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Fix implicit values in deltaM-mu
author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 19 Jan 2015 17:47:55 +0900
parents bcd4fe52a504
children d8cd880f1d78
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1 open import Level
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2
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3 open import basic
89
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4 open import delta
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5 open import delta.functor
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6 open import nat
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7 open import laws
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8
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9 module deltaM where
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10
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11 -- DeltaM definitions
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12
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13 data DeltaM {l : Level}
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14 (M : {l' : Level} -> Set l' -> Set l')
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15 {functorM : {l' : Level} -> Functor {l'} M}
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16 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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17 (A : Set l)
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18 : Set l where
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19 deltaM : Delta (M A) -> DeltaM M {functorM} {monadM} A
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20
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21
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22 -- DeltaM utils
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23
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24 headDeltaM : {l : Level} {A : Set l}
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25 {M : {l' : Level} -> Set l' -> Set l'}
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26 {functorM : {l' : Level} -> Functor {l'} M}
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27 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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28 -> DeltaM M {functorM} {monadM} A -> M A
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29 headDeltaM (deltaM (mono x)) = x
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30 headDeltaM (deltaM (delta x _)) = x
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31
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32 tailDeltaM : {l : Level} {A : Set l}
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33 {M : {l' : Level} -> Set l' -> Set l'}
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34 {functorM : {l' : Level} -> Functor {l'} M}
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35 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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36 -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A
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37 tailDeltaM (deltaM (mono x)) = deltaM (mono x)
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38 tailDeltaM (deltaM (delta _ d)) = deltaM d
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39
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40 appendDeltaM : {l : Level} {A : Set l}
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41 {M : {l' : Level} -> Set l' -> Set l'}
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42 {functorM : {l' : Level} -> Functor {l'} M}
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43 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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44 -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A
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45 appendDeltaM (deltaM d) (deltaM dd) = deltaM (deltaAppend d dd)
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46
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47
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48 checkOut : {l : Level} {A : Set l}
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49 {M : {l' : Level} -> Set l' -> Set l'}
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50 {functorM : {l' : Level} -> Functor {l'} M}
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51 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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52 -> Nat -> DeltaM M {functorM} {monadM} A -> M A
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53 checkOut O (deltaM (mono x)) = x
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54 checkOut O (deltaM (delta x _)) = x
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55 checkOut (S n) (deltaM (mono x)) = x
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56 checkOut {l} {A} {M} {functorM} {monadM} (S n) (deltaM (delta _ d)) = checkOut {l} {A} {M} {functorM} {monadM} n (deltaM d)
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57
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59
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60 -- functor definitions
90
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61 open Functor
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62 deltaM-fmap : {l : Level} {A B : Set l}
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63 {M : {l' : Level} -> Set l' -> Set l'}
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64 {functorM : {l' : Level} -> Functor {l'} M}
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65 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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66 -> (A -> B) -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} B
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67 deltaM-fmap {l} {A} {B} {M} {functorM} f (deltaM d) = deltaM (fmap delta-is-functor (fmap functorM f) d)
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68
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69 -- monad definitions
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70 open Monad
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71 deltaM-eta : {l : Level} {A B : Set l} {M : {l' : Level} -> Set l' -> Set l'}
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72 {functorM : {l' : Level} -> Functor {l'} M}
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73 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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74 -> A -> (DeltaM M {functorM} {monadM} A)
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75 deltaM-eta {_} {A} {_} {_} {_} {monadM} x = deltaM (mono (eta {_} {A} monadM x))
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76
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77 deltaM-bind : {l : Level} {A B : Set l} {M : {l' : Level} -> Set l' -> Set l'}
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78 {functorM : {l' : Level} -> Functor {l'} M}
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79 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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80 -> (DeltaM M {functorM} {monadM} A) -> (A -> DeltaM M {functorM} {monadM} B) -> DeltaM M {functorM} {monadM} B
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81 deltaM-bind {l} {A} {B} {M} {functorM} {monadM} (deltaM (mono x)) f = deltaM (mono (bind {l} {A} monadM x (headDeltaM ∙ f)))
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82 deltaM-bind {l} {A} {B} {M} {functorM} {monadM} (deltaM (delta x d)) f = appendDeltaM (deltaM (mono (bind {l} {A} monadM x (headDeltaM ∙ f))))
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83 (deltaM-bind (deltaM d) (tailDeltaM ∙ f))
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84
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85 deltaM-mu : {l : Level} {A : Set l} {M : {l' : Level} -> Set l' -> Set l'}
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86 {functorM : {l' : Level} -> Functor {l'} M}
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87 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
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88 -> (DeltaM M {functorM} {monadM} (DeltaM M {functorM} {monadM} A)) -> DeltaM M {functorM} {monadM} A
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89 deltaM-mu d = deltaM-bind d id