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| author | Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp> |
|---|---|
| date | Sat, 22 Nov 2014 18:31:33 +0900 |
| parents | 46b15f368905 |
| children | 0f308ddd6136 |
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open import list open import basic open import Level open import Relation.Binary.PropositionalEquality open ≡-Reasoning module delta where data Delta {l : Level} (A : Set l) : (Set (suc l)) where mono : A -> Delta A delta : A -> Delta A -> Delta A deltaAppend : {l : Level} {A : Set l} -> Delta A -> Delta A -> Delta A deltaAppend (mono x) d = delta x d deltaAppend (delta x d) ds = delta x (deltaAppend d ds) headDelta : {l : Level} {A : Set l} -> Delta A -> Delta A headDelta (mono x) = mono x headDelta (delta x _) = mono x tailDelta : {l : Level} {A : Set l} -> Delta A -> Delta A tailDelta (mono x) = mono x tailDelta (delta _ d) = d -- Functor fmap : {l ll : Level} {A : Set l} {B : Set ll} -> (A -> B) -> (Delta A) -> (Delta B) fmap f (mono x) = mono (f x) fmap f (delta x d) = delta (f x) (fmap f d) -- Monad (Category) eta : {l : Level} {A : Set l} -> A -> Delta A eta x = mono x bind : {l ll : Level} {A : Set l} {B : Set ll} -> (Delta A) -> (A -> Delta B) -> Delta B bind (mono x) f = f x bind (delta x d) f = deltaAppend (headDelta (f x)) (bind d (tailDelta ∙ f)) -- can not apply id. because different Level mu : {l : Level} {A : Set l} -> Delta (Delta A) -> Delta A mu d = bind d id returnS : {l : Level} {A : Set l} -> A -> Delta A returnS x = mono x returnSS : {l : Level} {A : Set l} -> A -> A -> Delta A returnSS x y = deltaAppend (returnS x) (returnS y) -- Monad (Haskell) return : {l : Level} {A : Set l} -> A -> Delta A return = eta _>>=_ : {l ll : Level} {A : Set l} {B : Set ll} -> (x : Delta A) -> (f : A -> (Delta B)) -> (Delta B) (mono x) >>= f = f x (delta x d) >>= f = deltaAppend (headDelta (f x)) (d >>= (tailDelta ∙ f)) -- proofs -- Functor-laws -- Functor-law-1 : T(id) = id' functor-law-1 : {l : Level} {A : Set l} -> (d : Delta A) -> (fmap id) d ≡ id d functor-law-1 (mono x) = refl functor-law-1 (delta x d) = cong (delta x) (functor-law-1 d) -- Functor-law-2 : T(f . g) = T(f) . T(g) functor-law-2 : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} -> (f : B -> C) -> (g : A -> B) -> (d : Delta A) -> (fmap (f ∙ g)) d ≡ ((fmap f) ∙ (fmap g)) d functor-law-2 f g (mono x) = refl functor-law-2 f g (delta x d) = cong (delta (f (g x))) (functor-law-2 f g d) -- Monad-laws (Category) -- monad-law-1 : join . fmap join = join . join monad-law-1 : {l : Level} {A : Set l} -> (d : Delta (Delta (Delta A))) -> ((mu ∙ (fmap mu)) d) ≡ ((mu ∙ mu) d) monad-law-1 (mono d) = refl monad-law-1 (delta (mono (mono x)) (mono (mono (mono x₁)))) = refl monad-law-1 (delta (mono (delta x x₁)) (mono (mono (mono x₂)))) = refl monad-law-1 (delta (delta (mono x) (mono x₁)) (mono (mono (mono x₂)))) = refl monad-law-1 (delta (delta (delta x x₁) (mono x₂)) (mono (mono (mono x₃)))) = refl monad-law-1 (delta (delta (mono x) (delta (mono x₁) x₂)) (mono (mono (mono x₃)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (mono x₂) x₃)) (mono (mono (mono x₄)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (mono (mono x₃)))) (mono (mono (mono x₄)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (mono x₃)) (mono (mono x₄)))) (mono (mono (mono x₅)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (mono x₃))) (mono (mono x₄)))) (mono (mono (mono x₅)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (mono x₄))) (mono (mono x₅)))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (mono x₄)))) (mono (mono x₅)))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (mono (mono x₆)))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))) (mono (mono x₆)))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (mono (mono x₇)))) (mono (mono (mono x₈)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ x₆))))) (mono (mono x₇)))) (mono (mono (mono x₈)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ x₇))))) (mono (mono x₈)))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (mono (delta x₃ (mono x₄))))) (mono (mono (mono x₅)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (mono x₃)) (mono (delta x₄ (mono x₅))))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ x₃)) (mono (delta x₄ (mono x₅))))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ x₄)) (mono (delta x₅ (mono x₆))))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (mono (delta x₃ (delta x₄ (mono x₅)))))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (mono x₃)) (mono (delta x₄ (delta x₅ (mono x₆)))))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (mono x₃))) (mono (delta x₄ (delta x₅ (mono x₆)))))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (delta x (mono x₁)) (delta (delta x₂ (delta x₃ (mono x₄))) (mono (delta x₅ (delta x₆ (mono x₇)))))) (mono (mono (mono x₈)))) = refl monad-law-1 (delta (delta (delta x (delta x₁ x₂)) (delta (delta x₃ (delta x₄ (mono x₅))) (mono (delta x₆ (delta x₇ (mono x₈)))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (mono x₄)))) (mono (delta x₅ (delta x₆ (mono x₇)))))) (mono (mono (mono x₈)))) = refl monad-law-1 (delta (delta (delta x (mono x₁)) (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (mono (delta x₆ (delta x₇ (mono x₈)))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (delta x (delta x₁ x₂)) (delta (delta x₃ (delta x₄ (delta x₅ (mono x₆)))) (mono (delta x₇ (delta x₈ (mono x₉)))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))) (mono (delta x₆ (delta x₇ (mono x₈)))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (delta x (mono x₁)) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (mono (delta x₇ (delta x₈ (mono x₉)))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (delta x (delta x₁ x₂)) (delta (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇))))) (mono (delta x₈ (delta x₉ (mono x₁₀)))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆)))))) (mono (delta x₇ (delta x₈ (mono x₉)))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (mono (delta x₈ (delta x₉ (mono x₁₀)))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇))))))) (mono (delta x₈ (delta x₉ (mono x₁₀)))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (mono (delta x₉ (delta x₁₀ (mono x₁₁)))))) (mono (mono (mono x₁₂)))) = refl -- x (Delta A)... x7 monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ x₈))))))) (mono (delta x₉ (delta x₁₀ (mono x₁₁)))))) (mono (mono (mono x₁₂)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ x₉))))))) (mono (delta x₁₀ (delta x₁₁ (mono x₁₂)))))) (mono (mono (mono x₁₃)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (mono (delta x₃ (delta x₄ (delta x₅ (mono x₆))))))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (mono x₃)) (mono (delta x₄ (delta x₅ (delta x₆ (mono x₇))))))) (mono (mono (mono x₈)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (mono x₃))) (mono (delta x₄ (delta x₅ (delta x₆ (mono x₇))))))) (mono (mono (mono x₈)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (mono x₄))) (mono (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (mono x₄)))) (mono (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (mono (delta x₆ (delta x₇ (delta x₈ (mono x₉))))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))) (mono (delta x₆ (delta x₇ (delta x₈ (mono x₉))))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (mono (delta x₇ (delta x₈ (delta x₉ (mono x₁₀))))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆)))))) (mono (delta x₇ (delta x₈ (delta x₉ (mono x₁₀))))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (mono (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁))))))) (mono (mono (mono x₁₂)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇))))))) (mono (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁))))))) (mono (mono (mono x₁₂)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (mono (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂))))))) (mono (mono (mono x₁₃)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ x₈))))))) (mono (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂))))))) (mono (mono (mono x₁₃)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ x₉))))))) (mono (delta x₁₀ (delta x₁₁ (delta x₁₂ (mono x₁₃))))))) (mono (mono (mono x₁₄)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (mono (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))))) (mono (mono (mono x₈)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (mono x₃)) (mono (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈)))))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (mono x₃))) (mono (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈)))))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (mono x₄))) (mono (delta x₅ (delta x₆ (delta x₇ (delta x₈ (mono x₉)))))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (mono x₄)))) (mono (delta x₅ (delta x₆ (delta x₇ (delta x₈ (mono x₉)))))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (mono (delta x₆ (delta x₇ (delta x₈ (delta x₉ (mono x₁₀)))))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))) (mono (delta x₆ (delta x₇ (delta x₈ (delta x₉ (mono x₁₀)))))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (mono (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁)))))))) (mono (mono (mono x₁₂)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆)))))) (mono (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁)))))))) (mono (mono (mono x₁₂)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (mono (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂)))))))) (mono (mono (mono x₁₃)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇))))))) (mono (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂)))))))) (mono (mono (mono x₁₃)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (mono (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (mono x₁₃)))))))) (mono (mono (mono x₁₄)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ x₈))))))) (mono (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (mono x₁₃)))))))) (mono (mono (mono x₁₄)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ x₉))))))) (mono (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (mono x₁₄)))))))) (mono (mono (mono x₁₅)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (mono (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ x₈)))))))) (mono (mono (mono x₉)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (mono x₃)) (mono (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ x₉)))))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (mono x₃))) (mono (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ x₉)))))))) (mono (mono (mono x₁₀)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (mono x₄))) (mono (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ x₁₀)))))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (mono x₄)))) (mono (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ x₁₀)))))))) (mono (mono (mono x₁₁)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (mono (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ x₁₁)))))))) (mono (mono (mono x₁₂)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))) (mono (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ x₁₁)))))))) (mono (mono (mono x₁₂)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (mono (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ x₁₂)))))))) (mono (mono (mono x₁₃)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆)))))) (mono (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ x₁₂)))))))) (mono (mono (mono x₁₃)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (mono (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ x₁₃)))))))) (mono (mono (mono x₁₄)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇))))))) (mono (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ x₁₃)))))))) (mono (mono (mono x₁₄)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (mono (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ x₁₄)))))))) (mono (mono (mono x₁₅)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ x₈))))))) (mono (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ x₁₄)))))))) (mono (mono (mono x₁₅)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ x₉))))))) (mono (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ x₁₅)))))))) (mono (mono (mono x₁₆)))) = refl -- 0, 2 monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (delta (mono x₃) (mono (mono x₄))))) (mono (mono (mono x₅)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (delta (mono x₃) (mono (delta x₄ (mono x₅)))))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (delta (mono x₃) (mono (delta x₄ (delta x₅ x₆)))))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (delta (mono x₃) (delta x₄ (mono x₅))))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (delta (mono x₃) (delta x₄ (delta x₅ x₆))))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (delta (delta x₃ x₄) (mono x₅)))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (mono x₂)) (delta (delta x₃ x₄) (delta x₅ x₆)))) (mono (mono (mono x₇)))) = refl monad-law-1 (delta (delta (mono x) (delta (delta x₁ (delta x₂ x₃)) (delta x₄ x₅))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta (delta x₂ x₃) (delta x₄ x₅))) (mono (mono (mono x₆)))) = refl monad-law-1 (delta (mono x) (mono (mono (delta x₁ d)))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (mono (mono (delta x₂ (mono x₃))))) = refl monad-law-1 (delta (delta (delta x x₁) (mono (mono x₂))) (mono (mono (delta x₃ (mono x₄))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (mono (mono (delta x₃ (mono x₄))))) = refl monad-law-1 (delta (delta (delta x x₁) (mono (delta x₂ (mono x₃)))) (mono (mono (delta x₄ (mono x₅))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ x₃)))) (mono (mono (delta x₄ (mono x₅))))) = refl monad-law-1 (delta (delta (delta x x₁) (mono (delta x₂ (delta x₃ x₄)))) (mono (mono (delta x₅ (mono x₆))))) = refl monad-law-1 (delta (delta (mono x) (mono x₁)) (mono (mono (delta x₂ (delta x₃ d))))) = refl monad-law-1 (delta (delta (delta x x₁) (mono x₂)) (mono (mono (delta x₃ (delta x₄ d))))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ (mono x₂))) (mono (mono (delta x₃ d)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta x₂ (mono x₃))) (mono (mono (delta x₄ d)))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ (delta x₂ x₃))) (mono (mono (delta x₄ d)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta x₂ (delta x₃ x₄))) (mono (mono (delta x₅ d)))) = refl monad-law-1 (delta (mono (mono x)) (mono (delta (mono x₁) d₁))) = refl monad-law-1 (delta (mono (mono x)) (mono (delta (delta x₁ d) d₁))) = refl monad-law-1 (delta (mono (delta x (mono x₁))) (mono (delta (mono x₂) (mono d₁)))) = refl monad-law-1 (delta (mono (delta x (mono x₁))) (mono (delta (delta x₂ d) (mono d₁)))) = refl monad-law-1 (delta (mono (delta x (delta x₁ x₂))) (mono (delta (mono x₃) (mono d₁)))) = refl monad-law-1 (delta (mono (delta x (delta x₁ x₂))) (mono (delta (delta x₃ d) (mono d₁)))) = refl monad-law-1 (delta (mono (delta x x₁)) (mono (delta (mono x₂) (delta d₁ (mono d₂))))) = refl monad-law-1 (delta (mono (delta x x₁)) (mono (delta (delta x₂ d) (delta d₁ (mono d₂))))) = refl monad-law-1 (delta (mono (delta x x₁)) (mono (delta (mono x₂) (delta d₁ (delta d₂ (mono d₃)))))) = refl monad-law-1 (delta (mono (delta x x₁)) (mono (delta (delta x₂ d) (delta d₁ (delta d₂ (mono d₃)))))) = refl monad-law-1 (delta (mono (delta x (mono x₁))) (mono (delta (mono x₂) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x (mono x₁))) (mono (delta (delta x₂ d) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x (delta x₁ (mono x₂)))) (mono (delta (mono x₃) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x (delta x₁ (mono x₂)))) (mono (delta (delta x₃ d) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x (delta x₁ (delta x₂ (mono x₃))))) (mono (delta (mono x₄) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x (delta x₁ (delta x₂ (mono x₃))))) (mono (delta (delta x₄ d) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x (delta x₁ (delta x₂ (delta x₃ x₄))))) (mono (delta (mono x₅) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x (delta x₁ (delta x₂ (delta x₃ x₄))))) (mono (delta (delta x₅ d) (delta d₁ (delta d₂ (delta d₃ d₄)))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (mono (delta (mono x₂) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (mono (delta (delta x₂ d) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (mono (delta (mono x₃) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (mono (delta (delta x₃ d) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (mono (delta (mono x₄) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (mono (delta (delta x₄ d) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (mono x₄)))))) (mono (delta (mono x₅) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (mono x₄)))))) (mono (delta (delta x₅ d) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ x₅)))))) (mono (delta (mono x₆) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ x₅)))))) (mono (delta (delta x₆ d) (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (mono (delta (mono x₂) (delta d₁ (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (mono (delta (delta x₂ d) (delta d₁ (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ x₂))) (mono (delta (mono x₃) (delta d₁ (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ x₂))) (mono (delta (delta x₃ d) (delta d₁ (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono x₁)) (mono (delta (mono x₂) (delta d₁ (delta d₂ d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono x₁)) (mono (delta (delta x₂ d) (delta d₁ (delta d₂ d₃))))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ x₂)) (mono (delta (mono x₃) d₁))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ x₂)) (mono (delta (delta x₃ d) d₁))) = refl monad-law-1 (delta (delta (delta x x₁) x₂) (mono (delta (mono x₃) d₁))) = refl monad-law-1 (delta (delta (delta x x₁) x₂) (mono (delta (delta x₃ d) d₁))) = refl -- monad-law-1 (delta (mono x) (delta (mono (mono x₁)) (mono (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (mono x₁)) (delta (mono (mono x₂)) (mono (mono d₁)))) = refl monad-law-1 (delta (delta (delta x x₁) (mono x₂)) (delta (mono (mono x₃)) (mono (mono d₁)))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ x₂)) (delta (mono (mono x₃)) (mono (mono d₁)))) = refl monad-law-1 (delta (delta (delta x x₁) (delta x₂ x₃)) (delta (mono (mono x₄)) (mono (mono d₁)))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (mono x₂) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (mono x₂) (delta (mono x₃) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (mono x₂) (delta (delta x₃ (mono x₄)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (mono x₂) (delta (delta x₃ (delta x₄ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (mono x₃)) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (mono x₃)) (delta (mono x₄) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (mono x₃)) (delta (delta x₄ (mono x₅)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (mono x₃)) (delta (delta x₄ (delta x₅ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (mono x₄))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (mono x₄))) (delta (mono x₅) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (mono x₄))) (delta (delta x₅ (mono x₆)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (mono x₄))) (delta (delta x₅ (delta x₆ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (delta (mono x₆) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (delta (delta x₆ (mono x₇)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (mono x₅)))) (delta (delta x₆ (delta x₇ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (delta (mono x₇) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (delta (delta x₇ (mono x₈)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆))))) (delta (delta x₇ (delta x₈ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (mono x₈) (mono (mono x₉))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (mono x₉)) (mono (mono x₁₀))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (delta x₉ d₂)) (mono (mono x₁₀))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (mono x₈) (mono (delta x₉ d₃))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (mono x₉)) (mono (delta x₁₀ (mono x₁₁)))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (delta x₉ d₂)) (mono (delta x₁₀ (mono x₁₁)))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (mono x₉)) (mono (delta x₁₀ (delta x₁₁ d₃)))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (delta x₉ d₂)) (mono (delta x₁₀ (delta x₁₁ d₃)))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (mono x₈) (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (mono x₉)) (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (mono x₇)))))) (delta (delta x₈ (delta x₉ d₂)) (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (mono x₉) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (mono x₁₀)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (delta x₁₀ d₂)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (mono x₁₀)) (delta d₃ (mono d₄))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (delta x₁₀ d₂)) (delta d₃ (mono d₄))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (mono x₁₀)) (delta (mono x₁₁) (delta (mono x₁₂) (mono (mono x₁₃))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (delta x₁₀ d₂)) (delta (mono x₁₁) (delta (mono x₁₂) (mono (mono x₁₃))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (mono x₁₀)) (delta (delta x₁₁ d₃) (delta (mono x₁₂) (mono (mono x₁₃))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (delta x₁₀ d₂)) (delta (delta x₁₁ d₃) (delta (mono x₁₂) (mono (mono x₁₃))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (mono x₁₀)) (delta d₃ (delta (delta x₁₁ d₄) (mono (mono x₁₂))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (delta x₁₀ d₂)) (delta d₃ (delta (delta x₁₁ d₄) (mono (mono x₁₂))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (mono x₁₀)) (delta d₃ (delta d₄ (mono (delta x₁₁ d₅))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (delta x₁₀ d₂)) (delta d₃ (delta d₄ (mono (delta x₁₁ d₅))))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (mono x₁₀)) (delta d₃ (delta d₄ (delta d₅ d₆)))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (mono x₈))))))) (delta (delta x₉ (delta x₁₀ d₂)) (delta d₃ (delta d₄ (delta d₅ d₆)))))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (mono x₉)))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (mono x₉)))))))) (delta (mono x₁₀) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (mono x₉)))))))) (delta (delta x₁₀ (mono x₁₁)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (mono x₉)))))))) (delta (delta x₁₀ (delta x₁₁ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (mono x₁₀))))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (mono x₁₀))))))))) (delta (mono x₁₁) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (mono x₁₀))))))))) (delta (delta x₁₁ (mono x₁₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (mono x₁₀))))))))) (delta (delta x₁₁ (delta x₁₂ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁)))))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁)))))))))) (delta (mono x₁₂) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁)))))))))) (delta (delta x₁₂ (mono x₁₃)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (mono x₁₁)))))))))) (delta (delta x₁₂ (delta x₁₃ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂))))))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂))))))))))) (delta (mono x₁₃) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂))))))))))) (delta (delta x₁₃ (mono x₁₄)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (mono x₁₂))))))))))) (delta (delta x₁₃ (delta x₁₄ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (mono x₁₃)))))))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (mono x₁₃)))))))))))) (delta (mono x₁₄) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (mono x₁₃)))))))))))) (delta (delta x₁₄ (mono x₁₅)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (mono x₁₃)))))))))))) (delta (delta x₁₄ (delta x₁₅ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (mono x₁₄))))))))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (mono x₁₄))))))))))))) (delta (mono x₁₅) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (mono x₁₄))))))))))))) (delta (delta x₁₅ (mono x₁₆)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (mono x₁₄))))))))))))) (delta (delta x₁₅ (delta x₁₆ d₂)) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ d₁))))))))))))) (mono d₂))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ d₁))))))))))))) (delta (mono x₁₅) d₃))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (mono x₁₅)))))))))))))) (delta (delta x₁₆ (mono x₁₇)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (mono x₁₅)))))))))))))) (delta (delta x₁₆ (delta x₁₇ d₂)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ (mono x₁₆))))))))))))))) (delta (delta x₁₇ (mono x₁₈)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ (mono x₁₆))))))))))))))) (delta (delta x₁₇ (delta x₁₈ d₂)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ (delta x₁₆ (mono x₁₇)))))))))))))))) (delta (delta x₁₈ (mono x₁₉)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ (delta x₁₆ (mono x₁₇)))))))))))))))) (delta (delta x₁₈ (delta x₁₉ d₂)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ (delta x₁₆ (delta x₁₇ d₁)))))))))))))))) (delta (delta x₁₈ (mono x₁₉)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ (delta x₁₆ (delta x₁₇ d₁)))))))))))))))) (delta (delta x₁₈ (delta x₁₉ d₂)) (mono d₃)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (mono x₁₅)))))))))))))) (delta (delta x₁₆ (mono x₁₇)) (delta (mono x₁₈) d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (mono x₁₅)))))))))))))) (delta (delta x₁₆ (delta x₁₇ d₂)) (delta (mono x₁₈) d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (mono x₁₅)))))))))))))) (delta (delta x₁₆ (mono x₁₇)) (delta (delta x₁₈ d₃) d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (mono x₁₅)))))))))))))) (delta (delta x₁₆ (delta x₁₇ d₂)) (delta (delta x₁₈ d₃) d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ d₁)))))))))))))) (delta (delta x₁₆ (mono x₁₇)) (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (mono x)) (delta (mono (mono x₁)) (mono (delta (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ (delta x₇ (delta x₈ (delta x₉ (delta x₁₀ (delta x₁₁ (delta x₁₂ (delta x₁₃ (delta x₁₄ (delta x₁₅ d₁)))))))))))))) (delta (delta x₁₆ (delta x₁₇ d₂)) (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (mono x₃) (mono d₂))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (mono x₃) (delta (mono x₄) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (mono x₃) (delta (delta x₄ (mono x₅)) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (mono x₃) (delta (delta x₄ (delta x₅ d₂)) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ d₁) (mono d₂))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (mono x₅) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (delta x₅ (mono x₆)) (mono d₃)))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (delta x₅ (delta x₆ d₂)) (mono d₃)))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (delta x₅ (mono x₆)) (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (delta x₅ (delta x₆ d₂)) (delta d₃ d₄)))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (delta x₄ (mono x₅))) (delta (mono x₆) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (delta x₄ (mono x₅))) (delta (delta x₆ (mono x₇)) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (delta x₄ (mono x₅))) (delta (delta x₆ (delta x₇ d₂)) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (delta x₄ (delta x₅ d₁))) (delta (mono x₆) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (delta x₄ (delta x₅ d₁))) (delta (delta x₆ (mono x₇)) d₃))))) = refl monad-law-1 (delta (mono (delta x x₁)) (delta (mono (mono x₂)) (mono (delta (delta x₃ (delta x₄ (delta x₅ d₁))) (delta (delta x₆ (delta x₇ d₂)) d₃))))) = refl -- monad-law-1 (delta (delta (mono x) (mono x₁)) (delta (mono (mono x₂)) (mono (delta (mono x₃) (mono (mono x₄)))))) = refl monad-law-1 (delta (delta (delta x x₁) (mono x₂)) (delta (mono (mono x₃)) (mono (delta (mono x₄) (mono (mono x₅)))))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ (mono x₂))) (delta (mono (mono x₃)) (mono (delta (mono x₄) (mono (mono x₅)))))) = refl monad-law-1 (delta (delta (delta x x₁) (delta x₂ (mono x₃))) (delta (mono (mono x₄)) (mono (delta (mono x₅) (mono (mono x₆)))))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ (delta x₂ x₃))) (delta (mono (mono x₄)) (mono (delta (mono x₅) (mono (mono x₆)))))) = refl monad-law-1 (delta (delta (delta x x₁) (delta x₂ (delta x₃ x₄))) (delta (mono (mono x₅)) (mono (delta (mono x₆) (mono (mono x₇)))))) = refl monad-law-1 (delta (delta (mono x) x₁) (delta (mono (mono x₂)) (mono (delta (mono x₃) (mono (delta x₄ d₂)))))) = refl monad-law-1 (delta (delta (delta x x₁) x₂) (delta (mono (mono x₃)) (mono (delta (mono x₄) (mono (delta x₅ d₂)))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (delta (mono (mono x₂)) (mono (delta (mono x₃) (delta (mono x₄) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (delta (mono (mono x₂)) (mono (delta (mono x₃) (delta (delta x₄ (mono x₅)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (delta (mono (mono x₂)) (mono (delta (mono x₃) (delta (delta x₄ (delta x₅ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (mono x₅) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (delta x₅ (mono x₆)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (delta x₅ (delta x₆ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (mono x₅) (delta (mono x₆) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (mono x₅) (delta (delta x₆ (mono x₇)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (mono x₅) (delta (delta x₆ (delta x₇ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (mono x₄)))))) (delta (mono (mono x₅)) (mono (delta (mono x₆) (delta (mono x₇) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (mono x₄)))))) (delta (mono (mono x₅)) (mono (delta (mono x₆) (delta (delta x₇ (mono x₈)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (mono x₄)))))) (delta (mono (mono x₅)) (mono (delta (mono x₆) (delta (delta x₇ (delta x₈ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))))) (delta (mono (mono x₆)) (mono (delta (mono x₇) (delta (mono x₈) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))))) (delta (mono (mono x₆)) (mono (delta (mono x₇) (delta (delta x₈ (mono x₉)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (mono x₅))))))) (delta (mono (mono x₆)) (mono (delta (mono x₇) (delta (delta x₈ (delta x₉ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆)))))))) (delta (mono (mono x₇)) (mono (delta (mono x₈) (delta (mono x₉) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆)))))))) (delta (mono (mono x₇)) (mono (delta (mono x₈) (delta (delta x₉ (mono x₁₀)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (mono x₆)))))))) (delta (mono (mono x₇)) (mono (delta (mono x₈) (delta (delta x₉ (delta x₁₀ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ x₇)))))))) (delta (mono (mono x₈)) (mono (delta (mono x₉) (delta (mono x₁₀) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ x₇)))))))) (delta (mono (mono x₈)) (mono (delta (mono x₉) (delta (delta x₁₀ (mono x₁₁)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ (delta x₅ (delta x₆ x₇)))))))) (delta (mono (mono x₈)) (mono (delta (mono x₉) (delta (delta x₁₀ (delta x₁₁ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ x₂)) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (mono x₅) d₃))))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ x₂)) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (delta x₅ (mono x₆)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (delta x₁ x₂)) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (delta x₅ (delta x₆ d₂)) d₃))))) = refl monad-law-1 (delta (delta (delta x x₁) x₂) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (mono x₅) d₃))))) = refl monad-law-1 (delta (delta (delta x x₁) x₂) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (delta x₅ (mono x₆)) d₃))))) = refl monad-law-1 (delta (delta (delta x x₁) x₂) (delta (mono (mono x₃)) (mono (delta (mono x₄) (delta (delta x₅ (delta x₆ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (mono x₅) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (delta x₅ (mono x₆)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (mono x₁))) (delta (mono (mono x₂)) (mono (delta (delta x₃ (mono x₄)) (delta (delta x₅ (delta x₆ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (delta (mono (mono x₃)) (mono (delta (delta x₄ (mono x₅)) (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (delta (mono (mono x₃)) (mono (delta (delta x₄ (mono x₅)) (delta (mono x₆) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (delta (mono (mono x₃)) (mono (delta (delta x₄ (mono x₅)) (delta (delta x₆ (mono x₇)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (mono x₂)))) (delta (mono (mono x₃)) (mono (delta (delta x₄ (mono x₅)) (delta (delta x₆ (delta x₇ d₂)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (delta x₅ (mono x₆)) (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (delta x₅ (mono x₆)) (delta (mono x₇) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (delta x₅ (mono x₆)) (delta (delta x₇ (mono x₈)) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (delta x₅ (mono x₆)) (delta (delta x₇ (delta x₈ (mono x₉))) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (mono x₃))))) (delta (mono (mono x₄)) (mono (delta (delta x₅ (mono x₆)) (delta (delta x₇ (delta x₈ (delta x₉ d₂))) d₃))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (mono x₄)))))) (delta (mono (mono x₅)) (mono (delta (delta x₆ (mono x₇)) (mono d₂))))) = refl monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (mono x₄)))))) (delta (mono (mono x₅)) (mono (delta (delta x₆ (mono x₇)) (delta d₂ d₃))))) = {!!} monad-law-1 (delta (delta (mono x) (mono (delta x₁ (delta x₂ (delta x₃ (delta x₄ x₅)))))) (delta (mono (mono x₆)) (mono (delta (delta x₇ (mono x₈)) d₂)))) = {!!} monad-law-1 (delta (delta (mono x) (delta x₁ x₂)) (delta (mono (mono x₃)) (mono (delta (delta x₄ (mono x₅)) d₂)))) = {!!} monad-law-1 (delta (delta (delta x x₁) x₂) (delta (mono (mono x₃)) (mono (delta (delta x₄ (mono x₅)) d₂)))) = {!!} monad-law-1 (delta (delta x x₁) (delta (mono (mono x₂)) (mono (delta (delta x₃ (delta x₄ d₁)) d₂)))) = {!!} -- monad-law-1 (delta x (delta (mono (mono x₁)) (delta d₁ d₂))) = {!!} monad-law-1 (delta x (delta (mono (delta x₁ d)) d₁)) = {!!} monad-law-1 (delta x (delta (delta d d₁) d₂)) = {!!} {- -- monad-law-2-2 : join . return = id monad-law-2-2 : {l : Level} {A : Set l } -> (s : Delta A) -> (mu ∙ eta) s ≡ id s monad-law-2-2 (similar lx x ly y) = refl -- monad-law-3 : return . f = fmap f . return monad-law-3 : {l : Level} {A B : Set l} (f : A -> B) (x : A) -> (eta ∙ f) x ≡ (fmap f ∙ eta) x monad-law-3 f x = refl -- monad-law-4 : join . fmap (fmap f) = fmap f . join monad-law-4 : {l ll : Level} {A : Set l} {B : Set ll} (f : A -> B) (s : Delta (Delta A)) -> (mu ∙ fmap (fmap f)) s ≡ (fmap f ∙ mu) s monad-law-4 f (similar lx (similar llx x _ _) ly (similar _ _ lly y)) = refl -- Monad-laws (Haskell) -- monad-law-h-1 : return a >>= k = k a monad-law-h-1 : {l ll : Level} {A : Set l} {B : Set ll} -> (a : A) -> (k : A -> (Delta B)) -> (return a >>= k) ≡ (k a) monad-law-h-1 a k = refl -- monad-law-h-2 : m >>= return = m monad-law-h-2 : {l : Level}{A : Set l} -> (m : Delta A) -> (m >>= return) ≡ m monad-law-h-2 (mono x) = refl monad-law-h-2 (delta x d) = cong (delta x) (monad-law-h-2 d) -- monad-law-h-3 : m >>= (\x -> k x >>= h) = (m >>= k) >>= h monad-law-h-3 : {l ll lll : Level} {A : Set l} {B : Set ll} {C : Set lll} -> (m : Delta A) -> (k : A -> (Delta B)) -> (h : B -> (Delta C)) -> (m >>= (\x -> k x >>= h)) ≡ ((m >>= k) >>= h) monad-law-h-3 (mono x) k h = refl monad-law-h-3 (delta x d) k h = begin (delta x d) >>= (\x -> k x >>= h) ≡⟨ refl ⟩ -- (delta x d) >>= f = deltaAppend (headDelta (f x)) (d >>= (tailDelta ∙ f)) deltaAppend (headDelta ((\x -> k x >>= h) x)) (d >>= (tailDelta ∙ (\x -> k x >>= h))) ≡⟨ refl ⟩ deltaAppend (headDelta (k x >>= h)) (d >>= (tailDelta ∙ (\x -> k x >>= h))) ≡⟨ {!!} ⟩ ((delta x d) >>= k) >>= h ∎ -}