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Yann Esposito 2012-12-03 17:15:40 +01:00
parent 9af0e64001
commit e5d455c2fd
23 changed files with 173 additions and 49 deletions
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61
categories.html
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@ -43,7 +43,7 @@
}
</script>
</head>
<body id="body" class="deck-container" style="width: 99%">
<body id="body" class="deck-container">
<div style="display:none">
\(\newcommand{\F}{\mathbf{F}}\)
@ -89,7 +89,7 @@
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>General overview</li>
<li class="yellow">General overview</li>
<li>Math <span class="and">&amp;</span> Abstraction</li>
<li>Programming <span class="and">&amp;</span> Abstraction</li>
<li>Categories <span class="and">&amp;</span> Abstraction</li>
@ -141,6 +141,21 @@
</ul>
</section>
<section class="slide">
<h2>Plan</h2>
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>General overview</li>
<li class="yellow">Math <span class="and">&amp;</span> Abstraction</li>
<li>Programming <span class="and">&amp;</span> Abstraction</li>
<li>Categories <span class="and">&amp;</span> Abstraction</li>
</ul>
</li>
<li>What?</li>
<li>How?</li>
</ul>
</section>
<section class="slide">
<h2>Math Abstraction</h2>
<p>A common concept you see in multiple instances.</p>
<div>
@ -178,6 +193,7 @@
</section>
<section class="slide">
<h2>Numbers ⇒ Sets</h2>
<blockquote><strong>Formalism</strong>: A <em>theory</em> is some strings (the axioms), some string manipulation rules, and all strings created by applying these rules to the axioms.</blockquote>
<table>
<tr>
<th>Numbers</th>
@ -250,16 +266,33 @@
</section>
<section class="slide">
<h2>Category Theory</h2>
<p>Categories package entire mathematical theories.</p>
<p>Categories package entire mathematical theories.<br/>
Theory=(Axioms,<span style="visibility:hidden">Strings</span>Rules,<span style="visibility:hidden">Stri</span>Theorems)<br/>
<span style="visibility:hidden">Theory=</span>(Strings,Strings → Strings, Strings)
</p>
<ul>
<li>Topology</li>
<li>Quantum Physics</li>
<li>Logic</li>
<li><b>Programming</b></li>
<li><b>Computer Science</b></li>
</ul>
<p>Recent field: <b>1942–45</b>, Samuel Eilenberg <span class="and">&amp;</span> Saunders Mac Lane
</section>
<section class="slide">
<h2>Plan</h2>
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>General overview</li>
<li>Math <span class="and">&amp;</span> Abstraction</li>
<li class="yellow">Programming <span class="and">&amp;</span> Abstraction</li>
<li>Categories <span class="and">&amp;</span> Abstraction</li>
</ul>
</li>
<li>What?</li>
<li>How?</li>
</ul>
<p><span style="visibility:hidden"><span class="and">&amp;</span></span> More <strong>general</strong>: more things are Categories.<br/>
<span class="and">&amp;</span> More <strong>precise</strong>: better distinction between concepts.</p>
<p>Young field: <b>1942–45</b>, Samuel Eilenberg <span class="and">&amp;</span> Saunders Mac Lane
</section>
<section class="slide">
<h2>Programming <span class="and">&amp;</span> Abstraction</h2>
@ -268,12 +301,14 @@
<ul>
<li>Encouraged by imperative paradigms.
</li><li>Actions <span class="and">&amp;</span> mutable objects.
</li><li>Time is <em>very</em> important: ex. linked list push
</li><li>Time is <em>very</em> important<sup>*</sup>.
</li><li>Synchronizing things is a challenge.
</li>
</ul>
<p class="yellow">Natural Abstractions: pointers, variables, loop, Objects, Classes...</p>
<p>Representation: a data structure changing other time.</p>
<p class="small">*: Push an element to a linked list for example</p>
</section>
<section class="slide">
<h2>Untyped Pure Programming</h2>
@ -281,7 +316,7 @@
<ul><li> Time is irrelevant by default.
</li><li> Mostly static constructions like pipes.
</li><li> All pipes can be plugged ⇒ all error at runtime
<ul><li> (+ ("foo" 27) 32)
<ul><li> (+ 37 "foo")
</li><li> Y = λf.(λx.f (x x)) (λx.f (x x))
</li><li> Y g = g (Y g)
</li></ul>
@ -290,6 +325,14 @@
<p class="yellow">Natural abstraction: higher level functions <span class="and">&amp;</span> equations</p>
</section>
<section class="slide">
<h2>Untyped Pure Programming</h2>
<p style="text-align:center"><code>(+ 42 "foo")</code></p>
<img src="categories/img/mp/pipe.png" />
</section>
<section class="slide">
<h2>Typed Pure Programming</h2>
<ul><li>Add shapes to pipes:
<ul><li> <code class="red">4 + ["foo",27]</code> forbidden

2
categories/10_Introduction/020_Plan.html
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@ -2,7 +2,7 @@
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>General overview</li>
<li class="yellow">General overview</li>
<li>Math &amp; Abstraction</li>
<li>Programming &amp; Abstraction</li>
<li>Categories &amp; Abstraction</li>

13
categories/10_Introduction/060_Plan.html Normal file
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@ -0,0 +1,13 @@
<h2>Plan</h2>
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>General overview</li>
<li class="yellow">Math &amp; Abstraction</li>
<li>Programming &amp; Abstraction</li>
<li>Categories &amp; Abstraction</li>
</ul>
</li>
<li>What?</li>
<li>How?</li>
</ul>

0
categories/10_Introduction/060_Abstraction.html → categories/10_Introduction/070_Math_Abstraction.html
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0
categories/10_Introduction/070_Generalization.html → categories/10_Introduction/080_Generalization.html
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1
categories/10_Introduction/080_Numbers_Sets.html → categories/10_Introduction/090_Numbers_Sets.html
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@ -1,4 +1,5 @@
<h2>Numbers ⇒ Sets</h2>
<blockquote><strong>Formalism</strong>: A <em>theory</em> is some strings (the axioms), some string manipulation rules, and all strings created by applying these rules to the axioms.</blockquote>
<table>
<tr>
<th>Numbers</th>

11
categories/10_Introduction/100_Category_Theory.html
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@ -1,11 +0,0 @@
<h2>Category Theory</h2>
<p>Categories package entire mathematical theories.</p>
<ul>
<li>Topology</li>
<li>Quantum Physics</li>
<li>Logic</li>
<li><b>Programming</b></li>
</ul>
<p><span style="visibility:hidden">&amp;</span> More <strong>general</strong>: more things are Categories.<br/>
&amp; More <strong>precise</strong>: better distinction between concepts.</p>
<p>Young field: <b>1942–45</b>, Samuel Eilenberg &amp; Saunders Mac Lane

0
categories/10_Introduction/090_Sets_Categories.html → categories/10_Introduction/100_Sets_Categories.html
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13
categories/10_Introduction/110_Category_Theory.html Normal file
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@ -0,0 +1,13 @@
<h2>Category Theory</h2>
<p>Categories package entire mathematical theories.<br/>
Theory=(Axioms,<span style="visibility:hidden">Strings</span>Rules,<span style="visibility:hidden">Stri</span>Theorems)<br/>
<span style="visibility:hidden">Theory=</span>(Strings,Strings → Strings, Strings)
</p>
<ul>
<li>Topology</li>
<li>Quantum Physics</li>
<li>Logic</li>
<li><b>Computer Science</b></li>
</ul>
<p>Recent field: <b>1942–45</b>, Samuel Eilenberg &amp; Saunders Mac Lane

13
categories/10_Introduction/120_Plan.html Normal file
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@ -0,0 +1,13 @@
<h2>Plan</h2>
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>General overview</li>
<li>Math &amp; Abstraction</li>
<li class="yellow">Programming &amp; Abstraction</li>
<li>Categories &amp; Abstraction</li>
</ul>
</li>
<li>What?</li>
<li>How?</li>
</ul>

4
categories/10_Introduction/110_Programming_Abstraction.html → categories/10_Introduction/130_Programming_Abstraction.html
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@ -4,9 +4,11 @@
<ul>
<li>Encouraged by imperative paradigms.
</li><li>Actions &amp; mutable objects.
</li><li>Time is <em>very</em> important: ex. linked list push
</li><li>Time is <em>very</em> important<sup>*</sup>.
</li><li>Synchronizing things is a challenge.
</li>
</ul>
<p class="yellow">Natural Abstractions: pointers, variables, loop, Objects, Classes...</p>
<p>Representation: a data structure changing other time.</p>
<p class="small">*: Push an element to a linked list for example</p>

2
categories/10_Introduction/120_Untyped_Pure_Programming.html → categories/10_Introduction/140_Untyped_Pure_Programming.html
View file

@ -3,7 +3,7 @@
<ul><li> Time is irrelevant by default.
</li><li> Mostly static constructions like pipes.
</li><li> All pipes can be plugged ⇒ all error at runtime
<ul><li> (+ ("foo" 27) 32)
<ul><li> (+ 37 "foo")
</li><li> Y = λf.(λx.f (x x)) (λx.f (x x))
</li><li> Y g = g (Y g)
</li></ul>

6
categories/10_Introduction/150_Untyped_Pure_Programming.html Normal file
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@ -0,0 +1,6 @@
<h2>Untyped Pure Programming</h2>
<p style="text-align:center"><code>(+ 42 "foo")</code></p>
<img src="categories/img/mp/pipe.png" />

0
categories/10_Introduction/130_Typed_Pure_Programming.html → categories/10_Introduction/160_Typed_Pure_Programming.html
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0
categories/10_Introduction/140_Polymorphism_mappend.html → categories/10_Introduction/170_Polymorphism_mappend.html
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0
categories/10_Introduction/150_Polymorphism.html → categories/10_Introduction/180_Polymorphism.html
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0
categories/10_Introduction/160_Programming_Paradigms.html → categories/10_Introduction/190_Programming_Paradigms.html
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0
categories/10_Introduction/170_Type_Theory_Categories.html → categories/10_Introduction/200_Type_Theory_Categories.html
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2
categories/head.html
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@ -43,7 +43,7 @@
}
</script>
</head>
<body id="body" class="deck-container" style="width: 99%">
<body id="body" class="deck-container">
<div style="display:none">
\(\newcommand{\F}{\mathbf{F}}\)

54
categories/img/mp/pipe.mp
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@ -19,7 +19,6 @@ vardef hiddenoutmouth(expr pos) =
enddef;
def drawoutmouth(expr pos) =
draw outmouth(pos);
draw hiddenoutmouth(pos) dashed evely;
enddef;
def drawtube(expr pos) =
@ -48,11 +47,8 @@ enddef;
def drawtwotubes(expr posintop,posinbot,posout) =
begingroup;
draw outmouth(posintop);
draw hiddenoutmouth(posintop) dashed evenly;
draw outmouth(posinbot);
draw hiddenoutmouth(posinbot) dashed evenly;
draw outmouth(posout);
draw hiddenoutmouth(posout) dashed evenly;
save intopt,intopb,inbott,inbotb,outt,outb;
pair intopt,intopb,inbott,inbotb,outt,outb;
@ -74,16 +70,18 @@ def drawtwotubeslabel(expr ptop,pbot,pout,l) =
drawtwotubes(ptop,pbot,pout);
save mid;
pair mid;
mid = 1/4ptop+1/4pbot+1/2pout;
mid = 6/30ptop+6/30pbot+18/30pout;
label(l,mid);
endgroup;
enddef;
def drawbegintube (expr pos) =
draw (subpath (4,8) of fullcircle rotated -90) scaled 2u shifted pos shifted (-2u,0);
draw (pos shifted (-2u,u)){right}..{right}(pos shifted (0,u));
draw (pos shifted (-2u,-u)){right}..{right}(pos shifted (0,-u));
def drawlongbegintube (expr pos,len) =
draw (subpath (4,8) of fullcircle rotated -90) scaled 2u shifted pos shifted (-len,0);
draw (pos shifted (-len,u)){right}..{right}(pos shifted (0,u));
draw (pos shifted (-len,-u)){right}..{right}(pos shifted (0,-u));
draw outmouth(pos);
draw hiddenoutmouth(pos) dashed evenly;
enddef;
def drawbegintube (expr pos) =
drawlongbegintube(pos,2u);
enddef;
def drawbegintubelabel(expr pos,l) =
@ -98,9 +96,7 @@ def drawtube(expr pos) =
midin := pos;
midout := pos shifted (gu,0);
draw outmouth(midin);
draw hiddenoutmouth(midin) dashed evenly;
draw outmouth(midout);
draw hiddenoutmouth(midout) dashed evenly;
save topin,topout,botin,botout;
pair topin,topout,botin,botout;
@ -118,14 +114,36 @@ def drawtubelabel(expr pos,l) =
enddef;
pair pos;
pos:=(gu,gu);
drawbegintubelabel(pos shifted (-gu,.5gu),btex $37$ etex);
drawbegintubelabel(pos shifted (-gu,-.5gu),btex $\mathtt{"foo"}$ etex);
pos:=origin;
z0=(2.5gu,.5gu);
z1=(0,-1.5gu);
z2=z1 shifted (3gu,0);
drawbegintubelabel(pos shifted (-.5gu,.5gu),btex $42$ etex);
drawbegintubelabel(pos shifted (-.5gu,-.5gu),btex $\mathtt{"foo"}$ etex);
drawtwotubeslabel(pos shifted (0,.5gu), pos shifted (0,-.5gu), pos shifted (gu,0),btex $+$ etex);
draw inmouth(pos shifted (0,.5gu) );
draw inmouth(pos shifted (0,-.5gu) );
z0=origin;
drawbegintubelabel(z0,btex $37$ etex);
drawbegintubelabel(z0 shifted (-2u,-gu),btex $\mathtt{"foo"}$ etex);
drawoptions(withcolor green);
drawbegintubelabel(z0,btex $42$ etex);
drawtwotubeslabel(z0, z0 shifted (0,-gu), z0 shifted (gu,-0.5gu),btex $+$ etex);
draw inmouth(z0 shifted (0,-gu));
drawtubelabel(z0 shifted (2gu,-.5gu),btex $37+$ etex);
drawoptions(withcolor green);
drawbegintubelabel(z1,btex $\mathtt{"foo"}$ etex);
drawtubelabel(z1,btex $\mathtt{(+\ 42)}$ etex)
drawoptions(withcolor red);
drawlongbegintube(z2,5u);
label(btex $\mathtt{(+\ 42\ "foo")}$ etex,z2 shifted (-3u,0));
draw z2 shifted (-4u,2u) -- z2 shifted (0,-2u) dashed evenly withpen pencircle scaled 1bp;
draw z2 shifted (-4u,-2u) -- z2 shifted (0,2u) dashed evenly withpen pencircle scaled 1bp;
drawoptions(withcolor base01);
drawarrow pos shifted (gu+2u,0) -- pos shifted (gu+4u,0);
drawarrow z0 shifted (-gu,-gu-u) .. z1 shifted (gu,2u);
drawarrow pos shifted (gu+u,-1.5gu) -- pos shifted (gu+3u,-1.5gu);

BIN
categories/img/mp/pipe.png
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Binary file not shown.
Side by side Swipe Overlay

Before

Width:  |  Height:  |  Size: 39 KiB

After

Width:  |  Height:  |  Size: 58 KiB

21
themes/style/y/main.css
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@ -33,6 +33,10 @@
font-weight: normal;
font-style: normal; }
body.deck-container {
width: 100%;
padding: 0; }
.deck-container {
font-family: "ComputerModernSansSerif", Helvetica, sans-serif;
/* Header Numbering */ }
@ -171,8 +175,10 @@
.deck-container blockquote {
font-style: italic;
padding: 0 1em;
border-left: solid 10px #586e75;
color: #93a1a1; }
border-left: solid 10px #586e75; }
.deck-container blockquote em {
font-style: normal;
color: #93a1a1; }
.deck-container blockquote ul {
padding-left: 1.5em; }
.deck-container abbr,
@ -806,7 +812,11 @@
margin-bottom: 1em; }
.deck-container table {
border: 1px solid #586e75;
width: 100%; }
width: 90%;
margin: 1.5em auto;
box-sizing: border-box;
-moz-box-sizing: border-box;
-webkit-box-sizing: border-box; }
.deck-container table tr td {
padding: 2px 0.5em; }
.deck-container table tr:nth-child(odd) {
@ -883,7 +893,7 @@
font-size: 4em; } }
@media only screen and (max-width: 1380px) {
.deck-container {
font-size: 2em; } }
font-size: 2.5em; } }
@media only screen and (max-width: 640px) {
.deck-container {
font-size: 1.5em; } }
@ -920,6 +930,9 @@ body.deck-container {
font-size: 0.5em; }
.deck-container .deck-prev-link,
.deck-container .deck-next-link {
position: absolute;
top: 90%;
bottom: 1em;
background-color: #073642;
color: #586e75; }
.deck-container .deck-prev-link:visited,

19
themes/style/y/main.sass
View file

@ -180,6 +180,10 @@ $secondTextColor: $base1
color: $base02
color: $base0
body.deck-container
width: 100%
padding: 0
.deck-container
.base03
color: $base03
@ -335,7 +339,9 @@ $secondTextColor: $base1
font-style: italic
padding: 0 1em
border-left: solid 10px $base01
color: $base1
em
font-style: normal
color: $base1
ul
padding-left: 1.5em
@ -1040,7 +1046,11 @@ $secondTextColor: $base1
table
border: 1px solid $borderColor
width: 100%
width: 90%
margin: 1.5em auto
box-sizing: border-box
-moz-box-sizing: border-box
-webkit-box-sizing: border-box
table tr td
padding: 2px .5em
table tr
@ -1124,7 +1134,7 @@ $secondTextColor: $base1
font-size: 4em
@media only screen and (max-width: 1380px)
.deck-container
font-size: 2em
font-size: 2.5em
@media only screen and (max-width: 640px)
.deck-container
font-size: 1.5em
@ -1164,6 +1174,9 @@ body.deck-container
.deck-prev-link,
.deck-next-link
position: absolute
top: 90%
bottom: 1em
&:visited
color: $base01
&:hover