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| -rw-r--r-- | pia/n.lyx | 40 | ||||
| -rw-r--r-- | pia/n4.lyx | 2706 |
2 files changed, 2745 insertions, 1 deletions
@@ -7,6 +7,10 @@ \textclass book \begin_preamble \input{../defs} +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codegray}{rgb}{0.5,0.5,0.5} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{backcolour}{rgb}{0.95,0.95,0.92} \end_preamble \use_default_options true \begin_modules @@ -78,7 +82,7 @@ algorithm2e \papercolumns 1 \papersides 1 \paperpagestyle empty -\listings_params "basicstyle={\ttfamily}" +\listings_params "basicstyle={\ttfamily},breaklines=true,backgroundcolor={\color{backcolour}},commentstyle={\color{codegreen}},keywordstyle={\color{magenta}},numberstyle={\tiny\color{codegray}},stringstyle={\color{codepurple}},breakatwhitespace=false,captionpos=b,keepspaces=true,numbers=left,numbersep=5pt" \tracking_changes false \output_changes false \html_math_output 0 @@ -162,6 +166,26 @@ https://en.wikipedia.org/wiki/Reduction_strategy el 25 de septiembre de 2022. \end_layout +\begin_layout Itemize +Simon Marlow (ed.) +\emph on +Haskell 2010 Language Report +\emph default + (2010). + Recuperado de +\begin_inset Flex URL +status open + +\begin_layout Plain Layout + +https://www.haskell.org/onlinereport/haskell2010/haskell.html +\end_layout + +\end_inset + +. +\end_layout + \begin_layout Chapter Introducción \end_layout @@ -204,5 +228,19 @@ filename "n3.lyx" \end_layout +\begin_layout Chapter +Haskell +\end_layout + +\begin_layout Standard +\begin_inset CommandInset include +LatexCommand input +filename "n4.lyx" + +\end_inset + + +\end_layout + \end_body \end_document diff --git a/pia/n4.lyx b/pia/n4.lyx new file mode 100644 index 0000000..f64f732 --- /dev/null +++ b/pia/n4.lyx @@ -0,0 +1,2706 @@ +#LyX 2.3 created this file. For more info see http://www.lyx.org/ +\lyxformat 544 +\begin_document +\begin_header +\save_transient_properties true +\origin unavailable +\textclass book +\begin_preamble +\input{../defs} +\end_preamble +\use_default_options true +\maintain_unincluded_children false +\language spanish +\language_package default +\inputencoding auto +\fontencoding global +\font_roman "default" "default" +\font_sans "default" "default" +\font_typewriter "default" "default" +\font_math "auto" "auto" +\font_default_family default +\use_non_tex_fonts false +\font_sc false +\font_osf false +\font_sf_scale 100 100 +\font_tt_scale 100 100 +\use_microtype false +\use_dash_ligatures true +\graphics default +\default_output_format default +\output_sync 0 +\bibtex_command default +\index_command default +\paperfontsize default +\spacing single +\use_hyperref false +\papersize default +\use_geometry false +\use_package amsmath 1 +\use_package amssymb 1 +\use_package cancel 1 +\use_package esint 1 +\use_package mathdots 1 +\use_package mathtools 1 +\use_package mhchem 1 +\use_package stackrel 1 +\use_package stmaryrd 1 +\use_package undertilde 1 +\cite_engine basic +\cite_engine_type default +\biblio_style plain +\use_bibtopic false +\use_indices false +\paperorientation portrait +\suppress_date false +\justification true +\use_refstyle 1 +\use_minted 0 +\index Index +\shortcut idx +\color #008000 +\end_index +\secnumdepth 3 +\tocdepth 3 +\paragraph_separation indent +\paragraph_indentation default +\is_math_indent 0 +\math_numbering_side default +\quotes_style french +\dynamic_quotes 0 +\papercolumns 1 +\papersides 1 +\paperpagestyle default +\tracking_changes false +\output_changes false +\html_math_output 0 +\html_css_as_file 0 +\html_be_strict false +\end_header + +\begin_body + +\begin_layout Standard +Haskell es un lenguaje de programación funcional puro y perezoso. +\end_layout + +\begin_layout Section +Estructura léxica +\begin_inset Foot +status open + +\begin_layout Plain Layout +Las reglas +\family typewriter +\emph on +nombre +\emph default + =~ +\emph on +regex +\family default +\emph default + definen una expresión regular en formato PCRE ampliado con dos reglas: + que +\family typewriter +< +\emph on +nombre +\emph default +> +\family default + incluye la expresión regular nombrada entre paréntesis y que un +\family typewriter + +\backslash + +\family default + antes de un salto de línea se salta todos los caracteres desde él mismo + hasta el primer caracter de la siguiente línea que no es un espacio en + blanco. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +program =~ (<lexeme>|<whitespace>)* +\end_layout + +\begin_layout Plain Layout + +lexeme =~ <qvarid>|<qconid>|<qvarsym>|<qconsym>|<literal>| +\backslash + +\end_layout + +\begin_layout Plain Layout + + <special>|<reservedop>|<reservedid> +\end_layout + +\begin_layout Plain Layout + +whitespace =~ <whitestuff>+ +\end_layout + +\begin_layout Plain Layout + +whitestuff =~ <whitechar>|<comment>|<ncomment> +\end_layout + +\begin_layout Plain Layout + +whitechar =~ <newline>|[ +\backslash +v +\backslash +t]| +\backslash +p{Separator} +\end_layout + +\begin_layout Plain Layout + +newline =~ +\backslash +r +\backslash +n|[ +\backslash +r +\backslash +n +\backslash +f] +\end_layout + +\begin_layout Plain Layout + +comment =~ --+(?!<symbol>)<anynb>*<newline> +\end_layout + +\begin_layout Plain Layout + +ncomment =~ +\backslash +{-<anyseq>(<ncomment><anyseq>)*- +\backslash +} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Las clases de caracteres son: +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +anyseq =~ (?!<any>*( +\backslash +{-|- +\backslash +})<any>*)<any>* +\end_layout + +\begin_layout Plain Layout + +any =~ <graphic>|<whitechar> +\end_layout + +\begin_layout Plain Layout + +anynb =~ <graphic>|[ +\backslash +t] +\end_layout + +\begin_layout Plain Layout + +graphic =~ <small>|<large>|<symbol>|<digit>|<special>|[ +\begin_inset Quotes cld +\end_inset + +'] +\end_layout + +\begin_layout Plain Layout + +small =~ +\backslash +p{Lowercase_Letter}|_ +\end_layout + +\begin_layout Plain Layout + +large =~ +\backslash +p{Uppercase_Letter}| +\backslash +p{Titlecase_Letter} +\end_layout + +\begin_layout Plain Layout + +symbol =~ [!#$%&*+./<=>?@ +\backslash + +\backslash +^|~:-]|(?!<special>|[_ +\begin_inset Quotes crd +\end_inset + +']) +\backslash +p{Symbol} +\end_layout + +\begin_layout Plain Layout + +digit =~ +\backslash +p{Decimal_Digit_Number} +\end_layout + +\begin_layout Plain Layout + +octit =~ [0-7] +\end_layout + +\begin_layout Plain Layout + +hexit =~ <digit>|[A-Fa-f] +\end_layout + +\begin_layout Plain Layout + +special =~ [() +\backslash +[ +\backslash +]{},;`] +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{samepage} +\end_layout + +\end_inset + +Las palabras reservadas son: +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +reservedid =~ case|class|data|default|deriving|do|else|foreign| +\backslash + +\end_layout + +\begin_layout Plain Layout + + if|import|in|infix|infixl|infixr|instance|let| +\backslash + +\end_layout + +\begin_layout Plain Layout + + module|newtype|of|then|type|where|_ +\end_layout + +\begin_layout Plain Layout + +reservedop =~ +\backslash +. +\backslash +.|:|::|=| +\backslash + +\backslash +| +\backslash +||<-|->|@|~|=> +\end_layout + +\end_inset + + +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +end{samepage} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Las variables pueden estar en espacios de nombres jerárquicos: +\begin_inset Note Comment +status open + +\begin_layout Plain Layout +tyvar=varid, tycon=tycls=conid, modid=qconid, qtycon=qtycls=qvarid +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +qvarid =~ (<conid> +\backslash +.)*<varid> +\end_layout + +\begin_layout Plain Layout + +qconid =~ (<conid> +\backslash +.)*<conid> +\end_layout + +\begin_layout Plain Layout + +qvarsym =~ (<conid> +\backslash +.)*<varsym> +\end_layout + +\begin_layout Plain Layout + +qconsym =~ (<conid> +\backslash +.)*<consym> +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Se escriben como sigue: +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +varid =~ (?!<reservedid>(?!<small>|<large>|<digit>|')) +\backslash + +\end_layout + +\begin_layout Plain Layout + + <small>(<small>|<large>|<digit>|')* +\end_layout + +\begin_layout Plain Layout + +conid =~ <large>(<small>|<large>|<digit>|')* +\end_layout + +\begin_layout Plain Layout + +varsym =~ (?!((--+|<reservedop>)(?!<symbol>))|:)<symbol>+ +\end_layout + +\begin_layout Plain Layout + +consym =~ (?!<reservedop>(?!<symbol>)):<symbol>* +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Los literales son: +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +literal =~ <integer>|<float>|<char>|<string> +\end_layout + +\begin_layout Plain Layout + +integer =~ <digit>+|0[oO]<octit>+|0[xX]<hexit>+ +\end_layout + +\begin_layout Plain Layout + +float =~ <digit>+ +\backslash +.<digit>+(<exponent>)?|<digit>+<exponent> +\end_layout + +\begin_layout Plain Layout + +exponent =~ [eE][+-]?<digit>+ +\end_layout + +\begin_layout Plain Layout + +char =~ '((?![' +\backslash + +\backslash +])<graphic>| |(?! +\backslash + +\backslash +&)<escape>)' +\end_layout + +\begin_layout Plain Layout + +string =~ +\begin_inset Quotes cld +\end_inset + +((?![ +\begin_inset Quotes cld +\end_inset + + +\backslash + +\backslash +])<graphic>| |<escape>| +\backslash + +\backslash +<whitechar>+ +\backslash + +\backslash +)* +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +escape =~ +\backslash + +\backslash +(<charesc>|<ascii>|<decimal>|o<octit>+|x<hexit>+) +\end_layout + +\begin_layout Plain Layout + +charesc =~ [abfnrtv +\backslash + +\backslash + +\begin_inset Quotes crd +\end_inset + +'&] +\end_layout + +\begin_layout Plain Layout + +ascii =~ +\backslash +^[A-Z@ +\backslash +[ +\backslash +] +\backslash + +\backslash +^_]|NUL|SOH|STX|ETX|EOT|ENQ|ACK|BEL|BS| +\backslash + +\end_layout + +\begin_layout Plain Layout + + HT|LF|VT|FF|CR|SO|SI|DLE|DC1|DC2|DC3|DC4|NAK|SYN|ETB| +\backslash + +\end_layout + +\begin_layout Plain Layout + + CAN|EM|SUB|ESC|FS|GS|RS|US|SP|DEL +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +En principio un programa se interpreta como una secuencia de lexemas, +\family typewriter +{ +\family default + entra en un nuevo contexto y +\family typewriter +} +\family default + sale del último contexto en que se ha entrado. + Sin embargo, se pueden evitar apariciones de +\family typewriter +{ +\family default +, +\family typewriter +} +\family default + y +\family typewriter +; +\family default + sangrando los lexemas de cierta forma y dejando que el +\emph on +\lang english +lexer +\emph default +\lang spanish + los inserte como sigue: +\end_layout + +\begin_layout Standard +\begin_inset Separator plain +\end_inset + + +\end_layout + +\begin_layout Enumerate +Tras un +\family typewriter +let +\family default +, +\family typewriter +where +\family default +, +\family typewriter +do +\family default + u +\family typewriter +of +\family default + no seguido de +\family typewriter +{ +\family default +, o al principio del cuerpo si este no empieza por +\family typewriter +module +\family default + o +\family typewriter +{ +\family default +, se inserta +\family typewriter +{ +\family default + y se abre un contexto implícito desde la columna por la que empieza el + siguiente lexema (si lo hay). + Este se cierra inmediatamente insertando +\family typewriter +} +\family default + si está directamente dentro (sin ningún contexto +\begin_inset Quotes cld +\end_inset + +en medio +\begin_inset Quotes crd +\end_inset + +) de un contexto implícito que empieza en una columna anterior. +\end_layout + +\begin_layout Enumerate +Si el primer lexema explícito en una línea no es el primero de su contexto, + mientras su contexto sea implícito, justo antes de la línea se inserta + +\family typewriter +; +\family default + si el lexema empieza en la misma columna que el contexto o +\family typewriter +} +\family default + y si empieza en una anterior, cerrando el contexto. +\end_layout + +\begin_layout Enumerate +Es un error cerrar un contexto implícito con un +\family typewriter +} +\family default + explícito. +\end_layout + +\begin_layout Enumerate +Mientras un lexema explícito en un contexto implícito cause un error sintáctico + (los lexemas explícitos o implícitos anteriores forman un prefijo válido + de la gramática libre de contexto pero al añadir el propio lexema ya no), + se inserta +\family typewriter +} +\family default + antes del lexema. +\end_layout + +\begin_layout Enumerate +Al final de la entrada se insertan +\family typewriter +} +\family default + suficientes para cerrar los contextos implícitos que queden abiertos. +\end_layout + +\begin_layout Section +Sesiones +\end_layout + +\begin_layout Standard +El programa +\family typewriter +ghci +\family default + lee expresiones o definiciones en Haskell, una por línea o entre una línea + +\begin_inset Quotes cld +\end_inset + + +\family typewriter +:{ +\family default + +\begin_inset Quotes crd +\end_inset + + y una +\begin_inset Quotes cld +\end_inset + + +\family typewriter +:} +\family default + +\begin_inset Quotes crd +\end_inset + +, las evalúa e imprime el resultado, y también puede interpretar comandos + de +\family typewriter +ghci +\family default +. + Una +\series bold +sesión +\series default + es la secuencia de iteraciones entre el usuario y este programa. + Las definiciones también se pueden guardar en ficheros, generalmente con + extensión +\family typewriter +.hs +\family default +, llamadas +\series bold +guiones +\series default + o +\series bold +\emph on +\lang english +scripts +\series default +\emph default +\lang spanish +, que se pueden cargar en el intérprete con el comando +\family typewriter +:l +\emph on +fichero +\family default +\emph default +. + El formato es: +\begin_inset Foot +status open + +\begin_layout Plain Layout +Las reglas +\family typewriter +\emph on +nombre +\emph default + = +\emph on +valor +\family default +\emph default + describen la gramática libre de contexto de Haskell en ABNF. + Cada cadena entre comillas representa un sólo lexema y entre dos lexemas + puede haber espacio. + Esta gramática tiene ambigüedades que se resuelven haciendo las frases + tan largas como sea posible de izquierda a derecha, resolviendo todos los + conflictos +\emph on +\lang english +shift-reduce +\emph default +\lang spanish + con +\emph on +\lang english +shift +\emph default +\lang spanish +. + Los +\emph on +\lang english +tokens +\emph default +\lang spanish + también se extienden lo máximo posible. +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +module = body +\end_layout + +\begin_layout Plain Layout + +body = +\begin_inset Quotes cld +\end_inset + +{ +\begin_inset Quotes cld +\end_inset + + topdecls +\begin_inset Quotes cld +\end_inset + +} +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +topdecls = [topdecl *( +\begin_inset Quotes cld +\end_inset + +; +\begin_inset Quotes crd +\end_inset + + topdecl)] +\end_layout + +\begin_layout Plain Layout + +topdecl = decl +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Un +\series bold +vínculo +\series default + es una asignación de un nombre a un valor, y un +\series bold +entorno +\series default + o +\series bold +contexto +\series default + es un conjunto de vínculos en que no hay más de un vínculo para el mismo + nombre. + Las expresiones se evalúan en un cierto contexto, y describen un valor + que depende de este. + Inicialmente el contexto global incluye las +\series bold +operaciones primitivas +\series default + incluidas en el evaluador, como las operaciones aritméticas básicas y las + incluidas en +\series bold +preludios +\series default +. +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +var = varid / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + varsym +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +varop = varsym / +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + varid +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Las variables se nombran como +\family typewriter +varid +\family default + y los +\series bold +operadores +\series default + infijos como +\family typewriter +varsym +\family default +, pero es posible usar un operador como nombre normal poniéndolo entre paréntesi +s y una función con nombre normal como operador poniéndola entre comillas + invertidas. + Se pueden definir nuevos operadores. +\end_layout + +\begin_layout Standard +La +\series bold +evaluación ansiosa +\series default + o +\series bold +llamada por valor +\series default + es como el orden aplicativo pero sin evaluar en el interior de abstracciones, + y la +\series bold +evaluación perezosa +\series default + o +\series bold +llamada por nombre +\series default + es como el orden normal pero sin evaluar en el interior de abstracciones. + Haskell usa evaluación perezosa, que al contrario que la ansiosa garantiza + la terminación si la expresión es normalizable. +\end_layout + +\begin_layout Section +Tipos +\end_layout + +\begin_layout Standard +Todo valor tiene un tipo con un cierto dominio, que incluye un +\series bold +valor indefinido +\series default + +\begin_inset Formula $\bot$ +\end_inset + + correspondiente a las expresiones de ese tipo cuya evaluación no termina, + aunque también se usa para notificar errores. +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +type = btype [ +\begin_inset Quotes cld +\end_inset + +-> +\begin_inset Quotes crd +\end_inset + + type] +\end_layout + +\begin_layout Plain Layout + +btype = [btype] atype +\end_layout + +\begin_layout Plain Layout + +atype = gtycon / varid / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + type *( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + type) +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +[ +\begin_inset Quotes cld +\end_inset + + type +\begin_inset Quotes cld +\end_inset + +] +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +gtycon = qtycon / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +[ +\begin_inset Quotes cld +\end_inset + + +\begin_inset Quotes cld +\end_inset + +] +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +El tipo +\family typewriter +\emph on +fuente +\emph default + -> +\emph on +resultado +\family default +\emph default + es el de las funciones que toman +\series bold +argumentos +\series default + del +\series bold +tipo fuente +\series default + y devuelven +\series bold +resultados +\series default + del +\series bold +tipo resultado +\series default +. + Una función +\begin_inset Formula $f$ +\end_inset + + es +\series bold +estricta +\series default + si +\begin_inset Formula $f\,\bot=\bot$ +\end_inset + +. + Dos funciones son +\series bold +iguales +\series default + si devuelven los mismos resultados para los mismos argumentos, y el compilador + es libre de cambiar una función por otra igual. + Normalmente las funciones están currificadas, pues esto reduce el número + de paréntesis y permite aplicar una función de varios argumentos a menos + argumentos para obtener otra función que puede ser útil por sí misma. + Es idiomático +\begin_inset Formula $\eta$ +\end_inset + +-reducir las definiciones de funciones. +\end_layout + +\begin_layout Standard +\begin_inset Note Note +status open + +\begin_layout Plain Layout +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +aexp /= +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + exp *( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + exp) +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +[ +\begin_inset Quotes cld +\end_inset + + exp *( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + exp) +\begin_inset Quotes cld +\end_inset + +] +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Note +status open + +\begin_layout Plain Layout +(*), (<=), ->, (+), div, (^), (/), (.), Float, pi, Integer, not, True, False, + (1*,), (), [*,], [], (:), otherwise, error, (-) +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Note Note +status open + +\begin_layout Plain Layout +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +funlhs /= +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + funlhs +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + 1*apat +\end_layout + +\begin_layout Plain Layout + +lpat /= gcon 1*apat +\end_layout + +\begin_layout Plain Layout + +guards /= +\begin_inset Quotes cld +\end_inset + +| +\begin_inset Quotes crd +\end_inset + + guard *( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + guard) +\end_layout + +\begin_layout Plain Layout + +apat /= +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + pat 1*( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + pat) +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +[ +\begin_inset Quotes cld +\end_inset + + pat *( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + pat) +\begin_inset Quotes cld +\end_inset + +] +\begin_inset Quotes crd +\end_inset + + / gcon +\end_layout + +\begin_layout Plain Layout + +aexp /= gcon +\end_layout + +\begin_layout Plain Layout + +gtycon /= +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + +\begin_inset Quotes cld +\end_inset + +-> +\begin_inset Quotes crd +\end_inset + + +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + 1* +\begin_inset Quotes crd +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +gcon = +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes crd +\end_inset + + +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +[ +\begin_inset Quotes cld +\end_inset + + +\begin_inset Quotes cld +\end_inset + +] +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + 1* +\begin_inset Quotes crd +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +op = varop / conop +\end_layout + +\begin_layout Plain Layout + +conop = +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + conid +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +qop = qvarop / qconop +\end_layout + +\begin_layout Plain Layout + +qvarop = qvarsym / +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + qvarid +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +qconop = gconsym / +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + qconid +\begin_inset Quotes cld +\end_inset + +` +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +gconsym = +\begin_inset Quotes cld +\end_inset + +: +\begin_inset Quotes crd +\end_inset + + / qconsym +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Section +Expresiones +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +exp = infixexp [ +\begin_inset Quotes cld +\end_inset + +:: +\begin_inset Quotes crd +\end_inset + + type] +\end_layout + +\begin_layout Plain Layout + +infixexp = lexp qop infixexp / +\begin_inset Quotes cld +\end_inset + +- +\begin_inset Quotes crd +\end_inset + + infixexp / lexp +\end_layout + +\begin_layout Plain Layout + +lexp = fexp +\end_layout + +\begin_layout Plain Layout + +fexp = [fexp] aexp / +\begin_inset Quotes cld +\end_inset + +let +\begin_inset Quotes crd +\end_inset + + decls +\begin_inset Quotes cld +\end_inset + +in +\begin_inset Quotes crd +\end_inset + + exp +\end_layout + +\begin_layout Plain Layout + +aexp = qvar / literal +\end_layout + +\begin_layout Plain Layout + +qvar = qvarid / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + qvarsym +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\begin_layout Plain Layout + +decls = +\begin_inset Quotes cld +\end_inset + +{ +\begin_inset Quotes cld +\end_inset + + [decl *( +\begin_inset Quotes cld +\end_inset + +; +\begin_inset Quotes crd +\end_inset + + decl)] +\begin_inset Quotes cld +\end_inset + +} +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Una variable ( +\family typewriter +qvar +\family default +) representa su valor en el contexto; un +\family typewriter +literal +\family default + se representa a sí mismo; +\family typewriter +fexp aexp +\family default + representa la aplicación de la función +\family typewriter +fexp +\family default + al valor +\family typewriter +aexp +\family default +; +\family typewriter +lexp qop infixexp +\family default + equivale a +\family typewriter +(qop) lexp infixexp +\family default +, aunque realmente distintos operadores tienen distinta precedencia y asociativi +dad, establecidas con la sintaxis: +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +gendecl /= fixity [integer] ops +\end_layout + +\begin_layout Plain Layout + +ops = op *( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + op) +\end_layout + +\begin_layout Plain Layout + +fixity = +\begin_inset Quotes cld +\end_inset + +infixl +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +infixr +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +infix +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +El entero opcional va del 0 al 9 y es mayor a mayor precedencia, y se usa + +\family typewriter +infixl +\family default + para indicar asociatividad por la izquierda o +\family typewriter +infixr +\family default + por la derecha. + El operador +\family typewriter +- +\family default + es el único unario, y representa la negación. +\end_layout + +\begin_layout Standard +Una +\series bold +sección +\series default + es un operador con una expresión delante o detrás: +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +aexp /= +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + infixexp qop +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + qop infixexp +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard + +\family typewriter +( +\emph on +infixexp qop +\emph default +) +\family default + equivale a +\family typewriter + +\backslash +y -> +\emph on +infixexp qop +\emph default + y +\family default + y +\family typewriter +( +\emph on +qop infixexp +\emph default +) +\family default + a +\family typewriter + +\backslash +x -> x +\emph on +qop infixexp +\family default +\emph default +. +\end_layout + +\begin_layout Section +Patrones +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +pat = lpat +\end_layout + +\begin_layout Plain Layout + +lpat = apat / +\begin_inset Quotes cld +\end_inset + +- +\begin_inset Quotes crd +\end_inset + + (integer / float) +\end_layout + +\begin_layout Plain Layout + +apat = var [ +\begin_inset Quotes cld +\end_inset + +@ +\begin_inset Quotes crd +\end_inset + + apat] / literal / +\begin_inset Quotes cld +\end_inset + +_ +\begin_inset Quotes crd +\end_inset + + / +\begin_inset Quotes cld +\end_inset + +( +\begin_inset Quotes cld +\end_inset + + pat +\begin_inset Quotes cld +\end_inset + +) +\begin_inset Quotes crd +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Un +\series bold +patrón +\series default + recibe un argumento y bien encaja, creando una serie de vínculos, o no. + El patrón +\family typewriter +_ +\family default + siempre encaja y no crea vínculos; una variable siempre encaja y crea un + vínculo de la variable al argumento; un patrón de forma +\family typewriter +\emph on +var +\emph default +@ +\emph on +apat +\family default +\emph default + es similar pero solo encaja si lo hace +\family typewriter +\emph on +apat +\family default +\emph default + y en tal caso crea un vínculo de +\family typewriter +\emph on +var +\family default +\emph default + al argumento que se añade a los vínculos que crea +\family typewriter +\emph on +apat +\family default +\emph default +. + Una misma variable no puede aparecer dos veces en la misma lista de patrones, + ni siquiera como subpatrón. + Un literal o su negación no crea vínculos y encaja sólo si el argumento + es igual a él. +\end_layout + +\begin_layout Standard +Un patrón no estándar es +\family typewriter +varid +\begin_inset Quotes qld +\end_inset + ++ +\begin_inset Quotes qrd +\end_inset + + integer +\family default +, que encaja con un entero de valor mayor o igual al +\family typewriter +integer +\family default + y asigna a la variable el entero menos ese +\family typewriter +integer +\family default +. +\end_layout + +\begin_layout Standard +Dada una lista de patrones o de listas de patrones del mismo tamaño cada + una con una expresión asociada, el +\series bold +encaje de patrones +\series default + consiste en seleccionar la expresión correspondiente al primer patrón que + encaje con cierto argumento, o la primera lista en que cada patrón encaje + con el correspondiente argumento de una lista de argumentos. +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +fexp /= +\begin_inset Quotes cld +\end_inset + +case +\begin_inset Quotes crd +\end_inset + + exp +\begin_inset Quotes cld +\end_inset + +of +\begin_inset Quotes crd +\end_inset + + +\begin_inset Quotes cld +\end_inset + +{ +\begin_inset Quotes cld +\end_inset + + alts +\begin_inset Quotes cld +\end_inset + +} +\begin_inset Quotes crd +\end_inset + + / +\end_layout + +\begin_layout Plain Layout + + / +\begin_inset Quotes cld +\end_inset + +if +\begin_inset Quotes crd +\end_inset + + exp [ +\begin_inset Quotes cld +\end_inset + +; +\begin_inset Quotes crd +\end_inset + +] +\begin_inset Quotes cld +\end_inset + +then +\begin_inset Quotes crd +\end_inset + + exp [ +\begin_inset Quotes cld +\end_inset + +; +\begin_inset Quotes crd +\end_inset + +] +\begin_inset Quotes cld +\end_inset + +else +\begin_inset Quotes crd +\end_inset + + exp / +\end_layout + +\begin_layout Plain Layout + + / +\begin_inset Quotes cld +\end_inset + + +\backslash + +\backslash + +\begin_inset Quotes crd +\end_inset + + 1*apat +\begin_inset Quotes cld +\end_inset + +-> +\begin_inset Quotes crd +\end_inset + + exp +\end_layout + +\begin_layout Plain Layout + +alts = alt *( +\begin_inset Quotes cld +\end_inset + +; +\begin_inset Quotes crd +\end_inset + + alt) +\end_layout + +\begin_layout Plain Layout + +alt = pat ( +\begin_inset Quotes cld +\end_inset + +-> +\begin_inset Quotes crd +\end_inset + + exp / 1*gdpat) [ +\begin_inset Quotes cld +\end_inset + +where +\begin_inset Quotes crd +\end_inset + + decls] +\end_layout + +\begin_layout Plain Layout + +gdpat = guards +\begin_inset Quotes cld +\end_inset + +-> +\begin_inset Quotes crd +\end_inset + + exp +\end_layout + +\begin_layout Plain Layout + +guards = +\begin_inset Quotes cld +\end_inset + +| +\begin_inset Quotes crd +\end_inset + + guard +\end_layout + +\begin_layout Plain Layout + +guard = infixexp +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +Si todas las +\family typewriter +alt +\family default + son del segundo tipo, +\family typewriter +case +\emph on +exp +\emph default + of +\emph on +alts +\family default +\emph default + evalúa +\family typewriter +\emph on +exp +\family default +\emph default +; selecciona la primera +\family typewriter +gdpat +\family default + tal que +\family typewriter +\emph on +exp +\family default +\emph default + encaja con el patrón de la +\family typewriter +alt +\family default + en la que está y, en un contexto extendido por las declaraciones en +\family typewriter +decls +\family default + y los vínculos de dicho patrón, la +\series bold +guarda +\series default + ( +\family typewriter +guard +\family default +) devuelve +\family typewriter +True +\family default +, y finalmente evalúa la expresión del +\family typewriter +gdpat +\family default + en el mismo contexto y devuelve su valor, o bien devuelve +\begin_inset Formula $\bot$ +\end_inset + + si ninguna +\family typewriter +gdpat +\family default + cumple la condición. + Una +\family typewriter +alt +\family default + de la forma +\family typewriter +-> +\emph on +exp +\family default +\emph default + equivale a +\family typewriter +| True -> +\emph on +exp +\family default +\emph default +. +\end_layout + +\begin_layout Standard +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{sloppypar} +\end_layout + +\end_inset + + +\family typewriter +if +\emph on +condition +\emph default + then +\emph on +when-true +\emph default + else +\emph on +when-false +\family default +\emph default + equivale a +\family typewriter +case +\emph on +condition +\emph default + of { True -> +\emph on +when-true +\emph default +; False -> +\emph on +when-false +\emph default + } +\family default +. +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +end{sloppypar} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard + +\family typewriter + +\backslash + +\emph on +apat +\begin_inset Formula $_{1}$ +\end_inset + + +\emph default + +\family default +... + +\family typewriter + +\emph on +apat +\begin_inset Formula $_{n}$ +\end_inset + + +\emph default + -> +\emph on +exp +\family default +\emph default + representa una función con parámetros definidos por patrones (generalmente + variables) cuya aplicación a +\begin_inset Formula $n$ +\end_inset + + parámetros encaja los parámetros si es posible y devuelve el valor de +\family typewriter +\emph on +exp +\family default +\emph default + en un contexto extendido por los vínculos creados por los patrones, y devuelve + +\begin_inset Formula $\bot$ +\end_inset + + en otro caso. +\end_layout + +\begin_layout Section +Definiciones +\end_layout + +\begin_layout Standard +Una +\series bold +definición +\series default + añade un vínculo al contexto en que se encuentra, en principio el contexto + global. + Está formada por una +\series bold +asignación de tipo +\series default + opcional, que indica el tipo de la variable, y una serie de ecuaciones. +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +decl = gendecl / (funlhs / pat) rhs +\end_layout + +\begin_layout Plain Layout + +gendecl = vars +\begin_inset Quotes cld +\end_inset + +:: +\begin_inset Quotes crd +\end_inset + + type +\end_layout + +\begin_layout Plain Layout + +vars = var *( +\begin_inset Quotes cld +\end_inset + +, +\begin_inset Quotes crd +\end_inset + + var) +\end_layout + +\begin_layout Plain Layout + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{samepage} +\end_layout + +\end_inset + +Las funciones se definen con una serie de +\series bold +ecuaciones +\series default + de la forma +\family typewriter +funlhs rhs +\family default +: +\end_layout + +\begin_layout Standard +\begin_inset listings +inline false +status open + +\begin_layout Plain Layout + +funlhs = var 1*apat / pat varop pat +\end_layout + +\begin_layout Plain Layout + +rhs = ( +\begin_inset Quotes cld +\end_inset + += +\begin_inset Quotes crd +\end_inset + + exp / 1*gdrhs) [ +\begin_inset Quotes cld +\end_inset + +where +\begin_inset Quotes crd +\end_inset + + decls] +\end_layout + +\begin_layout Plain Layout + +gdrhs = guards +\begin_inset Quotes cld +\end_inset + += +\begin_inset Quotes crd +\end_inset + + exp +\end_layout + +\end_inset + + +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +end{samepage} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +La +\series bold +aridad +\series default + de una ecuación es el número de parámetros (número de +\family typewriter +apat +\family default + en la primera sintaxis o 2 en la segunda), y todas las ecuaciones para + la misma función +\family typewriter +var +\family default + tienen la misma aridad. + La función se define currificada, y para evaluarla sobre ciertos argumentos, + se selecciona una +\series bold +cláusula +\series default + ( +\family typewriter +gdrhs +\family default +) de la misma forma que se seleccionaban los +\family typewriter +gdpat +\family default + en una expresión +\family typewriter +case +\family default +, usando ecuaciones en vez de +\family typewriter +alt +\family default +s y encajando tantos argumentos como sea la aridad, y se ejecuta la expresión + correspondiente. + Una ecuación +\family typewriter +\emph on +var apat +\family default +\emph default +... + +\family typewriter + = +\emph on +exp +\family default +\emph default + equivale a +\family typewriter +\emph on +var apat +\family default +\emph default +... + +\family typewriter + | True = +\emph on +exp +\family default +\emph default +. +\end_layout + +\begin_layout Standard +Las declaraciones de la forma +\family typewriter +pat rhs +\family default + definen variables globales añadiendo al contexto global los vínculos establecid +os al encajar el +\family typewriter +rhs +\family default + con el patrón, y es un error si no hay encaje. + Generalmente +\family typewriter +pat +\family default + es una variable. +\end_layout + +\end_body +\end_document |