{-# LANGUAGE AllowAmbiguousTypes, TypeApplications #-}

module Test.Credit.Heap.Base (HeapOp(..), Heap(..), BoundedHeap(..), H, BH) where

import Control.Monad.Credit
import Test.Credit
import Test.QuickCheck

data HeapOp a = Insert a | Merge | SplitMin
  deriving (HeapOp a -> HeapOp a -> Bool
(HeapOp a -> HeapOp a -> Bool)
-> (HeapOp a -> HeapOp a -> Bool) -> Eq (HeapOp a)
forall a. Eq a => HeapOp a -> HeapOp a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: forall a. Eq a => HeapOp a -> HeapOp a -> Bool
== :: HeapOp a -> HeapOp a -> Bool
$c/= :: forall a. Eq a => HeapOp a -> HeapOp a -> Bool
/= :: HeapOp a -> HeapOp a -> Bool
Eq, Eq (HeapOp a)
Eq (HeapOp a) =>
(HeapOp a -> HeapOp a -> Ordering)
-> (HeapOp a -> HeapOp a -> Bool)
-> (HeapOp a -> HeapOp a -> Bool)
-> (HeapOp a -> HeapOp a -> Bool)
-> (HeapOp a -> HeapOp a -> Bool)
-> (HeapOp a -> HeapOp a -> HeapOp a)
-> (HeapOp a -> HeapOp a -> HeapOp a)
-> Ord (HeapOp a)
HeapOp a -> HeapOp a -> Bool
HeapOp a -> HeapOp a -> Ordering
HeapOp a -> HeapOp a -> HeapOp a
forall a.
Eq a =>
(a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall a. Ord a => Eq (HeapOp a)
forall a. Ord a => HeapOp a -> HeapOp a -> Bool
forall a. Ord a => HeapOp a -> HeapOp a -> Ordering
forall a. Ord a => HeapOp a -> HeapOp a -> HeapOp a
$ccompare :: forall a. Ord a => HeapOp a -> HeapOp a -> Ordering
compare :: HeapOp a -> HeapOp a -> Ordering
$c< :: forall a. Ord a => HeapOp a -> HeapOp a -> Bool
< :: HeapOp a -> HeapOp a -> Bool
$c<= :: forall a. Ord a => HeapOp a -> HeapOp a -> Bool
<= :: HeapOp a -> HeapOp a -> Bool
$c> :: forall a. Ord a => HeapOp a -> HeapOp a -> Bool
> :: HeapOp a -> HeapOp a -> Bool
$c>= :: forall a. Ord a => HeapOp a -> HeapOp a -> Bool
>= :: HeapOp a -> HeapOp a -> Bool
$cmax :: forall a. Ord a => HeapOp a -> HeapOp a -> HeapOp a
max :: HeapOp a -> HeapOp a -> HeapOp a
$cmin :: forall a. Ord a => HeapOp a -> HeapOp a -> HeapOp a
min :: HeapOp a -> HeapOp a -> HeapOp a
Ord, Int -> HeapOp a -> ShowS
[HeapOp a] -> ShowS
HeapOp a -> String
(Int -> HeapOp a -> ShowS)
-> (HeapOp a -> String) -> ([HeapOp a] -> ShowS) -> Show (HeapOp a)
forall a. Show a => Int -> HeapOp a -> ShowS
forall a. Show a => [HeapOp a] -> ShowS
forall a. Show a => HeapOp a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: forall a. Show a => Int -> HeapOp a -> ShowS
showsPrec :: Int -> HeapOp a -> ShowS
$cshow :: forall a. Show a => HeapOp a -> String
show :: HeapOp a -> String
$cshowList :: forall a. Show a => [HeapOp a] -> ShowS
showList :: [HeapOp a] -> ShowS
Show)

instance Arbitrary a => Arbitrary (HeapOp a) where
  arbitrary :: Gen (HeapOp a)
arbitrary = [(Int, Gen (HeapOp a))] -> Gen (HeapOp a)
forall a. HasCallStack => [(Int, Gen a)] -> Gen a
frequency
    [ (Int
6, a -> HeapOp a
forall a. a -> HeapOp a
Insert (a -> HeapOp a) -> Gen a -> Gen (HeapOp a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen a
forall a. Arbitrary a => Gen a
arbitrary)
    , (Int
3, HeapOp a -> Gen (HeapOp a)
forall a. a -> Gen a
forall (f :: * -> *) a. Applicative f => a -> f a
pure HeapOp a
forall a. HeapOp a
SplitMin)
    , (Int
1, HeapOp a -> Gen (HeapOp a)
forall a. a -> Gen a
forall (f :: * -> *) a. Applicative f => a -> f a
pure HeapOp a
forall a. HeapOp a
Merge)
    ]

class Heap h where
  empty :: MonadLazy m => m (h a m)
  insert :: MonadCredit m => Ord a => a -> h a m -> m (h a m)
  merge :: MonadCredit m => Ord a => h a m -> h a m -> m (h a m)
  splitMin :: MonadCredit m => Ord a => h a m -> m (Maybe (a, h a m))

class Heap h => BoundedHeap h where
  hcost :: Size -> HeapOp a -> Credit

data H h a m = H (h (PrettyCell a) m)

instance (MemoryCell m (h (PrettyCell a) m)) => MemoryCell m (H h a m) where
  prettyCell :: H h a m -> m Memory
prettyCell (H h (PrettyCell a) m
h) = h (PrettyCell a) m -> m Memory
forall (m :: * -> *) a. MemoryCell m a => a -> m Memory
prettyCell h (PrettyCell a) m
h

instance (MemoryStructure (h (PrettyCell a))) => MemoryStructure (H h a) where
  prettyStructure :: forall (m :: * -> *). MonadMemory m => H h a m -> m Memory
prettyStructure (H h (PrettyCell a) m
h) = h (PrettyCell a) m -> m Memory
forall (m :: * -> *).
MonadMemory m =>
h (PrettyCell a) m -> m Memory
forall (t :: (* -> *) -> *) (m :: * -> *).
(MemoryStructure t, MonadMemory m) =>
t m -> m Memory
prettyStructure h (PrettyCell a) m
h

instance (Arbitrary a, Ord a, BoundedHeap h, Show a) => DataStructure (H h a) (HeapOp a) where
  cost :: Size -> HeapOp a -> Credit
cost Size
sz HeapOp a
Merge = Credit
0
  cost Size
sz HeapOp a
op = forall (h :: * -> (* -> *) -> *) a.
BoundedHeap h =>
Size -> HeapOp a -> Credit
hcost @h Size
sz HeapOp a
op
  create :: forall (m :: * -> *). MonadLazy m => m (H h a m)
create = h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H (h (PrettyCell a) m -> H h a m)
-> m (h (PrettyCell a) m) -> m (H h a m)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m (h (PrettyCell a) m)
forall (m :: * -> *) a. MonadLazy m => m (h a m)
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadLazy m) =>
m (h a m)
empty
  perform :: forall (m :: * -> *).
MonadInherit m =>
Size -> H h a m -> HeapOp a -> m (Size, H h a m)
perform Size
sz (H h (PrettyCell a) m
h) (Insert a
x) = (Size
sz Size -> Size -> Size
forall a. Num a => a -> a -> a
+ Size
1,) (H h a m -> (Size, H h a m))
-> (h (PrettyCell a) m -> H h a m)
-> h (PrettyCell a) m
-> (Size, H h a m)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H (h (PrettyCell a) m -> (Size, H h a m))
-> m (h (PrettyCell a) m) -> m (Size, H h a m)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> PrettyCell a -> h (PrettyCell a) m -> m (h (PrettyCell a) m)
forall (m :: * -> *) a.
(MonadCredit m, Ord a) =>
a -> h a m -> m (h a m)
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadCredit m, Ord a) =>
a -> h a m -> m (h a m)
insert (a -> PrettyCell a
forall a. a -> PrettyCell a
PrettyCell a
x) h (PrettyCell a) m
h
  perform Size
sz (H h (PrettyCell a) m
h) HeapOp a
Merge = (Size, H h a m) -> m (Size, H h a m)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Size
sz, h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H h (PrettyCell a) m
h) -- no op
  perform Size
sz (H h (PrettyCell a) m
h) HeapOp a
SplitMin = do
    Maybe (PrettyCell a, h (PrettyCell a) m)
m <- h (PrettyCell a) m -> m (Maybe (PrettyCell a, h (PrettyCell a) m))
forall (m :: * -> *) a.
(MonadCredit m, Ord a) =>
h a m -> m (Maybe (a, h a m))
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadCredit m, Ord a) =>
h a m -> m (Maybe (a, h a m))
splitMin h (PrettyCell a) m
h
    case Maybe (PrettyCell a, h (PrettyCell a) m)
m of
      Maybe (PrettyCell a, h (PrettyCell a) m)
Nothing -> (Size
sz,) (H h a m -> (Size, H h a m))
-> (h (PrettyCell a) m -> H h a m)
-> h (PrettyCell a) m
-> (Size, H h a m)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H (h (PrettyCell a) m -> (Size, H h a m))
-> m (h (PrettyCell a) m) -> m (Size, H h a m)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m (h (PrettyCell a) m)
forall (m :: * -> *) a. MonadLazy m => m (h a m)
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadLazy m) =>
m (h a m)
empty
      Just (PrettyCell a
_, h (PrettyCell a) m
h') -> (Size, H h a m) -> m (Size, H h a m)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Size
sz Size -> Size -> Size
forall a. Num a => a -> a -> a
- Size
1, h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H h (PrettyCell a) m
h')

data BH h a m = BH (H h a m) (H h a m)

instance (MemoryCell m (h (PrettyCell a) m)) => MemoryCell m (BH h a m) where
  prettyCell :: BH h a m -> m Memory
prettyCell (BH H h a m
h1 H h a m
h2) = do
    Memory
h1' <- H h a m -> m Memory
forall (m :: * -> *) a. MemoryCell m a => a -> m Memory
prettyCell H h a m
h1
    Memory
h2' <- H h a m -> m Memory
forall (m :: * -> *) a. MemoryCell m a => a -> m Memory
prettyCell H h a m
h2
    Memory -> m Memory
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Memory -> m Memory) -> Memory -> m Memory
forall a b. (a -> b) -> a -> b
$ String -> [Memory] -> Memory
mkMCell String
"Merge" [Memory
h1', Memory
h2']

instance (MemoryStructure (h (PrettyCell a))) => MemoryStructure (BH h a) where
  prettyStructure :: forall (m :: * -> *). MonadMemory m => BH h a m -> m Memory
prettyStructure (BH H h a m
h1 H h a m
h2) = do
    Memory
h1' <- H h a m -> m Memory
forall (m :: * -> *). MonadMemory m => H h a m -> m Memory
forall (t :: (* -> *) -> *) (m :: * -> *).
(MemoryStructure t, MonadMemory m) =>
t m -> m Memory
prettyStructure H h a m
h1
    Memory
h2' <- H h a m -> m Memory
forall (m :: * -> *). MonadMemory m => H h a m -> m Memory
forall (t :: (* -> *) -> *) (m :: * -> *).
(MemoryStructure t, MonadMemory m) =>
t m -> m Memory
prettyStructure H h a m
h2
    Memory -> m Memory
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Memory -> m Memory) -> Memory -> m Memory
forall a b. (a -> b) -> a -> b
$ String -> [Memory] -> Memory
mkMCell String
"Merge" [Memory
h1', Memory
h2']

instance (Arbitrary a, Ord a, BoundedHeap h, Show a) => DataStructure (BH h a) (HeapOp a) where
  cost :: Size -> HeapOp a -> Credit
cost = forall (h :: * -> (* -> *) -> *) a.
BoundedHeap h =>
Size -> HeapOp a -> Credit
hcost @h
  create :: forall (m :: * -> *). MonadLazy m => m (BH h a m)
create = do
    h (PrettyCell a) m
h1 <- m (h (PrettyCell a) m)
forall (m :: * -> *) a. MonadLazy m => m (h a m)
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadLazy m) =>
m (h a m)
empty
    h (PrettyCell a) m
h2 <- m (h (PrettyCell a) m)
forall (m :: * -> *) a. MonadLazy m => m (h a m)
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadLazy m) =>
m (h a m)
empty
    BH h a m -> m (BH h a m)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (BH h a m -> m (BH h a m)) -> BH h a m -> m (BH h a m)
forall a b. (a -> b) -> a -> b
$ H h a m -> H h a m -> BH h a m
forall {k} (h :: * -> k -> *) a (m :: k).
H h a m -> H h a m -> BH h a m
BH (h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H h (PrettyCell a) m
h1) (h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H h (PrettyCell a) m
h2)
  perform :: forall (m :: * -> *).
MonadInherit m =>
Size -> BH h a m -> HeapOp a -> m (Size, BH h a m)
perform Size
sz (BH H h a m
h1 H h a m
h2) (Insert a
a) = do
    (Size
sz, H h a m
h1) <- Size -> H h a m -> HeapOp a -> m (Size, H h a m)
forall (m :: * -> *).
MonadInherit m =>
Size -> H h a m -> HeapOp a -> m (Size, H h a m)
forall (t :: (* -> *) -> *) op (m :: * -> *).
(DataStructure t op, MonadInherit m) =>
Size -> t m -> op -> m (Size, t m)
perform Size
sz H h a m
h1 (a -> HeapOp a
forall a. a -> HeapOp a
Insert a
a)
    (Size, BH h a m) -> m (Size, BH h a m)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Size
sz, H h a m -> H h a m -> BH h a m
forall {k} (h :: * -> k -> *) a (m :: k).
H h a m -> H h a m -> BH h a m
BH H h a m
h1 H h a m
h2)
  perform Size
sz (BH H h a m
h1 H h a m
h2) HeapOp a
SplitMin = do
    (Size
sz, H h a m
h2) <- Size -> H h a m -> HeapOp a -> m (Size, H h a m)
forall (m :: * -> *).
MonadInherit m =>
Size -> H h a m -> HeapOp a -> m (Size, H h a m)
forall (t :: (* -> *) -> *) op (m :: * -> *).
(DataStructure t op, MonadInherit m) =>
Size -> t m -> op -> m (Size, t m)
perform Size
sz H h a m
h2 HeapOp a
forall a. HeapOp a
SplitMin
    (Size, BH h a m) -> m (Size, BH h a m)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Size
sz, H h a m -> H h a m -> BH h a m
forall {k} (h :: * -> k -> *) a (m :: k).
H h a m -> H h a m -> BH h a m
BH H h a m
h1 H h a m
h2)
  perform Size
sz (BH (H h (PrettyCell a) m
h1) (H h (PrettyCell a) m
h2)) HeapOp a
Merge = do
    h (PrettyCell a) m
h <- h (PrettyCell a) m -> h (PrettyCell a) m -> m (h (PrettyCell a) m)
forall (m :: * -> *) a.
(MonadCredit m, Ord a) =>
h a m -> h a m -> m (h a m)
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadCredit m, Ord a) =>
h a m -> h a m -> m (h a m)
merge h (PrettyCell a) m
h1 h (PrettyCell a) m
h2
    h (PrettyCell a) m
e <- m (h (PrettyCell a) m)
forall (m :: * -> *) a. MonadLazy m => m (h a m)
forall (h :: * -> (* -> *) -> *) (m :: * -> *) a.
(Heap h, MonadLazy m) =>
m (h a m)
empty
    (Size, BH h a m) -> m (Size, BH h a m)
forall a. a -> m a
forall (f :: * -> *) a. Applicative f => a -> f a
pure (Size
sz, H h a m -> H h a m -> BH h a m
forall {k} (h :: * -> k -> *) a (m :: k).
H h a m -> H h a m -> BH h a m
BH (h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H h (PrettyCell a) m
e) (h (PrettyCell a) m -> H h a m
forall {k} (h :: * -> k -> *) a (m :: k).
h (PrettyCell a) m -> H h a m
H h (PrettyCell a) m
h))