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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 a271f3ff1922
children 5bd5f4a7ce8d
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1 open import Level
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3 open import basic
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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 revision
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8 open import laws
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9
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10 module deltaM where
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11
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12 -- DeltaM definitions
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14 data DeltaM {l : Level}
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15 (M : {l' : Level} -> Set l' -> Set l')
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16 {functorM : {l' : Level} -> Functor {l'} M}
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17 {monadM : {l' : Level} {A : Set l'} -> Monad {l'} M functorM}
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18 (A : Set l)
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19 : (Rev -> Set l) where
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20 deltaM : {v : Rev} -> Delta (M A) v -> DeltaM M {functorM} {monadM} A v
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22
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23 -- DeltaM utils
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25 headDeltaM : {l : Level} {A : Set l} {v : Rev}
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26 {M : {l' : Level} -> Set l' -> Set l'}
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27 {functorM : {l' : Level} -> Functor {l'} M}
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28 {monadM : {l' : Level} -> Monad {l'} M functorM}
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29 -> DeltaM M {functorM} {monadM} A v -> M A
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30 headDeltaM (deltaM d) = headDelta d
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33 tailDeltaM : {l : Level} {A : Set l} {v : Rev}
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34 {M : {l' : Level} -> Set l' -> Set l'}
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35 {functorM : {l' : Level} -> Functor {l'} M}
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36 {monadM : {l' : Level} -> Monad {l'} M functorM}
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37 -> DeltaM {l} M {functorM} {monadM} A (commit v) -> DeltaM M {functorM} {monadM} A v
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38 tailDeltaM {_} {n} (deltaM d) = deltaM (tailDelta d)
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41 appendDeltaM : {l : Level} {A : Set l} {n m : Rev}
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42 {M : {l' : Level} -> Set l' -> Set l'}
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43 {functorM : {l' : Level} -> Functor {l'} M}
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44 {monadM : {l' : Level} -> Monad {l'} M functorM}
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45 -> DeltaM M {functorM} {monadM} A n -> DeltaM M {functorM} {monadM} A m -> DeltaM M {functorM} {monadM} A (merge n m)
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46 appendDeltaM (deltaM d) (deltaM dd) = deltaM (deltaAppend d dd)
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51 -- functor definitions
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52 open Functor
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53 deltaM-fmap : {l : Level} {A B : Set l} {n : Rev}
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54 {M : {l' : Level} -> Set l' -> Set l'}
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55 {functorM : {l' : Level} -> Functor {l'} M}
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56 {monadM : {l' : Level} -> Monad {l'} M functorM}
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57 -> (A -> B) -> DeltaM M {functorM} {monadM} A n -> DeltaM M {functorM} {monadM} B n
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58 deltaM-fmap {l} {A} {B} {n} {M} {functorM} f (deltaM d) = deltaM (fmap delta-is-functor (fmap functorM f) d)
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63 -- monad definitions
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64 open Monad
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66 deltaM-eta : {l : Level} {A : Set l} {v : Rev}
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67 {M : {l' : Level} -> Set l' -> Set l'}
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68 {functorM : {l' : Level} -> Functor {l'} M}
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69 {monadM : {l' : Level} -> Monad {l'} M functorM}
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70 -> A -> (DeltaM M {functorM} {monadM} A v)
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71 deltaM-eta {v = init} {monadM = mm} x = deltaM (mono (eta mm x))
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72 deltaM-eta {v = (commit v)} {monadM = mm} x = appendDeltaM (deltaM (mono (eta mm x)))
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73 (deltaM-eta {v = v} x)
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76 deltaM-bind : {l : Level} {A B : Set l} {v : Rev}
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77 {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} -> Monad {l'} M functorM}
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80 -> (DeltaM M {functorM} {monadM} A v) -> (A -> DeltaM M {functorM} {monadM} B v) -> DeltaM M {functorM} {monadM} B v
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81 deltaM-bind {v = init} {monadM = mm} (deltaM (mono x)) f = deltaM (mono (bind mm x (headDeltaM ∙ f)))
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82 deltaM-bind {v = commit v} {monadM = mm} (deltaM (delta x d)) f = appendDeltaM (deltaM (mono (bind mm x (headDeltaM ∙ f))))
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83 (deltaM-bind (deltaM d) (tailDeltaM ∙ f))
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86 deltaM-mu : {l : Level} {A : Set l} {v : Rev}
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87 {M : {l' : Level} -> Set l' -> Set l'}
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88 {functorM : {l' : Level} -> Functor {l'} M}
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89 {monadM : {l' : Level} -> Monad {l'} M functorM}
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90 -> (DeltaM M {functorM} {monadM} (DeltaM M {functorM} {monadM} A v) v) -> DeltaM M {functorM} {monadM} A v
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91 deltaM-mu d = deltaM-bind d id