-- This showed a couple of issues related to having ++ in types.

module RunLength

-- https://youtu.be/N4Z45Xg6_oc?t=1246

import Prelude

-- TODO this belongs in a library

data Void : U where

Not : U → U
Not x = x → Void

data Dec : U → U where
  Yes : ∀ prop. (prf : prop) → Dec prop
  No : ∀ prop. (contra : Not prop) → Dec prop

class DecEq t where
  decEq : (x₁ : t) → (x₂ : t) → Dec (x₁ ≡ x₂)

-- end lib

rep : ∀ a. Nat → a → List a
rep Z x = Nil
rep (S k) x = x :: rep k x

data RunLength : ∀ ty. List ty → U where
  Empty : ∀ ty. RunLength {ty} Nil
  Run : ∀ ty more. (n : Nat) →
        (x : ty) →
        RunLength more →
        RunLength (rep n x ++ more)

-- Idris has `?` here, but we're allowing metas on signatures to be solved later
testComp : RunLength {Char} _
testComp = Run (S (S (S Z))) 'x' $ Run (S (S (S (S Z)))) 'y' $ Empty

-- 24:20
uncompress : ∀ ty xs. RunLength {ty} xs → List ty

data Singleton : ∀ a. a → U where
  Val : ∀ a. (x : a) → Singleton x

-- Idris generates this
-- uncompress' : ∀ ty xs. RunLength {ty} xs → Singleton xs
-- uncompress' Empty = Val Nil
-- uncompress' (Run n x y) = let (Val ys) = uncompress' y in Val (rep n x ++ _)

solve : ∀ a. {{a}} -> a
solve {{a}} = a

-- adding ys back in, we still get a unification failure.
-- I think because the meta for ++ is not yet solved.
uncompress' : ∀ ty xs. RunLength {ty} xs → Singleton {List ty} xs
uncompress' Empty = Val Nil
uncompress' {ty} (Run n x y) = let (Val ys) = uncompress' y in Val (rep n x ++ ys)

rle : ∀ a. {{DecEq a}} → (xs : List a) → RunLength xs