mirrors/garage
1
0
Fork 0
mirror of https://git.deuxfleurs.fr/Deuxfleurs/garage.git synced 2024-11-25 09:31:00 +00:00
Code Issues Projects Releases Packages Wiki Activity

Different lattice figures

Browse source
This commit is contained in:
Alex Auvolat 2023-01-13 12:33:27 +01:00
parent 1f5e3aaf8e
commit cbb522e179
No known key found for this signature in database
GPG key ID: 0E496D15096376BE
14 changed files with 4269 additions and 349 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

14
doc/talks/2023-01-18-tocatta/Makefile
View file

@ -12,10 +12,16 @@ ASSETS=assets/consistent_hashing_1.pdf \
assets/lattice6.pdf_tex \ assets/lattice6.pdf_tex \
assets/lattice7.pdf_tex \ assets/lattice7.pdf_tex \
assets/lattice8.pdf_tex \ assets/lattice8.pdf_tex \
assets/lattice9.pdf_tex \ assets/latticeB_1.pdf_tex \
assets/latticeA.pdf_tex \ assets/latticeB_2.pdf_tex \
assets/latticeB.pdf_tex \ assets/latticeB_3.pdf_tex \
assets/latticeC.pdf_tex \ assets/latticeB_4.pdf_tex \
assets/latticeB_5.pdf_tex \
assets/latticeB_6.pdf_tex \
assets/latticeB_7.pdf_tex \
assets/latticeB_8.pdf_tex \
assets/latticeB_9.pdf_tex \
assets/latticeB_10.pdf_tex \
assets/deuxfleurs.pdf assets/deuxfleurs.pdf
talk.pdf: talk.tex $(ASSETS) talk.pdf: talk.tex $(ASSETS)

112
doc/talks/2023-01-18-tocatta/assets/lattice8.svg
View file

@ -25,8 +25,8 @@
inkscape:document-units="mm" inkscape:document-units="mm"
showgrid="false" showgrid="false"
inkscape:zoom="1.4734708" inkscape:zoom="1.4734708"
inkscape:cx="451.65469" inkscape:cx="399.39712"
inkscape:cy="272.14655" inkscape:cy="248.39311"
inkscape:window-width="1920" inkscape:window-width="1920"
inkscape:window-height="999" inkscape:window-height="999"
inkscape:window-x="0" inkscape:window-x="0"
@ -433,8 +433,8 @@
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663" id="path3663"
cx="147.35568" cx="132.33408"
cy="95.24971" cy="68.007973"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
@ -477,6 +477,17 @@
style="stroke-width:0.264583;fill:#000000" style="stroke-width:0.264583;fill:#000000"
x="6.9525447" x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text> y="13.702217">$write(\{a\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.261436"
id="text3707-1"><tspan
sodipodi:role="line"
id="tspan3705-5"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.261436">$read()$:</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
@ -501,15 +512,32 @@
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523" y="41.972523"
id="text3750-0"><tspan id="text3750-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6" id="tspan3748-6"
style="fill:#999999;stroke-width:0.264583" style="fill:#000000;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text> y="41.972523">$\sqsupseteq \{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-4"
cx="18.004833"
cy="70.942116"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="73.643356"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-65"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="73.643356">$\to \{\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
@ -521,67 +549,33 @@
style="fill:#000000;stroke-width:0.264583" style="fill:#000000;stroke-width:0.264583"
x="14.395845" x="14.395845"
y="52.022549">return OK</tspan></text> y="52.022549">return OK</tspan></text>
<circle <text
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" xml:space="preserve"
id="path3663-1-4" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
cx="18.004833" x="14.395845"
cy="90.979645" y="92.005798"
r="2.7302806" /> id="text4280-3"><tspan
<circle sodipodi:role="line"
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" id="tspan4278-7"
id="path3663-3-0-5" style="fill:#000000;stroke-width:0.264583"
cx="18.004833" x="14.395845"
cy="81.949104" y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text>
r="2.7302806" />
<circle <circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-2" id="path3663-1-5"
cx="18.004833" cx="18.004833"
cy="72.918564" cy="81.007744"
r="2.7302806" /> r="2.7302806" />
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447" x="23.457415"
y="65.279381" y="83.577797"
id="text3707-5"><tspan id="text3750-0-6"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3705-4" id="tspan3748-6-9"
style="fill:#000000;stroke-width:0.264583" style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-4"
style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text> y="83.577797">$\to \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="84.598038"
id="text3750-3-4"><tspan
sodipodi:role="line"
id="tspan3748-2-3"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969"
id="text3750-0-0"><tspan
sodipodi:role="line"
id="tspan3748-6-7"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
</g> </g>
</svg> </svg>

Side by side Swipe Overlay

Before

Width:  |  Height:  |  Size: 21 KiB

After

Width:  |  Height:  |  Size: 20 KiB

576
doc/talks/2023-01-18-tocatta/assets/latticeB_1.svg Normal file
View file

@ -0,0 +1,576 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
width="1000"
height="600"
viewBox="0 0 264.58333 158.75"
version="1.1"
id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeB_1.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg"
xmlns:svg="http://www.w3.org/2000/svg">
<sodipodi:namedview
id="namedview7"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:showpageshadow="2"
inkscape:pageopacity="0.0"
inkscape:pagecheckerboard="0"
inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm"
showgrid="false"
inkscape:zoom="1.0419012"
inkscape:cx="469.81422"
inkscape:cy="257.22209"
inkscape:window-width="1920"
inkscape:window-height="999"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="1"
inkscape:current-layer="layer2" />
<defs
id="defs2">
<marker
style="overflow:visible"
id="Arrow2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1-4"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8-7" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2-8"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6-4" />
</marker>
</defs>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
sodipodi:insensitive="true">
<rect
style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288"
width="262.58151"
height="156.82782"
x="0.77790999"
y="0.93738818" />
</g>
<g
inkscape:groupmode="layer"
id="layer2"
inkscape:label="Layer 2">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442"
id="text951"><tspan
sodipodi:role="line"
id="tspan949"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442">$\{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893"
id="text1005"><tspan
sodipodi:role="line"
id="tspan1003"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text>
<g
id="g1175"
transform="translate(51.996784,3.5774043)">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698"
id="text1009"><tspan
sodipodi:role="line"
id="tspan1007"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698">$\{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166"
id="text1009-3"><tspan
sodipodi:role="line"
id="tspan1007-6"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166">$\{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698"
id="text1009-7"><tspan
sodipodi:role="line"
id="tspan1007-5"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698">$\{c\}$</tspan></text>
</g>
<g
id="g1183"
transform="translate(51.996784,1.0317046)"
style="fill:#000000">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526"
id="text1117"><tspan
sodipodi:role="line"
id="tspan1115"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526"
id="text1117-3"><tspan
sodipodi:role="line"
id="tspan1115-5"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526"
id="text1117-6"><tspan
sodipodi:role="line"
id="tspan1115-2"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text>
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
d="M 153.33622,90.367682 118.34198,73.428915"
id="path1300" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
d="M 177.46016,90.367682 212.4544,73.428915"
id="path1300-2" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
d="M 153.33622,61.655656 118.34198,44.716889"
id="path1300-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
d="M 177.46016,61.655656 212.4544,44.716889"
id="path1300-2-6" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
d="M 118.34198,61.655656 153.33622,44.716889"
id="path1300-0-7" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
d="M 212.4544,61.655656 177.46016,44.716889"
id="path1300-2-6-9" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
d="M 118.34198,34.227412 153.33622,17.288645"
id="path1300-0-7-5" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
d="M 212.4544,34.227412 177.46016,17.288645"
id="path1300-2-6-9-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6-9"
sodipodi:nodetypes="cc" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663"
cx="147.35568"
cy="95.24971"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3"
cx="141.05479"
cy="95.316383"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="134.56244"
cy="94.993034"
r="2.7302806" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1"
cx="18.004833"
cy="39.402473"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0"
cx="18.004833"
cy="30.371933"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6"
cx="18.004833"
cy="21.341394"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217"
id="text3707"><tspan
sodipodi:role="line"
id="tspan3705"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="24.042637"
id="text3750"><tspan
sodipodi:role="line"
id="tspan3748"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="24.042637">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087"
id="text3750-3"><tspan
sodipodi:role="line"
id="tspan3748-2"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523"
id="text3750-0"><tspan
sodipodi:role="line"
id="tspan3748-6"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4"
cx="18.004833"
cy="90.979645"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-5"
cx="18.004833"
cy="81.949104"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-2"
cx="18.004833"
cy="72.918564"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381"
id="text3707-5"><tspan
sodipodi:role="line"
id="tspan3705-4"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-4"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="84.598038"
id="text3750-3-4"><tspan
sodipodi:role="line"
id="tspan3748-2-3"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969"
id="text3750-0-0"><tspan
sodipodi:role="line"
id="tspan3748-6-7"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
</g>
</svg>
Side by side

After

Width:  |  Height:  |  Size: 20 KiB

715
doc/talks/2023-01-18-tocatta/assets/latticeB_10.svg Normal file
View file

@ -0,0 +1,715 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
width="1000"
height="600"
viewBox="0 0 264.58333 158.75"
version="1.1"
id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeB_10.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg"
xmlns:svg="http://www.w3.org/2000/svg">
<sodipodi:namedview
id="namedview7"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:showpageshadow="2"
inkscape:pageopacity="0.0"
inkscape:pagecheckerboard="0"
inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm"
showgrid="false"
inkscape:zoom="1.0419012"
inkscape:cx="664.65036"
inkscape:cy="366.63745"
inkscape:window-width="1920"
inkscape:window-height="999"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="1"
inkscape:current-layer="layer2" />
<defs
id="defs2">
<marker
style="overflow:visible"
id="Arrow2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1-4"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8-7" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2-8"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6-4" />
</marker>
</defs>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
sodipodi:insensitive="true">
<rect
style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288"
width="262.58151"
height="156.82782"
x="0.77790999"
y="0.93738818" />
</g>
<g
inkscape:groupmode="layer"
id="layer2"
inkscape:label="Layer 2">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442"
id="text951"><tspan
sodipodi:role="line"
id="tspan949"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442">$\{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893"
id="text1005"><tspan
sodipodi:role="line"
id="tspan1003"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text>
<g
id="g1175"
transform="translate(51.996784,3.5774043)">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698"
id="text1009"><tspan
sodipodi:role="line"
id="tspan1007"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698">$\{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166"
id="text1009-3"><tspan
sodipodi:role="line"
id="tspan1007-6"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166">$\{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698"
id="text1009-7"><tspan
sodipodi:role="line"
id="tspan1007-5"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698">$\{c\}$</tspan></text>
</g>
<g
id="g1183"
transform="translate(51.996784,1.0317046)"
style="fill:#000000">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526"
id="text1117"><tspan
sodipodi:role="line"
id="tspan1115"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526"
id="text1117-3"><tspan
sodipodi:role="line"
id="tspan1115-5"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526"
id="text1117-6"><tspan
sodipodi:role="line"
id="tspan1115-2"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text>
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
d="M 153.33622,90.367682 118.34198,73.428915"
id="path1300" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
d="M 177.46016,90.367682 212.4544,73.428915"
id="path1300-2" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
d="M 153.33622,61.655656 118.34198,44.716889"
id="path1300-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
d="M 177.46016,61.655656 212.4544,44.716889"
id="path1300-2-6" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
d="M 118.34198,61.655656 153.33622,44.716889"
id="path1300-0-7" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
d="M 212.4544,61.655656 177.46016,44.716889"
id="path1300-2-6-9" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
d="M 118.34198,34.227412 153.33622,17.288645"
id="path1300-0-7-5" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
d="M 212.4544,34.227412 177.46016,17.288645"
id="path1300-2-6-9-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6-9"
sodipodi:nodetypes="cc" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663"
cx="147.35568"
cy="95.24971"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3"
cx="176.97627"
cy="68.155472"
r="2.7302806" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1"
cx="18.004833"
cy="39.402473"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0"
cx="18.004833"
cy="30.371933"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6"
cx="18.004833"
cy="21.341394"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217"
id="text3707"><tspan
sodipodi:role="line"
id="tspan3705"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637"
id="text3750"><tspan
sodipodi:role="line"
id="tspan3748"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087"
id="text3750-3"><tspan
sodipodi:role="line"
id="tspan3748-2"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523"
id="text3750-0"><tspan
sodipodi:role="line"
id="tspan3748-6"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4"
cx="18.004833"
cy="90.979645"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-5"
cx="18.004833"
cy="81.949104"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-2"
cx="18.004833"
cy="72.918564"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381"
id="text3707-5"><tspan
sodipodi:role="line"
id="tspan3705-4"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403"
id="text3707-5-3"><tspan
sodipodi:role="line"
id="tspan3705-4-6"
style="fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-4"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038"
id="text3750-3-4"><tspan
sodipodi:role="line"
id="tspan3748-2-3"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969"
id="text3750-0-0"><tspan
sodipodi:role="line"
id="tspan3748-6-7"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0"
cx="67.201363"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125"
id="text3750-9"><tspan
sodipodi:role="line"
id="tspan3748-3"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125">$\to \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="text4280-6"><tspan
sodipodi:role="line"
style="fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="tspan2630">return $\{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-7"
cx="67.201363"
cy="133.94179"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073"
id="text3750-3-6"><tspan
sodipodi:role="line"
id="tspan3748-2-0"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073">$\to \{\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0-6"
cx="174.36296"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="179.81555"
y="127.6125"
id="text3750-9-1"><tspan
sodipodi:role="line"
id="tspan3748-3-8"
style="fill:#000000;stroke-width:0.264583"
x="179.81555"
y="127.6125">$\to \{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403"
id="text3707-5-3-7"><tspan
sodipodi:role="line"
id="tspan3705-4-6-5"
style="fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
x="134.97845"
y="132.58472"
id="text3899"><tspan
sodipodi:role="line"
id="tspan3897"
style="stroke-width:0.264583"
x="134.97845"
y="132.58472">;</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="169.92604"
y="146.3129"
id="text4280-6-7"><tspan
sodipodi:role="line"
style="fill:#000000;stroke-width:0.264583"
x="169.92604"
y="146.3129"
id="tspan2630-9">return $\{b\}$</tspan></text>
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-7-2"
cx="174.36296"
cy="133.94179"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="179.81555"
y="136.59073"
id="text3750-3-6-0"><tspan
sodipodi:role="line"
id="tspan3748-2-0-2"
style="fill:#000000;stroke-width:0.264583"
x="179.81555"
y="136.59073">$\to \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:end;text-anchor:end;fill:#ff0000;stroke-width:0.264583"
x="259.75"
y="135.53111"
id="text9043"><tspan
sodipodi:role="line"
id="tspan9041"
style="fill:#ff0000;stroke-width:0.264583"
x="259.75"
y="135.53111">${\Large\textbf{??!}}$~~~~~</tspan><tspan
sodipodi:role="line"
style="fill:#ff0000;stroke-width:0.264583"
x="259.75"
y="146.11446"
id="tspan9372">$\{a\} \not\sqsubseteq \{b\}$</tspan></text>
</g>
</svg>
Side by side

After

Width:  |  Height:  |  Size: 25 KiB

116
doc/talks/2023-01-18-tocatta/assets/latticeC.svg → doc/talks/2023-01-18-tocatta/assets/latticeB_2.svg
View file

@ -3,12 +3,12 @@
<svg <svg
width="1000" width="1000"
height="400" height="600"
viewBox="0 0 264.58333 105.83333" viewBox="0 0 264.58333 158.75"
version="1.1" version="1.1"
id="svg5" id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)" inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeC.svg" sodipodi:docname="latticeB_2.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg"
@ -25,8 +25,8 @@
inkscape:document-units="mm" inkscape:document-units="mm"
showgrid="false" showgrid="false"
inkscape:zoom="1.4734708" inkscape:zoom="1.4734708"
inkscape:cx="450.97602" inkscape:cx="586.70996"
inkscape:cy="272.14655" inkscape:cy="321.01077"
inkscape:window-width="1920" inkscape:window-width="1920"
inkscape:window-height="999" inkscape:window-height="999"
inkscape:window-x="0" inkscape:window-x="0"
@ -270,10 +270,10 @@
id="layer1" id="layer1"
sodipodi:insensitive="true"> sodipodi:insensitive="true">
<rect <rect
style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000" style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288" id="rect288"
width="209.84705" width="262.58151"
height="104.42732" height="156.82782"
x="0.77790999" x="0.77790999"
y="0.93738818" /> y="0.93738818" />
</g> </g>
@ -283,24 +283,24 @@
inkscape:label="Layer 2"> inkscape:label="Layer 2">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442" y="99.307442"
id="text951"><tspan id="text951"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan949" id="tspan949"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442">$\{\}$</tspan></text> y="99.307442">$\{\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893" y="13.151893"
id="text1005"><tspan id="text1005"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1003" id="tspan1003"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text> y="13.151893">$\{a,b,c\}$</tspan></text>
<g <g
@ -308,35 +308,35 @@
transform="translate(51.996784,3.5774043)"> transform="translate(51.996784,3.5774043)">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698" y="67.008698"
id="text1009"><tspan id="text1009"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007" id="tspan1007"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698">$\{a\}$</tspan></text> y="67.008698">$\{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166" y="67.017166"
id="text1009-3"><tspan id="text1009-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-6" id="tspan1007-6"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166">$\{b\}$</tspan></text> y="67.017166">$\{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698" y="67.008698"
id="text1009-7"><tspan id="text1009-7"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-5" id="tspan1007-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698">$\{c\}$</tspan></text> y="67.008698">$\{c\}$</tspan></text>
</g> </g>
@ -346,35 +346,35 @@
style="fill:#000000"> style="fill:#000000">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526" y="40.841526"
id="text1117"><tspan id="text1117"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115" id="tspan1115"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text> y="40.841526">$\{a,c\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526" y="40.841526"
id="text1117-3"><tspan id="text1117-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-5" id="tspan1115-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text> y="40.841526">$\{a,b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526" y="40.841526"
id="text1117-6"><tspan id="text1117-6"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-2" id="tspan1115-2"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text> y="40.841526">$\{b,c\}$</tspan></text>
</g> </g>
@ -433,20 +433,20 @@
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663" id="path3663"
cx="117.08417" cx="147.35568"
cy="38.792969" cy="95.24971"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3" id="path3663-3"
cx="123.57843" cx="141.05479"
cy="39.100433" cy="95.316383"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6" id="path3663-6"
cx="130.27556" cx="118.63729"
cy="39.441635" cy="67.630196"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
@ -468,13 +468,13 @@
r="2.7302806" /> r="2.7302806" />
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217" y="13.702217"
id="text3707"><tspan id="text3707"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3705" id="tspan3705"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text> y="13.702217">$write(\{a\})$:</tspan></text>
<text <text
@ -490,48 +490,26 @@
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087" y="33.02087"
id="text3750-3"><tspan id="text3750-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-2" id="tspan3748-2"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523" y="41.972523"
id="text3750-0"><tspan id="text3750-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6" id="tspan3748-6"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523">$\sqsupseteq \{a\}$</tspan></text> y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549"
id="text4280"><tspan
sodipodi:role="line"
id="tspan4278"
style="fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549">return OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="14.395845"
y="102.48464"
id="text4280-8"><tspan
sodipodi:role="line"
id="tspan4278-8"
style="fill:#000000;stroke-width:0.264583"
x="14.395845"
y="102.48464">return OK</tspan></text>
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4" id="path3663-1-4"
@ -563,36 +541,36 @@
y="65.279381">$write(\{b\})$:</tspan></text> y="65.279381">$write(\{b\})$:</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="75.619804" y="75.619804"
id="text3750-7"><tspan id="text3750-7"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-4" id="tspan3748-4"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="75.619804">$\sqsupseteq \{b\}$</tspan></text> y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="84.598038" y="84.598038"
id="text3750-3-4"><tspan id="text3750-3-4"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-2-3" id="tspan3748-2-3"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text> y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969" y="93.54969"
id="text3750-0-0"><tspan id="text3750-0-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6-7" id="tspan3748-6-7"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969">$\sqsupseteq \{b\} \to$ OK</tspan></text> y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
</g> </g>
</svg> </svg>
Side by side Swipe Overlay

Before

Width:  |  Height:  |  Size: 21 KiB

After

Width:  |  Height:  |  Size: 20 KiB

109
doc/talks/2023-01-18-tocatta/assets/latticeA.svg → doc/talks/2023-01-18-tocatta/assets/latticeB_3.svg
View file

@ -3,12 +3,12 @@
<svg <svg
width="1000" width="1000"
height="400" height="600"
viewBox="0 0 264.58333 105.83333" viewBox="0 0 264.58333 158.75"
version="1.1" version="1.1"
id="svg5" id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)" inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeA.svg" sodipodi:docname="latticeB_3.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg"
@ -24,9 +24,9 @@
inkscape:deskcolor="#d1d1d1" inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm" inkscape:document-units="mm"
showgrid="false" showgrid="false"
inkscape:zoom="1.4734708" inkscape:zoom="2.0838024"
inkscape:cx="450.97602" inkscape:cx="465.25525"
inkscape:cy="272.14655" inkscape:cy="269.21938"
inkscape:window-width="1920" inkscape:window-width="1920"
inkscape:window-height="999" inkscape:window-height="999"
inkscape:window-x="0" inkscape:window-x="0"
@ -270,10 +270,10 @@
id="layer1" id="layer1"
sodipodi:insensitive="true"> sodipodi:insensitive="true">
<rect <rect
style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000" style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288" id="rect288"
width="209.84705" width="262.58151"
height="104.42732" height="156.82782"
x="0.77790999" x="0.77790999"
y="0.93738818" /> y="0.93738818" />
</g> </g>
@ -283,24 +283,24 @@
inkscape:label="Layer 2"> inkscape:label="Layer 2">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442" y="99.307442"
id="text951"><tspan id="text951"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan949" id="tspan949"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442">$\{\}$</tspan></text> y="99.307442">$\{\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893" y="13.151893"
id="text1005"><tspan id="text1005"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1003" id="tspan1003"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text> y="13.151893">$\{a,b,c\}$</tspan></text>
<g <g
@ -308,35 +308,35 @@
transform="translate(51.996784,3.5774043)"> transform="translate(51.996784,3.5774043)">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698" y="67.008698"
id="text1009"><tspan id="text1009"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007" id="tspan1007"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698">$\{a\}$</tspan></text> y="67.008698">$\{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166" y="67.017166"
id="text1009-3"><tspan id="text1009-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-6" id="tspan1007-6"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166">$\{b\}$</tspan></text> y="67.017166">$\{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698" y="67.008698"
id="text1009-7"><tspan id="text1009-7"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-5" id="tspan1007-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698">$\{c\}$</tspan></text> y="67.008698">$\{c\}$</tspan></text>
</g> </g>
@ -346,35 +346,35 @@
style="fill:#000000"> style="fill:#000000">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526" y="40.841526"
id="text1117"><tspan id="text1117"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115" id="tspan1115"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text> y="40.841526">$\{a,c\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526" y="40.841526"
id="text1117-3"><tspan id="text1117-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-5" id="tspan1115-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text> y="40.841526">$\{a,b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526" y="40.841526"
id="text1117-6"><tspan id="text1117-6"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-2" id="tspan1115-2"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text> y="40.841526">$\{b,c\}$</tspan></text>
</g> </g>
@ -433,20 +433,14 @@
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663" id="path3663"
cx="117.08417" cx="147.35568"
cy="38.792969" cy="95.24971"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3" id="path3663-3"
cx="126.08154" cx="176.97627"
cy="67.968384" cy="68.155472"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="119.58919"
cy="67.645035"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
@ -468,13 +462,13 @@
r="2.7302806" /> r="2.7302806" />
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217" y="13.702217"
id="text3707"><tspan id="text3707"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3705" id="tspan3705"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text> y="13.702217">$write(\{a\})$:</tspan></text>
<text <text
@ -490,37 +484,26 @@
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087" y="33.02087"
id="text3750-3"><tspan id="text3750-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-2" id="tspan3748-2"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523" y="41.972523"
id="text3750-0"><tspan id="text3750-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6" id="tspan3748-6"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523">$\sqsupseteq \{a\}$</tspan></text> y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549"
id="text4280"><tspan
sodipodi:role="line"
id="tspan4278"
style="fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549">return OK</tspan></text>
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4" id="path3663-1-4"
@ -563,25 +546,31 @@
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text> y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="84.598038" y="84.598038"
id="text3750-3-4"><tspan id="text3750-3-4"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-2-3" id="tspan3748-2-3"
style="fill:#999999;stroke-width:0.264583" style="fill:#000000;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text> y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969" y="93.54969"
id="text3750-0-0"><tspan id="text3750-0-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6-7" id="tspan3748-6-7"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969">$\sqsupseteq \{b\} \to$ OK</tspan></text> y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
</g> </g>
</svg> </svg>
Side by side Swipe Overlay

Before

Width:  |  Height:  |  Size: 21 KiB

After

Width:  |  Height:  |  Size: 20 KiB

114
doc/talks/2023-01-18-tocatta/assets/lattice9.svg → doc/talks/2023-01-18-tocatta/assets/latticeB_4.svg
View file

@ -3,12 +3,12 @@
<svg <svg
width="1000" width="1000"
height="400" height="600"
viewBox="0 0 264.58333 105.83333" viewBox="0 0 264.58333 158.75"
version="1.1" version="1.1"
id="svg5" id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)" inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="lattice9.svg" sodipodi:docname="latticeB_4.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg"
@ -24,9 +24,9 @@
inkscape:deskcolor="#d1d1d1" inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm" inkscape:document-units="mm"
showgrid="false" showgrid="false"
inkscape:zoom="1.4734708" inkscape:zoom="1.0419012"
inkscape:cx="451.65469" inkscape:cx="505.32622"
inkscape:cy="272.14655" inkscape:cy="316.72869"
inkscape:window-width="1920" inkscape:window-width="1920"
inkscape:window-height="999" inkscape:window-height="999"
inkscape:window-x="0" inkscape:window-x="0"
@ -270,10 +270,10 @@
id="layer1" id="layer1"
sodipodi:insensitive="true"> sodipodi:insensitive="true">
<rect <rect
style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000" style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288" id="rect288"
width="209.84705" width="262.58151"
height="104.42732" height="156.82782"
x="0.77790999" x="0.77790999"
y="0.93738818" /> y="0.93738818" />
</g> </g>
@ -283,24 +283,24 @@
inkscape:label="Layer 2"> inkscape:label="Layer 2">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442" y="99.307442"
id="text951"><tspan id="text951"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan949" id="tspan949"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442">$\{\}$</tspan></text> y="99.307442">$\{\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893" y="13.151893"
id="text1005"><tspan id="text1005"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1003" id="tspan1003"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text> y="13.151893">$\{a,b,c\}$</tspan></text>
<g <g
@ -308,35 +308,35 @@
transform="translate(51.996784,3.5774043)"> transform="translate(51.996784,3.5774043)">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698" y="67.008698"
id="text1009"><tspan id="text1009"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007" id="tspan1007"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698">$\{a\}$</tspan></text> y="67.008698">$\{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166" y="67.017166"
id="text1009-3"><tspan id="text1009-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-6" id="tspan1007-6"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166">$\{b\}$</tspan></text> y="67.017166">$\{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698" y="67.008698"
id="text1009-7"><tspan id="text1009-7"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-5" id="tspan1007-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698">$\{c\}$</tspan></text> y="67.008698">$\{c\}$</tspan></text>
</g> </g>
@ -346,35 +346,35 @@
style="fill:#000000"> style="fill:#000000">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526" y="40.841526"
id="text1117"><tspan id="text1117"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115" id="tspan1115"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text> y="40.841526">$\{a,c\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526" y="40.841526"
id="text1117-3"><tspan id="text1117-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-5" id="tspan1115-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text> y="40.841526">$\{a,b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526" y="40.841526"
id="text1117-6"><tspan id="text1117-6"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-2" id="tspan1115-2"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text> y="40.841526">$\{b,c\}$</tspan></text>
</g> </g>
@ -433,20 +433,14 @@
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663" id="path3663"
cx="177.03145" cx="147.35568"
cy="67.991631" cy="95.24971"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3" id="path3663-3"
cx="126.08154" cx="176.97627"
cy="67.968384" cy="68.155472"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="119.58919"
cy="67.645035"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
@ -468,13 +462,13 @@
r="2.7302806" /> r="2.7302806" />
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217" y="13.702217"
id="text3707"><tspan id="text3707"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3705" id="tspan3705"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text> y="13.702217">$write(\{a\})$:</tspan></text>
<text <text
@ -490,15 +484,15 @@
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087" y="33.02087"
id="text3750-3"><tspan id="text3750-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-2" id="tspan3748-2"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
@ -510,17 +504,6 @@
style="fill:#999999;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text> y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549"
id="text4280"><tspan
sodipodi:role="line"
id="tspan4278"
style="fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549">return OK</tspan></text>
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4" id="path3663-1-4"
@ -550,6 +533,17 @@
style="fill:#000000;stroke-width:0.264583" style="fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text> y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403"
id="text3707-5-3"><tspan
sodipodi:role="line"
id="tspan3705-4-6"
style="fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403">$read()$:</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
@ -563,25 +557,31 @@
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text> y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="84.598038" y="84.598038"
id="text3750-3-4"><tspan id="text3750-3-4"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-2-3" id="tspan3748-2-3"
style="fill:#999999;stroke-width:0.264583" style="fill:#000000;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text> y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969" y="93.54969"
id="text3750-0-0"><tspan id="text3750-0-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6-7" id="tspan3748-6-7"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969">$\sqsupseteq \{b\} \to$ OK</tspan></text> y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
</g> </g>
</svg> </svg>
Side by side Swipe Overlay

Before

Width:  |  Height:  |  Size: 21 KiB

After

Width:  |  Height:  |  Size: 21 KiB

140
doc/talks/2023-01-18-tocatta/assets/latticeB.svg → doc/talks/2023-01-18-tocatta/assets/latticeB_5.svg
View file

@ -3,12 +3,12 @@
<svg <svg
width="1000" width="1000"
height="400" height="600"
viewBox="0 0 264.58333 105.83333" viewBox="0 0 264.58333 158.75"
version="1.1" version="1.1"
id="svg5" id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)" inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeB.svg" sodipodi:docname="latticeB_5.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg" xmlns="http://www.w3.org/2000/svg"
@ -25,8 +25,8 @@
inkscape:document-units="mm" inkscape:document-units="mm"
showgrid="false" showgrid="false"
inkscape:zoom="1.4734708" inkscape:zoom="1.4734708"
inkscape:cx="450.97602" inkscape:cx="408.21983"
inkscape:cy="272.14655" inkscape:cy="319.65343"
inkscape:window-width="1920" inkscape:window-width="1920"
inkscape:window-height="999" inkscape:window-height="999"
inkscape:window-x="0" inkscape:window-x="0"
@ -270,10 +270,10 @@
id="layer1" id="layer1"
sodipodi:insensitive="true"> sodipodi:insensitive="true">
<rect <rect
style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000" style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288" id="rect288"
width="209.84705" width="262.58151"
height="104.42732" height="156.82782"
x="0.77790999" x="0.77790999"
y="0.93738818" /> y="0.93738818" />
</g> </g>
@ -283,24 +283,24 @@
inkscape:label="Layer 2"> inkscape:label="Layer 2">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442" y="99.307442"
id="text951"><tspan id="text951"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan949" id="tspan949"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="99.307442">$\{\}$</tspan></text> y="99.307442">$\{\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893" y="13.151893"
id="text1005"><tspan id="text1005"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1003" id="tspan1003"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="164.56372" x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text> y="13.151893">$\{a,b,c\}$</tspan></text>
<g <g
@ -308,35 +308,35 @@
transform="translate(51.996784,3.5774043)"> transform="translate(51.996784,3.5774043)">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698" y="67.008698"
id="text1009"><tspan id="text1009"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007" id="tspan1007"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="67.008698">$\{a\}$</tspan></text> y="67.008698">$\{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166" y="67.017166"
id="text1009-3"><tspan id="text1009-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-6" id="tspan1007-6"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="67.017166">$\{b\}$</tspan></text> y="67.017166">$\{b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698" y="67.008698"
id="text1009-7"><tspan id="text1009-7"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1007-5" id="tspan1007-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="67.008698">$\{c\}$</tspan></text> y="67.008698">$\{c\}$</tspan></text>
</g> </g>
@ -346,35 +346,35 @@
style="fill:#000000"> style="fill:#000000">
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526" y="40.841526"
id="text1117"><tspan id="text1117"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115" id="tspan1115"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="112.90984" x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text> y="40.841526">$\{a,c\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526" y="40.841526"
id="text1117-3"><tspan id="text1117-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-5" id="tspan1115-5"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="49.27084" x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text> y="40.841526">$\{a,b\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526" y="40.841526"
id="text1117-6"><tspan id="text1117-6"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan1115-2" id="tspan1115-2"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="176.20593" x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text> y="40.841526">$\{b,c\}$</tspan></text>
</g> </g>
@ -433,20 +433,14 @@
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663" id="path3663"
cx="117.08417" cx="147.35568"
cy="38.792969" cy="95.24971"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3" id="path3663-3"
cx="123.57843" cx="176.97627"
cy="39.100433" cy="68.155472"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="119.58919"
cy="67.645035"
r="2.7302806" /> r="2.7302806" />
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
@ -468,13 +462,13 @@
r="2.7302806" /> r="2.7302806" />
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217" y="13.702217"
id="text3707"><tspan id="text3707"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3705" id="tspan3705"
style="stroke-width:0.264583;fill:#000000" style="fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text> y="13.702217">$write(\{a\})$:</tspan></text>
<text <text
@ -490,48 +484,26 @@
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087" y="33.02087"
id="text3750-3"><tspan id="text3750-3"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-2" id="tspan3748-2"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text> y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523" y="41.972523"
id="text3750-0"><tspan id="text3750-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6" id="tspan3748-6"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="41.972523">$\sqsupseteq \{a\}$</tspan></text> y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549"
id="text4280"><tspan
sodipodi:role="line"
id="tspan4278"
style="fill:#000000;stroke-width:0.264583"
x="14.395845"
y="52.022549">return OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="14.395845"
y="102.48464"
id="text4280-8"><tspan
sodipodi:role="line"
id="tspan4278-8"
style="fill:#000000;stroke-width:0.264583"
x="14.395845"
y="102.48464">return OK</tspan></text>
<circle <circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000" style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4" id="path3663-1-4"
@ -561,6 +533,17 @@
style="fill:#000000;stroke-width:0.264583" style="fill:#000000;stroke-width:0.264583"
x="6.9525447" x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text> y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403"
id="text3707-5-3"><tspan
sodipodi:role="line"
id="tspan3705-4-6"
style="fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403">$read()$:</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
@ -585,14 +568,37 @@
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text> y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text <text
xml:space="preserve" xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583" style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969" y="93.54969"
id="text3750-0-0"><tspan id="text3750-0-0"><tspan
sodipodi:role="line" sodipodi:role="line"
id="tspan3748-6-7" id="tspan3748-6-7"
style="fill:#000000;stroke-width:0.264583" style="fill:#999999;stroke-width:0.264583"
x="23.457415" x="23.457415"
y="93.54969">$\sqsupseteq \{b\} \to$ OK</tspan></text> y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0"
cx="67.201363"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125"
id="text3750-9"><tspan
sodipodi:role="line"
id="tspan3748-3"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125">$\to \{a\}$</tspan></text>
</g> </g>
</svg> </svg>
Side by side Swipe Overlay

Before

Width:  |  Height:  |  Size: 21 KiB

After

Width:  |  Height:  |  Size: 21 KiB

632
doc/talks/2023-01-18-tocatta/assets/latticeB_6.svg Normal file
View file

@ -0,0 +1,632 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
width="1000"
height="600"
viewBox="0 0 264.58333 158.75"
version="1.1"
id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeB_6.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg"
xmlns:svg="http://www.w3.org/2000/svg">
<sodipodi:namedview
id="namedview7"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:showpageshadow="2"
inkscape:pageopacity="0.0"
inkscape:pagecheckerboard="0"
inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm"
showgrid="false"
inkscape:zoom="1.4734708"
inkscape:cx="408.21983"
inkscape:cy="319.65343"
inkscape:window-width="1920"
inkscape:window-height="999"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="1"
inkscape:current-layer="layer2" />
<defs
id="defs2">
<marker
style="overflow:visible"
id="Arrow2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1-4"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8-7" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2-8"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6-4" />
</marker>
</defs>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
sodipodi:insensitive="true">
<rect
style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288"
width="262.58151"
height="156.82782"
x="0.77790999"
y="0.93738818" />
</g>
<g
inkscape:groupmode="layer"
id="layer2"
inkscape:label="Layer 2">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442"
id="text951"><tspan
sodipodi:role="line"
id="tspan949"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442">$\{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893"
id="text1005"><tspan
sodipodi:role="line"
id="tspan1003"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text>
<g
id="g1175"
transform="translate(51.996784,3.5774043)">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698"
id="text1009"><tspan
sodipodi:role="line"
id="tspan1007"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698">$\{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166"
id="text1009-3"><tspan
sodipodi:role="line"
id="tspan1007-6"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166">$\{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698"
id="text1009-7"><tspan
sodipodi:role="line"
id="tspan1007-5"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698">$\{c\}$</tspan></text>
</g>
<g
id="g1183"
transform="translate(51.996784,1.0317046)"
style="fill:#000000">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526"
id="text1117"><tspan
sodipodi:role="line"
id="tspan1115"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526"
id="text1117-3"><tspan
sodipodi:role="line"
id="tspan1115-5"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526"
id="text1117-6"><tspan
sodipodi:role="line"
id="tspan1115-2"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text>
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
d="M 153.33622,90.367682 118.34198,73.428915"
id="path1300" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
d="M 177.46016,90.367682 212.4544,73.428915"
id="path1300-2" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
d="M 153.33622,61.655656 118.34198,44.716889"
id="path1300-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
d="M 177.46016,61.655656 212.4544,44.716889"
id="path1300-2-6" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
d="M 118.34198,61.655656 153.33622,44.716889"
id="path1300-0-7" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
d="M 212.4544,61.655656 177.46016,44.716889"
id="path1300-2-6-9" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
d="M 118.34198,34.227412 153.33622,17.288645"
id="path1300-0-7-5" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
d="M 212.4544,34.227412 177.46016,17.288645"
id="path1300-2-6-9-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6-9"
sodipodi:nodetypes="cc" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663"
cx="147.35568"
cy="95.24971"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3"
cx="176.97627"
cy="68.155472"
r="2.7302806" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1"
cx="18.004833"
cy="39.402473"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0"
cx="18.004833"
cy="30.371933"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6"
cx="18.004833"
cy="21.341394"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217"
id="text3707"><tspan
sodipodi:role="line"
id="tspan3705"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637"
id="text3750"><tspan
sodipodi:role="line"
id="tspan3748"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087"
id="text3750-3"><tspan
sodipodi:role="line"
id="tspan3748-2"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523"
id="text3750-0"><tspan
sodipodi:role="line"
id="tspan3748-6"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4"
cx="18.004833"
cy="90.979645"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-5"
cx="18.004833"
cy="81.949104"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-2"
cx="18.004833"
cy="72.918564"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381"
id="text3707-5"><tspan
sodipodi:role="line"
id="tspan3705-4"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403"
id="text3707-5-3"><tspan
sodipodi:role="line"
id="tspan3705-4-6"
style="fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-4"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038"
id="text3750-3-4"><tspan
sodipodi:role="line"
id="tspan3748-2-3"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969"
id="text3750-0-0"><tspan
sodipodi:role="line"
id="tspan3748-6-7"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0"
cx="67.201363"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125"
id="text3750-9"><tspan
sodipodi:role="line"
id="tspan3748-3"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125">$\to \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="text4280-6"><tspan
sodipodi:role="line"
style="fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="tspan2630">return $\{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-7"
cx="67.201363"
cy="133.94179"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073"
id="text3750-3-6"><tspan
sodipodi:role="line"
id="tspan3748-2-0"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073">$\to \{\}$</tspan></text>
</g>
</svg>
Side by side

After

Width:  |  Height:  |  Size: 22 KiB

654
doc/talks/2023-01-18-tocatta/assets/latticeB_7.svg Normal file
View file

@ -0,0 +1,654 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
width="1000"
height="600"
viewBox="0 0 264.58333 158.75"
version="1.1"
id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeB_7.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg"
xmlns:svg="http://www.w3.org/2000/svg">
<sodipodi:namedview
id="namedview7"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:showpageshadow="2"
inkscape:pageopacity="0.0"
inkscape:pagecheckerboard="0"
inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm"
showgrid="false"
inkscape:zoom="1.4734708"
inkscape:cx="553.45515"
inkscape:cy="346.80022"
inkscape:window-width="1920"
inkscape:window-height="999"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="1"
inkscape:current-layer="layer2" />
<defs
id="defs2">
<marker
style="overflow:visible"
id="Arrow2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1-4"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8-7" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2-8"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6-4" />
</marker>
</defs>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
sodipodi:insensitive="true">
<rect
style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288"
width="262.58151"
height="156.82782"
x="0.77790999"
y="0.93738818" />
</g>
<g
inkscape:groupmode="layer"
id="layer2"
inkscape:label="Layer 2">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442"
id="text951"><tspan
sodipodi:role="line"
id="tspan949"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442">$\{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893"
id="text1005"><tspan
sodipodi:role="line"
id="tspan1003"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text>
<g
id="g1175"
transform="translate(51.996784,3.5774043)">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698"
id="text1009"><tspan
sodipodi:role="line"
id="tspan1007"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698">$\{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166"
id="text1009-3"><tspan
sodipodi:role="line"
id="tspan1007-6"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166">$\{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698"
id="text1009-7"><tspan
sodipodi:role="line"
id="tspan1007-5"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698">$\{c\}$</tspan></text>
</g>
<g
id="g1183"
transform="translate(51.996784,1.0317046)"
style="fill:#000000">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526"
id="text1117"><tspan
sodipodi:role="line"
id="tspan1115"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526"
id="text1117-3"><tspan
sodipodi:role="line"
id="tspan1115-5"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526"
id="text1117-6"><tspan
sodipodi:role="line"
id="tspan1115-2"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text>
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
d="M 153.33622,90.367682 118.34198,73.428915"
id="path1300" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
d="M 177.46016,90.367682 212.4544,73.428915"
id="path1300-2" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
d="M 153.33622,61.655656 118.34198,44.716889"
id="path1300-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
d="M 177.46016,61.655656 212.4544,44.716889"
id="path1300-2-6" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
d="M 118.34198,61.655656 153.33622,44.716889"
id="path1300-0-7" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
d="M 212.4544,61.655656 177.46016,44.716889"
id="path1300-2-6-9" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
d="M 118.34198,34.227412 153.33622,17.288645"
id="path1300-0-7-5" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
d="M 212.4544,34.227412 177.46016,17.288645"
id="path1300-2-6-9-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6-9"
sodipodi:nodetypes="cc" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663"
cx="147.35568"
cy="95.24971"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3"
cx="176.97627"
cy="68.155472"
r="2.7302806" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1"
cx="18.004833"
cy="39.402473"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0"
cx="18.004833"
cy="30.371933"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6"
cx="18.004833"
cy="21.341394"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217"
id="text3707"><tspan
sodipodi:role="line"
id="tspan3705"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637"
id="text3750"><tspan
sodipodi:role="line"
id="tspan3748"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087"
id="text3750-3"><tspan
sodipodi:role="line"
id="tspan3748-2"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523"
id="text3750-0"><tspan
sodipodi:role="line"
id="tspan3748-6"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4"
cx="18.004833"
cy="90.979645"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-5"
cx="18.004833"
cy="81.949104"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-2"
cx="18.004833"
cy="72.918564"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381"
id="text3707-5"><tspan
sodipodi:role="line"
id="tspan3705-4"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403"
id="text3707-5-3"><tspan
sodipodi:role="line"
id="tspan3705-4-6"
style="fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-4"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038"
id="text3750-3-4"><tspan
sodipodi:role="line"
id="tspan3748-2-3"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969"
id="text3750-0-0"><tspan
sodipodi:role="line"
id="tspan3748-6-7"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0"
cx="67.201363"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125"
id="text3750-9"><tspan
sodipodi:role="line"
id="tspan3748-3"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125">$\to \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="text4280-6"><tspan
sodipodi:role="line"
style="fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="tspan2630">return $\{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-7"
cx="67.201363"
cy="133.94179"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073"
id="text3750-3-6"><tspan
sodipodi:role="line"
id="tspan3748-2-0"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073">$\to \{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403"
id="text3707-5-3-7"><tspan
sodipodi:role="line"
id="tspan3705-4-6-5"
style="fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
x="134.97845"
y="132.58472"
id="text3899"><tspan
sodipodi:role="line"
id="tspan3897"
style="stroke-width:0.264583"
x="134.97845"
y="132.58472">;</tspan></text>
</g>
</svg>
Side by side

After

Width:  |  Height:  |  Size: 23 KiB

671
doc/talks/2023-01-18-tocatta/assets/latticeB_8.svg Normal file
View file

@ -0,0 +1,671 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
width="1000"
height="600"
viewBox="0 0 264.58333 158.75"
version="1.1"
id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeB_8.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg"
xmlns:svg="http://www.w3.org/2000/svg">
<sodipodi:namedview
id="namedview7"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:showpageshadow="2"
inkscape:pageopacity="0.0"
inkscape:pagecheckerboard="0"
inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm"
showgrid="false"
inkscape:zoom="1.4734708"
inkscape:cx="448.94001"
inkscape:cy="322.36811"
inkscape:window-width="1920"
inkscape:window-height="999"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="1"
inkscape:current-layer="layer2" />
<defs
id="defs2">
<marker
style="overflow:visible"
id="Arrow2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1-4"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8-7" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2-8"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6-4" />
</marker>
</defs>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
sodipodi:insensitive="true">
<rect
style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288"
width="262.58151"
height="156.82782"
x="0.77790999"
y="0.93738818" />
</g>
<g
inkscape:groupmode="layer"
id="layer2"
inkscape:label="Layer 2">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442"
id="text951"><tspan
sodipodi:role="line"
id="tspan949"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442">$\{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893"
id="text1005"><tspan
sodipodi:role="line"
id="tspan1003"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text>
<g
id="g1175"
transform="translate(51.996784,3.5774043)">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698"
id="text1009"><tspan
sodipodi:role="line"
id="tspan1007"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698">$\{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166"
id="text1009-3"><tspan
sodipodi:role="line"
id="tspan1007-6"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166">$\{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698"
id="text1009-7"><tspan
sodipodi:role="line"
id="tspan1007-5"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698">$\{c\}$</tspan></text>
</g>
<g
id="g1183"
transform="translate(51.996784,1.0317046)"
style="fill:#000000">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526"
id="text1117"><tspan
sodipodi:role="line"
id="tspan1115"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526"
id="text1117-3"><tspan
sodipodi:role="line"
id="tspan1115-5"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526"
id="text1117-6"><tspan
sodipodi:role="line"
id="tspan1115-2"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text>
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
d="M 153.33622,90.367682 118.34198,73.428915"
id="path1300" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
d="M 177.46016,90.367682 212.4544,73.428915"
id="path1300-2" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
d="M 153.33622,61.655656 118.34198,44.716889"
id="path1300-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
d="M 177.46016,61.655656 212.4544,44.716889"
id="path1300-2-6" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
d="M 118.34198,61.655656 153.33622,44.716889"
id="path1300-0-7" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
d="M 212.4544,61.655656 177.46016,44.716889"
id="path1300-2-6-9" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
d="M 118.34198,34.227412 153.33622,17.288645"
id="path1300-0-7-5" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
d="M 212.4544,34.227412 177.46016,17.288645"
id="path1300-2-6-9-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6-9"
sodipodi:nodetypes="cc" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663"
cx="147.35568"
cy="95.24971"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3"
cx="176.97627"
cy="68.155472"
r="2.7302806" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1"
cx="18.004833"
cy="39.402473"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0"
cx="18.004833"
cy="30.371933"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6"
cx="18.004833"
cy="21.341394"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217"
id="text3707"><tspan
sodipodi:role="line"
id="tspan3705"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637"
id="text3750"><tspan
sodipodi:role="line"
id="tspan3748"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087"
id="text3750-3"><tspan
sodipodi:role="line"
id="tspan3748-2"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523"
id="text3750-0"><tspan
sodipodi:role="line"
id="tspan3748-6"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4"
cx="18.004833"
cy="90.979645"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-5"
cx="18.004833"
cy="81.949104"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-2"
cx="18.004833"
cy="72.918564"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381"
id="text3707-5"><tspan
sodipodi:role="line"
id="tspan3705-4"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403"
id="text3707-5-3"><tspan
sodipodi:role="line"
id="tspan3705-4-6"
style="fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-4"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038"
id="text3750-3-4"><tspan
sodipodi:role="line"
id="tspan3748-2-3"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969"
id="text3750-0-0"><tspan
sodipodi:role="line"
id="tspan3748-6-7"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0"
cx="67.201363"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125"
id="text3750-9"><tspan
sodipodi:role="line"
id="tspan3748-3"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125">$\to \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="text4280-6"><tspan
sodipodi:role="line"
style="fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="tspan2630">return $\{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-7"
cx="67.201363"
cy="133.94179"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073"
id="text3750-3-6"><tspan
sodipodi:role="line"
id="tspan3748-2-0"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073">$\to \{\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0-6"
cx="174.36296"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="179.81555"
y="127.6125"
id="text3750-9-1"><tspan
sodipodi:role="line"
id="tspan3748-3-8"
style="fill:#000000;stroke-width:0.264583"
x="179.81555"
y="127.6125">$\to \{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403"
id="text3707-5-3-7"><tspan
sodipodi:role="line"
id="tspan3705-4-6-5"
style="fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
x="134.97845"
y="132.58472"
id="text3899"><tspan
sodipodi:role="line"
id="tspan3897"
style="stroke-width:0.264583"
x="134.97845"
y="132.58472">;</tspan></text>
</g>
</svg>
Side by side

After

Width:  |  Height:  |  Size: 24 KiB

699
doc/talks/2023-01-18-tocatta/assets/latticeB_9.svg Normal file
View file

@ -0,0 +1,699 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
width="1000"
height="600"
viewBox="0 0 264.58333 158.75"
version="1.1"
id="svg5"
inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
sodipodi:docname="latticeB_9.svg"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns="http://www.w3.org/2000/svg"
xmlns:svg="http://www.w3.org/2000/svg">
<sodipodi:namedview
id="namedview7"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:showpageshadow="2"
inkscape:pageopacity="0.0"
inkscape:pagecheckerboard="0"
inkscape:deskcolor="#d1d1d1"
inkscape:document-units="mm"
showgrid="false"
inkscape:zoom="1.0419012"
inkscape:cx="664.65036"
inkscape:cy="366.63745"
inkscape:window-width="1920"
inkscape:window-height="999"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="1"
inkscape:current-layer="layer2" />
<defs
id="defs2">
<marker
style="overflow:visible"
id="Arrow2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-2"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-8" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-75-7-1"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-9-3-2" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-93-1-4"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-6-8-7" />
</marker>
<marker
style="overflow:visible"
id="Arrow2-9-7-2-8"
refX="0"
refY="0"
orient="auto-start-reverse"
inkscape:stockid="Arrow2"
markerWidth="7.6999998"
markerHeight="5.5999999"
viewBox="0 0 7.7 5.6"
inkscape:isstock="true"
inkscape:collect="always"
preserveAspectRatio="xMidYMid">
<path
transform="scale(0.7)"
d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
style="fill:context-stroke;fill-rule:evenodd;stroke:none"
id="arrow2L-1-0-6-4" />
</marker>
</defs>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
sodipodi:insensitive="true">
<rect
style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
id="rect288"
width="262.58151"
height="156.82782"
x="0.77790999"
y="0.93738818" />
</g>
<g
inkscape:groupmode="layer"
id="layer2"
inkscape:label="Layer 2">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442"
id="text951"><tspan
sodipodi:role="line"
id="tspan949"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="99.307442">$\{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893"
id="text1005"><tspan
sodipodi:role="line"
id="tspan1003"
style="fill:#000000;stroke-width:0.264583"
x="164.56372"
y="13.151893">$\{a,b,c\}$</tspan></text>
<g
id="g1175"
transform="translate(51.996784,3.5774043)">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698"
id="text1009"><tspan
sodipodi:role="line"
id="tspan1007"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="67.008698">$\{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166"
id="text1009-3"><tspan
sodipodi:role="line"
id="tspan1007-6"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="67.017166">$\{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698"
id="text1009-7"><tspan
sodipodi:role="line"
id="tspan1007-5"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="67.008698">$\{c\}$</tspan></text>
</g>
<g
id="g1183"
transform="translate(51.996784,1.0317046)"
style="fill:#000000">
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526"
id="text1117"><tspan
sodipodi:role="line"
id="tspan1115"
style="fill:#000000;stroke-width:0.264583"
x="112.90984"
y="40.841526">$\{a,c\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526"
id="text1117-3"><tspan
sodipodi:role="line"
id="tspan1115-5"
style="fill:#000000;stroke-width:0.264583"
x="49.27084"
y="40.841526">$\{a,b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526"
id="text1117-6"><tspan
sodipodi:role="line"
id="tspan1115-2"
style="fill:#000000;stroke-width:0.264583"
x="176.20593"
y="40.841526">$\{b,c\}$</tspan></text>
</g>
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
d="M 153.33622,90.367682 118.34198,73.428915"
id="path1300" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
d="M 177.46016,90.367682 212.4544,73.428915"
id="path1300-2" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
d="M 153.33622,61.655656 118.34198,44.716889"
id="path1300-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
d="M 177.46016,61.655656 212.4544,44.716889"
id="path1300-2-6" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
d="M 118.34198,61.655656 153.33622,44.716889"
id="path1300-0-7" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
d="M 212.4544,61.655656 177.46016,44.716889"
id="path1300-2-6-9" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
d="M 118.34198,34.227412 153.33622,17.288645"
id="path1300-0-7-5" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
d="M 212.4544,34.227412 177.46016,17.288645"
id="path1300-2-6-9-0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-9"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
id="path1300-2-2-6-9"
sodipodi:nodetypes="cc" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663"
cx="147.35568"
cy="95.24971"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3"
cx="176.97627"
cy="68.155472"
r="2.7302806" />
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1"
cx="18.004833"
cy="39.402473"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0"
cx="18.004833"
cy="30.371933"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6"
cx="18.004833"
cy="21.341394"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217"
id="text3707"><tspan
sodipodi:role="line"
id="tspan3705"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="13.702217">$write(\{a\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637"
id="text3750"><tspan
sodipodi:role="line"
id="tspan3748"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087"
id="text3750-3"><tspan
sodipodi:role="line"
id="tspan3748-2"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523"
id="text3750-0"><tspan
sodipodi:role="line"
id="tspan3748-6"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-1-4"
cx="18.004833"
cy="90.979645"
r="2.7302806" />
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-5"
cx="18.004833"
cy="81.949104"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-2"
cx="18.004833"
cy="72.918564"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381"
id="text3707-5"><tspan
sodipodi:role="line"
id="tspan3705-4"
style="fill:#000000;stroke-width:0.264583"
x="6.9525447"
y="65.279381">$write(\{b\})$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403"
id="text3707-5-3"><tspan
sodipodi:role="line"
id="tspan3705-4-6"
style="fill:#000000;stroke-width:0.264583"
x="59.340172"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804"
id="text3750-7"><tspan
sodipodi:role="line"
id="tspan3748-4"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038"
id="text3750-3-4"><tspan
sodipodi:role="line"
id="tspan3748-2-3"
style="fill:#000000;stroke-width:0.264583"
x="23.457415"
y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969"
id="text3750-0-0"><tspan
sodipodi:role="line"
id="tspan3748-6-7"
style="fill:#999999;stroke-width:0.264583"
x="23.457415"
y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6"
cx="118.63729"
cy="67.630196"
r="2.7302806" />
<circle
style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0"
cx="67.201363"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125"
id="text3750-9"><tspan
sodipodi:role="line"
id="tspan3748-3"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="127.6125">$\to \{a\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="text4280-6"><tspan
sodipodi:role="line"
style="fill:#000000;stroke-width:0.264583"
x="62.764446"
y="146.3129"
id="tspan2630">return $\{a\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-7"
cx="67.201363"
cy="133.94179"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073"
id="text3750-3-6"><tspan
sodipodi:role="line"
id="tspan3748-2-0"
style="fill:#000000;stroke-width:0.264583"
x="72.653946"
y="136.59073">$\to \{\}$</tspan></text>
<circle
style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-6-6-0-6"
cx="174.36296"
cy="124.91125"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="179.81555"
y="127.6125"
id="text3750-9-1"><tspan
sodipodi:role="line"
id="tspan3748-3-8"
style="fill:#000000;stroke-width:0.264583"
x="179.81555"
y="127.6125">$\to \{\}$</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403"
id="text3707-5-3-7"><tspan
sodipodi:role="line"
id="tspan3705-4-6-5"
style="fill:#000000;stroke-width:0.264583"
x="162.7999"
y="118.94403">$read()$:</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
x="134.97845"
y="132.58472"
id="text3899"><tspan
sodipodi:role="line"
id="tspan3897"
style="stroke-width:0.264583"
x="134.97845"
y="132.58472">;</tspan></text>
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="169.92604"
y="146.3129"
id="text4280-6-7"><tspan
sodipodi:role="line"
style="fill:#000000;stroke-width:0.264583"
x="169.92604"
y="146.3129"
id="tspan2630-9">return $\{b\}$</tspan></text>
<circle
style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
id="path3663-3-0-7-2"
cx="174.36296"
cy="133.94179"
r="2.7302806" />
<text
xml:space="preserve"
style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
x="179.81555"
y="136.59073"
id="text3750-3-6-0"><tspan
sodipodi:role="line"
id="tspan3748-2-0-2"
style="fill:#000000;stroke-width:0.264583"
x="179.81555"
y="136.59073">$\to \{b\}$</tspan></text>
</g>
</svg>
Side by side

After

Width:  |  Height:  |  Size: 25 KiB

BIN
doc/talks/2023-01-18-tocatta/talk.pdf
View file

Binary file not shown.

66
doc/talks/2023-01-18-tocatta/talk.tex
View file

@ -49,7 +49,7 @@
\title{Garage} \title{Garage}
\subtitle{a lightweight and robust geo-distributed data storage system} \subtitle{a lightweight and robust geo-distributed data storage system}
\author{Deuxfleurs Association} \author{Alex Auvolat, Deuxfleurs Association}
\date{Inria, 2023-01-18} \date{Inria, 2023-01-18}
\begin{document} \begin{document}
@ -59,7 +59,7 @@
\includegraphics[width=.3\linewidth]{../../sticker/Garage.pdf} \includegraphics[width=.3\linewidth]{../../sticker/Garage.pdf}
\vspace{1em} \vspace{1em}
{\large\bf Deuxfleurs Association} {\large\bf Alex Auvolat, Deuxfleurs Association}
\vspace{1em} \vspace{1em}
\url{https://garagehq.deuxfleurs.fr/} \url{https://garagehq.deuxfleurs.fr/}
@ -68,7 +68,7 @@
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{Who we are} \frametitle{Who I am}
\begin{columns}[t] \begin{columns}[t]
\begin{column}{.2\textwidth} \begin{column}{.2\textwidth}
\centering \centering
@ -82,21 +82,6 @@
~ ~
\end{column} \end{column}
\end{columns} \end{columns}
\vspace{1em}
\begin{columns}[t]
\begin{column}{.2\textwidth}
~
\end{column}
\begin{column}{.6\textwidth}
\textbf{Quentin Dufour}\\
PhD; co-founder of Deuxfleurs
\end{column}
\begin{column}{.2\textwidth}
\centering
\adjincludegraphics[width=.5\linewidth, valign=t]{assets/quentin.jpg}
\end{column}
\end{columns}
\vspace{2em} \vspace{2em}
\begin{columns}[t] \begin{columns}[t]
@ -546,7 +531,7 @@
\vspace{1em} \vspace{1em}
\textbf{CRDTs only}\\(conflict-free replicated data types) \textbf{Limited objects such as CRDTs}\\(conflict-free replicated data types)
\vspace{1em} \vspace{1em}
Part of the complexity is \textbf{reported to the consumer of the API}\\~ Part of the complexity is \textbf{reported to the consumer of the API}\\~
@ -647,6 +632,13 @@
\end{itemize} \end{itemize}
\end{frame} \end{frame}
\begin{frame}
\frametitle{Performance gains in practice}
\begin{center}
\includegraphics[width=.8\linewidth]{assets/endpoint-latency-dc.png}
\end{center}
\end{frame}
\begin{frame} \begin{frame}
\frametitle{What can we implement without consensus?} \frametitle{What can we implement without consensus?}
\begin{itemize} \begin{itemize}
@ -664,7 +656,7 @@
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{Understanding CRDTs and quorums} \frametitle{CRDTs and quorums: read-after-write consistency}
\begin{figure} \begin{figure}
\centering \centering
\def\svgwidth{.8\textwidth} \def\svgwidth{.8\textwidth}
@ -676,15 +668,11 @@
\only<6>{\import{assets/}{lattice6.pdf_tex}}% \only<6>{\import{assets/}{lattice6.pdf_tex}}%
\only<7>{\import{assets/}{lattice7.pdf_tex}}% \only<7>{\import{assets/}{lattice7.pdf_tex}}%
\only<8>{\import{assets/}{lattice8.pdf_tex}}% \only<8>{\import{assets/}{lattice8.pdf_tex}}%
\only<9>{\import{assets/}{lattice9.pdf_tex}}%
\only<10>{\import{assets/}{latticeA.pdf_tex}}%
\only<11>{\import{assets/}{latticeB.pdf_tex}}%
\only<12>{\import{assets/}{latticeC.pdf_tex}}%
\end{figure} \end{figure}
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{Read-after-write consistency:} \frametitle{CRDTs and quorums: read-after-write consistency}
\textbf{Property:} If node $A$ did an operation $write(x)$ and received an OK response,\\ \textbf{Property:} If node $A$ did an operation $write(x)$ and received an OK response,\\
\hspace{2cm} and node $B$ starts an operation $read()$ after $A$ received OK,\\ \hspace{2cm} and node $B$ starts an operation $read()$ after $A$ received OK,\\
\hspace{2cm} then $B$ will read a value $x' \sqsupseteq x$. \hspace{2cm} then $B$ will read a value $x' \sqsupseteq x$.
@ -718,7 +706,25 @@
\end{frame} \end{frame}
\begin{frame} \begin{frame}
\frametitle{Monotonical read consistency:} \frametitle{CRDTs and quorums: monotonic-reads consistency}
\begin{figure}
\centering
\def\svgwidth{.8\textwidth}
\only<1>{\import{assets/}{latticeB_1.pdf_tex}}%
\only<2>{\import{assets/}{latticeB_2.pdf_tex}}%
\only<3>{\import{assets/}{latticeB_3.pdf_tex}}%
\only<4>{\import{assets/}{latticeB_4.pdf_tex}}%
\only<5>{\import{assets/}{latticeB_5.pdf_tex}}%
\only<6>{\import{assets/}{latticeB_6.pdf_tex}}%
\only<7>{\import{assets/}{latticeB_7.pdf_tex}}%
\only<8>{\import{assets/}{latticeB_8.pdf_tex}}%
\only<9>{\import{assets/}{latticeB_9.pdf_tex}}%
\only<10>{\import{assets/}{latticeB_10.pdf_tex}}%
\end{figure}
\end{frame}
\begin{frame}
\frametitle{CRDTs and quorums: monotonic-reads consistency}
\textbf{Property:} If node $A$ did an operation $read()$ and received $x$ as a response,\\ \textbf{Property:} If node $A$ did an operation $read()$ and received $x$ as a response,\\
\hspace{2cm} and node $B$ starts an operation $read()$ after $A$ received $x$,\\ \hspace{2cm} and node $B$ starts an operation $read()$ after $A$ received $x$,\\
\hspace{2cm} then $B$ will read a value $x' \sqsupseteq x$. \hspace{2cm} then $B$ will read a value $x' \sqsupseteq x$.
@ -735,14 +741,8 @@
\end{enumerate} \end{enumerate}
\vspace{1em} \vspace{1em}
This makes reads slower in some cases, and is \textbf{not implemented in Garage}.
\end{frame}
\begin{frame} This makes reads slower in some cases, and is \textbf{not implemented in Garage}.
\frametitle{Performance gains in practice}
\begin{center}
\includegraphics[width=.8\linewidth]{assets/endpoint-latency-dc.png}
\end{center}
\end{frame} \end{frame}
\begin{frame} \begin{frame}