content: {-# LANGUAGE PatternGuards #-}
  {-# LANGUAGE FlexibleContexts #-}
  module Lambdabot.Plugin.Haskell.Pl.Transform (
      transform,
    ) where
  
  import Lambdabot.Plugin.Haskell.Pl.Common
  
  import qualified Data.Map as M
  
  import Data.Graph (stronglyConnComp, flattenSCC, flattenSCCs)
  import Control.Monad.State
  
  -- | Does a name occur in a pattern?
  occursP :: String -> Pattern -> Bool
  occursP v (PVar v') = v == v'
  occursP v (PTuple p1 p2) = v `occursP` p1 || v `occursP` p2
  occursP v (PCons  p1 p2) = v `occursP` p1 || v `occursP` p2
  
  -- | How often does the given name occur free in an expression?
  freeIn :: String -> Expr -> Int
  freeIn v (Var _ v') = fromEnum $ v == v'
  freeIn v (Lambda pat e) = if v `occursP` pat then 0 else freeIn v e
  freeIn v (App e1 e2) = freeIn v e1 + freeIn v e2
  freeIn v (Let ds e') = if v `elem` map declName ds then 0
    else freeIn v e' + sum [freeIn v e | Define _ e <- ds]
  
  -- | Does a name occur free in an expression?
  isFreeIn :: String -> Expr -> Bool
  isFreeIn v e = freeIn v e > 0
  
  tuple :: [Expr] -> Expr
  tuple es  = foldr1 (\x y -> Var Inf "," `App` x `App` y) es
  
  tupleP :: [String] -> Pattern
  tupleP vs = foldr1 PTuple $ PVar `map` vs
  
  -- | The subset of ds that d depends on
  dependsOn :: [Decl] -> Decl -> [Decl]
  dependsOn ds d = [d' | d' <- ds, declName d' `isFreeIn` declExpr d]
  
  -- | Convert recursive lets to lambdas with tuple patterns and fix calls
  unLet :: Expr -> Expr
  unLet (App e1 e2) = App (unLet e1) (unLet e2)
  unLet (Let [] e) = unLet e
  unLet (Let ds e) = unLet $
    (Lambda (tupleP $ declName `map` dsYes) (Let dsNo e)) `App`
      (fix' `App` (Lambda (tupleP $ declName `map` dsYes)
                          (tuple  $ declExpr `map` dsYes)))
      where
    comps = stronglyConnComp [(d',d',dependsOn ds d') | d' <- ds]
    dsYes = flattenSCC $ head comps
    dsNo = flattenSCCs $ tail comps
  
  unLet (Lambda v e) = Lambda v (unLet e)
  unLet (Var f x) = Var f x
  
  type Env = (M.Map String String, Int)
  -- note: The second component is the environment size, counting duplicate
  -- variables.
  
  -- | Rename all variables to (locally) unique fresh ones
  --
  -- It's a pity we still need that for the pointless transformation.
  -- Otherwise a newly created id/const/... could be bound by a lambda
  -- e.g. transform' (\id x -> x) ==> transform' (\id -> id) ==> id
  alphaRename :: Expr -> Expr
  alphaRename e = alpha e `evalState` (M.empty, 0) where
    alpha :: Expr -> State Env Expr
    alpha (Var f v)     = do (fm, _) <- get; return $ Var f $ maybe v id (M.lookup v fm)
    alpha (App e1 e2)   = liftM2 App (alpha e1) (alpha e2)
    alpha (Let _ _)     = assert False undefined
    alpha (Lambda v e') = inEnv $ liftM2 Lambda (alphaPat v) (alpha e')
  
    -- act like a reader monad
    inEnv :: State s a -> State s a
    inEnv f = state $ \s -> (fst $ runState f s, s)
  
    alphaPat (PVar v) = do
      (fm, i) <- get
      let v' = "$" ++ show i
      put (M.insert v v' fm, i+1)
      return $ PVar v'
    alphaPat (PTuple p1 p2) = liftM2 PTuple (alphaPat p1) (alphaPat p2)
    alphaPat (PCons  p1 p2) = liftM2 PCons  (alphaPat p1) (alphaPat p2)
  
  -- | Make an expression points free
  transform :: Expr -> Expr
  transform = transform' . alphaRename . unLet
  
  -- | Transform patterns to:
  --     fst/snd for tuple patterns
  --     head/tail for cons patterns
  --     id/const/flip/. for variable paterns
  transform' :: Expr -> Expr
  transform' (Let {}) = assert False undefined
  transform' (Var f v) = Var f v
  transform' (App e1 e2) = App (transform' e1) (transform' e2)
  transform' (Lambda (PTuple p1 p2) e)
    = transform' $ Lambda (PVar "z") $
        (Lambda p1 $ Lambda p2 $ e) `App` f `App` s where
      f = Var Pref "fst" `App` Var Pref "z"
      s = Var Pref "snd" `App` Var Pref "z"
  transform' (Lambda (PCons p1 p2) e)
    = transform' $ Lambda (PVar "z") $
        (Lambda p1 $ Lambda p2 $ e) `App` f `App` s where
      f = Var Pref "head" `App` Var Pref "z"
      s = Var Pref "tail" `App` Var Pref "z"
  transform' (Lambda (PVar v) e) = transform' $ getRidOfV e where
    getRidOfV (Var f v') | v == v'   = id'
                         | otherwise = const' `App` Var f v'
    getRidOfV l@(Lambda pat _) = assert (not $ v `occursP` pat) $
      getRidOfV $ transform' l
    getRidOfV (Let {}) = assert False bt
    getRidOfV e'@(App e1 e2)
      | fr1 && fr2 = scomb `App` getRidOfV e1 `App` getRidOfV e2
      | fr1 = flip' `App` getRidOfV e1 `App` e2
      | Var _ v' <- e2, v' == v = e1
      | fr2 = comp `App` e1 `App` getRidOfV e2
      | True = const' `App` e'
      where
        fr1 = v `isFreeIn` e1
        fr2 = v `isFreeIn` e2
  