{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE FlexibleContexts #-}
-- | Defunctionalization of typed, monomorphic Futhark programs without modules.
module Futhark.Internalise.Defunctionalise
  ( transformProg ) where

import qualified Control.Arrow as Arrow
import           Control.Monad.State
import           Control.Monad.RWS hiding (Sum)
import           Data.Bifunctor
import           Data.Foldable
import           Data.List (sortOn, nub, partition, tails)
import qualified Data.List.NonEmpty as NE
import           Data.Loc
import           Data.Maybe
import qualified Data.Map.Strict as M
import qualified Data.Set as S
import qualified Data.Sequence as Seq

import           Futhark.MonadFreshNames
import           Language.Futhark
import           Futhark.Representation.AST.Pretty ()

-- | An expression or an extended 'Lambda' (with size parameters,
-- which AST lambdas do not support).
data ExtExp = ExtLambda [TypeParam] [Pattern] Exp (Aliasing, StructType) SrcLoc
            | ExtExp Exp
  deriving (Show)

-- | A static value stores additional information about the result of
-- defunctionalization of an expression, aside from the residual expression.
data StaticVal = Dynamic PatternType
               | LambdaSV [VName] Pattern StructType ExtExp Env
                 -- ^ The 'VName's are shape parameters that are bound
                 -- by the 'Pattern'.
               | RecordSV [(Name, StaticVal)]
               | SumSV Name [StaticVal] [(Name, [PatternType])]
                 -- ^ The constructor that is actually present, plus
                 -- the others that are not.
               | DynamicFun (Exp, StaticVal) StaticVal
               | IntrinsicSV
  deriving (Show)

-- | Environment mapping variable names to their associated static value.
type Env = M.Map VName StaticVal

localEnv :: Env -> DefM a -> DefM a
localEnv env = local $ Arrow.second (env<>)

-- Even when using a "new" environment (for evaluating closures) we
-- still ram the global environment of DynamicFuns in there.
localNewEnv :: Env -> DefM a -> DefM a
localNewEnv env = local $ \(globals, old_env) ->
  (globals, M.filterWithKey (\k _ -> k `S.member` globals) old_env <> env)

extendEnv :: VName -> StaticVal -> DefM a -> DefM a
extendEnv vn sv = localEnv (M.singleton vn sv)

askEnv :: DefM Env
askEnv = asks snd

isGlobal :: VName -> DefM a -> DefM a
isGlobal v = local $ Arrow.first (S.insert v)

-- | Returns the defunctionalization environment restricted
-- to the given set of variable names and types.
restrictEnvTo :: NameSet -> DefM Env
restrictEnvTo (NameSet m) = restrict <$> ask
  where restrict (globals, env) = M.mapMaybeWithKey keep env
          where keep k sv = do guard $ not $ k `S.member` globals
                               u <- M.lookup k m
                               Just $ restrict' u sv
        restrict' Nonunique (Dynamic t) =
          Dynamic $ t `setUniqueness`  Nonunique
        restrict' _ (Dynamic t) =
          Dynamic t
        restrict' u (LambdaSV dims pat t e env) =
          LambdaSV dims pat t e $ M.map (restrict' u) env
        restrict' u (RecordSV fields) =
          RecordSV $ map (fmap $ restrict' u) fields
        restrict' u (SumSV c svs fields) =
          SumSV c (map (restrict' u) svs) fields
        restrict' u (DynamicFun (e, sv1) sv2) =
          DynamicFun (e, restrict' u sv1) $ restrict' u sv2
        restrict' _ IntrinsicSV = IntrinsicSV

-- | Defunctionalization monad.  The Reader environment tracks both
-- the current Env as well as the set of globally defined dynamic
-- functions.  This is used to avoid unnecessarily large closure
-- environments.
newtype DefM a = DefM (RWS (S.Set VName, Env) (Seq.Seq ValBind) VNameSource a)
  deriving (Functor, Applicative, Monad,
            MonadReader (S.Set VName, Env),
            MonadWriter (Seq.Seq ValBind),
            MonadFreshNames)

-- | Run a computation in the defunctionalization monad. Returns the result of
-- the computation, a new name source, and a list of lifted function declations.
runDefM :: VNameSource -> DefM a -> (a, VNameSource, Seq.Seq ValBind)
runDefM src (DefM m) = runRWS m mempty src

collectFuns :: DefM a -> DefM (a, Seq.Seq ValBind)
collectFuns m = pass $ do
  (x, decs) <- listen m
  return ((x, decs), const mempty)

-- | Looks up the associated static value for a given name in the environment.
lookupVar :: SrcLoc -> VName -> DefM StaticVal
lookupVar loc x = do
  env <- askEnv
  case M.lookup x env of
    Just sv -> return sv
    Nothing -- If the variable is unknown, it may refer to the 'intrinsics'
            -- module, which we will have to treat specially.
      | baseTag x <= maxIntrinsicTag -> return IntrinsicSV
      | otherwise -> -- Anything not in scope is going to be an
                     -- existential size.
          return $ Dynamic $ Scalar $ Prim $ Signed Int32
      | otherwise ->  error $ "Variable " ++ pretty x ++ " at "
                          ++ locStr loc ++ " is out of scope."

-- Like patternDimNames, but ignores sizes that are only found in
-- funtion types.
arraySizes :: StructType -> S.Set VName
arraySizes (Scalar Arrow{}) = mempty
arraySizes (Scalar (Record fields)) = foldMap arraySizes fields
arraySizes (Scalar (Sum cs)) = foldMap (foldMap arraySizes) cs
arraySizes (Scalar TypeVar{}) = mempty
arraySizes (Scalar Prim{}) = mempty
arraySizes (Array _ _ t shape) =
  arraySizes (Scalar t) <> foldMap dimName (shapeDims shape)
  where dimName :: DimDecl VName -> S.Set VName
        dimName (NamedDim qn) = S.singleton $ qualLeaf qn
        dimName _             = mempty

patternArraySizes :: Pattern -> S.Set VName
patternArraySizes = arraySizes . patternStructType

dimMapping :: Monoid a =>
              TypeBase (DimDecl VName) a
           -> TypeBase (DimDecl VName) a
           -> M.Map VName VName
dimMapping t1 t2 = execState (matchDims f t1 t2) mempty
  where f (NamedDim d1) (NamedDim d2) = do
          modify $ M.insert (qualLeaf d1) (qualLeaf d2)
          return $ NamedDim d1
        f d _ = return d

defuncFun :: [TypeParam] -> [Pattern] -> Exp -> (Aliasing, StructType) -> SrcLoc
          -> DefM (Exp, StaticVal)
defuncFun tparams pats e0 (closure, ret) loc = do
  when (any isTypeParam tparams) $
    error $ "Received a lambda with type parameters at " ++ locStr loc
         ++ ", but the defunctionalizer expects a monomorphic input program."
  -- Extract the first parameter of the lambda and "push" the
  -- remaining ones (if there are any) into the body of the lambda.
  let (dims, pat, ret', e0') = case pats of
        [] -> error "Received a lambda with no parameters."
        [pat'] -> (map typeParamName tparams, pat', ret, ExtExp e0)
        (pat' : pats') ->
          -- Split shape parameters into those that are determined by
          -- the first pattern, and those that are determined by later
          -- patterns.
          let bound_by_pat = (`S.member` patternArraySizes pat') . typeParamName
              (pat_dims, rest_dims) = partition bound_by_pat tparams
          in (map typeParamName pat_dims, pat',
              foldFunType (map (toStruct . patternType) pats') ret,
              ExtLambda rest_dims pats' e0 (closure, ret) loc)

  -- Construct a record literal that closes over the environment of
  -- the lambda.  Closed-over 'DynamicFun's are converted to their
  -- closure representation.
  let used = freeVars (Lambda pats e0 Nothing (Info (closure, ret)) loc)
             `without` mconcat (map oneName dims)
  used_env <- restrictEnvTo used

  -- The closure parts that are sizes are proactively turned into size
  -- parameters.
  let sizes_of_arrays = foldMap (arraySizes . toStruct . typeFromSV) used_env <>
                        patternArraySizes pat
      notSize = not . (`S.member` sizes_of_arrays)
      (fields, env) = unzip $ map closureFromDynamicFun $
                      filter (notSize . fst) $ M.toList used_env
      env' = M.fromList env
      closure_dims = S.toList sizes_of_arrays

  return (RecordLit fields loc,
          LambdaSV (nub $ dims<>closure_dims) pat ret' e0' env')

  where closureFromDynamicFun (vn, DynamicFun (clsr_env, sv) _) =
          let name = nameFromString $ pretty vn
          in (RecordFieldExplicit name clsr_env noLoc, (vn, sv))

        closureFromDynamicFun (vn, sv) =
          let name = nameFromString $ pretty vn
              tp' = typeFromSV sv
          in (RecordFieldExplicit name
               (Var (qualName vn) (Info tp') noLoc) noLoc, (vn, sv))

-- | Defunctionalization of an expression. Returns the residual expression and
-- the associated static value in the defunctionalization monad.
defuncExp :: Exp -> DefM (Exp, StaticVal)

defuncExp e@Literal{} =
  return (e, Dynamic $ typeOf e)

defuncExp e@IntLit{} =
  return (e, Dynamic $ typeOf e)

defuncExp e@FloatLit{} =
  return (e, Dynamic $ typeOf e)

defuncExp e@StringLit{} =
  return (e, Dynamic $ typeOf e)

defuncExp (Parens e loc) = do
  (e', sv) <- defuncExp e
  return (Parens e' loc, sv)

defuncExp (QualParens qn e loc) = do
  (e', sv) <- defuncExp e
  return (QualParens qn e' loc, sv)

defuncExp (TupLit es loc) = do
  (es', svs) <- unzip <$> mapM defuncExp es
  return (TupLit es' loc, RecordSV $ zip tupleFieldNames svs)

defuncExp (RecordLit fs loc) = do
  (fs', names_svs) <- unzip <$> mapM defuncField fs
  return (RecordLit fs' loc, RecordSV names_svs)

  where defuncField (RecordFieldExplicit vn e loc') = do
          (e', sv) <- defuncExp e
          return (RecordFieldExplicit vn e' loc', (vn, sv))
        defuncField (RecordFieldImplicit vn _ loc') = do
          sv <- lookupVar loc' vn
          case sv of
            -- If the implicit field refers to a dynamic function, we
            -- convert it to an explicit field with a record closing over
            -- the environment and bind the corresponding static value.
            DynamicFun (e, sv') _ -> let vn' = baseName vn
                                     in return (RecordFieldExplicit vn' e loc',
                                                (vn', sv'))
            -- The field may refer to a functional expression, so we get the
            -- type from the static value and not the one from the AST.
            _ -> let tp = Info $ typeFromSV sv
                 in return (RecordFieldImplicit vn tp loc', (baseName vn, sv))

defuncExp (ArrayLit es t@(Info t') loc) = do
  es' <- mapM defuncExp' es
  return (ArrayLit es' t loc, Dynamic t')

defuncExp (Range e1 me incl t@(Info t', _) loc) = do
  e1' <- defuncExp' e1
  me' <- mapM defuncExp' me
  incl' <- mapM defuncExp' incl
  return (Range e1' me' incl' t loc, Dynamic t')

defuncExp e@(Var qn _ loc) = do
  sv <- lookupVar loc (qualLeaf qn)
  case sv of
    -- If the variable refers to a dynamic function, we return its closure
    -- representation (i.e., a record expression capturing the free variables
    -- and a 'LambdaSV' static value) instead of the variable itself.
    DynamicFun closure _ -> return closure
    -- Intrinsic functions used as variables are eta-expanded, so we
    -- can get rid of them.
    IntrinsicSV -> do
      (pats, body, tp) <- etaExpand (typeOf e) e
      defuncExp $ Lambda pats body Nothing (Info (mempty, tp)) noLoc
    _ -> let tp = typeFromSV sv
         in return (Var qn (Info tp) loc, sv)

defuncExp (Ascript e0 tydecl loc)
  | orderZero (typeOf e0) = do (e0', sv) <- defuncExp e0
                               return (Ascript e0' tydecl loc, sv)
  | otherwise = defuncExp e0

defuncExp (Coerce e0 tydecl t loc)
  | orderZero (typeOf e0) = do (e0', sv) <- defuncExp e0
                               return (Coerce e0' tydecl t loc, sv)
  | otherwise = defuncExp e0

defuncExp (LetPat pat e1 e2 (Info t, retext) loc) = do
  (e1', sv1) <- defuncExp e1
  let env  = matchPatternSV pat sv1
      pat' = updatePattern pat sv1
  (e2', sv2) <- localEnv env $ defuncExp e2
  -- To maintain any sizes going out of scope, we need to compute the
  -- old size substitution induced by retext and also apply it to the
  -- newly computed body type.
  let mapping = dimMapping (typeOf e2) t
      subst v = fromMaybe v $ M.lookup v mapping
      t' = first (fmap subst) $ typeOf e2'
  return (LetPat pat' e1' e2' (Info t', retext) loc, sv2)

-- Local functions are handled by rewriting them to lambdas, so that
-- the same machinery can be re-used.
defuncExp (LetFun vn (dims, pats, _, Info ret, e1) e2 _ loc) = do
  (e1', sv1) <- defuncFun dims pats e1 (mempty, ret) loc
  (e2', sv2) <- localEnv (M.singleton vn sv1) $ defuncExp e2
  return (LetPat (Id vn (Info (typeOf e1')) loc) e1' e2' (Info $ typeOf e2', Info []) loc,
          sv2)

defuncExp (If e1 e2 e3 tp loc) = do
  (e1', _ ) <- defuncExp e1
  (e2', sv) <- defuncExp e2
  (e3', _ ) <- defuncExp e3
  return (If e1' e2' e3' tp loc, sv)

defuncExp e@(Apply f@(Var f' _ _) arg d (t, ext) loc)
  | baseTag (qualLeaf f') <= maxIntrinsicTag,
    TupLit es tuploc <- arg = do
      -- defuncSoacExp also works fine for non-SOACs.
      es' <- mapM defuncSoacExp es
      return (Apply f (TupLit es' tuploc) d (t, ext) loc,
              Dynamic $ typeOf e)

defuncExp e@Apply{} = defuncApply 0 e

defuncExp (Negate e0 loc) = do
  (e0', sv) <- defuncExp e0
  return (Negate e0' loc, sv)

defuncExp (Lambda pats e0 _ (Info (closure, ret)) loc) =
  defuncFun [] pats e0 (closure, ret) loc

-- Operator sections are expected to be converted to lambda-expressions
-- by the monomorphizer, so they should no longer occur at this point.
defuncExp OpSection{}      = error "defuncExp: unexpected operator section."
defuncExp OpSectionLeft{}  = error "defuncExp: unexpected operator section."
defuncExp OpSectionRight{} = error "defuncExp: unexpected operator section."
defuncExp ProjectSection{} = error "defuncExp: unexpected projection section."
defuncExp IndexSection{}   = error "defuncExp: unexpected projection section."

defuncExp (DoLoop sparams pat e1 form e3 ret loc) = do
  (e1', sv1) <- defuncExp e1
  let env1 = matchPatternSV pat sv1
  (form', env2) <- case form of
    For v e2      -> do e2' <- defuncExp' e2
                        return (For v e2', envFromIdent v)
    ForIn pat2 e2 -> do e2' <- defuncExp' e2
                        return (ForIn pat2 e2', envFromPattern pat2)
    While e2      -> do e2' <- localEnv env1 $ defuncExp' e2
                        return (While e2', mempty)
  (e3', sv) <- localEnv (env1 <> env2) $ defuncExp e3
  return (DoLoop sparams pat e1' form' e3' ret loc, sv)
  where envFromIdent (Ident vn (Info tp) _) =
          M.singleton vn $ Dynamic tp

-- We handle BinOps by turning them into ordinary function applications.
defuncExp (BinOp (qn, qnloc) (Info t)
           (e1, Info (pt1, ext1)) (e2, Info (pt2, ext2))
           (Info ret) (Info retext) loc) =
  defuncExp $ Apply (Apply (Var qn (Info t) qnloc)
                     e1 (Info (diet pt1, ext1))
                     (Info (Scalar $ Arrow mempty Unnamed (fromStruct pt2) ret), Info []) loc)
                    e2 (Info (diet pt2, ext2)) (Info ret, Info retext) loc

defuncExp (Project vn e0 tp@(Info tp') loc) = do
  (e0', sv0) <- defuncExp e0
  case sv0 of
    RecordSV svs -> case lookup vn svs of
      Just sv -> return (Project vn e0' (Info $ typeFromSV sv) loc, sv)
      Nothing -> error "Invalid record projection."
    Dynamic _ -> return (Project vn e0' tp loc, Dynamic tp')
    _ -> error $ "Projection of an expression with static value " ++ show sv0

defuncExp (LetWith id1 id2 idxs e1 body t loc) = do
  e1' <- defuncExp' e1
  sv1 <- lookupVar (identSrcLoc id2) $ identName id2
  idxs' <- mapM defuncDimIndex idxs
  (body', sv) <- extendEnv (identName id1) sv1 $ defuncExp body
  return (LetWith id1 id2 idxs' e1' body' t loc, sv)

defuncExp expr@(Index e0 idxs info loc) = do
  e0' <- defuncExp' e0
  idxs' <- mapM defuncDimIndex idxs
  return (Index e0' idxs' info loc, Dynamic $ typeOf expr)

defuncExp (Update e1 idxs e2 loc) = do
  (e1', sv) <- defuncExp e1
  idxs' <- mapM defuncDimIndex idxs
  e2' <- defuncExp' e2
  return (Update e1' idxs' e2' loc, sv)

-- Note that we might change the type of the record field here.  This
-- is not permitted in the type checker due to problems with type
-- inference, but it actually works fine.
defuncExp (RecordUpdate e1 fs e2 _ loc) = do
  (e1', sv1) <- defuncExp e1
  (e2', sv2) <- defuncExp e2
  let sv = staticField sv1 sv2 fs
  return (RecordUpdate e1' fs e2' (Info $ typeFromSV sv1) loc,
          sv)
  where staticField (RecordSV svs) sv2 (f:fs') =
          case lookup f svs of
            Just sv -> RecordSV $
                       (f, staticField sv sv2 fs') : filter ((/=f) . fst) svs
            Nothing -> error "Invalid record projection."
        staticField (Dynamic t@(Scalar Record{})) sv2 fs'@(_:_) =
          staticField (svFromType t) sv2 fs'
        staticField _ sv2 _ = sv2

defuncExp (Unsafe e1 loc) = do
  (e1', sv) <- defuncExp e1
  return (Unsafe e1' loc, sv)

defuncExp (Assert e1 e2 desc loc) = do
  (e1', _) <- defuncExp e1
  (e2', sv) <- defuncExp e2
  return (Assert e1' e2' desc loc, sv)

defuncExp (Constr name es (Info (Scalar (Sum all_fs))) loc) = do
  (es', svs) <- unzip <$> mapM defuncExp es
  let sv = SumSV name svs $ M.toList $
           name `M.delete` M.map (map defuncType) all_fs
  return (Constr name es' (Info (typeFromSV sv)) loc, sv)
  where defuncType :: Monoid als =>
                      TypeBase (DimDecl VName) als
                   -> TypeBase (DimDecl VName) als
        defuncType (Array as u t shape) = Array as u (defuncScalar t) shape
        defuncType (Scalar t) = Scalar $ defuncScalar t

        defuncScalar :: Monoid als =>
                        ScalarTypeBase (DimDecl VName) als
                     -> ScalarTypeBase (DimDecl VName) als
        defuncScalar (Record fs) = Record $ M.map defuncType fs
        defuncScalar Arrow{} = Record mempty
        defuncScalar (Sum fs) = Sum $ M.map (map defuncType) fs
        defuncScalar (Prim t) = Prim t
        defuncScalar (TypeVar as u tn targs) = TypeVar as u tn targs

defuncExp (Constr name _ (Info t) loc) =
  error $ "Constructor " ++ pretty name ++ " given type " ++
  pretty t ++ " at " ++ locStr loc

defuncExp (Match e cs t loc) = do
  (e', sv) <- defuncExp e
  csPairs  <- mapM (defuncCase sv) cs
  let cs' = fmap fst csPairs
      sv' = snd $ NE.head csPairs
  return (Match e' cs' t loc, sv')

-- | Same as 'defuncExp', except it ignores the static value.
defuncExp' :: Exp -> DefM Exp
defuncExp' = fmap fst . defuncExp

defuncExtExp :: ExtExp -> DefM (Exp, StaticVal)
defuncExtExp (ExtExp e) = defuncExp e
defuncExtExp (ExtLambda tparams pats e0 (closure, ret) loc) =
  defuncFun tparams pats e0 (closure, ret) loc

defuncCase :: StaticVal -> Case -> DefM (Case, StaticVal)
defuncCase sv (CasePat p e loc) = do
  let p'  = updatePattern p sv
      env = matchPatternSV p sv
  (e', sv') <- localEnv env $ defuncExp e
  return (CasePat p' e' loc, sv')

-- | Defunctionalize the function argument to a SOAC by eta-expanding if
-- necessary and then defunctionalizing the body of the introduced lambda.
defuncSoacExp :: Exp -> DefM Exp
defuncSoacExp e@OpSection{}      = return e
defuncSoacExp e@OpSectionLeft{}  = return e
defuncSoacExp e@OpSectionRight{} = return e
defuncSoacExp e@ProjectSection{} = return e

defuncSoacExp (Parens e loc) =
  Parens <$> defuncSoacExp e <*> pure loc

defuncSoacExp (Lambda params e0 decl tp loc) = do
  let env = foldMap envFromPattern params
  e0' <- localEnv env $ defuncSoacExp e0
  return $ Lambda params e0' decl tp loc

defuncSoacExp e
  | Scalar Arrow{} <- typeOf e = do
      (pats, body, tp) <- etaExpand (typeOf e) e
      let env = foldMap envFromPattern pats
      body' <- localEnv env $ defuncExp' body
      return $ Lambda pats body' Nothing (Info (mempty, tp)) noLoc
  | otherwise = defuncExp' e

etaExpand :: PatternType -> Exp -> DefM ([Pattern], Exp, StructType)
etaExpand e_t e = do
  let (ps, ret) = getType e_t
  (pats, vars) <- fmap unzip . forM ps $ \(p, t) -> do
    x <- case p of Named x -> pure x
                   Unnamed -> newNameFromString "x"
    return (Id x (Info t) noLoc,
            Var (qualName x) (Info t) noLoc)
  let e' = foldl' (\e1 (e2, t2, argtypes) ->
                     Apply e1 e2 (Info (diet t2, Nothing))
                     (Info (foldFunType argtypes ret), Info []) noLoc)
           e $ zip3 vars (map snd ps) (drop 1 $ tails $ map snd ps)
  return (pats, e', toStruct ret)

  where getType (Scalar (Arrow _ p t1 t2)) =
          let (ps, r) = getType t2 in ((p,t1) : ps, r)
        getType t = ([], t)

-- | Defunctionalize an indexing of a single array dimension.
defuncDimIndex :: DimIndexBase Info VName -> DefM (DimIndexBase Info VName)
defuncDimIndex (DimFix e1) = DimFix . fst <$> defuncExp e1
defuncDimIndex (DimSlice me1 me2 me3) =
  DimSlice <$> defunc' me1 <*> defunc' me2 <*> defunc' me3
  where defunc' = mapM defuncExp'

-- | Defunctionalize a let-bound function, while preserving parameters
-- that have order 0 types (i.e., non-functional).
defuncLet :: [TypeParam] -> [Pattern] -> Exp -> StructType
          -> DefM ([TypeParam], [Pattern], Exp, StaticVal)
defuncLet dims ps@(pat:pats) body rettype
  | patternOrderZero pat = do

      let bound_by_pat = (`S.member` patternDimNames pat) . typeParamName
          -- Take care to not include more size parameters than necessary.
          (pat_dims, rest_dims) = partition bound_by_pat dims
          env = envFromPattern pat <> envFromShapeParams pat_dims
      (rest_dims', pats', body', sv) <- localEnv env $ defuncLet rest_dims pats body rettype
      closure <- defuncFun dims ps body (mempty, rettype) noLoc
      return (pat_dims ++ rest_dims', pat : pats', body', DynamicFun closure sv)
  | otherwise = do
      (e, sv) <- defuncFun dims ps body (mempty, rettype) noLoc
      return ([], [], e, sv)

defuncLet _ [] body rettype = do
  (body', sv) <- defuncExp body
  return ([], [], body', imposeType sv rettype)
  where imposeType Dynamic{} t =
          Dynamic $ fromStruct t
        imposeType (RecordSV fs1) (Scalar (Record fs2)) =
          RecordSV $ M.toList $ M.intersectionWith imposeType (M.fromList fs1) fs2
        imposeType sv _ = sv

-- | Defunctionalize an application expression at a given depth of application.
-- Calls to dynamic (first-order) functions are preserved at much as possible,
-- but a new lifted function is created if a dynamic function is only partially
-- applied.
defuncApply :: Int -> Exp -> DefM (Exp, StaticVal)
defuncApply depth e@(Apply e1 e2 d t@(Info ret, Info ext) loc) = do
  let (argtypes, _) = unfoldFunType ret
  (e1', sv1) <- defuncApply (depth+1) e1
  (e2', sv2) <- defuncExp e2
  let e' = Apply e1' e2' d t loc
  case sv1 of
    LambdaSV dims pat e0_t e0 closure_env -> do
      let env' = matchPatternSV pat sv2
          env_dim = envFromDimNames dims
      (e0', sv) <- localNewEnv (env' <> closure_env <> env_dim) $ defuncExtExp e0

      let closure_pat = buildEnvPattern closure_env
          pat' = updatePattern pat sv2

      -- Lift lambda to top-level function definition.  We put in
      -- a lot of effort to try to infer the uniqueness attributes
      -- of the lifted function, but this is ultimately all a sham
      -- and a hack.  There is some piece we're missing.
      let params = [closure_pat, pat']
          params_for_rettype = params ++ svParams sv1 ++ svParams sv2
          svParams (LambdaSV _ sv_pat _ _ _) = [sv_pat]
          svParams _                         = []
          rettype = buildRetType closure_env params_for_rettype e0_t $ typeOf e0'

          already_bound = S.fromList dims <>
                          S.map identName (foldMap patternIdents params)
          more_dims = S.toList $
                      S.filter (`S.notMember` already_bound) $
                      foldMap patternArraySizes params

          -- Embed some information about the original function
          -- into the name of the lifted function, to make the
          -- result slightly more human-readable.
          liftedName i (Var f _ _) =
            "lifted_" ++ show i ++ "_" ++ baseString (qualLeaf f)
          liftedName i (Apply f _ _ _ _) =
            liftedName (i+1) f
          liftedName _ _ = "lifted"

      fname <- newNameFromString $ liftedName (0::Int) e1
      liftValDec fname rettype (dims ++ more_dims) params e0'

      let t1 = toStruct $ typeOf e1'
          t2 = toStruct $ typeOf e2'
          fname' = qualName fname
          fname'' = Var fname' (Info (Scalar $ Arrow mempty Unnamed (fromStruct t1) $
                                      Scalar $ Arrow mempty Unnamed (fromStruct t2) rettype))
                    loc

          -- FIXME: what if this application returns both a function
          -- and a value?
          callret | orderZero ret = (Info ret, Info ext)
                  | otherwise     = (Info rettype, Info ext)

      return (Parens (Apply (Apply fname'' e1'
                              (Info (Observe, Nothing))
                              (Info $ Scalar $ Arrow mempty Unnamed (fromStruct t2) rettype,
                               Info [])
                              loc)
                      e2' d callret loc) noLoc, sv)

    -- If e1 is a dynamic function, we just leave the application in place,
    -- but we update the types since it may be partially applied or return
    -- a higher-order term.
    DynamicFun _ sv ->
      let (argtypes', rettype) = dynamicFunType sv argtypes
          restype = foldFunType argtypes' rettype `setAliases` aliases ret
          -- FIXME: what if this application returns both a function
          -- and a value?
          callret | orderZero ret = (Info ret, Info ext)
                  | otherwise     = (Info restype, Info ext)
          apply_e = Apply e1' e2' d callret loc
      in return (apply_e, sv)

    -- Propagate the 'IntrinsicsSV' until we reach the outermost application,
    -- where we construct a dynamic static value with the appropriate type.
    IntrinsicSV
      | depth == 0 ->
          -- If the intrinsic is fully applied, then we are done.
          -- Otherwise we need to eta-expand it and recursively
          -- defunctionalise. XXX: might it be better to simply
          -- eta-expand immediately any time we encounter a
          -- non-fully-applied intrinsic?
          if null argtypes
            then return (e', Dynamic $ typeOf e)
            else do (pats, body, tp) <- etaExpand (typeOf e') e'
                    defuncExp $ Lambda pats body Nothing (Info (mempty, tp)) noLoc
      | otherwise -> return (e', IntrinsicSV)

    _ -> error $ "Application of an expression that is neither a static lambda "
              ++ "nor a dynamic function, but has static value: " ++ show sv1

defuncApply depth e@(Var qn (Info t) loc) = do
    let (argtypes, _) = unfoldFunType t
    sv <- lookupVar loc (qualLeaf qn)
    case sv of
      DynamicFun _ _
        | fullyApplied sv depth ->
            -- We still need to update the types in case the dynamic
            -- function returns a higher-order term.
            let (argtypes', rettype) = dynamicFunType sv argtypes
            in return (Var qn (Info (foldFunType argtypes' rettype)) loc, sv)

        | otherwise -> do
            fname <- newName $ qualLeaf qn
            let (dims, pats, e0, sv') = liftDynFun sv depth
                pats_names = S.map identName $ mconcat $ map patternIdents pats
                notInPats = (`S.notMember` pats_names)
                dims' = filter notInPats dims
                (argtypes', rettype) = dynamicFunType sv' argtypes
            liftValDec fname (fromStruct rettype) dims' pats e0
            return (Var (qualName fname)
                    (Info (foldFunType argtypes' $ fromStruct rettype)) loc, sv')

      IntrinsicSV -> return (e, IntrinsicSV)

      _ -> return (Var qn (Info (typeFromSV sv)) loc, sv)

defuncApply depth (Parens e _) = defuncApply depth e

defuncApply _ expr = defuncExp expr

-- | Check if a 'StaticVal' and a given application depth corresponds
-- to a fully applied dynamic function.
fullyApplied :: StaticVal -> Int -> Bool
fullyApplied (DynamicFun _ sv) depth
  | depth == 0   = False
  | depth >  0   = fullyApplied sv (depth-1)
fullyApplied _ _ = True

-- | Converts a dynamic function 'StaticVal' into a list of
-- dimensions, a list of parameters, a function body, and the
-- appropriate static value for applying the function at the given
-- depth of partial application.
liftDynFun :: StaticVal -> Int -> ([VName], [Pattern], Exp, StaticVal)
liftDynFun (DynamicFun (e, sv) _) 0 = ([], [], e, sv)
liftDynFun (DynamicFun clsr@(_, LambdaSV dims pat _ _ _) sv) d
  | d > 0 =  let (dims', pats, e', sv') = liftDynFun sv (d-1)
             in (nub $ dims ++ dims', pat : pats, e', DynamicFun clsr sv')
liftDynFun sv _ = error $ "Tried to lift a StaticVal " ++ show sv
                       ++ ", but expected a dynamic function."

-- | Converts a pattern to an environment that binds the individual names of the
-- pattern to their corresponding types wrapped in a 'Dynamic' static value.
envFromPattern :: Pattern -> Env
envFromPattern pat = case pat of
  TuplePattern ps _       -> foldMap envFromPattern ps
  RecordPattern fs _      -> foldMap (envFromPattern . snd) fs
  PatternParens p _       -> envFromPattern p
  Id vn (Info t) _        -> M.singleton vn $ Dynamic t
  Wildcard _ _            -> mempty
  PatternAscription p _ _ -> envFromPattern p
  PatternLit{}            -> mempty
  PatternConstr _ _ ps _  -> foldMap envFromPattern ps

-- | Create an environment that binds the shape parameters.
envFromShapeParams :: [TypeParamBase VName] -> Env
envFromShapeParams = envFromDimNames . map dim
  where dim (TypeParamDim vn _) = vn
        dim tparam = error $
          "The defunctionalizer expects a monomorphic input program,\n" ++
          "but it received a type parameter " ++ pretty tparam ++
          " at " ++ locStr (srclocOf tparam) ++ "."

envFromDimNames :: [VName] -> Env
envFromDimNames = M.fromList . flip zip (repeat $ Dynamic $ Scalar $ Prim $ Signed Int32)

-- | Create a new top-level value declaration with the given function name,
-- return type, list of parameters, and body expression.
liftValDec :: VName -> PatternType -> [VName] -> [Pattern] -> Exp -> DefM ()
liftValDec fname rettype dims pats body = tell $ Seq.singleton dec
  where dims' = map (flip TypeParamDim noLoc) dims
        -- FIXME: this pass is still not correctly size-preserving, so
        -- forget those return sizes that we forgot to propagate along
        -- the way.  Hopefully the internaliser is conservative and
        -- will insert reshapes...
        bound_here = S.fromList dims <> S.map identName (foldMap patternIdents pats)
        anyDimIfNotBound (NamedDim v)
          | qualLeaf v `S.member` bound_here = NamedDim v
          | otherwise = AnyDim
        anyDimIfNotBound d = d
        rettype_st = first anyDimIfNotBound $ toStruct rettype

        dec = ValBind
          { valBindEntryPoint = Nothing
          , valBindName       = fname
          , valBindRetDecl    = Nothing
          , valBindRetType    = Info (rettype_st, [])
          , valBindTypeParams = dims'
          , valBindParams     = pats
          , valBindBody       = body
          , valBindDoc        = Nothing
          , valBindLocation   = noLoc
          }

-- | Given a closure environment, construct a record pattern that
-- binds the closed over variables.
buildEnvPattern :: Env -> Pattern
buildEnvPattern env = RecordPattern (map buildField $ M.toList env) noLoc
  where buildField (vn, sv) =
          (nameFromString (pretty vn),
           Id vn (Info $ typeFromSV sv) noLoc)

-- | Given a closure environment pattern and the type of a term,
-- construct the type of that term, where uniqueness is set to
-- `Nonunique` for those arrays that are bound in the environment or
-- pattern (except if they are unique there).  This ensures that a
-- lifted function can create unique arrays as long as they do not
-- alias any of its parameters.  XXX: it is not clear that this is a
-- sufficient property, unfortunately.
buildRetType :: Env -> [Pattern] -> StructType -> PatternType -> PatternType
buildRetType env pats = comb
  where bound = foldMap oneName (M.keys env) <> foldMap patternVars pats
        boundAsUnique v =
          maybe False (unique . unInfo . identType) $
          find ((==v) . identName) $ S.toList $ foldMap patternIdents pats
        problematic v = (v `member` bound) && not (boundAsUnique v)
        comb (Scalar (Record fs_annot)) (Scalar (Record fs_got)) =
          Scalar $ Record $ M.intersectionWith comb fs_annot fs_got
        comb (Scalar (Sum cs_annot)) (Scalar (Sum cs_got)) =
          Scalar $ Sum $ M.intersectionWith (zipWith comb) cs_annot cs_got
        comb (Scalar Arrow{}) t =
          descend t
        comb got et =
          descend $ fromStruct got `setAliases` aliases et

        descend t@Array{}
          | any (problematic . aliasVar) (aliases t) = t `setUniqueness` Nonunique
        descend (Scalar (Record t)) = Scalar $ Record $ fmap descend t
        descend t = t

-- | Compute the corresponding type for a given static value.
typeFromSV :: StaticVal -> PatternType
typeFromSV (Dynamic tp) = tp
typeFromSV (LambdaSV sizes _ _ _ env) =
  unscopeType (S.fromList sizes) $ typeFromEnv env
typeFromSV (RecordSV ls) =
  Scalar $ Record $ M.fromList $ map (fmap typeFromSV) ls
typeFromSV (DynamicFun (_, sv) _) =
  typeFromSV sv
typeFromSV (SumSV name svs fields) =
  Scalar $ Sum $ M.insert name (map typeFromSV svs) $ M.fromList fields
typeFromSV IntrinsicSV =
  error "Tried to get the type from the static value of an intrinsic."

typeFromEnv :: Env -> PatternType
typeFromEnv = Scalar . Record . M.fromList .
              map (bimap (nameFromString . pretty) typeFromSV) . M.toList

-- | Construct the type for a fully-applied dynamic function from its
-- static value and the original types of its arguments.
dynamicFunType :: StaticVal -> [PatternType] -> ([PatternType], PatternType)
dynamicFunType (DynamicFun _ sv) (p:ps) =
  let (ps', ret) = dynamicFunType sv ps in (p : ps', ret)
dynamicFunType sv _ = ([], typeFromSV sv)

-- | Match a pattern with its static value. Returns an environment with
-- the identifier components of the pattern mapped to the corresponding
-- subcomponents of the static value.
matchPatternSV :: PatternBase Info VName -> StaticVal -> Env
matchPatternSV (TuplePattern ps _) (RecordSV ls) =
  mconcat $ zipWith (\p (_, sv) -> matchPatternSV p sv) ps ls
matchPatternSV (RecordPattern ps _) (RecordSV ls)
  | ps' <- sortOn fst ps, ls' <- sortOn fst ls,
    map fst ps' == map fst ls' =
      mconcat $ zipWith (\(_, p) (_, sv) -> matchPatternSV p sv) ps' ls'
matchPatternSV (PatternParens pat _) sv = matchPatternSV pat sv
matchPatternSV (Id vn (Info t) _) sv =
  -- When matching a pattern with a zero-order STaticVal, the type of
  -- the pattern wins out.  This is important when matching a
  -- nonunique pattern with a unique value.
  if orderZeroSV sv
  then M.singleton vn $ Dynamic t
  else M.singleton vn sv
matchPatternSV (Wildcard _ _) _ = mempty
matchPatternSV (PatternAscription pat _ _) sv = matchPatternSV pat sv
matchPatternSV PatternLit{} _ = mempty
matchPatternSV (PatternConstr c1 _ ps _) (SumSV c2 ls fs)
  | c1 == c2 =
      mconcat $ zipWith matchPatternSV ps ls
  | Just ts <- lookup c1 fs =
      mconcat $ zipWith matchPatternSV ps $ map svFromType ts
  | otherwise =
      error $ "matchPatternSV: missing constructor in type: " ++ pretty c1
matchPatternSV (PatternConstr c1 _ ps _) (Dynamic (Scalar (Sum fs)))
  | Just ts <- M.lookup c1 fs =
      mconcat $ zipWith matchPatternSV ps $ map svFromType ts
  | otherwise =
      error $ "matchPatternSV: missing constructor in type: " ++ pretty c1
matchPatternSV pat (Dynamic t) = matchPatternSV pat $ svFromType t
matchPatternSV pat sv = error $ "Tried to match pattern " ++ pretty pat
                             ++ " with static value " ++ show sv ++ "."

orderZeroSV :: StaticVal -> Bool
orderZeroSV Dynamic{} = True
orderZeroSV (RecordSV fields) = all (orderZeroSV . snd) fields
orderZeroSV _ = False

-- | Given a pattern and the static value for the defunctionalized argument,
-- update the pattern to reflect the changes in the types.
updatePattern :: Pattern -> StaticVal -> Pattern
updatePattern (TuplePattern ps loc) (RecordSV svs) =
  TuplePattern (zipWith updatePattern ps $ map snd svs) loc
updatePattern (RecordPattern ps loc) (RecordSV svs)
  | ps' <- sortOn fst ps, svs' <- sortOn fst svs =
      RecordPattern (zipWith (\(n, p) (_, sv) ->
                                (n, updatePattern p sv)) ps' svs') loc
updatePattern (PatternParens pat loc) sv =
  PatternParens (updatePattern pat sv) loc
updatePattern pat@(Id vn (Info tp) loc) sv
  | orderZero tp = pat
  | otherwise = Id vn (Info $ typeFromSV sv `setUniqueness` Nonunique) loc
updatePattern pat@(Wildcard (Info tp) loc) sv
  | orderZero tp = pat
  | otherwise = Wildcard (Info $ typeFromSV sv) loc
updatePattern (PatternAscription pat tydecl loc) sv
  | orderZero . unInfo $ expandedType tydecl =
      PatternAscription (updatePattern pat sv) tydecl loc
  | otherwise = updatePattern pat sv
updatePattern p@PatternLit{} _ = p
updatePattern pat@(PatternConstr c1 (Info t) ps loc) sv@(SumSV _ svs _)
  | orderZero t = pat
  | otherwise = PatternConstr c1 (Info t') ps' loc
  where t' = typeFromSV sv `setUniqueness` Nonunique
        ps' = zipWith updatePattern ps svs
updatePattern (PatternConstr c1 _ ps loc) (Dynamic t) =
  PatternConstr c1 (Info t) ps loc
updatePattern pat (Dynamic t) = updatePattern pat (svFromType t)
updatePattern pat sv =
  error $ "Tried to update pattern " ++ pretty pat
       ++ "to reflect the static value " ++ show sv

-- | Convert a record (or tuple) type to a record static value. This is used for
-- "unwrapping" tuples and records that are nested in 'Dynamic' static values.
svFromType :: PatternType -> StaticVal
svFromType (Scalar (Record fs)) = RecordSV . M.toList $ M.map svFromType fs
svFromType t                    = Dynamic t

-- A set of names where we also track uniqueness.
newtype NameSet = NameSet (M.Map VName Uniqueness) deriving (Show)

instance Semigroup NameSet where
  NameSet x <> NameSet y = NameSet $ M.unionWith max x y

instance Monoid NameSet where
  mempty = NameSet mempty

without :: NameSet -> NameSet -> NameSet
without (NameSet x) (NameSet y) = NameSet $ x `M.difference` y

member :: VName -> NameSet -> Bool
member v (NameSet m) = v `M.member` m

ident :: Ident -> NameSet
ident v = NameSet $ M.singleton (identName v) (uniqueness $ unInfo $ identType v)

oneName :: VName -> NameSet
oneName v = NameSet $ M.singleton v Nonunique

names :: S.Set VName -> NameSet
names = foldMap oneName

-- | Compute the set of free variables of an expression.
freeVars :: Exp -> NameSet
freeVars expr = case expr of
  Literal{}            -> mempty
  IntLit{}             -> mempty
  FloatLit{}           -> mempty
  StringLit{}          -> mempty
  Parens e _           -> freeVars e
  QualParens _ e _     -> freeVars e
  TupLit es _          -> foldMap freeVars es

  RecordLit fs _       -> foldMap freeVarsField fs
    where freeVarsField (RecordFieldExplicit _ e _)  = freeVars e
          freeVarsField (RecordFieldImplicit vn t _) = ident $ Ident vn t noLoc

  ArrayLit es t _      -> foldMap freeVars es <>
                          names (typeDimNames $ unInfo t)
  Range e me incl _ _  -> freeVars e <> foldMap freeVars me <>
                          foldMap freeVars incl
  Var qn (Info t) _    -> NameSet $ M.singleton (qualLeaf qn) $ uniqueness t
  Ascript e t _        -> freeVars e <> names (typeDimNames $ unInfo $ expandedType t)
  Coerce e t _ _       -> freeVars e <> names (typeDimNames $ unInfo $ expandedType t)
  LetPat pat e1 e2 _ _ -> freeVars e1 <> ((names (patternDimNames pat) <> freeVars e2)
                                          `without` patternVars pat)

  LetFun vn (_, pats, _, _, e1) e2 _ _ ->
    ((freeVars e1 <> names (foldMap patternDimNames pats))
      `without` foldMap patternVars pats) <>
    (freeVars e2 `without` oneName vn)

  If e1 e2 e3 _ _           -> freeVars e1 <> freeVars e2 <> freeVars e3
  Apply e1 e2 _ _ _         -> freeVars e1 <> freeVars e2
  Negate e _                -> freeVars e
  Lambda pats e0 _ _ _      -> (names (foldMap patternDimNames pats) <> freeVars e0)
                               `without` foldMap patternVars pats
  OpSection{}                 -> mempty
  OpSectionLeft _  _ e _ _ _  -> freeVars e
  OpSectionRight _ _ e _ _ _  -> freeVars e
  ProjectSection{}            -> mempty
  IndexSection idxs _ _       -> foldMap freeDimIndex idxs

  DoLoop sparams pat e1 form e3 _ _ ->
    let (e2fv, e2ident) = formVars form
    in freeVars e1 <> e2fv <>
       (freeVars e3 `without`
        (names (S.fromList sparams) <> patternVars pat <> e2ident))
    where formVars (For v e2) = (freeVars e2, ident v)
          formVars (ForIn p e2)   = (freeVars e2, patternVars p)
          formVars (While e2)     = (freeVars e2, mempty)

  BinOp (qn, _) _ (e1, _) (e2, _) _ _ _ -> oneName (qualLeaf qn) <>
                                           freeVars e1 <> freeVars e2
  Project _ e _ _                -> freeVars e

  LetWith id1 id2 idxs e1 e2 _ _ ->
    ident id2 <> foldMap freeDimIndex idxs <> freeVars e1 <>
    (freeVars e2 `without` ident id1)

  Index e idxs _ _    -> freeVars e  <> foldMap freeDimIndex idxs
  Update e1 idxs e2 _ -> freeVars e1 <> foldMap freeDimIndex idxs <> freeVars e2
  RecordUpdate e1 _ e2 _ _ -> freeVars e1 <> freeVars e2

  Unsafe e _          -> freeVars e
  Assert e1 e2 _ _    -> freeVars e1 <> freeVars e2
  Constr _ es _ _     -> foldMap freeVars es
  Match e cs _ _      -> freeVars e <> foldMap caseFV cs
    where caseFV (CasePat p eCase _) = (names (patternDimNames p) <> freeVars eCase)
                                       `without` patternVars p

freeDimIndex :: DimIndexBase Info VName -> NameSet
freeDimIndex (DimFix e) = freeVars e
freeDimIndex (DimSlice me1 me2 me3) =
  foldMap (foldMap freeVars) [me1, me2, me3]

-- | Extract all the variable names bound in a pattern.
patternVars :: Pattern -> NameSet
patternVars = mconcat . map ident . S.toList . patternIdents

-- | Defunctionalize a top-level value binding. Returns the
-- transformed result as well as an environment that binds the name of
-- the value binding to the static value of the transformed body.  The
-- boolean is true if the function is a 'DynamicFun'.
defuncValBind :: ValBind -> DefM (ValBind, Env, Bool)

-- Eta-expand entry points with a functional return type.
defuncValBind (ValBind entry name _ (Info (rettype, retext)) tparams params body _ loc)
  | Scalar Arrow{} <- rettype = do
      (body_pats, body', rettype') <- etaExpand (fromStruct rettype) body
      -- FIXME: we should also handle non-constant size annotations
      -- here.
      defuncValBind $ ValBind entry name Nothing
        (Info (rettype', retext))
        tparams (params <> body_pats) body' Nothing loc

defuncValBind valbind@(ValBind _ name retdecl (Info (rettype, retext)) tparams params body _ _) = do
  (tparams', params', body', sv) <- defuncLet tparams params body rettype
  let rettype' = anySizes $ toStruct $ typeOf body'
  return ( valbind { valBindRetDecl    = retdecl
                   , valBindRetType    = Info (combineTypeShapes rettype rettype',
                                               retext)
                   , valBindTypeParams = tparams'
                   , valBindParams     = params'
                   , valBindBody       = body'
                   }
         , M.singleton name sv
         , case sv of DynamicFun{} -> True
                      _            -> False)

-- | Defunctionalize a list of top-level declarations.
defuncVals :: [ValBind] -> DefM (Seq.Seq ValBind)
defuncVals [] = return mempty
defuncVals (valbind : ds) = do
  ((valbind', env, dyn), defs) <- collectFuns $ defuncValBind valbind
  ds' <- localEnv env $ if dyn
                        then isGlobal (valBindName valbind') $ defuncVals ds
                        else defuncVals ds
  return $ defs <> Seq.singleton valbind' <> ds'

-- | Transform a list of top-level value bindings. May produce new
-- lifted function definitions, which are placed in front of the
-- resulting list of declarations.
transformProg :: MonadFreshNames m => [ValBind] -> m [ValBind]
transformProg decs = modifyNameSource $ \namesrc ->
  let (decs', namesrc', liftedDecs) = runDefM namesrc $ defuncVals decs
  in (toList $ liftedDecs <> decs', namesrc')