Created
April 3, 2011 08:25
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merge fails, why?
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module InsertionSort where | |
open import Data.Nat | |
open import Data.Product | |
data Order : Set where | |
le : Order | |
ge : Order | |
data List (X : Set) : Set where | |
nil : List X | |
_∷_ : X -> List X -> List X | |
order : (x : ℕ) (y : ℕ) -> Order | |
order zero y = le | |
order (suc n) zero = ge | |
order (suc n) (suc n') = order n n' | |
merge : List ℕ -> List ℕ -> List ℕ | |
merge nil ys = ys | |
merge xs nil = xs | |
merge (x ∷ xs') (y ∷ ys') with order x y | |
merge (x ∷ xs') (y ∷ ys') | le = x ∷ merge xs' (y ∷ ys') | |
merge (x ∷ xs') (y ∷ ys') | ge = y ∷ merge (x ∷ xs') ys' | |
deal : {X : Set} (xs : List X) -> List X × List X | |
deal nil = nil , nil | |
deal (y ∷ nil) = y ∷ nil , nil | |
deal (y ∷ (y' ∷ y0)) with deal y0 | |
deal (y' ∷ (y1 ∷ y0)) | proj₁ , y = y' ∷ proj₁ , y1 ∷ y | |
sort : List ℕ -> List ℕ | |
sort xs with deal xs | |
sort xs | proj₁ , nil = proj₁ | |
sort xs | proj₁ , y ∷ y' = merge (sort proj₁) (sort (y ∷ y')) | |
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