Distribution/Types/Condition.hs

    {-# LANGUAGE DeriveDataTypeable #-}
    {-# LANGUAGE DeriveGeneric #-}

    module Distribution.Types.Condition (
        Condition(..),
        cNot,
        cAnd,
        cOr,
        simplifyCondition,
    ) where

    import Prelude ()
    import Distribution.Compat.Prelude

    -- | A boolean expression parameterized over the variable type used.
    data Condition c = Var c
                     | Lit Bool
                     | CNot (Condition c)
                     | COr (Condition c) (Condition c)
                     | CAnd (Condition c) (Condition c)
        deriving (Show, Eq, Typeable, Data, Generic)

    -- | Boolean negation of a 'Condition' value.
    cNot :: Condition a -> Condition a
    cNot (Lit b)  = Lit (not b)
    cNot (CNot c) = c
    cNot c        = CNot c

    -- | Boolean AND of two 'Condtion' values.
    cAnd :: Condition a -> Condition a -> Condition a
    cAnd (Lit False) _           = Lit False
    cAnd _           (Lit False) = Lit False
    cAnd (Lit True)  x           = x
    cAnd x           (Lit True)  = x
    cAnd x           y           = CAnd x y

    -- | Boolean OR of two 'Condition' values.
    cOr :: Eq v => Condition v -> Condition v -> Condition v
    cOr  (Lit True)  _           = Lit True
    cOr  _           (Lit True)  = Lit True
    cOr  (Lit False) x           = x
    cOr  x           (Lit False) = x
    cOr  c           (CNot d)
      | c == d                   = Lit True
    cOr  (CNot c)    d
      | c == d                   = Lit True
    cOr  x           y           = COr x y

    instance Functor Condition where
      f `fmap` Var c    = Var (f c)
      _ `fmap` Lit c    = Lit c
      f `fmap` CNot c   = CNot (fmap f c)
      f `fmap` COr c d  = COr  (fmap f c) (fmap f d)
      f `fmap` CAnd c d = CAnd (fmap f c) (fmap f d)

    instance Foldable Condition where
      f `foldMap` Var c    = f c
      _ `foldMap` Lit _    = mempty
      f `foldMap` CNot c   = foldMap f c
      f `foldMap` COr c d  = foldMap f c `mappend` foldMap f d
      f `foldMap` CAnd c d = foldMap f c `mappend` foldMap f d

    instance Traversable Condition where
      f `traverse` Var c    = Var `fmap` f c
      _ `traverse` Lit c    = pure $ Lit c
      f `traverse` CNot c   = CNot `fmap` traverse f c
      f `traverse` COr c d  = COr  `fmap` traverse f c <*> traverse f d
      f `traverse` CAnd c d = CAnd `fmap` traverse f c <*> traverse f d

    instance Applicative Condition where
      pure  = Var
      (<*>) = ap

    instance Monad Condition where
      return = pure
      -- Terminating cases
      (>>=) (Lit x) _ = Lit x
      (>>=) (Var x) f = f x
      -- Recursing cases
      (>>=) (CNot  x  ) f = CNot (x >>= f)
      (>>=) (COr   x y) f = COr  (x >>= f) (y >>= f)
      (>>=) (CAnd  x y) f = CAnd (x >>= f) (y >>= f)

    instance Monoid (Condition a) where
      mempty = Lit False
      mappend = (<>)

    instance Semigroup (Condition a) where
      (<>) = COr

    instance Alternative Condition where
      empty = mempty
      (<|>) = mappend

    instance MonadPlus Condition where
      mzero = mempty
      mplus = mappend

    instance Binary c => Binary (Condition c)

    -- | Simplify the condition and return its free variables.
    simplifyCondition :: Condition c
                      -> (c -> Either d Bool)   -- ^ (partial) variable assignment
                      -> (Condition d, [d])
    simplifyCondition cond i = fv . walk $ cond
      where
        walk cnd = case cnd of
          Var v   -> either Var Lit (i v)
          Lit b   -> Lit b
          CNot c  -> case walk c of
                       Lit True -> Lit False
                       Lit False -> Lit True
                       c' -> CNot c'
          COr c d -> case (walk c, walk d) of
                       (Lit False, d') -> d'
                       (Lit True, _)   -> Lit True
                       (c', Lit False) -> c'
                       (_, Lit True)   -> Lit True
                       (c',d')         -> COr c' d'
          CAnd c d -> case (walk c, walk d) of
                        (Lit False, _) -> Lit False
                        (Lit True, d') -> d'
                        (_, Lit False) -> Lit False
                        (c', Lit True) -> c'
                        (c',d')        -> CAnd c' d'
        -- gather free vars
        fv c = (c, fv' c)
        fv' c = case c of
          Var v     -> [v]
          Lit _      -> []
          CNot c'    -> fv' c'
          COr c1 c2  -> fv' c1 ++ fv' c2
          CAnd c1 c2 -> fv' c1 ++ fv' c2