-- |
-- Module for exhaustivity checking over pattern matching definitions
-- The algorithm analyses the clauses of a definition one by one from top
-- to bottom, where in each step it has the cases already missing (uncovered),
-- and it generates the new set of missing cases.
--
module Language.PureScript.Linter.Exhaustive
  ( checkExhaustiveExpr
  ) where

import Prelude.Compat
import Protolude (ordNub)

import Control.Applicative
import Control.Arrow (first, second)
import Control.Monad (unless)
import Control.Monad.Writer.Class
import Control.Monad.Supply.Class (MonadSupply, fresh, freshName)

import Data.Function (on)
import Data.List (foldl', sortBy)
import Data.Maybe (fromMaybe)
import Data.Monoid ((<>))
import qualified Data.Map as M
import Data.Text (Text)
import qualified Data.Text as T

import Language.PureScript.AST.Binders
import Language.PureScript.AST.Declarations
import Language.PureScript.AST.Literals
import Language.PureScript.Crash
import Language.PureScript.Environment
import Language.PureScript.Errors
import Language.PureScript.Kinds
import Language.PureScript.Names as P
import Language.PureScript.Pretty.Values (prettyPrintBinderAtom)
import Language.PureScript.Traversals
import Language.PureScript.Types as P
import qualified Language.PureScript.Constants as C

-- | There are two modes of failure for the redundancy check:
--
-- 1. Exhaustivity was incomplete due to too many cases, so we couldn't determine redundancy.
-- 2. We didn't attempt to determine redundancy for a binder, e.g. an integer binder.
--
-- We want to warn the user in the first case.
data RedundancyError = Incomplete | Unknown

-- |
-- Qualifies a propername from a given qualified propername and a default module name
--
qualifyName
  :: ProperName a
  -> ModuleName
  -> Qualified (ProperName b)
  -> Qualified (ProperName a)
qualifyName n defmn qn = Qualified (Just mn) n
  where
  (mn, _) = qualify defmn qn

-- |
-- Given an environment and a datatype or newtype name,
-- this function returns the associated data constructors if it is the case of a datatype
-- where: - ProperName is the name of the constructor (for example, "Nothing" in Maybe)
--        - [Type] is the list of arguments, if it has (for example, "Just" has [TypeVar "a"])
--
getConstructors :: Environment -> ModuleName -> Qualified (ProperName 'ConstructorName) -> [(ProperName 'ConstructorName, [Type])]
getConstructors env defmn n = extractConstructors lnte
  where

  extractConstructors :: Maybe (Kind, TypeKind) -> [(ProperName 'ConstructorName, [Type])]
  extractConstructors (Just (_, DataType _ pt)) = pt
  extractConstructors _ = internalError "Data name not in the scope of the current environment in extractConstructors"

  lnte :: Maybe (Kind, TypeKind)
  lnte = M.lookup qpn (types env)

  qpn :: Qualified (ProperName 'TypeName)
  qpn = getConsDataName n

  getConsDataName :: Qualified (ProperName 'ConstructorName) -> Qualified (ProperName 'TypeName)
  getConsDataName con =
    case getConsInfo con of
      Nothing -> internalError $ "Constructor " ++ T.unpack (showQualified runProperName con) ++ " not in the scope of the current environment in getConsDataName."
      Just (_, pm, _, _) -> qualifyName pm defmn con

  getConsInfo :: Qualified (ProperName 'ConstructorName) -> Maybe (DataDeclType, ProperName 'TypeName, Type, [Ident])
  getConsInfo con = M.lookup con (dataConstructors env)

-- |
-- Replicates a wildcard binder
--
initialize :: Int -> [Binder]
initialize l = replicate l NullBinder

-- |
-- Applies a function over two lists of tuples that may lack elements
--
genericMerge :: Ord a =>
  (a -> Maybe b -> Maybe c -> d) ->
  [(a, b)] ->
  [(a, c)] ->
  [d]
genericMerge _ [] [] = []
genericMerge f bs [] = map (\(s, b) -> f s (Just b) Nothing) bs
genericMerge f [] bs = map (\(s, b) -> f s Nothing (Just b)) bs
genericMerge f bsl@((s, b):bs) bsr@((s', b'):bs')
  | s < s' = f s (Just b) Nothing : genericMerge f bs bsr
  | s > s' = f s' Nothing (Just b') : genericMerge f bsl bs'
  | otherwise = f s (Just b) (Just b') : genericMerge f bs bs'

-- |
-- Find the uncovered set between two binders:
-- the first binder is the case we are trying to cover, the second one is the matching binder
--
missingCasesSingle :: Environment -> ModuleName -> Binder -> Binder -> ([Binder], Either RedundancyError Bool)
missingCasesSingle _ _ _ NullBinder = ([], return True)
missingCasesSingle _ _ _ (VarBinder _) = ([], return True)
missingCasesSingle env mn (VarBinder _) b = missingCasesSingle env mn NullBinder b
missingCasesSingle env mn br (NamedBinder _ bl) = missingCasesSingle env mn br bl
missingCasesSingle env mn NullBinder cb@(ConstructorBinder con _) =
  (concatMap (\cp -> fst $ missingCasesSingle env mn cp cb) allPatterns, return True)
  where
  allPatterns = map (\(p, t) -> ConstructorBinder (qualifyName p mn con) (initialize $ length t))
                  $ getConstructors env mn con
missingCasesSingle env mn cb@(ConstructorBinder con bs) (ConstructorBinder con' bs')
  | con == con' = let (bs'', pr) = missingCasesMultiple env mn bs bs' in (map (ConstructorBinder con) bs'', pr)
  | otherwise = ([cb], return False)
missingCasesSingle env mn NullBinder (LiteralBinder (ObjectLiteral bs)) =
  (map (LiteralBinder . ObjectLiteral . zip (map fst bs)) allMisses, pr)
  where
  (allMisses, pr) = missingCasesMultiple env mn (initialize $ length bs) (map snd bs)
missingCasesSingle env mn (LiteralBinder (ObjectLiteral bs)) (LiteralBinder (ObjectLiteral bs')) =
  (map (LiteralBinder . ObjectLiteral . zip sortedNames) allMisses, pr)
  where
  (allMisses, pr) = uncurry (missingCasesMultiple env mn) (unzip binders)

  sortNames = sortBy (compare `on` fst)

  (sbs, sbs') = (sortNames bs, sortNames bs')

  compB :: a -> Maybe a -> Maybe a -> (a, a)
  compB e b b' = (fm b, fm b')
    where
    fm = fromMaybe e

  compBS :: b -> a -> Maybe b -> Maybe b -> (a, (b, b))
  compBS e s b b' = (s, compB e b b')

  (sortedNames, binders) = unzip $ genericMerge (compBS NullBinder) sbs sbs'
missingCasesSingle _ _ NullBinder (LiteralBinder (BooleanLiteral b)) = ([LiteralBinder . BooleanLiteral $ not b], return True)
missingCasesSingle _ _ (LiteralBinder (BooleanLiteral bl)) (LiteralBinder (BooleanLiteral br))
  | bl == br = ([], return True)
  | otherwise = ([LiteralBinder $ BooleanLiteral bl], return False)
missingCasesSingle env mn b (PositionedBinder _ _ cb) = missingCasesSingle env mn b cb
missingCasesSingle env mn b (TypedBinder _ cb) = missingCasesSingle env mn b cb
missingCasesSingle _ _ b _ = ([b], Left Unknown)

-- |
-- Returns the uncovered set of binders
-- the first argument is the list of uncovered binders at step i
-- the second argument is the (i+1)th clause of a pattern matching definition
--
-- The idea of the algorithm is as follows:
-- it processes each binder of the two lists (say, `x` and `y`) one by one
-- at each step two cases arises:
--   - there are no missing cases between `x` and `y`: this is very straightforward, it continues with the remaining cases
--       but keeps the uncovered binder in its position.
--   - there are missing cases, let us call it the set `U`: on the one hand, we mix each new uncovered case in `U`
--       with the current tail of uncovered set. On the other hand, it continues with the remaining cases: here we
--       can use `x` (but it will generate overlapping cases), or `y`, which will generate non-overlapping cases.
--
--     As an example, consider:
--
--       data N = Z | S N
--       f Z Z = Z   --> {[S _, _], [Z, S _]} which are the right non-overlapping cases (GHC uses this).
--
--       if we use `x` instead of `y` (in this case, `y` stands for `Z` and `x` for `_`) we obtain:
--       f Z Z = Z   --> {[S _, _], [_, S _]} you can see that both cases overlaps each other.
--
--       Up to now, we've decided to use `x` just because we expect to generate uncovered cases which might be
--       redundant or not, but uncovered at least. If we use `y` instead, we'll need to have a redundancy checker
--       (which ought to be available soon), or increase the complexity of the algorithm.
--
missingCasesMultiple :: Environment -> ModuleName -> [Binder] -> [Binder] -> ([[Binder]], Either RedundancyError Bool)
missingCasesMultiple env mn = go
  where
  go (x:xs) (y:ys) = (map (: xs) miss1 ++ map (x :) miss2, liftA2 (&&) pr1 pr2)
    where
    (miss1, pr1) = missingCasesSingle env mn x y
    (miss2, pr2) = go xs ys
  go _ _ = ([], pure True)

-- |
-- Guard handling
--
-- We say a guard is exhaustive iff it has an `otherwise` (or `true`) expression.
-- Example:
--   f x | x < 0 = 0
--       | otherwise = 1
--   is exhaustive, whereas `f x | x < 0` is not
--
-- The function below say whether or not a guard has an `otherwise` expression
-- It is considered that `otherwise` is defined in Prelude
--
isExhaustiveGuard :: [GuardedExpr] -> Bool
isExhaustiveGuard [GuardedExpr [] _] = True
isExhaustiveGuard gs  =
  not . null $ filter (\(GuardedExpr grd _) -> isExhaustive grd) gs
  where
    checkGuard :: Guard -> Bool
    checkGuard (ConditionGuard cond) = isTrueExpr cond
    checkGuard (PatternGuard bind _) = isIrrefutable bind

    isExhaustive :: [Guard] -> Bool
    isExhaustive = all checkGuard

-- |
-- Returns the uncovered set of case alternatives
--
missingCases :: Environment -> ModuleName -> [Binder] -> CaseAlternative -> ([[Binder]], Either RedundancyError Bool)
missingCases env mn uncovered ca = missingCasesMultiple env mn uncovered (caseAlternativeBinders ca)

missingAlternative :: Environment -> ModuleName -> CaseAlternative -> [Binder] -> ([[Binder]], Either RedundancyError Bool)
missingAlternative env mn ca uncovered
  | isExhaustiveGuard (caseAlternativeResult ca) = mcases
  | otherwise = ([uncovered], snd mcases)
  where
  mcases = missingCases env mn uncovered ca

-- |
-- Main exhaustivity checking function
-- Starting with the set `uncovered = { _ }` (nothing covered, one `_` for each function argument),
-- it partitions that set with the new uncovered cases, until it consumes the whole set of clauses.
-- Then, returns the uncovered set of case alternatives.
--
checkExhaustive
  :: forall m
   . (MonadWriter MultipleErrors m, MonadSupply m)
   => Environment
   -> ModuleName
   -> Int
   -> [CaseAlternative]
   -> Expr
   -> m Expr
checkExhaustive env mn numArgs cas expr = makeResult . first ordNub $ foldl' step ([initialize numArgs], (pure True, [])) cas
  where
  step :: ([[Binder]], (Either RedundancyError Bool, [[Binder]])) -> CaseAlternative -> ([[Binder]], (Either RedundancyError Bool, [[Binder]]))
  step (uncovered, (nec, redundant)) ca =
    let (missed, pr) = unzip (map (missingAlternative env mn ca) uncovered)
        (missed', approx) = splitAt 10000 (ordNub (concat missed))
        cond = or <$> sequenceA pr
    in (missed', ( if null approx
                     then liftA2 (&&) cond nec
                     else Left Incomplete
                 , if either (const True) id cond
                     then redundant
                     else caseAlternativeBinders ca : redundant
                 )
       )

  makeResult :: ([[Binder]], (Either RedundancyError Bool, [[Binder]])) -> m Expr
  makeResult (bss, (rr, bss')) =
    do unless (null bss') tellRedundant
       case rr of
         Left Incomplete -> tellIncomplete
         _ -> return ()
       if null bss
         then return expr
         else addPartialConstraint (second null (splitAt 5 bss)) expr
    where
      tellRedundant = tell . errorMessage . uncurry OverlappingPattern . second null . splitAt 5 $ bss'
      tellIncomplete = tell . errorMessage $ IncompleteExhaustivityCheck

  -- | We add a Partial constraint by adding a call to the following identity function:
  --
  -- partial :: forall a. Partial => a -> a
  --
  -- The binder information is provided so that it can be embedded in the constraint,
  -- and then included in the error message.
  addPartialConstraint :: ([[Binder]], Bool) -> Expr -> m Expr
  addPartialConstraint (bss, complete) e = do
    tyVar <- ("p" <>) . T.pack . show <$> fresh
    var <- freshName
    return $
      Let
        [ partial var tyVar ]
        $ App (Var (Qualified Nothing (Ident C.__unused))) e
    where
      partial :: Text -> Text -> Declaration
      partial var tyVar =
        ValueDeclaration (Ident C.__unused) Private [] $
        [MkUnguarded
          (TypedValue
           True
           (Abs (VarBinder (Ident var)) (Var (Qualified Nothing (Ident var))))
           (ty tyVar))
        ]

      ty :: Text -> Type
      ty tyVar =
        ForAll tyVar
          ( ConstrainedType
              (Constraint C.Partial [] (Just constraintData))
              $ TypeApp (TypeApp tyFunction (TypeVar tyVar)) (TypeVar tyVar)
          )
          Nothing

      constraintData :: ConstraintData
      constraintData =
        PartialConstraintData (map (map prettyPrintBinderAtom) bss) complete

-- |
-- Exhaustivity checking
--
checkExhaustiveExpr
  :: forall m
   . (MonadWriter MultipleErrors m, MonadSupply m)
   => Environment
   -> ModuleName
   -> Expr
   -> m Expr
checkExhaustiveExpr env mn = onExpr
  where
  onDecl :: Declaration -> m Declaration
  onDecl (BindingGroupDeclaration bs) = BindingGroupDeclaration <$> mapM (thirdM onExpr) bs
  onDecl (ValueDeclaration name x y [MkUnguarded e]) = ValueDeclaration name x y . mkUnguardedExpr <$> censor (addHint (ErrorInValueDeclaration name)) (onExpr e)
  onDecl (PositionedDeclaration pos x dec) = PositionedDeclaration pos x <$> censor (addHint (PositionedError pos)) (onDecl dec)
  onDecl decl = return decl

  onExpr :: Expr -> m Expr
  onExpr (UnaryMinus e) = UnaryMinus <$> onExpr e
  onExpr (Literal (ArrayLiteral es)) = Literal . ArrayLiteral <$> mapM onExpr es
  onExpr (Literal (ObjectLiteral es)) = Literal . ObjectLiteral <$> mapM (sndM onExpr) es
  onExpr (TypeClassDictionaryConstructorApp x e) = TypeClassDictionaryConstructorApp x <$> onExpr e
  onExpr (Accessor x e) = Accessor x <$> onExpr e
  onExpr (ObjectUpdate o es) = ObjectUpdate <$> onExpr o <*> mapM (sndM onExpr) es
  onExpr (Abs x e) = Abs x <$> onExpr e
  onExpr (App e1 e2) = App <$> onExpr e1 <*> onExpr e2
  onExpr (IfThenElse e1 e2 e3) = IfThenElse <$> onExpr e1 <*> onExpr e2 <*> onExpr e3
  onExpr (Case es cas) = do
    case' <- Case <$> mapM onExpr es <*> mapM onCaseAlternative cas
    checkExhaustive env mn (length es) cas case'
  onExpr (TypedValue x e y) = TypedValue x <$> onExpr e <*> pure y
  onExpr (Let ds e) = Let <$> mapM onDecl ds <*> onExpr e
  onExpr (PositionedValue pos x e) = PositionedValue pos x <$> censor (addHint (PositionedError pos)) (onExpr e)
  onExpr expr = return expr

  onCaseAlternative :: CaseAlternative -> m CaseAlternative
  onCaseAlternative (CaseAlternative x [MkUnguarded e]) = CaseAlternative x . mkUnguardedExpr <$> onExpr e
  onCaseAlternative (CaseAlternative x es) = CaseAlternative x <$> mapM onGuardedExpr es

  onGuardedExpr :: GuardedExpr -> m GuardedExpr
  onGuardedExpr (GuardedExpr guard rhs) = GuardedExpr guard <$> onExpr rhs

  mkUnguardedExpr = pure . MkUnguarded