72 lines
1.9 KiB
TeX
72 lines
1.9 KiB
TeX
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\documentclass{article}
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\usepackage[utf8x]{inputenc}
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\usepackage{amssymb}
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\usepackage{color}
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\definecolor{keywordcolor}{rgb}{0.7, 0.1, 0.1} % red
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\definecolor{tacticcolor}{rgb}{0.1, 0.2, 0.6} % blue
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\definecolor{commentcolor}{rgb}{0.4, 0.4, 0.4} % grey
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\definecolor{symbolcolor}{rgb}{0.0, 0.1, 0.6} % blue
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\definecolor{sortcolor}{rgb}{0.1, 0.5, 0.1} % green
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\usepackage{listings}
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\def\lstlanguagefiles{lstlean.tex}
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\lstset{language=lean}
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\title{The Lean listing style}
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\author{Jeremy Avigad}
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\begin{document}
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\maketitle
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This is an example of how to use \verb=lstlean.tex= to typeset your Lean code. Here is some code: \lstinline{theorem foo (x y : ℕ), x + y = y + x}. Here are the translations of some unicode symbols:
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\begin{lstlisting}
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Some symbols: ℕ ℤ ∩ ⊂ ∀ ∃ Π α β γ ∈ ⦃ ⦄
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\end{lstlisting}
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Here is a block of code:
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\begin{lstlisting}
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/-
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Basic properties of lists.
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-/
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import logic tools.helper_tactics data.nat.basic algebra.function
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open eq.ops helper_tactics nat prod function option
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inductive list (T : Type) : Type :=
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| nil {} : list T
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| cons : T → list T → list T
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namespace list
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notation h :: t := cons h t
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notation `[` l:(foldr `,` (h t, cons h t) nil `]`) := l
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variable {T : Type}
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/- append -/
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definition append : list T → list T → list T
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| [] l := l
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| (h :: s) t := h :: (append s t)
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notation l₁ ++ l₂ := append l₁ l₂
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theorem append_nil_left (t : list T) : [] ++ t = t
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theorem append_cons (x : T) (s t : list T) : (x::s) ++ t = x::(s ++ t)
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theorem append_nil_right : ∀ (t : list T), t ++ [] = t
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| [] := rfl
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| (a :: l) := calc
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(a :: l) ++ [] = a :: (l ++ []) : rfl
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... = a :: l : append_nil_right l
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theorem append.assoc : ∀ (s t u : list T), s ++ t ++ u = s ++ (t ++ u)
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| [] t u := rfl
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| (a :: l) t u :=
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show a :: (l ++ t ++ u) = (a :: l) ++ (t ++ u),
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by rewrite (append.assoc l t u)
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\end{lstlisting}
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\end{document}
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