91/111110p 10 | 80jXf0p10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | 80zs10 | ZTf0 | \enddata{raster, 539447368} \view{rasterview,539447368,70,0,0} determines whether the candidate is divisible by a known prime. The check in the square terminates the graph--succeeding--if the current list element exceeds the upper bound. The octagon terminates with failure if the division produces a remainder of zero. \subsection{1.4 Show and Tell (STL) - Takayuki Dan Kimura} \formatnote{ }Show and Tell (STL) is a data flowgraph language with the distinction that arbitrary images can be utilized as function names; in Figure 2, these images are handwritten names. The upper left window shows the STL drawing panel and the lower right the list of objects used in this solution. The output (3 5 7 11) is in the middle bottom window. \formatnote{ }The notation is this:\leftindent{ Empty box = variable Thick box = formal parameters Dotted box = predicate Double box = iteration control Pair of open triangles = iterate value Meshed rectangle = element by element} \formatnote{ }The "Prime" panel is the main program, which finds the primes in the first five odd integers. On the left "3,5,7.." is invoked to create the list 3, 5, 7, 9, 11. This list serves as the initial value through the paired open triangles on the upper-line through the iteration box; the entire list, as modified by "Sieve" is the value on this line and serves as input to the next iteration. At each cycle, the first element of the current upper-line list is extracted with "top". When there are no more elements, "top" will fail and the iteration in "Prime" terminates. Otherwise, the first element is a prime and is appended to the output list in the lower left. That same first element and the current upper-line list are passed as parameters to "Sieve" which produces a new list omitting the first element and its multiples. \formatnote{ }In the other cases of paired open triangles--in "3,5,7..." and "mod"--a single value is passed in, modified, and passed on to the next iteration. The list output from "3,5,7..." is via the meshed rectangle port at the bottom, which assembles the values from successive iterations in which the predicate (>0) succeeds. "Mod" repeatedly subtracts its second (rightmost) parameter from the iterating first parameter; the output is the last value before the predicate (<=0) fails. \formatnote{ }The upper line through "Sieve" is through meshed rectangles, so each element of the list value is processed in a separate iteration. If the predicate (>0) succeeds, the current iteration value is appended to the output list under construction. "Top" is an inefficient version of what should be a primitive to find the first element of a sequence. Its first iteration succeeds because the first element from the list is greater than zero; subsequent iterations fail because the input element is not equal to the element from the previous iteration. \subsection{1.5 VisaVis - Joerg Poswig} \formatnote{ }VisaVis is a data-flow language with second order functions as a special focus. Such a function takes a function and a collection of data as arguments and applies the function to the data in some manner. Users can define their own second order functions in the language. \formatnote{ }The algorithm for primes is shown in Figure 3 and is in four parts, one in each quadrant. In the upper left, VisaVis's "interval" operator generates a list of the integers from 2 to k and this list is processed through the "primes" operator. The latter is in the upper right quadrant and is a recursive function which terminates when the list is empty. Otherwise the first element is taken to be the next prime number and is merged with the results of the subsequent computations. The rest of the sequence and the first element become the two parameters of "sift", the output of which serves as input for the next recursive call (circle 3). The final step is "Merge", another VisaVis operator, which attaches the prime from the current iteration to the list from the recursive call. \formatnote{ }The "sift" process is in the lower left quadrant where the built-in second order function "FilterWithArg" applies the function "ModEqualNot" to the list and the current prime. "ModEqualNot" in the lower right returns True if the current list element is not divisible by the current prime. \formatnote{ }The relation of the parts of the program are not clear in Figure 3, but can be made clear with the VisaVis "hierarchy tool", a simulated three dimensional image which depicts the nesting of program parts and the data values in transit. For an illustration of the animation of execution, see [Poswig, 1993]. \formatnote{ }In addition to the solution in Figure 3, which uses division, a solution was constructed with the hierarchy tool that employed a true sieve using addition instead of division. This solution proved slower, however, possibly due to simulation overheads. \formatnote{ }\section{2. Checkbook} \formatnote{ }The second problem aimed at traditional business computing requirements and especially the need for long term storage of information in files: \quotation{Write a simple program for checkbook accounting. It should accept user input for deposits and withdrawals to the account. Withdrawal information should include check number, date, payable to, reason, and amount. Deposit information should include date, reason/origin, and amount. Design a GUI with user interaction in a suitable layout that allows entry of the data and selection of the actions in any reasonable sequence. The program should maintain a list of all transactions and allow it to be reviewed.} \formatnote{ }The two commercial vendors--LabVIEW and Prograph--presented solutions to this problem, but space limitations prevent displaying them here. Both vendors took advantage of their special strengths. \formatnote{ }LabVIEW's solution features realistic and colorful forms for check register, withdrawal, and deposit. These are front panels to data flow diagrams implementing the algorithms. When idle, the algorithm polls for input every quarter second. \formatnote{ }In Prograph the interface editor was used to create screen interfaces for checks, deposits, and the transaction list shown in Figure 4. The algorithm is implemented with the aid of a simple class hierarchy: The Transaction class is an abstract class with two subclasses, Check and Deposit. The Account class has attributes for the current balance and a list of Transactions. Methods in the Account class add transactions to the list and update the balance. Each window in the application is a subclass of Prograph's Window class, while the transaction list is an instance of class Grid, from Prograph's class library. \section{3. Rolling wagon wheel} \formatnote{ }Since visual languages are inherently graphical, it seemed appropriate to determine if they could perform a computation whose primary purpose was animation of a graphical image: \quotation{Write a program to display a simulation of a spoked wagon wheel rolling down a ramp whose slope can be varied by the user. }\ \formatnote{ }The trivial ChemTrains program for the rolling wheel has only two rules: an initial diagram with the wheel at the top and a final diagram with it at the bottom. ChemTrains automatically animates motion between two states. In fact, however, a more elaborate solution was created which divides the ramp into a series of sections and has a rule that moves the wheel from one section to the next. \formatnote{ }LabVIEW programs draw pictures by appending drawing codes together and providing a control that can render them on the front panel. The codes are 2D primitives--circles, lines, bitmaps, and so on--and are appended by wiring together icons with appropriate parameters for diameter, color, etc. The draw wheel program encapsulates these drawing commands into a module that appends the drawing commands for a parameterized wheel. Similarly, other icons draw the ramp, calculate the effect that gravity has on the wheel position, and update the wheel rotation for a given wheel position. See Figure 5, which is a black/white rendering of the colorful original. The associated data flow diagram does the kinematics to accelerate the wheel due to gravity. \formatnote{ }In Prograph the wheel was programmed by creating classes for the ramp window and the wheel. Attributes in these classes include the height of the ramp, the position of the wheel, and the orientation of the spokes (diagonal or orthogonal). Methods of the ramp class provide for drawing or dragging the ramp and for animating the wheel, while the wheel class has methods for drawing the wheel and for drawing its spokes. Movement down the slope is at constant speed. \section{4. Observations} \formatnote{ }Various statistics were elicited from the submitters and are summarized in Tables 1 and 2. For comparison the sieve was coded in C in under half an hour. Execution on a DECstation 5000/20 required 3.6 milliseconds to find the 168 primes among the first thousand integers. The complete program required 53 operators, but only 13 of them would be required in a visual version. (In the statistics, loops and conditionals are not counted as operators.) Thus the C version is comparable in number of operators to the visual versions. The heart of the routine is \leftindent{/* find primes in 2...k \ s is an array of booleans, initially TRUE */ p = 2; lim = sqrt(k); while (p < lim) \{ for (i = p+p; i <= k; i += p) /* delete multiple of p */ s[i] = FALSE;; /* assert: for j in 2 <= j <= p**2 s[j] is true iff j is prime */ while ( ! s[++p]) \{\} /* find next prime */ \}} Since arrays are such a vital component of the sieve approach, it is interesting that C is better suited to dealing with arrays than many visual languages. The latter tend instead to deal with higher-level (and more generally useful) constructs such as sets and lists. \formatnote{ }More than one observer has noted that the various visual programs are not easy to read, despite the alleged advantages of visual expression. This is a problem with visual languages; there is not yet enough shared learning about what computational icons mean. After all, most of us went through high school algebra which taught the meaning of expressions like ax\superscript{2}+c and C programmers have learned to understand compound operations like while ( ! s[p++]) \{\} \formatnote{ }The most interesting aspect of the various flow diagram solutions are the conventions for iteration. Most have some notion that a line going in one side is connected from the output from the previous iteration at the opposite side of the box. In three of the systems a predicate determines whether the iteration continues. VisaVis utilizes recursion and second order functions instead of iteration. ChemTrains has only one loop, the one in the central execution driver; it is conceivable that an extension to ChemTrains would have multiple rule sets through which looping would be independent; this might reduce the importance of rule order. \formatnote{ }Most of the solutions exploited one or more built-in facilities of the particular programming system. For instance, \description{\ LabVIEW and Prograph's solutions used existing graphical elements to create visually attractive interfaces. LabVIEW's prime program utilizes built-in array access and display operators. Prograph's prime solution utilizes built-in list handling. In all the prime programs, storage management was simpler than in the C version. Prograph's check book is based on its Grid class. VisaVis' Primes utilized the FilterWithArg 2nd order function. ChemTrains could have solved the wheel problem trivially because ChemTrains automatically animates motion between states. } \formatnote{ }It may be that built-in facilities are a major advantage of visual programming systems; since programs these days need to have graphical components, visual systems can integrate these in a program more readily than can a textual-only language system. It is interesting to speculate that the advantages of visual systems may not be in the programming itself, but rather in more convenient integration of programming, testing, and using the result. \bold{Acknowledgements:} The moderator is grateful for the aid of the committee for the 1994 Visual Languages Comparison: Kris Blom, NASA, JPL; Ron Dolin, Univ. Calif., Santa Barbara; Joe Pfeiffer, New Mexico State Univ.; Catalin Roman, Washington Univ.; Ephraim Glinert, RPI. Brigham Bell's early enthusiasm was crucial. \center{\bigger{\onesmaller{\bold{References}}}} \onesmaller{ [Bell, 1992a] Bell, B., \italic{Using Programming Walkthroughs to Design a Visual Language}, Ph.D. Dissertation, Technical Report CU-CS-581-92, University of Colorado, January 1992. [Bell, 1993] Bell, B. & Lewis, C., "ChemTrains: A Language for Creating Behaving Pictures," \italic{Proceedings of the IEEE Symposium on Visual Languages,} August 1993. [Cox, 1989] Cox, P.T.; Giles, F.R.; Pietrzykowski, T., "Prograph: a step towards liberating programming from textual conditioning",\italic{ Proc. 1989 IEEE Workshop on Visual Programming}, Rome (Oct, 1989), 150-156. [Daley, 1992] P. Daley, "Automated Monitoring of a Soil Vapor Remediation System," \italic{Scientific Computing & Automation}, May 1992. [Jagadeesh, 1993] J. Jagadeesh & Y. Wang, "LabVIEW" Product Review, \italic{Computer}, February 1993. [Kodosky, 1991] J. Kodosky, J. MacCrisken, & G. Rymar, "Visual Programming Using Structured Data Flow," \italic{Proceedings of the IEEE Workshop on Visual Languages}, October 1991. [Poswig, 1993] J. Poswig, G. Vrankar & C. Moraga, "Interactive animation of visual program execution," \italic{IEEE Symposium on Visual Languages}, 1993, 180-187. [Poswig, 1994] J. Poswig, G. Vrankar & C. Moraga, "VisaVis - A higher order functional visual programming language", \italic{Journal on Visual Languages and Computing 5}, (1994), 83-111.} \begindata{bp,539408968} \enddata{bp,539408968} \view{bpv,539408968,71,0,0} \sansserif{\ \begindata{table,539447544} \cols 91 51 53 53 68 46 "ChemTrains "LabVIEW "Prograph "Show and Tell "VisaVis - - - - - 'Components "8 "2 "5 "5 "4 'Pixels/100,000 "6.0 "2.9 "2.3 "4.9 "1.5 'Operators "n.a. "14 "8 "10 "13 - - - - - Creation time, expert "2 hrs "1 hr "10 min "2 hrs "15 min Creation time, tyro "2-3 hrs "15-20 min "25 min - - - - - Storage space "4K "124K "20K "12K "19 K 'Time (primes<1000) "0.034 * "0.23 # "80 & \enddata{table,539447544} \view{spread,539447544,72,0,0} }\sansserif{\bold{Table 1. Data for Primes problem. } Component - a connected graph or a rule. For the primes program, ChemTrains and LabVIEWs reuse a single window to show successive components, Prograph utilizes one window per component, and both Show and Tell and VisaVis manage to display all components simultaneously. Operator - an icon in the graph, not counting loop control. Times for tyros are crude estimates by the panelists. Empty cells are values not reported. * seconds on a Mac IIfx. An improved algorithm takes .019 seconds. # seconds on a Quadra 700 ( 25 MHz, 68040). & seconds estimated for PC 486/33MH. Observed time was 3 sec for primes in 1...100. Another solution in VisaVis using addition instead of division took 9 sec for primes up to 100.} \sansserif{\ \begindata{table,539452280} \cols 96 46 11 41 11 55 13 48 10 40 ^Checkbook = = ^Wagon Wheel = = = = - - - - - - - - "LabVIEW "Prograph "ChemTrains "LabVIEW "Prograph - - - - - 'Components "3 "24 * "2 "8 "5 * 'Pixels/100,000 "3.4 "30.3 "12.2 "19.4 - - - - - - - - - Creation time, expert "2.5 hrs "4 hrs "0.5 hrs "15 hrs "2 hrs Creation time, tyro "3-4 hrs "6-8 hrs "~ 40 hrs "4-6 hrs - - - - - - - - - Storage space "111K "39K "3K "400K "36K \enddata{table,539452280} \view{spread,539452280,73,0,0} }\sansserif{\bold{Table 2. Data for Checkbook and Wagon wheel problems.} *The checkbook program has 8 classes with a total of 24 methods. The wagon wheel program has 2 classes with a total of 5 methods. 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h08r01G | fet30ic0y07c0 04g04g20g!10g 81p08g1fjc0h02 30i0ci03jc0i30 81h08sG | fet30ic0y0780 88g84g20g!10g 81p08g1fjc0h02 30i0ci0304ic2 e0h308180g08r 01G | fet30ic0y07c0 70g78g20g!10g Gp08g1fjc0h02 30hf00ch3c030e ic3a0h308180g 08r01G | fet30ic0y07c0 z08g1djc0h0230 h880ch220318h f0c230h3081hc8 r01G | fet30ic0y07c0 z08g1fh06gc0h 02308001880c20 g620330h90c210 g0c3083g01e8r 01G | fet30ic0y0780 z08g0fg033egc0 h1e3080f1080c 203c420320g06 f0c220600e3086 g0128r01G | fet3fIc0y07c0 z08g1f3c1e02g c1670f1230b189 180c2c62460320 4014e0c620g2a 3098180168r01 G | fet3fIc0y07c0 z08g1f241006g c1f50d9231e109 100c7842440320 479480c440026a 30f001f9c8r01 G | fezx0780z08g1f 041004gc19d18 a2338109e00ce0 42780338051c80 c4c882ee308001 6908r01G | fezx07c0z08g1d 1c3004gc11910 a2308109800c20 4260030c4b18f0 c589a368308389 2908sG | fezx07c0z08g1f 380804gc11910 a2308119g0c20 464003044e1840 c707236c308a19 2888r01G | fezx0780z08g1f 0c!082ac1!11be 308111g0c2044 4003048c98gc4 062367b08e1128 e8r01G | fezx07c0z08g1f 04!082ac1111f 023081f3g0c20 7cc003048f80g c40622f3308c13 !68r01G | fezx07c0z08g1d 04080920c11180 g308062g0c2018 80030680hc406 22103084124808 r01G | fezx07c0z08g1f 042919gc010h30 d802g0c36g8003 0680hc4042210 308c10g08r01G | fezx0780z08g1f !3901gc0i3070 02g0c1cg800304 ic40440g30i08 r01G | fezx07c0z08g1d !01hc0i30g06g 0cg0180032cicc i30i08r01G | fezx07c0z08g1f 01ic0i30i0ci03 38ic8i30i08r01 G | fezx0780z08g1f jc0i30i0ci03j c0i30i08r01G | fezx07c0z08g1d jc0i30i0ci03j c0i30i08r01G | fezx07c0z08g1f ZOf8r01G | fezx0780z08g1e zzh01G | fezx07ZIfczzh 01G | fezx07c0z08g1e zzh01G | fezx07c0z08g1e zzh01G | fezx0780z08g1c zzh01G | fezx07c0z08g1e zzh01G | fezx07c0z08g1e zzh01G | fezx0780z08g1c zzh01G | fezx07c0z08g1e zzh01G | fezx07c0z08g1e zzh01G | fezx0780z08g1c zzh01G | fezx07c0z08g1e zzh01G | fezx07c0z08g1e zzh01G | fezx07c0z08g1c zzh01G | fezx0780z08g1e zzh01G | fezx07c0z08g1e zzh01G | feb7ZWfbZIefZZH feG | \enddata{raster, 540799064} \view{rasterview,540799064,75,0,0} Figure 2. Show and Tell primes}} \bold{ }\ \begindata{raster,540799240} 2 0 68266 68266 0 0 483 237 bits 540799240 483 237 ZZZc0 | 80zzy60 | 80zzy60 | 80zzy60 | bfZIf8p0fZJ60 | 80zj078ch1801 f0g0180zk60 | bfZIf80c4ch18 0198g01800fZJ 60 | 80zj0c0f!8719 8198f0f198zk60 | bfZIf8!0c!cc9b 01"99b00fZJ60 | 80zj!0c!cc1e01 f1!99e0zk60 | bfZIf8!0ccfcc 1c01"99c00fZJ 60 | 80zj!0ccc0c1e 01"99e0zk60 | bfZIf80c4ccc4c 9b01"99b00fZJ 60 | 80zj078cc78719 81!f0f198zk60 | bfZIf8p0fZJ60 | 80zzy60 | 80zzy60 | 80zzy60 | ZZZe0 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 8001e006j0760 h03e0p03e0hc3 800fc0j1ehccc0 h3c018330if807 n60 | 8001b006j0760 h0330p0330hc1 8003k33h!c0h36 018030icc03n60 | 800199cf38i07 e7h03338e3ce7 80l03339b1cf1 9c030ej307ce3 dde0h3339e778 icce339e38ek60 | 800198666ci07 ed80g03e6c361 b6c0l03e0db06 d9b6031bj3071 b6ccc0h336db3 30if8330db6db k60 | 800199e67ci06 ed80g03c7cf39 b6c0l!03db1ed9 be031bj3061f6 ccc0h337db330 iccf33db61fk60 | 8001b36660i06 ed80g03661b0d b6c0l0306db36 d9b0031bj3361 86ccc0h3661b3 30icdb36db6d8 k60 | 8001e1e338i06 67h03338f78e6 c0l!03cf1ef19c 030ej1e60e3cc 60h3c39e318if8 f33db38ek60 | 80zk03zs60 | 80zk0ezs60 | 80zzy60 | 8007ZZVf8g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l040c 08g60 | 8004g20g08h10 i08q08q80k01l 02l041208g60 | 8004f8221c09c1 g10i08e030o08 q80ge38e381c71 l02g038e38e071 c42108g60 | 80041046221223 g10i09!10o08q 80011451442289 l02g045145108a 244088g60 | 80042042221225 g10i0903132d20 m08q80g105144 2289l02h414510 8a248048g60 | 800470822221e9 g10i08e090b120 m08q80g209144 2289l02h824510 8a25e1e8g60 | 8004088222202f 8010i081393a1 20m08q80g4111 442289l02g0104 45108a242108g 60 | 80048902224041 g10i091494a120 m08q80g821144 2289l02g020845 108a242108g60 | 800471021c4181 g10i08e393a0e0 m08q8001f7ce38 9c71l02g07df38 e271c42108g60 | 8004l10i08i20 m08q80k01l02l 043f08g60 | 8004l10i08ic0 m08q80k01l02l 04g08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l07G f8g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004g20g08h10 i08q08q80k01l 02l04g08g60 | 8004f8223e09c1 g10h0108e0g10 n0823671008m80 k01h073e7038e2 g010e7ce071c4 g08g60 | 80041046201223 g10h030910g10 n0821289008m80 k01h08a0884512 g031141108a24 g08g60 | 800420423c1225 g10h0109032c17 1d2b338c60i08 5128399cc0l80 k01h08bc884512 g!0179108a24g 08g60 | 800470820221e9 g10h0109gb014 a12c0a5290i08 5127104920l80 k01h0782884512 g010205108a24 g08g60 | 8004088202202f 8010h010903a0 1499283a50f0i 08f92091c9e0l 80k01i82884512 g010405108a24 g08g60 | 80048902224041 g10h010914a014 85284a5280i08 89289249m80k01 h0122884512g01 0845108a24g08 g60 | 800471021c4181 g10h0108e3a014 b8e83a4c60i08 892709c4c0l80 k01h061c7138e2 g011f38e271c4 g08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l07G f8g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l043f 08g60 | 8004l10i08q08 q80k01l02l0421 08g60 | 8004l10i08q08 q80k01l02l0421 08g60 | 8004l10i08q08 q80k01l02l0421 08g60 | 8004l10i08q08 q80k01l02l05e1 e8g60 | 8004l10i08q08 q80k01l02l0480 48g60 | 8004l10i08q08 q80k01l02l0440 88g60 | 8004l10i08q08 q80k01l02l0421 08g60 | 8004l10i08q08 q80k01l02l0412 08g60 | 8004l10i08q08 q80k01l02l040c 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8004l10i08q08 q80k01l02l04g 08g60 | 8007ZZVf8g60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80x07Nfej1fNf8 w60 | 80x18n0180i60 n06w60 | 80x10o80i40n02 w60 | 80x20o40i80n01 w60 | 80x20o40i80n01 w60 | 80x20g3ej63h40 i80g03c6h0ch01 w60 | 80x20g33j03h40 i80g0626h0ch01 w60 | 80x20g331e3e1e 1c6780g40i80g 0607!c38cc0g01 w60 | 80x20g#333263 h40i80g!06!66 4d80g01w60 | 80x20g#333863 h40i80g!06!66 0fh01w60 | 80x20g333f!33 1c63h40i80g!06 67e60eh01w60 | 80x20g3330!33 0e63h40i80g!06 66060fh01w60 | 80x20g3331!33 2663h40i80g06 2666264d80g01 w60 | 80x20g3e1e3e1e 1c6180g40i80g 03c663c38cc0g 01w60 | 80x20i30k40i80 n01w60 | 80x20i30k40i80 n01w60 | 80x20o40i80n01 w60 | 80x10o80i40n02 w60 | 80x18n0180i60 n06w60 | 80x07Nfej1fNf8 w60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | 80zzy60 | ZZZe0 | 7fZZYe0 | \enddata{raster, 540799240} \view{rasterview,540799240,76,0,0} \sansserif{\bold{Figure 4. Prograph check register} \bold{ Figure 1a. LabVIEW primes, \ front panel} \formatnote{\bold{ Figure 1b. LabVIEW primes, block diagram} }\bold{Figure 3. VisaVis primes} \formatnote{ }\bold{Figure 5. LabVIEW wagon wheel, front panel} }\enddata{text,538702508}