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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>reveal.js – The HTML Presentation Framework</title>
<meta name="description" content="A framework for easily creating beautiful presentations using HTML">
<meta name="author" content="Hakim El Hattab">
<meta name="apple-mobile-web-app-capable" content="yes">
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" href="dist/reset.css">
<link rel="stylesheet" href="dist/reveal.css">
<link rel="stylesheet" href="dist/theme/black.css" id="theme">
<!-- Theme used for syntax highlighting of code -->
<link rel="stylesheet" href="plugin/highlight/monokai.css">
</head>
<style>
[src*="https://mermaid.ink/svg/"],
.invert {
filter: invert(100%);
}
.cols {
display: grid;
grid-auto-flow: row;
grid-template-columns: 1fr 1fr;
}
.cols>* {
align-self: center;
place-self: center;
}
.cols>img {
margin: 0
}
.cols3 {
display: grid;
grid-auto-flow: row;
grid-template-columns: 1fr 1fr 1fr;
}
.cols3>* {
align-self: center;
place-self: center;
}
.cols-left>* {
align-self: left;
place-self: 0px;
}
.cols3>img {
margin: 0
}
</style>
<body>
<div class="reveal">
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section>
<p>Agenda 1ra clase:
<ol>
<li>Teoría semántica operacional</li>
<li>Metodología de la práctica</li>
<li>Actividad con nota</li>
</ol>
</p>
</section>
<section>
<h1>Semántica operacional</h1>
<div class="cols" style="font-size: 0.8em;">
<div>
<p>Temas:
<ol>
<li>Árboles</li>
<li>Árbol sintáctico abstracto</li>
<li>Sistema de transición</li>
<li>Big step vs small step</li>
<li>Notación secuente</li>
</ol>
</p>
</div>
<div>
<p>Bibliografía:
<ol>
<li>Plotkin. A Structural Approach to Operational
Semantics. (descarga <a
href="https://homepages.inf.ed.ac.uk/gdp/publications/sos_jlap.pdf">aquí</a>
legalmente)
</li>
<li>Pierce. Types and programming languages.</li>
</ol>
</p>
</div>
</div>
</section>
<section data-auto-animate>
<h2>Árboles en ocaml</h2>
<div class="cols" style="font-size: 30px;">
<pre><code class="hljs language-ocaml" data-line-numbers="1,2" data-trim data-noescape >
type tree = Node of tree * tree
| Leave of string
let a1:tree = Leave "hola"
let a2:tree = Node(
Leave "izq",
Leave "der"
)
let a3:tree = Node(
Node(
Leave "izq",
Leave "der"
),
Leave "masder"
)
</code></pre>
</div>
</section>
<section data-auto-animate>
<h2>Árboles en ocaml</h2>
<div class="cols" style="font-size: 30px;">
<pre><code class="hljs language-ocaml" data-line-numbers="1,2,4" data-trim data-noescape >
type tree = Node of tree * tree
| Leave of string
let a1:tree = Leave "hola"
let a2:tree = Node(
Leave "izq",
Leave "der"
)
let a3:tree = Node(
Node(
Leave "izq",
Leave "der"
),
Leave "masder"
)
</code></pre>
<img src="https://mermaid.ink/svg/pako:eNoljTsOwjAQBa9ivYIqJzAVUko66FiKVbzBkfwJZo2EotydRbxqijeaDVMNAo9H4zW660jF2U43wln4Le7w7FWPsSb-E-GOAVla5iWYt_0EgkbJQvCGQWbuSQlUdrty13r5lAleW5cBfQ2sMi5sxQw_c3rJ_gWJCSz0?type=png)](https://mermaid.live/edit#pako:eNoljTsOwjAQBa9ivYIqJzAVUko66FiKVbzBkfwJZo2EotydRbxqijeaDVMNAo9H4zW660jF2U43wln4Le7w7FWPsSb-E-GOAVla5iWYt_0EgkbJQvCGQWbuSQlUdrty13r5lAleW5cBfQ2sMi5sxQw_c3rJ_gWJCSz0"
height="300" />
</div>
</section>
<section data-auto-animate>
<h2>Árboles en ocaml</h2>
<div class="cols" style="font-size: 30px;">
<pre><code class="hljs language-ocaml" data-line-numbers="1,2,6-9" data-trim data-noescape >
type tree = Node of tree * tree
| Leave of string
let a1:tree = Leave "hola"
let a2:tree = Node(
Leave "izq",
Leave "der"
)
let a3:tree = Node(
Node(
Leave "izq",
Leave "der"
),
Leave "masder"
)
</code></pre>
<img src="https://mermaid.ink/svg/pako:eNplj8EKwjAMhl-l5CAK2wv0IKg76i56sx7CmrnCum41FXTs3Y3zopjLHz4-SP4RqmAJNFwj9o06FaZTMptzKfii8ny9XRrYE95JLYYU2D2HOQ2s_tTdr2opfquQgafo0Vk5N76JAW7IkwEtq6UaUyuy6SZRMXE4ProKNMdEGaTeIlPhUB71oGtsb0LJOg7x8KkwN5leGWlD1Q"
height="300" />
</div>
</section>
<section data-auto-animate>
<h2>Árboles en ocaml</h2>
<div class="cols" style="font-size: 30px;">
<pre><code class="hljs language-ocaml" data-line-numbers="1,2,11-17" data-trim data-noescape >
type tree = Node of tree * tree
| Leave of string
let a1:tree = Leave "hola"
let a2:tree = Node(
Leave "izq",
Leave "der"
)
let a3:tree = Node(
Node(
Leave "izq",
Leave "der"
),
Leave "masder"
)
</code></pre>
<img src="https://mermaid.ink/svg/pako:eNp1kMEKwjAMhl-l5CAK8wV6EKY7qhe9WQ9hzVxhXbeuFXTs3Y1TkInm9PPxEZK_h9xpAgkXj00pjpmqBU-Kpz3zs1guVyL9wbK5gi3hlcSsjS5Y7DT5MSpYvP2Pvp7a5t7-VTdT9WsrJGDJWzSaT-6fREEoyZICyVFTgbFiWdUDqxiDO9zqHGTwkRKIjcZAmUF-1oIssOqYkjbB-d2rhrGN4QFd_1gS"
height="300" />
</div>
</section>
<section>
<h2>AST: Árbol de sintaxis abstracto</h2>
<div>
<pre><code class="hljs language-c">
float matchO(char *s) { /* find a zero */
if (!strncmp(s, "0.0", 3))
return 0.;
}
</code></pre>
<img src="./assets/ast.png" />
</div>
</section>
<section>
<h3>AST: Árbol de sintaxis abstracto</h3>
<aside class="notes">Se analiza/lee cada AST al revelarlo y por qué son mejores que la representación
textual.</aside>
<pre style="width: 100%; margin:0; text-align: center;" class="fragment" data-fragment-index="4"><code style="width: 100%; margin:0" class="hljs language-ocaml" data-trim data-noescape >
type expr = Lit of int | Sum of expr * expr | Times of expr * expr
</code></pre>
<div class="cols3" class="fragment" data-fragment-index="1">
<div>
<pre><code class="hljs language-c" data-trim data-noescape>
2 * 3 + 1
</code></pre>
<img src="https://mermaid.ink/svg/pako:eNodjTEOwjAQBL9yuoICkgLoXCAB5gXQnV2c4guJFDuRsQsU5e_YdLuj0e6K3ewEFb4jLwO8tAkAVzpYaNsL3GhvYQd3OtrK_7VyTafKH3S22KCX6Hl0ZWStlsE0iBeDqkQnPecpGTRhKyrnND-_oUOVYpYG8-I4iR653HtUPU8f2X5Diy02"
height="300" />
<pre class="fragment" data-fragment-index="5"><code style="width: 100%; margin:0" class="hljs language-ocaml" data-trim data-noescape >
Sum(
Times(Lit 2, Lit 3),
Lit 1
)
</code></pre>
</div>
<div class="fragment" data-fragment-index="2">
<pre><code class="language-c" data-trim data-noescape>
1 * 2 * 3
</code></pre>
<img src="https://mermaid.ink/svg/pako:eNo1jbEOgzAQQ3_l5KFDBUPbLUOlFv6AboThRI6CRAJKk6FC_HuPoZv9bMsb-sUJDN6R15FetQ1Ej_bcUVne6dleOjpRpf7g1Z9fFd5QwEv0PDmdb0dukUbxYmFUOhk4z8nChl2rnNPSfEMPk2KWAnl1nKSeWI89zMDzR_YfPDkrPQ"
height="300" />
<pre class="fragment" data-fragment-index="6"><code style="width: 100%; margin:0" class="hljs language-ocaml" data-trim data-noescape >
Times(
Lit 1
Times(Lit 2, Lit 3),
)
</code></pre>
</div>
<div class="fragment" data-fragment-index="3">
<pre><code class="language-c" data-trim data-noescape>
(1 * 2) * 3
</code></pre>
<img src="https://mermaid.ink/svg/pako:eNo1jTEOgzAQBL9y2iIFgiKhcxEphB-QDlOc8BGQsEGOXUSIv8cu0o1md7UHxs0IFN6e95lerXZEj74YqKru1GS40LOvh-ybv78meUMJK97yYtL8yLlGmMWKhkpoZOK4Bg3tzlTlGLbu60ao4KOUiLvhIO3C6dhCTbx-5PwBO8krPA"
height="300" />
<pre class="fragment" data-fragment-index="7"><code style="width: 100%; margin:0" class="hljs language-ocaml" data-trim data-noescape >
Times(
Times(Lit 1, Lit 2),
Lit 3
)
</code></pre>
</div>
</div>
</section>
<section
data-background-iframe="https://replit.com/@jisbruzzi/ex1-structural-recursion-ocaml?v=1&embed=true#main.ml"
data-background-interactive>
<h2>Ejercicio interactivo</h2>
<p>https://replit.com/@jisbruzzi/ex1-structural-recursion-ocaml</p>
<aside class="notes">
<p>Vamos a hacer un par de ejercicios con recursividad estructural:</p>
<ul>
<li>eval</li>
<li>contar cantidad de suma</li>
<li>algún eval alternativo?</li>
<li>transición small step?</li>
</ul>
</aside>
</section>
<section style="font-size: 28px;">
<h3>Sistemas de transición[Plotkin 1.2]</h3>
<aside class="notes">Plotkin, G D. A structural approach to operational semantics. Sección 1.2.</aside>
<p>
<ul>
<li>Dupla $(\Gamma,\to)$</li>
<li>$\Gamma$ conjunto de <i>configuraciones</i></li>
<li>$\to$ relación entre elementos de $\Gamma$.</li>
<li>$\to \subset \Gamma \times \Gamma$</li>
</ul>
</p>
<div class="fragment">
<h3>ST terminales[Plotkin 1.2]</h3>
<p>
<ul>
<li>Tripla $(\Gamma,\to,T)$</li>
<li>No se puede transicionar desde un elemento de $T\subset\Gamma$ </li>
<li>$\forall \gamma \in T \forall \gamma' \in \Gamma. \gamma \not\to \gamma'$</li>
</ul>
</p>
</div>
<div class="fragment">
<h3>ST determinísticos [TAPL 3.5.4]</h3>
<ul>
<li>$\to$ es una función</li>
<li>$ \gamma\to\gamma' \land \gamma\to\gamma'' \implies \gamma'=\gamma''$</li>
</ul>
</div>
</section>
<section>
<h2>Ejemplo: lenguaje Switch</h2>
<section data-auto-animate>
<pre data-id="code"><code class="hljs language-ocaml" data-trim data-noescape data-line-numbers>
type operatons = Switch operations | End
type state = On|Off
type sconfig = operations*state
</code></pre>
<div class="cols">
<img src="./assets/switch.webp" height="400" />
<div>
<p>
<pre style="width: 100%; margin:0">
<code class="hljs language-ocaml" data-trim data-noescape data-line-numbers="1|2|3|4">
let c1=(Switch (Switch (Switch End)),On);;
let c2=(Switch (Switch End),Off);;
let c3=(Switch End,On);;
let c4=(End,Off);;
</code>
</pre>
</p>
<ul class="fragment" style="font-size: 30px;">
<li><code>(Switch(x),On)</code>$\to$<code>(x,Off)</code></li>
<li><code>(Switch(x),Off)</code>$\to$<code>(x,On)</code></li>
<li>$T=\{$ <code>(End,On)</code> , <code>(End,Off)</code> $\}$</li>
</ul>
</div>
</div>
</section>
<section data-auto-animate>
<ul style="font-size: 30px;">
<li><code>(Switch(x),On)</code>$\to$<code>(x,Off)</code></li>
<li><code>(Switch(x),Off)</code>$\to$<code>(x,On)</code></li>
<li>$T=\{$ <code>(End,On)</code> , <code>(End,Off)</code> $\}$</li>
</ul>
<pre data-id="code"><code class="hljs language-ocaml" data-trim data-noescape data-line-numbers="1-3|7-11|13-19" >
type operatons = Switch operations | End
type state = On|Off
type sconfig = operations*state
exception Terminal
let small_step (config:sconfig):sconfig =
match config with
| (Switch x, On) -> (x, Off)
| (Switch x, Off) -> (x, On)
| (End, _) -> raise Terminal;;
let rec big_step (config:sconfig):sconfig =
match config with
| (Switch End, On) -> (End,Off)
| (Switch End, Off) -> (End, On)
| (Switch x, On) -> big_step (x,Off)
| (Switch x, Off) -> big_step (x, On)
| (End, _) -> raise Terminal;;
</code></pre>
</section>
</section>
<section>
<h2>Ejemplo: lenguage pp</h2>
<section>
<h3>Aclaración: listas</h3>
<iframe src="./ocaml-toplevel.html" width="800" height="400"></iframe>
<aside class="notes">
Ejemplos:
- []
- 1::[]
- [1;2;3]
- 1::2::3::[]
- 1::[2,3,4,5]
</aside>
</section>
<section>
<pre data-id="code"><code class="hljs language-ocaml" data-trim data-noescape data-line-numbers>
type operation = Push of int | Times | Add
type ppconfig = (operation list * int list)
</code></pre>
<div style="font-size: 25px;">
<ul>
<li><code>(Push x::tl,s)</code> $\to$ <code>(tl,x::s)</code></li>
<li><code>(Add::tl,a::b::s)</code> $\to$ <code>(tl,(a+b)::s)</code></li>
<li><code>(Times::tl,a::b::s)</code> $\to$ <code>(tl,(a*b)::s)</code></li>
<li>$T=\{$ <code>([],x)</code> $\}$</li>
</ul>
</div>
<div class="fragment fade-in" data-fragment-index="1">
<pre data-id="code" style="width: 100%;"><code class="hljs language-ocaml" data-trim data-noescape data-line-numbers="1|2|3|4|5|6|7|9|10">
let e1 = ( Push 3::Push 2::Push 4::Add::Times::Times::[] , [8]);;
let e2 = ( Push 2::Push 4::Add::Times::Times::[] , [3;8]);;
let e3 = ( Push 4::Add::Times::Times::[] , [2;3;8]);;
let e4 = ( Add::Times::Times::[] , [4;2;3;8]);;
let e5 = ( Times::Times::[] , [6;3;8]);;
let e6 = ( Times::[] , [18;8]);;
let e6 = ( [] , [144]);;(* e6 pertenece a T *)
let x = ( Add::[] , [99]);;(* ? *)
let y = ( [] , [37;15;2]);;(* ? *)
</code></pre>
</div>
</section>
</section>
<section>
<h3>Big step vs small step</h3>
<section data-auto-animate style="padding-top: 1em;">
<ul style="font-size:24px; text-align: left;">
<li class="fragment fade-in-then-semi-out">
<p>Lenguage PP:</p>
<p><code>([Push 1; Push 2;Add];[])</code>$\xrightarrow[]{PPs}$<code>([Push 2;Add];[1])</code>
</p>
<p><code>([Push 1; Push 2;Add];[])</code>$\xrightarrow[]{PPb}$<code>([];[3])</code></p>
</li>
<li class="fragment fade-in-then-semi-out">
<p>Lenguage Switch:</p>
<p><code>(Switch (Switch (Switch End)),On)</code>$\xrightarrow[]{Ss}$<code>((Switch (Switch End),Off)</code>
</p>
<p><code>(Switch (Switch (Switch End)),On)</code>$\xrightarrow[]{Sb}$<code>(End,Off)</code>
</p>
</li>
<li data-id="interesting-grampa" class="fragment fade-in-then-semi-out">
<p>Lenguage lits:</p>
<p data-id="interesting-parent"><code data-id="interesting">3*4+2*3</code>
$\xrightarrow[]{Ls}$ <code>12+2*3</code></p>
<p><code>3*4+2*3</code> $\xrightarrow[]{Lb}$ <code>18</code></p>
</li>
</ul>
</section>
<section data-auto-animate style="font-size:28px; margin-top: 30px;">
<ul data-id="interesting-grampa" style="text-align: center;">
<p data-id="interesting-parent"><code data-id="interesting">3*4+2*3</code></p>
<div class="fragment">
<p><code>12+2*3</code></p>
<p><code>12+6</code></p>
<p><code>18</code></p>
</div>
</ul>
<p class="fragment">$T=\{$ <code>Lit(_)</code> $\}$</p>
<pre class="fragment" data-id="code" style="font-size:19px;"><code class="hljs language-ocaml" data-trim data-noescape data-line-numbers="1-2|6-8|7|8|10-13|11|12">
type expr = Lit of int | Sum of expr * expr | Times of expr * expr
type litconfig = expr
exception Terminal
exception Implementar
let big_step (c:litconfig):litconfig = match c with
| Lit(_) -> raise Terminal
| x -> Lit(eval x);;
let small_step (c:litconfig):litconfig = match c with
| Lit(_) -> raise Terminal
| Sum(Lit x, Lit y) -> Lit (x + y)
| _ -> raise Implementar;;
</code></pre>
</section>
<section
data-background-iframe="https://replit.com/@jisbruzzi/ex2-small-step-lits?v=1&embed=true#main.ml"
data-background-interactive>
<h2>Ejercicio interactivo</h2>
<p>https://replit.com/@jisbruzzi/ex2-small-step-lits</p>
</section>
</section>
<section>
<h3>Notación secuente (<a href="https://en.wikipedia.org/wiki/Sequent_calculus">sequent calculus</a>)
</h3>
<style>
.notacion-secuente .orange {
color: orange
}
.notacion-secuente .green {
color: yellowgreen
}
.notacion-secuente .katex-display {
font-size: 0.6em;
}
</style>
<section>
$$
A \land B \land C \implies D
$$
<p>Se escribe:</p>
$$
\begin{array}{c c c} A & B & C \end{array} \over D
$$
</section>
<section data-auto-animate class="notacion-secuente">
<div class="cols" style="grid-template-columns: 1fr;">
<div data-id="sum">
$$
{\htmlClass{orange}{x} \to \htmlClass{green}{x'}}\over{Sum(\htmlClass{orange}{x},y)\to
Sum(\htmlClass{green}{x'},y)}
$$
$$
{\htmlClass{orange}{y} \to \htmlClass{green}{y'}}\over{Sum(Lit(x),\htmlClass{orange}{y})\to
Sum(Lit(x),\htmlClass{green}{y'})}
$$
$$
{}\over{Sum(Lit(\htmlClass{orange}{x}),Lit(\htmlClass{green}{y}))\to
Lit(\htmlClass{orange}{x}+\htmlClass{green}{y})}
$$
</div>
</div>
</section>
<section data-auto-animate class="notacion-secuente" style="padding-top: 3em;">
<h4>Sistema de transición de lits</h4>
<pre><code class="hljs language-ocaml" data-trim>
type litconfig = Lit of int
| Sum of litconfig * litconfig
| Times of litconfig * litconfig
</code></pre>
<div class="cols">
<div data-id="sum">
$$
{\htmlClass{orange}{x} \to \htmlClass{green}{x'}}\over{Sum(\htmlClass{orange}{x},y)\to
Sum(\htmlClass{green}{x'},y)}
$$
$$
{\htmlClass{orange}{y} \to \htmlClass{green}{y'}}\over{Sum(Lit(x),\htmlClass{orange}{y})\to
Sum(Lit(x),\htmlClass{green}{y'})}
$$
$$
{}\over{Sum(Lit(\htmlClass{orange}{x}),Lit(\htmlClass{green}{y}))\to
Lit(\htmlClass{orange}{x}+\htmlClass{green}{y})}
$$
</div>
<div data-id="times">
$$
{\htmlClass{orange}{x} \to \htmlClass{green}{x'}}\over{Times(\htmlClass{orange}{x},y)\to
Times(\htmlClass{green}{x'},y)}
$$
$$
{\htmlClass{orange}{y} \to
\htmlClass{green}{y'}}\over{Times(Lit(x),\htmlClass{orange}{y})\to
Times(Lit(x),\htmlClass{green}{y'})}
$$
$$
{}\over{Times(Lit(\htmlClass{orange}{x}),Lit(\htmlClass{green}{y}))\to
Lit(\htmlClass{orange}{x}*\htmlClass{green}{y})}
$$
</div>
</div>
<div>$T=\{$ <code>Lit(_)</code> $\}$</div>
</section>
</section>
<section style="font-size: 0.8em;">
<h1>¿Preguntas?</h1>
<p>A continuación, laboratorio.</p>
</section>
</div>
</div>
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