243 lines
13 KiB
Text
243 lines
13 KiB
Text
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%================= Standard packages ==========================================%
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\usepackage{fleqn}
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\usepackage[portuguese]{babel}
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\usepackage[utf8]{inputenc}
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\usepackage{mathptmx} % math font
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\usepackage{tabularx}
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%----------------- testing ----------------------------------------------------%
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\newtheorem{teste}{\underline{Teste unitário}}%
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\newtheorem{propriedade}{\relax{Propriedade [\href{https://hackage.haskell.org/package/QuickCheck}{QuickCheck}]}}%
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%----------------- verbatim ---------------------------------------------------%
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\usepackage{fancyvrb}
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%----------------- Using xy ---------------------------------------------------%
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\usepackage[all]{xy}
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\def\larrow#1#2#3{\xymatrix{ #3 & #1 \ar[l]_-{#2} }}
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\def\rarrow#1#2#3{\xymatrix{ #1 \ar[r]^-{#2} & #3 }}
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\def\u{u} % unidade de um mónade
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\def\fun#1{{\sf #1}\index{Functor}}
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%----------------- Colors -----------------------------------------------------%
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\usepackage{color}
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\usepackage[dvipsnames]{xcolor}
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\definecolor{url}{HTML}{0F80FF}
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\hypersetup{
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linkcolor=url,
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citecolor=url,
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urlcolor=url
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}
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\definecolor{codegreen}{rgb}{0,0.6,0}
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\definecolor{codegray}{rgb}{0.5,0.5,0.5}
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\definecolor{codepurple}{rgb}{0.58,0,0.82}
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\definecolor{backcolour}{HTML}{fcf4e8}
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%----------------- Listings ---------------------------------------------------%
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\usepackage{listings}
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\lstset{
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backgroundcolor=\color{backcolour},
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commentstyle=\color{codegreen},
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keywordstyle=\color{magenta},
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numberstyle=\tiny\color{codegray},
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stringstyle=\color{codepurple},
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basicstyle=\ttfamily\footnotesize,
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breakatwhitespace=false,
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breaklines=true,
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captionpos=b,
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keepspaces=true,
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numbers=left,
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numbersep=5pt,
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showspaces=false,
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showstringspaces=false,
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showtabs=false,
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tabsize=2
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}
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%----------------- tikz -------------------------------------------------------%
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\usepackage{tikz}
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\usepackage{tikz-qtree}
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\usetikzlibrary{trees}
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%----------------- anamorphism's brackets -------------------------------------%
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\newcommand{\lanabracket}{\mathopen{[\!\!\!\:(}}
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\newcommand{\ranabracket}{\mathopen{)\!\!\!\:]}}
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%---------------- boxes -------------------------------------------------------%
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\usepackage[many]{tcolorbox}
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\tcbset{
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sharp corners,
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colback = white,
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before skip = 0.5cm,
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after skip = 0.5cm,
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breakable
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}
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\newtcolorbox{alert}{
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colback = Dandelion!7.5,
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enhanced,
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colframe = Dandelion!7.5,
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borderline west = {4pt}{0pt}{Dandelion!50},
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breakable
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}
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\newtcolorbox{bquote}{
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colback = url!5,
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enhanced,
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colframe = url!5,
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borderline west = {4pt}{0pt}{RoyalBlue!50},
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breakable
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}
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\tcbset{
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sharp corners,
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colback = white,
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before skip = 0.5cm,
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after skip = 0.5cm,
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boxsep=0mm,
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breakable
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}
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\newtcolorbox{normalbox}{
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colback = white,
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enhanced,
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colframe = black,
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boxrule = 0.5pt,
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breakable
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}
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%----------------- Using makeidx ----------------------------------------------%
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\usepackage{makeidx}
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\def\tree#1{\href{https://en.wikipedia.org/wiki/Tree_(data_structure)}{#1}\index{Árvore (Estrutura de Dados)}}
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\def\dijkstra#1{\href{https://en.wikipedia.org/wiki/Edsger_W._Dijkstra}{#1}\index{Edsger W. Dijkstra}}
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\def\shuntingYard#1{\href{https://en.wikipedia.org/wiki/Shunting_yard_algorithm}{#1}\index{Shunting Yard}}
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\def\sierpCarpet#1{\href{https://en.wikipedia.org/wiki/Sierpinski_carpet}{#1}\index{Fractal!Tapete de Sierpinski}}
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\def\sierpTriangle#1{\href{http://en.wikipedia.org/wiki/Sierpinski_triangle}{#1}\index{Fractal!Tri\^angulo de Sierpinski}}
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\def\fractal{\href{http://pt.wikipedia.org/wiki/Fractal}{fractal}\index{Fractal}}
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\def\svg{\href{https://svgwg.org/svg2-draft/}{SVG}\index{SVG (Scalable Vector Graphics)}}
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\def\xml{\href{https://en.wikipedia.org/wiki/XML}{XML}\index{XML (Extensible Markup Language)}}
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\def\DSL{\href{https://www.researchgate.net/publication/254462947_Experience_report_A_do-it-yourself_high-assurance_compiler}{DSL}\index{DSL (linguaguem específica para domínio)}}
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\def\DL{\href{https://roberttlange.github.io/posts/2019/08/blog-post-6/}{Deep Learning}\index{Deep Learning)}}
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\def\Fsharp{\href{https://fsharp.org}{F\#}\index{F\#}}
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\def\catalan#1{\href{https://en.wikipedia.org/wiki/Catalan_number}{#1}\index{Números de Catalan}}
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\def\bezier#1{\href{https://en.wikipedia.org/wiki/B\%C3\%A9zier_curve}{#1}\index{Curvas de Bézier}}
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\def\Nat{\href{https://haslab.github.io/CP/Material/Nat.hs}{Nat}\index{Cálculo de Programas!Material Pedagógico!Nat.hs}}
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\def\Cp{\href{https://haslab.github.io/CP/Material/Cp.hs}{Cp}\index{Cálculo de Programas!Material Pedagógico!Cp.hs}}
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%-------
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\def\random#1{\href{https://hackage.haskell.org/package/random-1.1/docs/System-Random.html}{#1}\index{Haskell!Monad!Random}}
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\def\truchet#1{\href{https://en.wikipedia.org/wiki/Truchet_tiles}{#1}\index{Mosaico de Truchet}}
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\def\BTree{\href{https://haslab.github.io/CP/Material/BTree.hs}{BTree}\index{Cálculo de Programas!Material Pedagógico!BTree.hs}}
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\def\Bibtex{\href{http://www.bibtex.org/}{Bib\TeX}\index{\LaTeX!\texttt{bibtex}}}
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\def\Exp{\href{https://haslab.github.io/CP/Material/Exp.hs}{Exp}\index{Cálculo de Programas!Material Pedagógico!Exp.hs}}
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\def\Rose{\href{https://haslab.github.io/CP/2223/Material/Rose.hs}{Rose Tree}\index{Cálculo de Programas!Material Pedagógico!Rose.hs}}
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\def\GHCi{\ghci{GHCi}}
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\def\IO{IO\index{Mónade!{IO}}}
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\def\Dist{Dist\index{Mónade!{Dist}}}
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\def\listM#1{#1\index{Mónade!Listas}}
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\def\Html{\textsc{Html}\index{HTML}}
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\def\LTree{\href{https://haslab.github.io/CP/Material/LTree.hs}{\textit{LTree}}\index{Cálculo de Programas!Material Pedagógico!LTree.hs}}
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\def\FTree{\href{https://haslab.github.io/CP/Material/FTree.hs}{\textit{FTree}}\index{Cálculo de Programas!Material Pedagógico!FTree.hs}}
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\def\mTree#1{\href{https://en.wikipedia.org/wiki/Merkle_tree}{#1}\index{Merkle tree}}
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\def\MerkleTree{\mTree{Merkle tree}}
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\def\Latex{\href{http://www.tug.org/index.html}{\LaTeX}\index{\LaTeX}}
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\def\LhsToTeX{\lhstotex{lhs2tex}}
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\def\List{\href{http://wiki.di.uminho.pt/twiki/pub/Education/CP/MaterialPedagogico/List.hs}{List}\index{Cálculo de Programas!Material Pedagógico!List.hs}}
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\def\Makeindex{\href{https://www.ctan.org/pkg/makeindex}{\texttt{makeindex}}\index{\LaTeX!\texttt{makeindex}}}
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\def\MaterialPedagogico{\material{material pedagógico}}
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\def\blockchain{\href{https://pt.wikipedia.org/wiki/Blockchain}{blockchain}\index{Blockchain}}
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\def\PFP{\href{http://web.engr.oregonstate.edu/~erwig/pfp}{PHP}\index{Haskell!Biblioteca!PFP}}
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\def\Probability{\href{http://wiki.di.uminho.pt/twiki/bin/view/Education/CP/MaterialPedagogico}{Probability}\index{Haskell!Biblioteca!Probability}}
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\def\QuickCheck{\href{https://wiki.haskell.org/Introduction_to_QuickCheck1}{QuickCheck}\index{Haskell!QuickCheck}}
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\def\Unix{\href{https://en.wikipedia.org/wiki/Unix}{Unix}\index{Unix}}
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\def\R{I\!\!R\index{Números reais ($I\!\!R$)}}
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\def\TUG{TUG\index{TeX!TeX Users Group (TUG)}}
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\def\alt#1#2{\mathopen{[}#1 , #2\mathclose{]}\index{Combinador ``pointfree''!\emph{either}}} % "either" is reserved...
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\def\ap#1#2{#1\,#2}
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\def\bang{{!}\index{Função!\emph{bang}}}
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\def\btree#1{\href{https://en.wikipedia.org/wiki/B-tree}{#1}\index{B-tree}}
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\def\B{\mathbb{B}\index{Booleans}}
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\def\CP{\href{https://haslab.github.io/CP/}{Cálculo de Programas}\index{Cálculo de Programas}}
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\def\N{\mathbb{N}\index{Números naturais ($I\!\!N$)}}
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\def\Q{\mathbb{Q}\index{Racionais}}
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\def\cata#1{\mathopen{\llparenthesis}#1\mathclose{\rrparenthesis}\index{Combinador ``pointfree''!\emph{cata}}}
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\def\cataList#1{\mathopen{\llparenthesis}#1\mathclose{\rrparenthesis}\index{Combinador ``pointfree''!\emph{cata}!Listas}}
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\def\anaList#1{\lanabracket#1\ranabracket\index{Combinador ``pointfree''!\emph{ana}!Listas}}
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\def\cataNat#1{\mathopen{\llparenthesis}#1\mathclose{\rrparenthesis}\index{Combinador ``pointfree''!\emph{cata}!Naturais}}
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\def\cp#1{\href{https://haslab.github.io/CP/}{#1}\index{Cálculo de Programas}}
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\def\dium{\htmladdnormallink{Departamento de Informática}{http://www.di.uminho.pt/}\index{U.Minho!Departamento de Informática}}
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\def\gloss#1{\href{https://hackage.haskell.org/package/gloss-1.13.1.1/docs/Graphics-Gloss.html}{#1}\index{Haskell!Gloss}}
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\def\graphviz#1{\href{https://www.graphviz.org/}{#1}\index{Graphviz}}
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\def\pd#1{\href{https://en.wikipedia.org/wiki/Dynamic_programming}{#1}\index{Programação!dinâmica}}
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\def\stack#1{\href{https://docs.haskellstack.org/en/stable/README/}{#1}\index{Haskell!Stack}}
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\def\xfig#1{\href{https://sourceforge.net/projects/mcj/}{#1}\index{X-fig}}
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\def\file#1{\texttt{#1}\index{Ficheiro!\texttt{#1}}}
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\def\ghci#1{\href{https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/ghci.html}{#1}\index{Haskell!interpretador!GHCi}}
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\def\graphviz#1{\href{http://graphviz.org/}{#1}\index{Graphviz}}
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\def\webgraphviz#1{\href{http://www.webgraphviz.com/}{#1}\index{Graphviz!WebGraphviz}}
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\def\gcc#1{\href{https://www.gnu.org/software/gcc/}{#1}\index{GCC}}
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\def\pda#1{\href{https://en.wikipedia.org/wiki/Stack_machine\#Simple_compilers}{#1}\index{Stack machine}}
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\def\haskell#1{\href{http://www.haskell.org}{#1}\index{Haskell}}
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\def\haskellf#1{\texttt{#1}\index{Função!\texttt{#1}}}
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\def\hcata{cata\index{Combinador ``pointfree''!\emph{cata}}}
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\def\iso{\mathbin{\cong}\index{Relação de isomorfismo}}
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\def\kons#1{\underline{#1}\index{Combinador ``pointfree''!função constante}}
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\def\length{\mathit{length}\index{Função!\emph{length}}}
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\def\lhaskell#1{#1\index{Haskell!Literate Haskell}}
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\def\lhstotex#1{\href{https://hackage.haskell.org/package/lhs2tex}{#1}\index{\LaTeX!\texttt{lhs2TeX}}}
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\def\litp#1{\href{http://www.literateprogramming.com}{#1}\index{Programação!literária}}
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\def\lsystem#1{\href{https://en.wikipedia.org/wiki/L-system}{#1}\index{L-system}}
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\def\map#1{\mathsf{map}\ #1\index{Função!\emph{map}}}
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\def\for#1#2{\mathsf{for}\ #1 #2\index{Função!\emph{for}}}
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\def\material#1{\href{https://haslab.github.io/CP/Material/}{#1}\index{Cálculo de Programas!Material Pedagógico}}
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\def\p#1{\pi_{#1}\index{Função!$\pi_#1$}}
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\def\ana#1{\lanabracket#1\ranabracket\index{Combinador ``pointfree''!\emph{ana}}}
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\def\split#1#2{\mathopen{\langle}#1 , #2\mathclose{\rangle}\index{Combinador ``pointfree''!\emph{split}}} % <a,b,...z>
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\def\succ#1{\mathsf{succ}\ #1\index{Função!\emph{succ}}}
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\def\taylor#1{\href{https://en.wikipedia.org/wiki/Taylor_series}{#1}\index{Taylor series!Maclaurin series}}
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\def\texcmd#1{\texttt{#1}\index{\LaTeX!macro!\texttt{#1}}}
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\def\trans#1{\overline{#1\rule{0pt}{.6em}}\index{Combinador ``pointfree''!transposição}}
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\def\uncurry #1{\widehat{#1}\index{Função!\emph{uncurry}}}
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\def\wc#1{\href{http://pubs.opengroup.org/onlinepubs/9699919799/utilities/wc.html}{#1}\index{Unix shell!wc}}
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\def\xypic#1{\textsc{#1}\index{\LaTeX!pacote!XY-pic}}
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%----------------- Extracted from jnobasics.sty -------------------------------%
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\long\def\pdfout#1{\relax}
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\def\mcond#1#2#3{#1 \rightarrow #2 , #3}
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\newenvironment{lcbr}{\left\{\begin{array}{l}}{\end{array}\right.}
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\newenvironment{calculation}{\begin{eqnarray*}&&}{\end{eqnarray*}}
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\def\eg{\emph{eg.}}
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\def\esimo#1{#1${.\kern-.1em}^{\super{o}}$}
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\def\esima#1{#1${.\kern-.1em}^{\super{a}}$}
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\def\super#1{\mbox{{\scriptsize #1}}}
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\def\comp{\mathbin{\cdot}}
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\def\implied{\mathbin\Leftarrow}
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\def\deff{\stackrel{\rm def}{=}} % Function definition symbol
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\def\kcomp{\mathbin{\bullet}}
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\def\conj#1#2{\mathopen{\langle} #1, #2 \mathclose{\rangle}}
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\def\start{&&}
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\def\more{\\&&}
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\def\qed{\\&\Box&}
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\def\just#1#2{\\ & \rule{2em}{0pt} \{ \mbox{\rule[-.7em]{0pt}{1.8em} \small #2 \/} \} \nonumber\\ && }
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%----------------- Cross references -------------------------------------------%
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\newlabel{eq:fokkinga}{{3.95}{112}{The mutual-recursion law}{section.3.17}{}}
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%----------------- Importing/modifying isolatin1 ------------------------------%
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%\usepackage{isolatin1}
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%\catcode181=13 \def^^b5{\mu} % 181, '265, "b5
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%\@ifundefined{lguill}{\def^^ab{``}}{\def^^ab{\lguill}}
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%\@ifundefined{rguill}{\def^^bb{''}}{\def^^bb{\rguill}}
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%\catcode186=13 \def^^ba{${\kern-.1em}^{\mbox{\scriptsize o}}$} % 186, '272, "ba
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%\catcode183=13 \def^^b7{\comp} % 183, '267, "b7
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%----------------- WWW interfacing desabled -----------------------------------%
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\let\pisca=\relax
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\def\quoteId#1#2{\textsl{#1}}
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\def\quoteUrl#1#2{\texttt{#2}}
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\let\htmladdnormallink=\quoteId % HTML links disabled by default
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%----------------- Shortcuts --------------------------------------------------%
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\def\Haskell{\haskell{Haskell}}
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\def\Graphviz{\graphviz{Graphviz}}
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\def\WebGraphviz{\webgraphviz{WebGraphviz}}
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\def\LSystems{\lsystem{L-Systems}}
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\def\LSystem{\lsystem{L-System}}
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%----------------- Date -------------------------------------------------------%
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\def\mydate{
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\ifcase\month\or
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Janeiro\or Fevereiro\or Março\or Abril\or Maio\or Junho\or Julho\or Agosto\or Setembro\or Outubro\or Novembro\or Dezembro\fi \ de \number\year
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}
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%----------------- Problemas ----------------------------------------------------%
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\newcount\pn \pn=1 % Problem number
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%\def\Problema{\section*{Problema \number\pn}\global\advance\pn by 1}
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\def\Problema{\section*{Problema \number\pn}\global\advance\pn by 1}
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%----------------- fim ----------------------------------------------------------%
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