content: {-# LANGUAGE DeriveDataTypeable,FlexibleInstances #-}
  module Test where
  
  import HipSpec
  import Prelude(Eq, Ord, return, div, (-))
  
  data Bool = True | False deriving (Eq, Typeable, Ord)
  
  instance Names Bool where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary Bool where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              return True
            ),
            (1, do
              return False
            )
          ]
        arb n = frequency
          [
            (1, do
              return True
            ),
            (1, do
              return False
            )
          ]
  
  instance Partial Bool where
    unlifted True = return True
    unlifted False = return False
  
  
  data Unit = Null deriving (Eq, Typeable, Ord)
  
  instance Names Unit where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary Unit where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              return Null
            )
          ]
        arb n = frequency
          [
            (1, do
              return Null
            )
          ]
  
  instance Partial Unit where
    unlifted Null = return Null
  
  
  data Nat = Zero | Succ Nat deriving (Eq, Typeable, Ord)
  
  instance Names Nat where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary Nat where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              return Zero
            )
          ]
        arb n = frequency
          [
            (1, do
              return Zero
            ),
            (n, do
              let n' = n - 1
              x0 <- arb n'
              return (Succ x0)
            )
          ]
  
  instance Partial Nat where
    unlifted Zero = return Zero
    unlifted (Succ x0) = do
      x0' <- lifted x0
      return (Succ x0')
  
  
  data List = Nil Unit | Cons Nat List deriving (Eq, Typeable, Ord)
  
  instance Names List where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary List where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Nil x0)
            )
          ]
        arb n = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Nil x0)
            ),
            (n, do
              let n' = n - 1
              x0 <- arbitrary
              x1 <- arb n'
              return (Cons x0 x1)
            )
          ]
  
  instance Partial List where
    unlifted (Nil x0) = do
      x0' <- lifted x0
      return (Nil x0')
    unlifted (Cons x0 x1) = do
      x0' <- lifted x0
      x1' <- lifted x1
      return (Cons x0' x1')
  
  
  data CList = Cnil Unit | Single Nat | Concat CList CList deriving (Eq, Typeable, Ord)
  
  instance Names CList where
    names _ = ["var0_0", "var0_1", "var0_2"]
  
  instance Arbitrary CList where
    arbitrary = sized arb
      where
        arb 0 = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Cnil x0)
            ),
            (1, do
              x0 <- arbitrary
              return (Single x0)
            )
          ]
        arb n = frequency
          [
            (1, do
              x0 <- arbitrary
              return (Cnil x0)
            ),
            (1, do
              x0 <- arbitrary
              return (Single x0)
            ),
            (n, do
              let n' = n `div` 2
              x0 <- arb n'
              x1 <- arb n'
              return (Concat x0 x1)
            )
          ]
  
  instance Partial CList where
    unlifted (Cnil x0) = do
      x0' <- lifted x0
      return (Cnil x0')
    unlifted (Single x0) = do
      x0' <- lifted x0
      return (Single x0')
    unlifted (Concat x0 x1) = do
      x0' <- lifted x0
      x1' <- lifted x1
      return (Concat x0' x1')
  
  
  plus :: Nat -> Nat -> Nat
  plus Zero x = x
  plus (Succ x) y = (Succ (plus x y))
  
  times :: Nat -> Nat -> Nat
  times Zero x = Zero
  times (Succ x) y = (plus (times x y) y)
  
  tf1 :: List -> Nat
  tf1 (Nil tv3) = (Succ Zero)
  tf1 (Cons tv4 tv5) = (times tv4 (tf0 tv5))
  
  tf0 :: List -> Nat
  tf0 tv1 = (tf1 tv1)
  
  spec :: List -> Nat
  spec tv0 = (tf0 tv0)
  
  tf3 :: List -> List -> List
  tf3 tv11 (Nil tv12) = tv11
  tf3 tv11 (Cons tv13 tv14) = (Cons tv13 (tf2 tv14 tv11))
  
  tf2 :: List -> List -> List
  tf2 tv8 tv9 = (tf3 tv9 tv8)
  
  cat :: List -> List -> List
  cat tv6 tv7 = (tf2 tv6 tv7)
  
  tf5 :: CList -> List
  tf5 (Cnil tv18) = (Nil Null)
  tf5 (Single tv19) = (Cons tv19 (Nil Null))
  tf5 (Concat tv20 tv21) = (cat (tf4 tv20) (tf4 tv21))
  
  tf4 :: CList -> List
  tf4 tv16 = (tf5 tv16)
  
  repr :: CList -> List
  repr tv15 = (tf4 tv15)
  
  main :: CList -> Nat
  main tv22 = (spec (repr tv22))
  
  tf7 :: CList -> Nat
  tf7 (Cnil tv26) = (Succ Zero)
  tf7 (Single tv27) = tv27
  tf7 (Concat tv28 tv29) = (times (tf6 tv29) (tf6 tv28))
  
  tf6 :: CList -> Nat
  tf6 tv24 = (tf7 tv24)
  
  reprNew :: CList -> Nat
  reprNew tv23 = (tf6 tv23)
  
  mainNew :: CList -> Nat
  mainNew tv30 = (reprNew tv30)
  
  optimize inp0 = (main inp0)=:=(mainNew inp0)
  