#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 544
\begin_document
\begin_header
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\language spanish
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\index Index
\shortcut idx
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\end_header

\begin_body

\begin_layout Standard
Una 
\series bold
secuencia
\series default
 es un conjunto ordenado de valores.
 Se expresa como 
\begin_inset Formula $[a_{1},\dots,a_{n}]$
\end_inset

.
 La función 
\begin_inset Quotes cld
\end_inset


\begin_inset Formula $long(S)$
\end_inset


\begin_inset Quotes crd
\end_inset

 devuelve la longitud de la secuencia 
\begin_inset Formula $S$
\end_inset

.
 Si 
\begin_inset Formula $S=[a_{1},\dots,a_{n}]$
\end_inset

 y 
\begin_inset Formula $S'=[b_{1},\dots,b_{m}]$
\end_inset

 y 
\begin_inset Formula $e$
\end_inset

 es un elemento, definimos conceptualmente las siguientes operaciones:
\end_layout

\begin_layout Itemize

\series bold
Añadir un elemento:
\series default
 
\begin_inset Formula $S\bullet e=[a_{1},\dots,a_{n},e]$
\end_inset

; 
\begin_inset Formula $e\circ S=[e,a_{1},\dots,a_{n}]$
\end_inset

.
\end_layout

\begin_layout Itemize

\series bold
Concatenar secuencias:
\series default
 
\begin_inset Formula $S\&S'=[a_{1},\dots,a_{n},b_{1},\dots,b_{m}]$
\end_inset

.
\end_layout

\begin_layout Itemize
\begin_inset Formula $primero(S)=a_{1}$
\end_inset

; 
\begin_inset Formula $último(S)=a_{n}$
\end_inset

.
\end_layout

\begin_layout Itemize

\series bold
Sucesor:
\series default
 
\begin_inset Formula $sucesor(S,i)=S_{i+1}$
\end_inset

.
\end_layout

\begin_layout Itemize

\series bold
Cola
\series default
 y 
\series bold
cabeza:
\series default
 
\begin_inset Formula $cola(S)=[S_{2},\dots,S_{n}]$
\end_inset

; 
\begin_inset Formula $cabeza(S)=[S_{1},\dots,S_{n-1}]$
\end_inset

.
\end_layout

\begin_layout Itemize

\series bold
¿Vacía?
\series default
: 
\begin_inset Formula $esvacía(S)=\begin{cases}
\text{Verdadero} & S=[]\\
\text{Falso} & S\neq[]
\end{cases}$
\end_inset


\end_layout

\begin_layout Subsection
Primer modelo
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="7" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
E.
 inicial
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
E.
 final
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Efecto
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comenzar(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Marcada/Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comienza desde el principio.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Avanzar(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Avanza un elemento.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
EA(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Obtiene el elemento actual.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Crear(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Cualquiera
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Creación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Crea una secuencia vacía.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Registrar(S,e)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Creación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Creación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Añade un elemento.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Marcar(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Creación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Marcada
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Añade una marca de fin de secuencia.
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Por defecto una secuencia no está en ningún estado, por lo que solo podemos
 usar Crear(S).
 En Pascal, estas operaciones se encuentran en los archivos 
\family typewriter
unitmse1
\family default
, 
\family typewriter
unitmsc1
\family default
 y 
\family typewriter
unitmsr1
\family default
 para enteros, caracteres y reales.
 Debemos añadir el código justo después de la línea con el nombre del programa,
 con el nombre del archivo correspondiente:
\end_layout

\begin_layout Standard
\begin_inset Box Boxed
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
thickness "0.4pt"
separation "3pt"
shadowsize "4pt"
framecolor "black"
backgroundcolor "none"
status open

\begin_layout Plain Layout

\family typewriter
uses
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\emph on
unitms
\series bold
x
\series default
1
\emph default
;
\end_layout

\end_inset


\end_layout

\begin_layout Standard
El tipo de dato es 
\begin_inset Formula $MS_{x}1$
\end_inset

 (siendo 
\begin_inset Formula $_{x}$
\end_inset

 una 
\family typewriter
e
\family default
, 
\family typewriter
c
\family default
 o 
\family typewriter
r
\family default
), y las funciones se denominan
\begin_inset Newline newline
\end_inset


\begin_inset Formula $Comenzar\_MS_{x}1$
\end_inset

, etc.
 Además, se añaden 
\begin_inset Formula $Encender\_Maquina\_MS_{x}1(S)$
\end_inset

, que debe ser llamada una y sólo una vez antes de cualquier otra operación
 sobre la secuencia (el 
\begin_inset Quotes cld
\end_inset

constructor
\begin_inset Quotes crd
\end_inset

) y 
\begin_inset Formula $Cargar\_Fichero\_MS_{x}1(S,s)$
\end_inset

, donde 
\begin_inset Formula $s$
\end_inset

 es una cadena de caracteres (capítulo 5), y carga en la secuencia los datos
 leídos del fichero indicado en 
\begin_inset Formula $s$
\end_inset

.
\end_layout

\begin_layout Subsection
Segundo modelo
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="4">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
E.
 inicial
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
E.
 final
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Efecto
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Iniciar(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Cr./Inic./Cons.
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Comienza desde antes del 
\begin_inset Formula $1^{er}$
\end_inset

 elemento.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Avanzar(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Iniciada/Cons.
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Avanza un elemento.
 Error si EsÚltimo.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
EA(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Consulta
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Obtiene el elemento actual.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
EsVacía(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Cualquiera
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
(E.
 inicial)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Devuelve si la secuencia es vacía.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
EsÚltimo(S,e)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Inic./Cons.
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
(E.
 inicial)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Devuelve si el elem.
 actual es el último.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Crear(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Cualquiera
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Creación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Crea una secuencia vacía.
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Registrar(S)
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Creación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Creación
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Añade un elemento a la secuencia.
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
Estas secuencias son similares a las del primer modelo, y en Pascal se usan
 igual, pero no tienen marca de fin y empiezan antes del primer elemento.
\end_layout

\begin_layout Section
Composición iterativa
\end_layout

\begin_layout Standard
Las iteraciones tienen un 
\series bold
invariante
\series default
 (INV), que se cumple tras cada ciclo y es un subconjunto de la post-condición,
 además de tener una 
\series bold
precondición
\series default
 (PRE) y una 
\series bold
postcondición
\series default
 (POST).
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="4" columns="2">
<features tabularvalignment="middle">
<column alignment="left" valignment="top" width="50text%">
<column alignment="left" valignment="top" width="40text%">
<row>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Lenguaje algorítmico
\end_layout

\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Pascal
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\series bold
MIENTRAS
\series default
 
\begin_inset Formula $c$
\end_inset

 
\series bold
HACER
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $e$
\end_inset


\end_layout

\begin_layout Plain Layout

\series bold
FIN_MIENTRAS
\end_layout

\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family typewriter
while 
\begin_inset Formula $c$
\end_inset

 do
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $e$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\series bold
REPETIR
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $s$
\end_inset


\end_layout

\begin_layout Plain Layout

\series bold
HASTA_QUE
\series default
 
\begin_inset Formula $c$
\end_inset


\end_layout

\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family typewriter
repeat
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $s$
\end_inset


\family default
 (no es necesario 
\family typewriter
begin
\family default
..
\family typewriter
end
\family default
).
\end_layout

\begin_layout Plain Layout

\family typewriter
until 
\begin_inset Formula $c$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\series bold
ITERAR
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $s_{1}$
\end_inset


\end_layout

\begin_layout Plain Layout

\series bold
DETENER
\series default
 
\begin_inset Formula $c$
\end_inset


\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $s_{2}$
\end_inset


\end_layout

\begin_layout Plain Layout

\series bold
FIN_ITERAR
\end_layout

\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family typewriter
repeat
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $s_{1}$
\end_inset

;
\end_layout

\begin_layout Plain Layout

\family typewriter
if 
\begin_inset Formula $c$
\end_inset

 then break;
\end_layout

\begin_layout Plain Layout

\family typewriter
\begin_inset space \hspace{}
\length 8ex
\end_inset


\begin_inset Formula $s_{2}$
\end_inset

;
\end_layout

\begin_layout Plain Layout

\family typewriter
until false
\end_layout

\end_inset
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
En exámenes y prácticas, no podemos utilizar 
\family typewriter
break
\family default
 salvo en este caso.
\end_layout

\begin_layout Standard
Cualquier composición iterativa se puede expresar en términos de cualquier
 otra, pero hay que saber elegir la más apropiada en cada caso.
\end_layout

\end_body
\end_document