content: {-@ LIQUID "--expect-any-error" @-}
  {-@ LIQUID "--no-adt" 	                           @-}
  {-@ LIQUID "--exact-data-con"                      @-}
  {-@ LIQUID "--higherorder"                         @-}
  {-@ LIQUID "--no-termination"                      @-}
  {-@ LIQUID "--ple" @-}
  
  {-# LANGUAGE ExistentialQuantification, KindSignatures, TypeFamilies, GADTs #-}
  
  module ExactGADT5 where
  
  import Prelude hiding (filter)
  
  data PersistFilter = EQUAL | LE | GE
  
  class PersistEntity record where
      data EntityField record :: * -> *
  
  {-@ data Filter record typ = Filter { filterField :: EntityField record typ, filterValue :: typ, filterFilter :: PersistFilter } @-}
  data Filter record typ = Filter
      { filterField  :: EntityField record typ
      , filterValue  :: typ
      , filterFilter :: PersistFilter
      }
  
  
  {-@ reflect createEqQuery @-}
  {-
  createEqQuery :: (PersistEntity record, Eq typ) =>
  	         EntityField record typ -> typ -> Filter record typ
  createEqQuery field value =
    Filter {
      filterField = field
    , filterValue = value
    , filterFilter = EQUAL
    }
  -}
  
  createEqQuery :: EntityField record typ -> typ -> Filter record typ
  createEqQuery field value = Filter field value EQUAL
  
  createLeQuery :: (PersistEntity record, Eq typ) =>
                   EntityField record typ -> typ -> Filter record typ
  createLeQuery field value =
    Filter {
      filterField = field
    , filterValue = value
    , filterFilter = LE
    }
  
  {-@ data Blob  = B { xVal :: Int, yVal :: Int } @-}
  data Blob  = B { xVal :: Int, yVal :: Int }
  
  instance PersistEntity Blob where
    {-@ data EntityField Blob typ where
            BlobXVal :: EntityField Blob Int
            BlobYVal :: EntityField Blob Int
      @-}
      data EntityField Blob typ where
          BlobXVal :: EntityField Blob Int
          BlobYVal :: EntityField Blob Int
  
  {-@ filter :: f:(a -> Bool) -> [a] -> [{v:a | f v}] @-}
  filter :: (a -> Bool) -> [a] -> [a]
  filter f (x:xs)
    | f x         = x : filter f xs
    | otherwise   =     filter f xs
  filter _ []     = []
  
  {-@ reflect evalQBlobXVal @-}
  evalQBlobXVal :: PersistFilter -> Int -> Int -> Bool
  evalQBlobXVal EQUAL filter given = filter == given
  evalQBlobXVal LE filter given = given <= filter
  evalQBlobXVal GE filter given = given >= filter
  
  {-@ reflect evalQBlobYVal @-}
  evalQBlobYVal :: PersistFilter -> Int -> Int -> Bool
  evalQBlobYVal EQUAL filter given = filter == given
  evalQBlobYVal LE filter given = given <= filter
  evalQBlobYVal GE filter given = given >= filter
  
  {-@ reflect evalQBlob @-}
  evalQBlob :: Filter Blob typ -> Blob -> Bool
  evalQBlob filter blob = case filterField filter of
    BlobXVal -> evalQBlobXVal (filterFilter filter) (filterValue filter) (xVal blob)
    BlobYVal -> evalQBlobYVal (filterFilter filter) (filterValue filter) (yVal blob)
  
  {-@ filterQBlob :: f:(Filter Blob a) -> [Blob] -> [{b:Blob | evalQBlob f b}] @-}
  filterQBlob :: Filter Blob a -> [Blob] -> [Blob]
  filterQBlob q = filter (evalQBlob q)
  
  {-@ assume select :: f:(Filter Blob a) -> [{b:Blob | evalQBlob f b}] @-}
  select :: Filter Blob a -> [Blob]
  select _ = undefined
  
  -- Client code:
  
  -- Should typecheck:
  {-@ getZeros1 :: [Blob] -> [{b:Blob | xVal b == 10}] @-}
  getZeros1 :: [Blob] -> [Blob]
  getZeros1 = filterQBlob (Filter BlobXVal 0 EQUAL)
  
  {-@ getZeros2 :: () -> [{b:Blob | xVal b == 0}] @-}
  getZeros2 :: () -> [Blob]
  getZeros2 () = select (Filter BlobXVal 0 EQUAL)
  
  {-@ getZeros3 :: [Blob] -> [{b:Blob | xVal b == 0}] @-}
  getZeros3 :: [Blob] -> [Blob]
  getZeros3 blobs = filterQBlob (createEqQuery BlobXVal 0) blobs
  
  {-@ getZeros4 :: () -> [{b:Blob | xVal b == 0}] @-}
  getZeros4 :: () -> [Blob]
  getZeros4 () = select (createEqQuery BlobXVal 0)
  