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annotate agda/deltaM.agda @ 90:55d11ce7e223

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Unify levels on data type. only use suc to proofs
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 19 Jan 2015 12:11:38 +0900
parents 5411ce26d525
children bcd4fe52a504
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5411ce26d525 Defining DeltaM in Agda...
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1 open import Level
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2
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3 open import delta
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4 open import delta.functor
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5 open import nat
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6 open import laws
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7
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8 module deltaM where
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9
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10 -- DeltaM definitions
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11
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12 data DeltaM {l : Level}
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13 (M : {l' : Level} -> Set l' -> Set l')
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14 {functorM : {l' : Level} -> Functor {l'} M}
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15 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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16 (A : Set l)
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17 : Set l where
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18 deltaM : Delta (M A) -> DeltaM M {functorM} {monadM} A
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19
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20
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21 -- DeltaM utils
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22
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23 headDeltaM : {l : Level} {A : Set l}
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24 {M : {l' : Level} -> Set l' -> Set l'}
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25 {functorM : {l' : Level} -> Functor {l'} M}
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26 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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27 -> DeltaM M {functorM} {monadM} A -> M A
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28 headDeltaM (deltaM (mono x)) = x
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29 headDeltaM (deltaM (delta x _)) = x
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30
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31 tailDeltaM : {l : Level} {A : Set l}
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32 {M : {l' : Level} -> Set l' -> Set l'}
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33 {functorM : {l' : Level} -> Functor {l'} M}
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34 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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35 -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A
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36 tailDeltaM (deltaM (mono x)) = deltaM (mono x)
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37 tailDeltaM (deltaM (delta _ d)) = deltaM d
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38
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39 appendDeltaM : {l : Level} {A : Set l}
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40 {M : {l' : Level} -> Set l' -> Set l'}
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41 {functorM : {l' : Level} -> Functor {l'} M}
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42 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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43 -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A
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44 appendDeltaM (deltaM d) (deltaM dd) = deltaM (deltaAppend d dd)
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45
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46
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47 checkOut : {l : Level} {A : Set l}
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48 {M : {l' : Level} -> Set l' -> Set l'}
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49 {functorM : {l' : Level} -> Functor {l'} M}
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50 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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51 -> Nat -> DeltaM M {functorM} {monadM} A -> M A
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52 checkOut O (deltaM (mono x)) = x
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53 checkOut O (deltaM (delta x _)) = x
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54 checkOut (S n) (deltaM (mono x)) = x
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55 checkOut {l} {A} {M} {functorM} {monadM} (S n) (deltaM (delta _ d)) = checkOut {l} {A} {M} {functorM} {monadM} n (deltaM d)
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58 open Functor
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59 deltaM-fmap : {l : Level} {A B : Set l}
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60 {M : {l' : Level} -> Set l' -> Set l'}
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61 {functorM : {l' : Level} -> Functor {l'} M}
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62 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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63 -> (A -> B) -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} B
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64 deltaM-fmap {l} {A} {B} {M} {functorM} f (deltaM d) = deltaM (fmap delta-is-functor (fmap functorM f) d)