PGF.Expr

module PGF.Expr(Tree, BindType(..), Expr(..), Literal(..), Patt(..), Equation(..),
                readExpr, showExpr, pExpr, pBinds, ppExpr, ppPatt, pattScope,

                mkAbs,    unAbs,
                mkApp,    unApp, unAppForm,
                mkStr,    unStr,
                mkInt,    unInt,
                mkDouble, unDouble,
                mkMeta,   unMeta,

                normalForm,

                -- needed in the typechecker
                Value(..), Env, Sig, eval, apply, applyValue, value2expr,

                MetaId,

                -- helpers
                pMeta,pArg,pLit,freshName,ppMeta,ppLit,ppParens
               ) where

import PGF.CId
import PGF.Type
import PGF.ByteCode

import Data.Char
--import Data.Maybe
import Data.List as List
import qualified Data.Map as Map hiding (showTree)
import Control.Monad
import qualified Text.PrettyPrint as PP
import qualified Text.ParserCombinators.ReadP as RP

type MetaId = Int

data BindType = 
    Explicit
  | Implicit
  deriving (Eq,Ord,Show)

-- | Tree is the abstract syntax representation of a given sentence
-- in some concrete syntax. Technically 'Tree' is a type synonym
-- of 'Expr'.
type Tree = Expr

-- | An expression in the abstract syntax of the grammar. It could be
-- both parameter of a dependent type or an abstract syntax tree for
-- for some sentence.
data Expr =
   EAbs BindType CId Expr           -- ^ lambda abstraction
 | EApp Expr Expr                   -- ^ application
 | ELit Literal                     -- ^ literal
 | EMeta  {-# UNPACK #-} !MetaId    -- ^ meta variable
 | EFun   CId                       -- ^ function or data constructor
 | EVar   {-# UNPACK #-} !Int       -- ^ variable with de Bruijn index
 | ETyped Expr Type                 -- ^ local type signature
 | EImplArg Expr                    -- ^ implicit argument in expression
  deriving (Eq,Ord,Show)

-- | The pattern is used to define equations in the abstract syntax of the grammar.
data Patt =
   PApp CId [Patt]                  -- ^ application. The identifier should be constructor i.e. defined with 'data'
 | PLit Literal                     -- ^ literal
 | PVar CId                         -- ^ variable
 | PAs  CId Patt                    -- ^ variable@pattern
 | PWild                            -- ^ wildcard
 | PImplArg Patt                    -- ^ implicit argument in pattern
 | PTilde Expr
  deriving Show

-- | The equation is used to define lambda function as a sequence
-- of equations with pattern matching. The list of 'Expr' represents
-- the patterns and the second 'Expr' is the function body for this
-- equation.
data Equation =
   Equ [Patt] Expr
  deriving Show

-- | parses 'String' as an expression
readExpr :: String -> Maybe Expr
readExpr s = case [x | (x,cs) <- RP.readP_to_S pExpr s, all isSpace cs] of
               [x] -> Just x
               _   -> Nothing

-- | renders expression as 'String'. The list
-- of identifiers is the list of all free variables
-- in the expression in order reverse to the order
-- of binding.
showExpr :: [CId] -> Expr -> String
showExpr vars = PP.render . ppExpr 0 vars

instance Read Expr where
    readsPrec _ = RP.readP_to_S pExpr

mkAbs :: BindType -> CId -> Expr -> Expr
mkAbs = EAbs

unAbs :: Expr -> Maybe (BindType, CId, Expr)
unAbs (EAbs bt x e) = Just (bt,x,e)
unAbs (ETyped e ty) = unAbs e
unAbs (EImplArg e)  = unAbs e
unAbs _             = Nothing

-- | Constructs an expression by applying a function to a list of expressions
mkApp :: CId -> [Expr] -> Expr
mkApp f es = foldl EApp (EFun f) es

-- | Decomposes an expression into application of function
unApp :: Expr -> Maybe (CId,[Expr])
unApp e = case unAppForm e of
  (EFun f,es) -> Just (f,es)
  _           -> Nothing

-- | Decomposes an expression into an application of a constructor such as a constant or a metavariable
unAppForm :: Expr -> (Expr,[Expr])
unAppForm = extract []
  where
    extract es f@(EFun _)   = (f,es)
    extract es (EApp e1 e2) = extract (e2:es) e1
    extract es (ETyped e ty)= extract es e
    extract es (EImplArg e) = extract es e
    extract es h            = (h,es)

-- | Constructs an expression from string literal
mkStr :: String -> Expr
mkStr s = ELit (LStr s)

-- | Decomposes an expression into string literal
unStr :: Expr -> Maybe String
unStr (ELit (LStr s)) = Just s
unStr (ETyped e ty)   = unStr e
unStr (EImplArg e)    = unStr e
unStr _               = Nothing

-- | Constructs an expression from integer literal
mkInt :: Int -> Expr
mkInt i = ELit (LInt i)

-- | Decomposes an expression into integer literal
unInt :: Expr -> Maybe Int
unInt (ELit (LInt i)) = Just i
unInt (ETyped e ty)   = unInt e
unInt (EImplArg e)    = unInt e
unInt _               = Nothing

-- | Constructs an expression from real number literal
mkDouble :: Double -> Expr
mkDouble f = ELit (LFlt f)

-- | Decomposes an expression into real number literal
unDouble :: Expr -> Maybe Double
unDouble (ELit (LFlt f)) = Just f
unDouble (ETyped e ty)   = unDouble e
unDouble (EImplArg e)    = unDouble e
unDouble _               = Nothing

-- | Constructs an expression which is meta variable
mkMeta :: Int -> Expr
mkMeta i = EMeta i

-- | Checks whether an expression is a meta variable
unMeta :: Expr -> Maybe Int
unMeta (EMeta i)     = Just i
unMeta (ETyped e ty) = unMeta e
unMeta (EImplArg e)  = unMeta e
unMeta _             = Nothing

-----------------------------------------------------
-- Parsing
-----------------------------------------------------

pExpr :: RP.ReadP Expr
pExpr = RP.skipSpaces >> (pAbs RP.<++ pTerm)
  where
    pTerm = do f <- pFactor
               RP.skipSpaces
               as <- RP.sepBy pArg RP.skipSpaces
               return (foldl EApp f as)

    pAbs = do xs <- RP.between (RP.char '\\') (RP.skipSpaces >> RP.string "->") pBinds
              e  <- pExpr
              return (foldr (\(b,x) e -> EAbs b x e) e xs)

pBinds :: RP.ReadP [(BindType,CId)]
pBinds = do xss <- RP.sepBy1 (RP.skipSpaces >> pBind) (RP.skipSpaces >> RP.char ',')
            return (concat xss)
  where
    pCIdOrWild = pCId `mplus` (RP.char '_' >> return wildCId)

    pBind = 
      do x <- pCIdOrWild
         return [(Explicit,x)]
      `mplus`
      RP.between (RP.char '{')
                 (RP.skipSpaces >> RP.char '}')
                 (RP.sepBy1 (RP.skipSpaces >> pCIdOrWild >>= \id -> return (Implicit,id)) (RP.skipSpaces >> RP.char ','))

pArg = fmap EImplArg (RP.between (RP.char '{') (RP.char '}') pExpr)
       RP.<++
       pFactor

pFactor =       fmap EFun  pCId
        RP.<++  fmap ELit  pLit
        RP.<++  fmap EMeta pMeta
        RP.<++  RP.between (RP.char '(') (RP.skipSpaces >> RP.char ')') pExpr
        RP.<++  RP.between (RP.char '<') (RP.skipSpaces >> RP.char '>') pTyped

pTyped = do RP.skipSpaces
            e <- pExpr
            RP.skipSpaces
            RP.char ':'
            RP.skipSpaces
            ty <- pType
            return (ETyped e ty)

pMeta = do RP.char '?'
           ds <- RP.munch isDigit
           return (read ('0':ds))

pLit :: RP.ReadP Literal
pLit = liftM LStr (RP.readS_to_P reads)
       RP.<++
       liftM LInt (RP.readS_to_P reads)
       RP.<++
       liftM LFlt (RP.readS_to_P reads)


-----------------------------------------------------
-- Printing
-----------------------------------------------------

ppExpr :: Int -> [CId] -> Expr -> PP.Doc
ppExpr d scope (EAbs b x e) = let (bs,xs,e1) = getVars [] [] (EAbs b x e)
                              in ppParens (d > 1) (PP.char '\\' PP.<>
                                                   PP.hsep (PP.punctuate PP.comma (reverse (List.zipWith ppBind bs xs))) PP.<+>
                                                   PP.text "->" PP.<+>
                                                   ppExpr 1 (xs++scope) e1)
                              where
                                getVars bs xs (EAbs b x e) = getVars (b:bs) ((freshName x xs):xs) e
                                getVars bs xs e            = (bs,xs,e)
ppExpr d scope (EApp e1 e2) = ppParens (d > 3) ((ppExpr 3 scope e1) PP.<+> (ppExpr 4 scope e2))
ppExpr d scope (ELit l)     = ppLit l
ppExpr d scope (EMeta n)    = ppMeta n
ppExpr d scope (EFun f)     = ppCId f
ppExpr d scope (EVar i)     = ppCId (scope !! i)
ppExpr d scope (ETyped e ty)= PP.char '<' PP.<> ppExpr 0 scope e PP.<+> PP.colon PP.<+> ppType 0 scope ty PP.<> PP.char '>'
ppExpr d scope (EImplArg e) = PP.braces (ppExpr 0 scope e)

ppPatt :: Int -> [CId] -> Patt -> PP.Doc
ppPatt d scope (PApp f ps)  = let ds = List.map (ppPatt 2 scope) ps
                              in ppParens (not (List.null ps) && d > 1) (ppCId f PP.<+> PP.hsep ds)
ppPatt d scope (PLit l)     = ppLit l
ppPatt d scope (PVar f)     = ppCId f
ppPatt d scope (PAs x p)    = ppCId x PP.<> PP.char '@' PP.<> ppPatt 3 scope p
ppPatt d scope PWild        = PP.char '_'
ppPatt d scope (PImplArg p) = PP.braces (ppPatt 0 scope p)
ppPatt d scope (PTilde e)   = PP.char '~' PP.<> ppExpr 6 scope e

pattScope :: [CId] -> Patt -> [CId]
pattScope scope (PApp f ps)  = foldl pattScope scope ps
pattScope scope (PLit l)     = scope
pattScope scope (PVar f)     = f:scope
pattScope scope (PAs x p)    = pattScope (x:scope) p
pattScope scope PWild        = scope
pattScope scope (PImplArg p) = pattScope scope p                               
pattScope scope (PTilde e)   = scope

ppBind Explicit x = ppCId x
ppBind Implicit x = PP.braces (ppCId x)

ppMeta :: MetaId -> PP.Doc
ppMeta n
  | n == 0    = PP.char '?'
  | otherwise = PP.char '?' PP.<> PP.int n

ppParens True  = PP.parens
ppParens False = id

freshName :: CId -> [CId] -> CId
freshName x xs0 = loop 1 x
  where
    xs = wildCId : xs0

    loop i y
      | elem y xs = loop (i+1) (mkCId (show x++show i))
      | otherwise = y


-----------------------------------------------------
-- Computation
-----------------------------------------------------

-- | Compute an expression to normal form
normalForm :: Sig -> Int -> Env -> Expr -> Expr
normalForm sig k env e = value2expr sig k (eval sig env e)

value2expr sig i (VApp f vs)                 = foldl EApp (EFun f)       (List.map (value2expr sig i) vs)
value2expr sig i (VGen j vs)                 = foldl EApp (EVar (i-j-1)) (List.map (value2expr sig i) vs)
value2expr sig i (VMeta j env vs)            = case snd sig j of
                                                 Just e  -> value2expr sig i (apply sig env e vs)
                                                 Nothing -> foldl EApp (EMeta j) (List.map (value2expr sig i) vs)
value2expr sig i (VSusp j env vs k)          = value2expr sig i (k (VGen j vs))
value2expr sig i (VConst f vs)               = foldl EApp (EFun f)       (List.map (value2expr sig i) vs)
value2expr sig i (VLit l)                    = ELit l
value2expr sig i (VClosure env (EAbs b x e)) = EAbs b (mkCId ('v':show i)) (value2expr sig (i+1) (eval sig ((VGen i []):env) e))
value2expr sig i (VImplArg v)                = EImplArg (value2expr sig i v)

data Value
  = VApp CId [Value]
  | VLit Literal
  | VMeta {-# UNPACK #-} !MetaId Env [Value]
  | VSusp {-# UNPACK #-} !MetaId Env [Value] (Value -> Value)
  | VGen  {-# UNPACK #-} !Int [Value]
  | VConst CId [Value]
  | VClosure Env Expr
  | VImplArg Value

type Sig = ( Map.Map CId (Type,Int,Maybe ([Equation],[[Instr]]),Double) -- type and def of a fun
           , Int -> Maybe Expr                                          -- lookup for metavariables
           )
type Env = [Value]

eval :: Sig -> Env -> Expr -> Value
eval sig env (EVar i)     = env !! i
eval sig env (EFun f)     = case Map.lookup f (fst sig) of
                              Just (_,a,meqs,_) -> case meqs of
                                                       Just (eqs,_)
                                                               -> if a == 0
                                                                    then case eqs of
                                                                           Equ [] e : _ -> eval sig [] e
                                                                           _            -> VConst f []
                                                                    else VApp f []
                                                       Nothing -> VApp f []
                              Nothing             -> error ("unknown function "++showCId f)
eval sig env (EApp e1 e2) = apply sig env e1 [eval sig env e2]
eval sig env (EAbs b x e) = VClosure env (EAbs b x e)
eval sig env (EMeta i)    = case snd sig i of
                              Just e  -> eval sig env e
                              Nothing -> VMeta i env []
eval sig env (ELit l)     = VLit l
eval sig env (ETyped e _) = eval sig env e
eval sig env (EImplArg e) = VImplArg (eval sig env e)

apply :: Sig -> Env -> Expr -> [Value] -> Value
apply sig env e            []     = eval sig env e
apply sig env (EVar i)     vs     = applyValue sig (env !! i) vs
apply sig env (EFun f)     vs     = case Map.lookup f (fst sig) of
                                      Just (_,a,meqs,_) -> case meqs of
                                                             Just (eqs,_) -> if a <= length vs
                                                                               then match sig f eqs vs
                                                                               else VApp f vs
                                                             Nothing      -> VApp f vs
                                      Nothing           -> error ("unknown function "++showCId f)
apply sig env (EApp e1 e2) vs     = apply sig env e1 (eval sig env e2 : vs)
apply sig env (EAbs b x e) (v:vs) = case (b,v) of
                                      (Implicit,VImplArg v) -> apply sig (v:env) e vs
                                      (Explicit,         v) -> apply sig (v:env) e vs
apply sig env (EMeta i)    vs     = case snd sig i of
                                      Just e  -> apply sig env e vs
                                      Nothing -> VMeta i env vs
apply sig env (ELit l)     vs     = error "literal of function type"
apply sig env (ETyped e _) vs     = apply sig env e vs
apply sig env (EImplArg _) vs     = error "implicit argument in function position"

applyValue sig v                         []       = v
applyValue sig (VApp f  vs0)             vs       = apply sig [] (EFun f) (vs0++vs)
applyValue sig (VLit _)                  vs       = error "literal of function type"
applyValue sig (VMeta i env vs0)         vs       = VMeta i env (vs0++vs)
applyValue sig (VGen  i vs0)             vs       = VGen  i (vs0++vs)
applyValue sig (VSusp i env vs0 k)       vs       = VSusp i env vs0 (\v -> applyValue sig (k v) vs)
applyValue sig (VConst f vs0)            vs       = VConst f (vs0++vs)
applyValue sig (VClosure env (EAbs b x e)) (v:vs) = case (b,v) of
                                                      (Implicit,VImplArg v) -> apply sig (v:env) e vs
                                                      (Explicit,         v) -> apply sig (v:env) e vs
applyValue sig (VImplArg _)              vs       = error "implicit argument in function position"

-----------------------------------------------------
-- Pattern matching
-----------------------------------------------------

match :: Sig -> CId -> [Equation] -> [Value] -> Value
match sig f eqs as0 =
  case eqs of
    []               -> VConst f as0
    (Equ ps res):eqs -> tryMatches eqs ps as0 res []
  where
    tryMatches eqs []     as     res env = apply sig env res as
    tryMatches eqs (p:ps) (a:as) res env = tryMatch p a env
      where
        tryMatch (PVar x     ) (v                ) env            = tryMatches eqs  ps        as  res (v:env)
        tryMatch (PAs  x p   ) (v                ) env            = tryMatch p v (v:env)
        tryMatch (PWild      ) (_                ) env            = tryMatches eqs  ps        as  res env
        tryMatch (p          ) (VMeta i envi vs  ) env            = VSusp i envi vs (\v -> tryMatch p v env)
        tryMatch (p          ) (VGen  i vs       ) env            = VConst f as0
        tryMatch (p          ) (VSusp i envi vs k) env            = VSusp i envi vs (\v -> tryMatch p (k v) env)
        tryMatch (p          ) v@(VConst _ _     ) env            = VConst f as0
        tryMatch (PApp f1 ps1) (VApp f2 vs2      ) env | f1 == f2 = tryMatches eqs (ps1++ps) (vs2++as) res env
        tryMatch (PLit l1    ) (VLit l2          ) env | l1 == l2 = tryMatches eqs  ps        as  res env
        tryMatch (PImplArg p ) (VImplArg v       ) env            = tryMatch p v env
        tryMatch (PTilde _   ) (_                ) env            = tryMatches eqs  ps        as  res env
        tryMatch _             _                   env            = match sig f eqs as0