Internal.hs

{-# LANGUAGE CPP #-}
{-# LANGUAGE TemplateHaskellQuotes #-}

{-|
Module:      Data.Functor.Invariant.TH.Internal
Copyright:   (C) 2012-2017 Nicolas Frisby, (C) 2015-2017 Ryan Scott
License:     BSD-style (see the file LICENSE)
Maintainer:  Ryan Scott
Portability: Template Haskell

Template Haskell-related utilities.
-}
module Data.Functor.Invariant.TH.Internal where

import           Data.Coerce (coerce)
import           Data.Foldable (foldr')
import           Data.Functor.Invariant (Invariant(..), Invariant2(..))
import qualified Data.List as List
import qualified Data.Map as Map (singleton)
import           Data.Map (Map)
import           Data.Maybe (fromMaybe, mapMaybe)
import qualified Data.Set as Set
import           Data.Set (Set)

import           Language.Haskell.TH.Datatype
import           Language.Haskell.TH.Lib
import           Language.Haskell.TH.Syntax

-------------------------------------------------------------------------------
-- Expanding type synonyms
-------------------------------------------------------------------------------

applySubstitutionKind :: Map Name Kind -> Type -> Type
applySubstitutionKind = applySubstitution

substNameWithKind :: Name -> Kind -> Type -> Type
substNameWithKind n k = applySubstitutionKind (Map.singleton n k)

substNamesWithKindStar :: [Name] -> Type -> Type
substNamesWithKindStar ns t = foldr' (flip substNameWithKind starK) t ns

-------------------------------------------------------------------------------
-- Class-specific constants
-------------------------------------------------------------------------------

-- | A representation of which @Invariant@ is being used.
data InvariantClass = Invariant | Invariant2
  deriving (Eq, Ord)

instance Enum InvariantClass where
    fromEnum Invariant  = 1
    fromEnum Invariant2 = 2

    toEnum 1 = Invariant
    toEnum 2 = Invariant2
    toEnum i = error $ "No Invariant class for number " ++ show i

invmapConstName :: InvariantClass -> Name
invmapConstName Invariant  = invmapConstValName
invmapConstName Invariant2 = invmap2ConstValName

invariantClassName :: InvariantClass -> Name
invariantClassName Invariant  = invariantTypeName
invariantClassName Invariant2 = invariant2TypeName

invmapName :: InvariantClass -> Name
invmapName Invariant  = invmapValName
invmapName Invariant2 = invmap2ValName

-- | A type-restricted version of 'const'. This constrains the map functions
-- that are autogenerated by Template Haskell to be the correct type, even
-- if they aren't actually used in an invmap(2) expression. This is useful
-- in makeInvmap(2), since a map function might have its type inferred as
-- @a@ instead of @a -> b@ (which is clearly wrong).
invmapConst :: f b -> (a -> b) -> (b -> a) -> f a -> f b
invmapConst = const . const . const
{-# INLINE invmapConst #-}

invmap2Const :: f c d
             -> (a -> c) -> (c -> a)
             -> (b -> d) -> (d -> b)
             -> f a b -> f c d
invmap2Const = const . const . const . const . const
{-# INLINE invmap2Const #-}

-------------------------------------------------------------------------------
-- StarKindStatus
-------------------------------------------------------------------------------

-- | Whether a type is not of kind *, is of kind *, or is a kind variable.
data StarKindStatus = NotKindStar
                    | KindStar
                    | IsKindVar Name
  deriving Eq

-- | Does a Type have kind * or k (for some kind variable k)?
canRealizeKindStar :: Type -> StarKindStatus
canRealizeKindStar t
  | hasKindStar t = KindStar
  | otherwise = case t of
                     SigT _ (VarT k) -> IsKindVar k
                     _               -> NotKindStar

-- | Returns 'Just' the kind variable 'Name' of a 'StarKindStatus' if it exists.
-- Otherwise, returns 'Nothing'.
starKindStatusToName :: StarKindStatus -> Maybe Name
starKindStatusToName (IsKindVar n) = Just n
starKindStatusToName _             = Nothing

-- | Concat together all of the StarKindStatuses that are IsKindVar and extract
-- the kind variables' Names out.
catKindVarNames :: [StarKindStatus] -> [Name]
catKindVarNames = mapMaybe starKindStatusToName

-------------------------------------------------------------------------------
-- Assorted utilities
-------------------------------------------------------------------------------

-- | Returns True if a Type has kind *.
hasKindStar :: Type -> Bool
hasKindStar VarT{}         = True
hasKindStar (SigT _ StarT) = True
hasKindStar _              = False

-- Returns True is a kind is equal to *, or if it is a kind variable.
isStarOrVar :: Kind -> Bool
isStarOrVar StarT  = True
isStarOrVar VarT{} = True
isStarOrVar _      = False

-- | @hasKindVarChain n kind@ Checks if @kind@ is of the form
-- k_0 -> k_1 -> ... -> k_(n-1), where k0, k1, ..., and k_(n-1) can be * or
-- kind variables.
hasKindVarChain :: Int -> Type -> Maybe [Name]
hasKindVarChain kindArrows t =
  let uk = uncurryKind (tyKind t)
  in if (length uk - 1 == kindArrows) && all isStarOrVar uk
        then Just (freeVariables uk)
        else Nothing

-- | If a Type is a SigT, returns its kind signature. Otherwise, return *.
tyKind :: Type -> Kind
tyKind (SigT _ k) = k
tyKind _          = starK

-- | A mapping of type variable Names to their map function Names. For example, in a
-- Invariant declaration, a TyVarMap might look like:
--
--   (a ~> (covA, contraA), b ~> (covB, contraB))
--
-- where a and b are the last two type variables of the datatype, and covA and covB
-- are the two map functions for a and b in covariant positions, and contraA and
-- contraB are the two map functions for a and b in contravariant positions.
type TyVarMap = Map Name (Name, Name)

fst3 :: (a, b, c) -> a
fst3 (a, _, _) = a

thd3 :: (a, b, c) -> c
thd3 (_, _, c) = c

-- Like 'lookup', but for lists of triples.
lookup2 :: Eq a => a -> [(a, b, c)] -> Maybe (b, c)
lookup2 _ [] = Nothing
lookup2 key ((x,y,z):xyzs)
    | key == x  = Just (y, z)
    | otherwise = lookup2 key xyzs

-- | Generate a list of fresh names with a common prefix, and numbered suffixes.
newNameList :: String -> Int -> Q [Name]
newNameList prefix n = mapM (newName . (prefix ++) . show) [1..n]

createKindChain :: Int -> Kind
createKindChain = go starK
  where
    go :: Kind -> Int -> Kind
    go k 0 = k
    go k n = n `seq` go (arrowKCompat starK k) (n - 1)

-- | Applies a typeclass constraint to a type.
applyClass :: Name -> Name -> Pred
applyClass con t = AppT (ConT con) (VarT t)

-- | Checks to see if the last types in a data family instance can be safely eta-
-- reduced (i.e., dropped), given the other types. This checks for three conditions:
--
-- (1) All of the dropped types are type variables
-- (2) All of the dropped types are distinct
-- (3) None of the remaining types mention any of the dropped types
canEtaReduce :: [Type] -> [Type] -> Bool
canEtaReduce remaining dropped =
       all isTyVar dropped
    && allDistinct droppedNames -- Make sure not to pass something of type [Type], since Type
                                -- didn't have an Ord instance until template-haskell-2.10.0.0
    && not (any (`mentionsName` droppedNames) remaining)
  where
    droppedNames :: [Name]
    droppedNames = map varTToName dropped

-- | Extract Just the Name from a type variable. If the argument Type is not a
-- type variable, return Nothing.
varTToName_maybe :: Type -> Maybe Name
varTToName_maybe (VarT n)   = Just n
varTToName_maybe (SigT t _) = varTToName_maybe t
varTToName_maybe _          = Nothing

-- | Extract the Name from a type variable. If the argument Type is not a
-- type variable, throw an error.
varTToName :: Type -> Name
varTToName = fromMaybe (error "Not a type variable!") . varTToName_maybe

-- | Peel off a kind signature from a Type (if it has one).
unSigT :: Type -> Type
unSigT (SigT t _) = t
unSigT t          = t

-- | Is the given type a variable?
isTyVar :: Type -> Bool
isTyVar (VarT _)   = True
isTyVar (SigT t _) = isTyVar t
isTyVar _          = False

-- | Detect if a Name in a list of provided Names occurs as an argument to some
-- type family. This makes an effort to exclude /oversaturated/ arguments to
-- type families. For instance, if one declared the following type family:
--
-- @
-- type family F a :: Type -> Type
-- @
--
-- Then in the type @F a b@, we would consider @a@ to be an argument to @F@,
-- but not @b@.
isInTypeFamilyApp :: [Name] -> Type -> [Type] -> Q Bool
isInTypeFamilyApp names tyFun tyArgs =
  case tyFun of
    ConT tcName -> go tcName
    _           -> return False
  where
    go :: Name -> Q Bool
    go tcName = do
      info <- reify tcName
      case info of
        FamilyI (OpenTypeFamilyD (TypeFamilyHead _ bndrs _ _)) _
          -> withinFirstArgs bndrs
        FamilyI (ClosedTypeFamilyD (TypeFamilyHead _ bndrs _ _) _) _
          -> withinFirstArgs bndrs
        _ -> return False
      where
        withinFirstArgs :: [a] -> Q Bool
        withinFirstArgs bndrs =
          let firstArgs = take (length bndrs) tyArgs
              argFVs    = freeVariables firstArgs
          in return $ any (`elem` argFVs) names

-- | Are all of the items in a list (which have an ordering) distinct?
--
-- This uses Set (as opposed to nub) for better asymptotic time complexity.
allDistinct :: Ord a => [a] -> Bool
allDistinct = allDistinct' Set.empty
  where
    allDistinct' :: Ord a => Set a -> [a] -> Bool
    allDistinct' uniqs (x:xs)
        | x `Set.member` uniqs = False
        | otherwise            = allDistinct' (Set.insert x uniqs) xs
    allDistinct' _ _           = True

-- | Does the given type mention any of the Names in the list?
mentionsName :: Type -> [Name] -> Bool
mentionsName = go
  where
    go :: Type -> [Name] -> Bool
    go (AppT t1 t2) names = go t1 names || go t2 names
    go (SigT t k)   names = go t names || go k names
    go (VarT n)     names = n `elem` names
    go _            _     = False

-- | Does an instance predicate mention any of the Names in the list?
predMentionsName :: Pred -> [Name] -> Bool
predMentionsName = mentionsName

-- | Construct a type via curried application.
applyTy :: Type -> [Type] -> Type
applyTy = List.foldl' AppT

-- | Fully applies a type constructor to its type variables.
applyTyCon :: Name -> [Type] -> Type
applyTyCon = applyTy . ConT

-- | Split an applied type into its individual components. For example, this:
--
-- @
-- Either Int Char
-- @
--
-- would split to this:
--
-- @
-- [Either, Int, Char]
-- @
unapplyTy :: Type -> (Type, [Type])
unapplyTy ty = go ty ty []
  where
    go :: Type -> Type -> [Type] -> (Type, [Type])
    go _      (AppT ty1 ty2)     args = go ty1 ty1 (ty2:args)
    go origTy (SigT ty' _)       args = go origTy ty' args
    go origTy (InfixT ty1 n ty2) args = go origTy (ConT n `AppT` ty1 `AppT` ty2) args
    go origTy (ParensT ty')      args = go origTy ty' args
    go origTy _                  args = (origTy, args)

-- | Split a type signature by the arrows on its spine. For example, this:
--
-- @
-- forall a b. (a ~ b) => (a -> b) -> Char -> ()
-- @
--
-- would split to this:
--
-- @
-- (a ~ b, [a -> b, Char, ()])
-- @
uncurryTy :: Type -> (Cxt, [Type])
uncurryTy (AppT (AppT ArrowT t1) t2) =
  let (ctxt, tys) = uncurryTy t2
  in (ctxt, t1:tys)
uncurryTy (SigT t _) = uncurryTy t
uncurryTy (ForallT _ ctxt t) =
  let (ctxt', tys) = uncurryTy t
  in (ctxt ++ ctxt', tys)
uncurryTy t = ([], [t])

-- | Like uncurryType, except on a kind level.
uncurryKind :: Kind -> [Kind]
uncurryKind = snd . uncurryTy

-------------------------------------------------------------------------------
-- Quoted names
-------------------------------------------------------------------------------

invariantTypeName :: Name
invariantTypeName = ''Invariant

invariant2TypeName :: Name
invariant2TypeName = ''Invariant2

invmapValName :: Name
invmapValName = 'invmap

invmap2ValName :: Name
invmap2ValName = 'invmap2

invmapConstValName :: Name
invmapConstValName = 'invmapConst

invmap2ConstValName :: Name
invmap2ConstValName = 'invmap2Const

coerceValName :: Name
coerceValName = 'coerce

errorValName :: Name
errorValName = 'error

seqValName :: Name
seqValName = 'seq