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<html> <head><meta http-equiv="content-type" content="text/html;charset=utf-8"> <title>Rationalized APL</title> <link href="adoc.css" rel=stylesheet> </head> <body> <p align=center><b>Rationalized APL</b><br> Kenneth E. Iverson</p> <table> <tr><td colspan=3><font size=-1><a target=main href="RationalizedAPL1.htm#intro">Introduction</font></a></td></tr> <tr><td valign=top><font size=-1>A. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#a">Bracket and Semicolon Indexing, and Index Assignment</font></a></td></tr> <tr><td valign=top><font size=-1>B. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#b">Name Assignment</font></a></td></tr> <tr><td valign=top><font size=-1>C. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#c">Function Valence</font></a></td></tr> <tr><td valign=top><font size=-1>D. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#d">Function Definition</font></a></td></tr> <tr><td valign=top><font size=-1>E. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#e">Syntax and Order of Execution</font></a></td></tr> <tr><td valign=top><font size=-1>F. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#f">Extensions to Higher Rank Arrays</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top nowrap><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#f1">Rank</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#f2">Conformance</font></a></td></tr> <tr><td valign=top nowrap><font size=-1>G. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#g">Operators on Nonscalar Functions</font></a></td></tr> <tr><td valign=top><font size=-1>H. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#h">Miscellaneous</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#h1">The Type Attribute</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#h2">The Bracket Axis Operator</font></a></td></tr> <tr><td valign=top><font size=-1>I. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#i">New Operators</font></a></td></tr> <tr><td valign=top><font size=-1>J. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#j">New Functions</font></a></td></tr> <tr><td valign=top><font size=-1>K. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#k">Further Operators</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#k1">Til</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#k2">Dot</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#k3">Supernumerary Axes</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#k4">Scan</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#k5">Cut Operator</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#k6">With</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#k7">Compression</font></a></td></tr> <tr><td valign=top><font size=-1>L. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#l">Summary</font></a></td></tr> <tr><td><font size=-1> </font></td></tr> <tr><td colspan=3><font size=-1><a target=main href="RationalizedAPL1.htm#xa">Appendices</font></a></td></tr> <tr><td valign=top nowrap><font size=-1>A. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#xa">Ranks of Primitive Functions</font></a></td></tr> <tr><td valign=top><font size=-1>B. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#xb">Table of Dyadic Operators</font></a></td></tr> <tr><td valign=top><font size=-1>C. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#xc">Examples and Brief Definitions</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xc1">Function Ranks and Disposition of Axes</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xc2">The Transpose Operator</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xc3">Dyadic Functions</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xc4">The Cartesian Product</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xc5">Operators on Non-Scalar Functions</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xc6">Til, Cut, and Bind</font></a></td></tr> <tr><td valign=top><font size=-1>D. </td><td colspan=2><font size=-1><a target=main href="RationalizedAPL1.htm#xd">APL2 versus a Comparable Subset</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd1">Syntax</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd2">Function Classes</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd3">Depth Functions</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd4">Array Formation</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd5">Domain of Operators</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd6">Prototypes</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd7">Heterogeneous Arrays</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd8">Primitive Enclose</font></a></td></tr> <tr><td><font size=-1> </font></td><td valign=top><font size=-1>• </font></td><td><font size=-1><a target=main href="RationalizedAPL1.htm#xd9">General Remarks</font></a></td></tr> <tr><td><font size=-1> </font></td></tr> <tr><td colspan=3><font size=-1><a target=main href="RationalizedAPL1.htm#ref">References</font></a></td></tr> <tr><td colspan=3><font size=-1><a target=main href="RationalizedAPL1.htm#ack">Acknowledgements</font></a></td></tr> <tr><td><font size=-1> </font></td></tr> <tr><td colspan=3><font size=-1><a target=main href="RationalizedAPL1.htm#err">Errata</font></a></td></tr> </table> <br><br><br> </body> </html>