1044 lines
78 KiB
HTML
1044 lines
78 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<head>
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<title></title>
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<script type="text/javascript" src="outliner.js"></script><style type="text/css">
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img.status {
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margin-left: 2px; margin-right: 2px; margin-top: 2px; height: 11px; width: 11px;
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}
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img.checkbox-column {
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height: 11px; width: 11px; vertical-align: top; margin-top: 3px;
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}
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img.leaf {
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margin-left: 3px; margin-right:3px; margin-top: 2px; margin-bottom: 3px; height: 6px; width 6px;
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}
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img.parent {
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margin-left: 3px; margin-right:3px; margin-top: 2px; height: 10px; width: 10px;
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}
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th {
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vertical-align: bottom;
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}
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td {
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vertical-align: top;
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}
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td,th {
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empty-cells: show;
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}
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.top-right-border {
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}
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.no-border {
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border-bottom: 0px;
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border-left: 0px;
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}
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table {
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font-family: Helvetica, sans-serif;
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font-size: 12px;
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font-family: "Helvetica Neue", sans-serif; font-size: 13px;
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}
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.wholeDocument {
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font-family: "Helvetica Neue", sans-serif; font-size: 13px;
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}
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td.subcell {
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border: none;
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}
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td.content {
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padding-left: 4px;
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padding-bottom: 2px;
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padding-top: 1px;
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padding-right: 3px;
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}
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.full {
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height: 100%;
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}
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.heighthack {
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height: 17px;
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}
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div.titlepadding {
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padding-right:3px;
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padding-left:6px;
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padding-bottom:3px;
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padding-top: 2px;
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}
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.summary_node {
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background: rgba(0,0,0,.12);
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margin-bottom: 1px;
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}
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div.column {
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padding-right: 3px;
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padding-left: 4px;
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padding-top: 0px;
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padding-bottom: 0px;
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margin-right: 1px;
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}
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.labelpadding {
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padding-right: 3px;
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padding-top: 1px;
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padding-left: 2px;
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}
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.indicator {
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white-space: nowrap;
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text-align:right;
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margin-right: 0px;
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vertical-align: top;
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padding-top: 1px;
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padding-left: 0px;
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}
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.wholedocgutter {
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}
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div.row {
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}
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div.headerRow {
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}
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.expanded {
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display: inline;
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}
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.collapsed {
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display: none;
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}
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div.palette-hit-zone {
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position: fixed;
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bottom: 0px;
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height: 33%;
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left:50%;
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width: 66%;
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margin-left: -33%;
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}
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div.floating-palette {
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-webkit-border-radius: 5px;
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-webkit-transition: opacity is fade-in-out;
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-webkit-transition-duration: 1s;
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background-color: rgb(64, 64, 64);
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opacity:0.7;
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width: 88px;
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height: 44px;
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position: fixed;
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bottom: 20px;
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left: 50%;
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margin-left: -44px;
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}
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div.palette-cell {
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opacity:1;
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margin-top: 6px;
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margin-bottom: 6px;
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position: absolute;
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height: 32px;
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width: 32px;
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}
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div.cell-divider {
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position: absolute;
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margin-top: 6px;
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margin-bottom: 6px;
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margin-left: 44px;
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height: 32px;
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width:0px;
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position:absolute;
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left:0px;
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border-right:rgb(207, 207, 207) 2px solid;
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}
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.note {
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padding-left: 5px;
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padding-right: 3px;
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border: none;
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color:rgb(84,84,84) ; font-size: 11px;font-size: 11px;
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}
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.note-bg {
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}
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/* Total table width is 924
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Adjusted table width is 979 */
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.wholething {
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width: auto;
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}
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table.row {
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width: 924px;
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}
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.col_width1 {
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width: 924px; /* Actual width is 924 */
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}
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.col1 {
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}
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.colbackground1 {
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}
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/* Level Styles */
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.columntitle {
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font-weight: 600;
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}
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.ns-eUsXLp0Pv1g-Heading1 {
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color:rgb(50,50,50) ; font-family: "Helvetica Neue", sans-serif; font-weight: 300; font-size: 30px;}
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.ns-d4-frBYwy2X-Heading2 {
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color:rgb(50,50,50) ; font-family: "Helvetica Neue", sans-serif; font-size: 18px;}
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.ns-kRw332h0q-G-Heading3 {
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font-family: "Helvetica Neue", sans-serif; font-weight: 600; font-size: 13px;}
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.ns-nU7Pax9sHwm-HighlightYellow {
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}
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.ns-m6c_M2fT6yP-HighlightRed {
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}
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.ns-auoqZ5xVKeG-HighlightGreen {
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}
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.ns-hE9mXgl4a8m-Purple {
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color:rgb(150,97,207) ; }
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.ns-l2kopvXC4ak-Blue {
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color:rgb(58,142,237) ; }
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.ns-f7F2187eZ56-Bondi {
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color:rgb(0,191,192) ; }
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.ns-kJhkVDl2Xsd-Green {
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color:rgb(103,187,53) ; }
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.ns-inNRQJ-da6E-Yellow {
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color:rgb(255,187,0) ; }
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||
.ns-nAm7imW-teW-Orange {
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color:rgb(255,144,77) ; }
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.ns-jtC-ndQ7Pcw-Red {
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color:rgb(242,96,119) ; }
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.ns-dI8s4BxgdIs-Graphite {
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color:rgb(107,124,165) ; }
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.ns-bg-eUsXLp0Pv1g-Heading1 {
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||
}
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.ns-bg-d4-frBYwy2X-Heading2 {
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}
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.ns-bg-kRw332h0q-G-Heading3 {
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}
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.ns-bg-nU7Pax9sHwm-HighlightYellow {
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background-color:rgba(255,187,0,0.25) ; }
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.ns-bg-m6c_M2fT6yP-HighlightRed {
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background-color:rgba(242,96,119,0.25) ; }
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.ns-bg-auoqZ5xVKeG-HighlightGreen {
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background-color:rgba(103,187,53,0.25) ; }
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.ns-bg-hE9mXgl4a8m-Purple {
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}
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.ns-bg-l2kopvXC4ak-Blue {
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}
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||
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||
.ns-bg-f7F2187eZ56-Bondi {
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}
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.ns-bg-kJhkVDl2Xsd-Green {
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}
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.ns-bg-inNRQJ-da6E-Yellow {
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}
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.ns-bg-nAm7imW-teW-Orange {
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}
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.ns-bg-jtC-ndQ7Pcw-Red {
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}
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||
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.ns-bg-dI8s4BxgdIs-Graphite {
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}
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||
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||
.ns-gutter-eUsXLp0Pv1g-Heading1 {
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||
}
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||
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.ns-gutter-d4-frBYwy2X-Heading2 {
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}
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.ns-gutter-kRw332h0q-G-Heading3 {
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}
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.ns-gutter-nU7Pax9sHwm-HighlightYellow {
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}
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||
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||
.ns-gutter-m6c_M2fT6yP-HighlightRed {
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||
}
|
||
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||
.ns-gutter-auoqZ5xVKeG-HighlightGreen {
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||
}
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||
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||
.ns-gutter-hE9mXgl4a8m-Purple {
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||
}
|
||
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||
.ns-gutter-l2kopvXC4ak-Blue {
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||
}
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||
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||
.ns-gutter-f7F2187eZ56-Bondi {
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||
}
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||
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||
.ns-gutter-kJhkVDl2Xsd-Green {
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}
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||
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||
.ns-gutter-inNRQJ-da6E-Yellow {
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}
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||
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||
.ns-gutter-nAm7imW-teW-Orange {
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}
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||
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||
.ns-gutter-jtC-ndQ7Pcw-Red {
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||
}
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||
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.ns-gutter-dI8s4BxgdIs-Graphite {
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}
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</style>
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</head>
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<body class="wholeDocument"><table cellspacing="0" cellpadding="0" class="top-right-border"><tr><td class="wholething no-border">
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<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="n9Cr4BPjkMA"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor1"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
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<td class=" subcell wholedocgutter level1 levelguttercolor1" style="width: 9px;"></td>
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<td class=" subcell wholedocgutter indicator level1 levelguttercolor1" style="width: 15px;"><img onmousedown="ioSwitch('pn9Cr4BPjkMA', event.shiftKey)" id="in9Cr4BPjkMA" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
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<td class=" subcell wholedocgutter labelpadding level1 levelguttercolor1" style=" width: 1px; "></td>
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<td class=" content level1 subcell">Datalog<br>
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</td>
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</tr></table></div></td></tr></table>
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<div id="pn9Cr4BPjkMA" class="expanded">
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<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="jw6i7QfKlHP"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor2"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
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<td class=" subcell wholedocgutter level2 levelguttercolor2" style="width: 25px;"></td>
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<td class=" subcell wholedocgutter indicator level2 levelguttercolor2" style="width: 15px;"><img onmousedown="ioSwitch('pjw6i7QfKlHP', event.shiftKey)" id="ijw6i7QfKlHP" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
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<td class=" subcell wholedocgutter labelpadding level2 levelguttercolor2" style=" width: 1px; "></td>
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<td class=" content level2 subcell">Propositional Calculus (0th order logic)<br>
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</td>
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</tr></table></div></td></tr></table>
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<div id="pjw6i7QfKlHP" class="expanded">
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<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="eCh11dKzQhG"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
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<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
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<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
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<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
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<td class=" content level3 subcell">Facts (P), Basic operations: (Not, And, Or), Implication<br>
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</td>
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</tr></table></div></td></tr></table>
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<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="ooeE4Az34-X"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
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||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
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||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
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<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
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<td class=" content level3 subcell">Example Facts: AliceWentToTheStore, BobWentToTheStore, AliceWentToHome<br>
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</td>
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</tr></table></div></td></tr></table>
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<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="aeKcnMpGIXB"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
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<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
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<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img onmousedown="ioSwitch('paeKcnMpGIXB', event.shiftKey)" id="iaeKcnMpGIXB" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
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<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
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<td class=" content level3 subcell">Implication:<br>
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</td>
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</tr></table></div></td></tr></table>
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<div id="paeKcnMpGIXB" class="expanded">
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||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="nA-infjIW8W"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
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||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
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<td class=" content level4 subcell"> (if P and Q then R)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="fLAa2UWCvl0"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">=== R \or \not P \or \not Q<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="bUtEc-RwiCO"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">=== “Horn Clause”<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="iJ88YrQNa7u"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor2"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level2 levelguttercolor2" style="width: 25px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level2 levelguttercolor2" style="width: 15px;"><img onmousedown="ioSwitch('piJ88YrQNa7u', event.shiftKey)" id="iiJ88YrQNa7u" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level2 levelguttercolor2" style=" width: 1px; "></td>
|
||
<td class=" content level2 subcell">1st order logic<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="piJ88YrQNa7u" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="h-iLrTm783e"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Goal: Quantification <br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="nBGJtVI5CmJ"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Challenge, need way to enumerate classes/sets of facts<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="jGpim8AN38q"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Groups of facts: WentTo(Store,<span class="" style='font-family: "Helvetica", sans-serif; font-size: 12px;'> </span>Alice), WentTo(Store<span class="" style='font-family: "Helvetica", sans-serif; font-size: 12px;'>, </span>Bob), WentTo(Home, Alice)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="eZEmpGRaOik"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">For all facts in a group (\forall) a property holds<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="lcsRHWqfuhi"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">There exists a fact in a group (\exists) such that a property holds<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gOdPCIIC9sG"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img onmousedown="ioSwitch('pgOdPCIIC9sG', event.shiftKey)" id="igOdPCIIC9sG" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">New way to discuss implication:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pgOdPCIIC9sG" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gXQ0QMT-vY3"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Given one or more facts P(X,Y), Q(X), …., “infer” a new fact R(Y)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="mbaCb02g0T9"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">If WentTo(X, Y) and ShoppingAt(X) then ShoppingDone(Y)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="osK_9_fqcSd"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">\forall Y, \exists X: If P(X,Y) and Q(X) then R(Y)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="nz9QDa-aXeQ"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">\forall Y, \exists X: \not P(X,Y) \or \not Q(X) \or R(Y)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="avkzsbfGmMb"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Which elements of R must be true?<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="ajGs-gTvL4k"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">SELECT Y FROM P NATURAL JOIN Q INTO R<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="jeGl0l7Rdey"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img onmousedown="ioSwitch('pjeGl0l7Rdey', event.shiftKey)" id="ijeGl0l7Rdey" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Datalog<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pjeGl0l7Rdey" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="oYmm-AzjM9O"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">R(Y) -= P(X,Y), Q(X)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gcN8Py1KRaz"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Head, Body<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="bGZQApaQkYY"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('pbGZQApaQkYY', event.shiftKey)" id="ibGZQApaQkYY" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Find values of Y for which R is true?<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pbGZQApaQkYY" class="expanded"><table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="mZ-7PZ9Bkas"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Find a value of X for which P(X,Y) and Q(X) are true<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table></div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="bWx3NV7B2Pm"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">What about R(Y, Z) -= P(X,Y), Q(X)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="oFTodIptICr"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img onmousedown="ioSwitch('poFTodIptICr', event.shiftKey)" id="ioFTodIptICr" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Alternative View:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="poFTodIptICr" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gHXPGB1wXRT"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('pgHXPGB1wXRT', event.shiftKey)" id="igHXPGB1wXRT" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">R(Y) is a function<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pgHXPGB1wXRT" class="expanded"><table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="hSUjzSfyFbn"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Dom => Bool<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table></div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="hugjrxU7oon"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Given Y, find a value of X for which P(X,Y) and Q(X) evaluate to true.<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="eT_EdhyAdUC"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('peT_EdhyAdUC', event.shiftKey)" id="ieT_EdhyAdUC" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Support<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="peT_EdhyAdUC" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="bRhKXPN0Yz2"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Support: The set of values of Y for which R(Y) evaluates to true<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="dk0zwPkQ_FF"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Finite Support: The support set has a fixed size<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="iLhBsqk95Yt"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">If P(X,Y), Q(X) have finite support, so does R(Y)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="hZVTOb9Phg1"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">actually, we can do a bit better… to be discussed shortly<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="ksfHm21-zVt"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('pksfHm21-zVt', event.shiftKey)" id="iksfHm21-zVt" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Natural consequence:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pksfHm21-zVt" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="bBLJ0f6nqrU"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">R(Y,Z) is true for any value of Z as long as R(Y) would be true.<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="oobjV_NSPgV"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">R(Y,Z) has an infinite support!<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gyQnIAsPzMZ"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Z is “unsafe” or “unbound"<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="lZBf9zcZvf8"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Y is “bound” or “safe”<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="dpEPsz-Ds74"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img onmousedown="ioSwitch('pdpEPsz-Ds74', event.shiftKey)" id="idpEPsz-Ds74" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Safety and Support<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pdpEPsz-Ds74" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="mr1iR_cGpCd"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Assume we have a S(Y,Z) with finite support.<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="kj36nzDRxov"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">R(Y,Z) dies not have finite support<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="aHDcPVNUGVD"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">What about ( S(Y,Z) and R(Y,Z) )<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="pX0FppIbsRh"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Interestingly enough, this actually does have finite support: Because Z is safe in S, it does not need to be safe in R.<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="mhwWRR9FxQn"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">In general, a variable is safe in a conjunction of terms IFF it is safe in at least one of the terms.<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="lF-3JjQcMej"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img onmousedown="ioSwitch('plF-3JjQcMej', event.shiftKey)" id="ilF-3JjQcMej" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">What else can you do with this idea?<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="plF-3JjQcMej" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="dm14r_F1Cdb"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Functions F(X) -> ???<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="mIXp4kXNCi-"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('pmIXp4kXNCi-', event.shiftKey)" id="imIXp4kXNCi-" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">What about other functions?<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pmIXp4kXNCi-" class="expanded"><table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="aQ1ObuTv76h"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">F(X,Y) -> true if (X < Y)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table></div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="jWxaUXIaJg7"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('pjWxaUXIaJg7', event.shiftKey)" id="ijWxaUXIaJg7" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">How about to natural numbers?<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pjWxaUXIaJg7" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="lglqhrOo_r-"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Simple way to express Bags!<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gELskVltVC1"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">R(X) -> N = number of instances of X in R (multiplicity)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="aciCu3Gp_-L"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img onmousedown="ioSwitch('paciCu3Gp_-L', event.shiftKey)" id="iaciCu3Gp_-L" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Leads to some interesting math:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="paciCu3Gp_-L" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="oAw5top8oeU"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">R(X) U S(X) === R(X) + S(X)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="lPt9wYWe0Mi"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">R(X) |><| S(X) === R(X) * S(X)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="hGIWY9IdLw_"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Q(X) -= R(X,Y) * S(X, Y) === Aggregation: Sum[Y] R(X,Y) * S(X,Y)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="g5EPynHfryU"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">SELECT COUNT(*) FROM R NATURAL JOIN S<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="oQz41OAQAFB"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('poQz41OAQAFB', event.shiftKey)" id="ioQz41OAQAFB" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">How about real numbers?<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="poQz41OAQAFB" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gw1gbYq8vcH"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">R(X) -> Multiplicity<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="c90ZzHbybG_"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">F(X) -> {X}<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="aR9IujNEKk6"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Q() -= SUM[X] ( R(X) * {X} )<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="fEfIyq_4I1M"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">SELECT SUM(X) FROM R<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="aLA_vNDmdy-"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Q() -= SUM[X] ( R(X,Y) * S(Y,Z) * {Z < 10} * {X} )<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="cZEVYe-HKV9"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">SELECT SUM(R.X) FROM R NATURAL JOIN S WHERE S.Z < 10<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="kYpB0lRkwG_"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">OR: Aggregate { Start with R, Join with S, Filter on Z < 10, Multiply multiplicity by X }<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="a26K3pn-Gho"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img onmousedown="ioSwitch('pa26K3pn-Gho', event.shiftKey)" id="ia26K3pn-Gho" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Sequence of transformations, each modifying the output of the last<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pa26K3pn-Gho" class="expanded"><table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="l1xzcQk5MNO"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">Pipelining technique sometimes referred to as a “Monad"<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table></div>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="oSku2D1T-1u"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">^— all actually used in practice. DBToaster’s AGCA and LogicBlox LogiQL<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="hMAR0UnJLxG"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img onmousedown="ioSwitch('phMAR0UnJLxG', event.shiftKey)" id="ihMAR0UnJLxG" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">Connections to Rings:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="phMAR0UnJLxG" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="nmheoy1IS07"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img onmousedown="ioSwitch('pnmheoy1IS07', event.shiftKey)" id="inmheoy1IS07" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Semiring:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pnmheoy1IS07" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="jqROof035Jk"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">Set/Type, +: SxS->S, 0, *: SxS->, 1<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="nr7ajZDV3fp"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">+/* associative, commutative<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="d_TZ-eY8xYM"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">+ distributive over *<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="mZgexSgRflO"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">0+x = x<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="nunNyp2z_-M"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">0*x = 0<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="kG_REcFNwfo"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">1*x = x<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gyHY6GBgGy7"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img onmousedown="ioSwitch('pgyHY6GBgGy7', event.shiftKey)" id="igyHY6GBgGy7" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">Ring = Semiring + Invertor:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pgyHY6GBgGy7" class="expanded"><table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="o2-RWNupg1H"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor6"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level6 levelguttercolor6" style="width: 89px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level6 levelguttercolor6" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level6 levelguttercolor6" style=" width: 1px; "></td>
|
||
<td class=" content level6 subcell">-x + x = 0<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table></div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="ptxoRU_WCxD"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor5"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level5 levelguttercolor5" style="width: 73px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level5 levelguttercolor5" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level5 levelguttercolor5" style=" width: 1px; "></td>
|
||
<td class=" content level5 subcell">U = + // |><| = *<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="e0LymDE9OZh"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor1"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level1 levelguttercolor1" style="width: 9px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level1 levelguttercolor1" style="width: 15px;"><img onmousedown="ioSwitch('pe0LymDE9OZh', event.shiftKey)" id="ie0LymDE9OZh" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level1 levelguttercolor1" style=" width: 1px; "></td>
|
||
<td class=" content level1 subcell">Monad Algebra<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pe0LymDE9OZh" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="h47GJYbWTgh"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor2"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level2 levelguttercolor2" style="width: 25px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level2 levelguttercolor2" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level2 levelguttercolor2" style=" width: 1px; "></td>
|
||
<td class=" content level2 subcell">Problem: Nested data! We want to transform it in bulk<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="eYU3eMb5Dcg"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor2"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level2 levelguttercolor2" style="width: 25px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level2 levelguttercolor2" style="width: 15px;"><img onmousedown="ioSwitch('peYU3eMb5Dcg', event.shiftKey)" id="ieYU3eMb5Dcg" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level2 levelguttercolor2" style=" width: 1px; "></td>
|
||
<td class=" content level2 subcell">Same idea of pipelining operations:<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="peYU3eMb5Dcg" class="expanded"><table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="attOKY1Rxmm"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Applied to <br>
|
||
</td>
|
||
</tr></table></div></td></tr></table></div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="eYSl5UMOv2W"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor2"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level2 levelguttercolor2" style="width: 25px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level2 levelguttercolor2" style="width: 15px;"><img onmousedown="ioSwitch('peYSl5UMOv2W', event.shiftKey)" id="ieYSl5UMOv2W" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level2 levelguttercolor2" style=" width: 1px; "></td>
|
||
<td class=" content level2 subcell">Overview<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="peYSl5UMOv2W" class="expanded">
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gP-Xrv1F0dE"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Types: Dom, Tuple(X,Y), List(X)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="bvYthQyJO0j"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Basic Ops: Const, Emptyset, Singleton, Map, Union, Tuple, DeTuple, f(DOM)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="gN_-HOnWWHR"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img onmousedown="ioSwitch('pgN_-HOnWWHR', event.shiftKey)" id="igN_-HOnWWHR" border="0" alt="V" class="parent" src="Expanded.png" title="collapse"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Key Features: Fold<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<div id="pgN_-HOnWWHR" class="expanded"><table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="maal-EBYpdf"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor4"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level4 levelguttercolor4" style="width: 57px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level4 levelguttercolor4" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level4 levelguttercolor4" style=" width: 1px; "></td>
|
||
<td class=" content level4 subcell">If/Then/Else<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table></div>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="pmAIE4lc4Bc"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell">Key Features: Tensor Strength — PairWith (equiv: Cross Product)<br>
|
||
</td>
|
||
</tr></table></div></td></tr></table>
|
||
<table cellspacing="0" border="0" cellpadding="0" class="row heighthack"><tr id="fDR8eKg8MDQ"><td class=" col1 colbackground1 col_width1" style=""><div class=" full levelcolor3"><table border="0" cellspacing="0" cellpadding="0" style="height:100%" class=" col_width1 col1"><tr>
|
||
<td class=" subcell wholedocgutter level3 levelguttercolor3" style="width: 41px;"></td>
|
||
<td class=" subcell wholedocgutter indicator level3 levelguttercolor3" style="width: 15px;"><img border="0" alt="*" class="leaf" src="LeafRowHandle.png"></td>
|
||
<td class=" subcell wholedocgutter labelpadding level3 levelguttercolor3" style=" width: 1px; "></td>
|
||
<td class=" content level3 subcell"></td>
|
||
</tr></table></div></td></tr></table>
|
||
</div>
|
||
</div>
|
||
</td></tr></table></body>
|
||
</html>
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