{-|
Module      : What4.Solver.SimpleBackend.Simplify
Description : Simplification procedure for distributing operations through if/then/else
Copyright   : (c) Galois, Inc 2016-2020
License     : BSD3
Maintainer  : Joe Hendrix <jhendrix@galois.com>

This module provides a minimalistic interface for manipulating Boolean formulas
and execution contexts in the symbolic simulator.
-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE ViewPatterns #-}
module What4.Expr.Simplify
  ( simplify
  , count_subterms
  ) where

import           Control.Lens ((^.))
import           Control.Monad.ST
import           Control.Monad.State
import           Data.Map.Strict (Map)
import qualified Data.Map.Strict as Map
import           Data.Maybe
import qualified Data.Parameterized.HashTable as PH
import           Data.Parameterized.Nonce
import           Data.Parameterized.TraversableFC
import           Data.Word

import           What4.Interface
import qualified What4.SemiRing as SR
import           What4.Expr.Builder
import qualified What4.Expr.WeightedSum as WSum

------------------------------------------------------------------------
-- simplify

data NormCache t st fs
   = NormCache { ncBuilder :: !(ExprBuilder t st fs)
               , ncTable :: !(PH.HashTable RealWorld (Expr t) (Expr t))
               }

norm :: NormCache t st fs -> Expr t tp -> IO (Expr t tp)
norm c e = do
  mr <- stToIO $ PH.lookup (ncTable c) e
  case mr of
    Just r -> return r
    Nothing -> do
      r <- norm' c e
      stToIO $ PH.insert (ncTable c) e r
      return r

bvIteDist :: (BoolExpr t -> r -> r -> IO r)
          -> Expr t i
          -> (Expr t i -> IO r)
          -> IO r
bvIteDist muxFn (asApp -> Just (BaseIte _ _ c t f)) atomFn = do
  t' <- bvIteDist muxFn t atomFn
  f' <- bvIteDist muxFn f atomFn
  muxFn c t' f'
bvIteDist _ u atomFn = atomFn u

newtype Or x = Or {unOr :: Bool}

instance Functor Or where
  fmap _f (Or b) = (Or b)
instance Applicative Or where
  pure _ = Or False
  (Or a) <*> (Or b) = Or (a || b)

norm' :: forall t st fs tp . PH.HashableF (Expr t) => NormCache t st fs -> Expr t tp -> IO (Expr t tp)
norm' nc (AppExpr a0) = do
  let sb = ncBuilder nc
  case appExprApp a0 of
    SemiRingSum s
      | let sr = WSum.sumRepr s
      , SR.SemiRingBVRepr SR.BVArithRepr w <- sr
      , unOr (WSum.traverseVars @(Expr t) (\x -> Or (iteSize x >= 1)) s)
      -> do let tms = WSum.eval (++) (\c x -> [(c,x)]) (const []) s
            let f [] k = bvLit sb w (s^.WSum.sumOffset) >>= k
                f ((c,x):xs) k =
                   bvIteDist (bvIte sb) x $ \x' ->
                   scalarMul sb sr c x' >>= \cx' ->
                   f xs $ \xs' ->
                   bvAdd sb cx' xs' >>= k
            f tms (norm nc)

    BaseEq (BaseBVRepr _w) (asApp -> Just (BaseIte _ _ x_c x_t x_f)) y -> do
      z_t <- bvEq sb x_t y
      z_f <- bvEq sb x_f y
      norm nc =<< itePred sb x_c z_t z_f
    BaseEq (BaseBVRepr _w) x (asApp -> Just (BaseIte _ _ y_c y_t y_f)) -> do
      z_t <- bvEq sb x y_t
      z_f <- bvEq sb x y_f
      norm nc =<< itePred sb y_c z_t z_f
    BVSlt (asApp -> Just (BaseIte _ _ x_c x_t x_f)) y -> do
      z_t <- bvSlt sb x_t y
      z_f <- bvSlt sb x_f y
      norm nc =<< itePred sb x_c z_t z_f
    BVSlt x (asApp -> Just (BaseIte _ _ y_c y_t y_f)) -> do
      z_t <- bvSlt sb x y_t
      z_f <- bvSlt sb x y_f
      norm nc =<< itePred sb y_c z_t z_f
    app -> do
      app' <- traverseApp (norm nc) app
      if app' == app then
        return (AppExpr a0)
       else
        norm nc =<< sbMakeExpr sb app'
norm' nc (NonceAppExpr p0) = do
  let predApp = nonceExprApp p0
  p <- traverseFC (norm nc) predApp
  if p == predApp then
    return $! NonceAppExpr p0
   else
    norm nc =<< sbNonceExpr (ncBuilder nc) p
norm' _ e = return e

-- | Simplify a Boolean expression by distributing over ite.
simplify :: ExprBuilder t st fs -> BoolExpr t -> IO (BoolExpr t)
simplify sb p = do
  tbl <- stToIO $ PH.new
  let nc = NormCache { ncBuilder = sb
                     , ncTable = tbl
                     }
  norm nc p

------------------------------------------------------------------------
-- count_subterm

type Counter = State (Map Word64 Int)

-- | Record an element occurs, and return condition indicating if it is new.
recordExpr :: Nonce t (tp::k) -> Counter Bool
recordExpr n = do
  m <- get
  let (mr, m') = Map.insertLookupWithKey (\_ -> (+)) (indexValue n) 1 m
  put $ m'
  return $! isNothing mr

count_subterms' :: Expr t tp -> Counter ()
count_subterms' e0 =
  case e0 of
    BoolExpr{} -> pure () 
    SemiRingLiteral{} -> pure ()
    StringExpr{} -> pure ()
    FloatExpr{} -> pure ()
    AppExpr ae -> do
      is_new <- recordExpr (appExprId ae)
      when is_new $ do
        traverseFC_ count_subterms' (appExprApp ae)
    NonceAppExpr nae -> do
      is_new <- recordExpr (nonceExprId nae)
      when is_new $ do
        traverseFC_ count_subterms' (nonceExprApp nae)
    BoundVarExpr v -> do
      void $ recordExpr (bvarId v)

-- | Return a map from nonce indices to the number of times an elt with that
-- nonce appears in the subterm.
count_subterms :: Expr t tp -> Map Word64 Int
count_subterms e = execState (count_subterms' e) Map.empty

{-
------------------------------------------------------------------------
-- nnf

-- | Convert formula into negation normal form.
nnf :: SimpleBuilder Expr t BoolType -> IO (Expr T BoolType)
nnf e =
-}