{-# LANGUAGE ScopedTypeVariables #-}
{-@ LIQUID "--no-termination" @-}
module Class () where
import Language.Haskell.Liquid.Prelude
import Prelude hiding (sum, length, (!!), Functor(..))
data MList a = Nil | Cons a (MList a)
{-@ (!!) :: xs:MList a -> {v:Nat | v < sz xs} -> a @-}
(!!) :: MList a -> Int -> a
(Cons x _) !! 0 = x
(Cons _ xs) !! i = xs !! (i - 1)
{-@ class measure sz :: forall a. a -> Int @-}
{-@ class Sized s where
size :: forall a. x:s a -> {v:Nat | v = sz x}
@-}
class Sized s where
size :: s a -> Int
instance Sized MList where
{-@ instance measure sz :: MList a -> Int
sz (Nil) = 0
sz (Cons x xs) = 1 + sz xs
@-}
size = length
{-@ length :: xs:MList a -> {v:Nat | v = sz xs} @-}
length :: MList a -> Int
length Nil = 0
length (Cons _ xs) = 1 + length xs
{-@ bob :: xs:MList a -> {v:Nat | v = sz xs} @-}
bob :: MList a -> Int
bob = length
instance Sized [] where
{-@ instance measure sz :: [a] -> Int
sz ([]) = 0
sz (x:xs) = 1 + (sz xs)
@-}
size [] = 0
size (_:xs) = 1 + size xs
{-@ class (Sized s) => Indexable s where
index :: forall a. x:s a -> {v:Nat | v < sz x} -> a
@-}
class (Sized s) => Indexable s where
index :: s a -> Int -> a
instance Indexable MList where
index = (!!)
{-@ sum :: Indexable s => s Int -> Int @-}
sum :: Indexable s => s Int -> Int
sum xs = go n 0
where
n = size xs
go (d::Int) i
| i < n = index xs i + go (d-1) (i+1)
| otherwise = 0
{-@ sumMList :: MList Int -> Int @-}
sumMList :: MList Int -> Int
sumMList xs = go max 0
where
max = size xs
go (d::Int) i
| i < max = index xs i + go (d-1) (i+1)
| otherwise = 0
{-@ mlist3 :: {v:MList Int | sz v = 3} @-}
mlist3 :: MList Int
mlist3 = 1 `Cons` (2 `Cons` (3 `Cons` Nil))
foo = liquidAssert $ size (Cons 1 Nil) == size [1]