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Trying redenition Delta with length constraints
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 26 Jan 2015 23:00:05 +0900
parents f26a954cd068
children e6499a50ccbd
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6789c65a75bc Split functor-proofs into delta.functor
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1 open import Level
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2 open import Relation.Binary.PropositionalEquality
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3
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5 open import basic
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6 open import delta
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7 open import laws
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8 open import nat
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9 open import revision
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10
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6789c65a75bc Split functor-proofs into delta.functor
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13 module delta.functor where
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14
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15 -- Functor-laws
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16
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17 -- Functor-law-1 : T(id) = id'
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18 functor-law-1 : {l : Level} {A : Set l} {n : Rev} -> (d : Delta A n) -> (delta-fmap id) d ≡ id d
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19 functor-law-1 (mono x) = refl
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20 functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d)
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21
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22 -- Functor-law-2 : T(f . g) = T(f) . T(g)
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23 functor-law-2 : {l : Level} {n : Rev} {A B C : Set l} ->
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24 (f : B -> C) -> (g : A -> B) -> (d : Delta A n) ->
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8d92ed54a94f Prove functor-laws for deltaM
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25 (delta-fmap (f ∙ g)) d ≡ ((delta-fmap f) ∙ (delta-fmap g)) d
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26 functor-law-2 f g (mono x) = refl
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27 functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d)
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29 delta-is-functor : {l : Level} {n : Rev} -> Functor {l} (\A -> Delta A n)
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5411ce26d525 Defining DeltaM in Agda...
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30 delta-is-functor = record { fmap = delta-fmap ;
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31 preserve-id = functor-law-1;
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32 covariant = \f g -> functor-law-2 g f}