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annotate agda/list.agda @ 25:a5aadebc084d

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Define List in Agda
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Tue, 07 Oct 2014 10:38:57 +0900
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children 5ba82f107a95
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a5aadebc084d Define List in Agda
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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1 module list where
a5aadebc084d Define List in Agda
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2
a5aadebc084d Define List in Agda
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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3 open import Relation.Binary.PropositionalEquality
a5aadebc084d Define List in Agda
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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4 open ≡-Reasoning
a5aadebc084d Define List in Agda
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5
a5aadebc084d Define List in Agda
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6 infixr 40 _::_
a5aadebc084d Define List in Agda
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7 data List (A : Set) : Set where
a5aadebc084d Define List in Agda
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8 [] : List A
a5aadebc084d Define List in Agda
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9 _::_ : A -> List A -> List A
a5aadebc084d Define List in Agda
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a5aadebc084d Define List in Agda
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a5aadebc084d Define List in Agda
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12 infixl 30 _++_
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13 _++_ : {A : Set} -> List A -> List A -> List A
a5aadebc084d Define List in Agda
Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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14 [] ++ ys = ys
a5aadebc084d Define List in Agda
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15 (x :: xs) ++ ys = x :: (xs ++ ys)
a5aadebc084d Define List in Agda
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18 empty-append : {A : Set} -> (xs : List A) -> xs ++ [] ≡ [] ++ xs
a5aadebc084d Define List in Agda
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19 empty-append [] = refl
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20 empty-append (x :: xs) = begin
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21 x :: (xs ++ [])
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Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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22 ≡⟨ cong (_::_ x) (empty-append xs) ⟩
a5aadebc084d Define List in Agda
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23 x :: xs
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24 ∎