{- |

Module : $Header$

Description : Helper functions for coding out polymorphism

Copyright : (c) J. von Schroeder, DFKI Bremen 2012

License : GPLv2 or higher, see LICENSE.txt

Maintainer : Jonathan von Schroeder <jonathan.von_schroeder@dfki.de>

Stability : provisional

Portability : non-portable

-}

module THF.Poly

where

import THF.Cons

import THF.Sign

import THF.Utils

import THF.As

import THF.PrintTHF ()

import THF.Print ()

import Common.Result

import Common.Id

import Common.AS_Annotation

import Common.DocUtils

import Control.Monad.State

import qualified Data.Map (Map, lookup, insert, empty,

mapAccumWithKey, foldWithKey,

mapWithKey)

import qualified Data.List (mapAccumL, elemIndex)

sh :: Pretty a => a -> String

sh = show . pretty

data Constraint = NormalC (String, Range, Type)

| WeakC (String, Range, Type) deriving Show

instance GetRange Constraint where

getRange (NormalC (_, r, _)) = r

getRange (WeakC (_, r, _)) = r

instance GetRange Type where

getRange _ = nullRange

occursType :: Token -> Type -> Bool

occursType t tp = case tp of

MapType tp1 tp2 ->

occursType t tp1 || occursType t tp2

ProdType tps ->

any (occursType t) tps

VType t1 -> t == t1

ParType tp2 -> occursType t tp2

_ -> False

constraintToType :: Constraint -> (Bool, (String, Range, Type))

constraintToType (WeakC d) = (True, d)

constraintToType (NormalC d) = (False, d)

toConstraint :: Bool -> (String, Range, Type) -> Constraint

toConstraint weak = if weak then WeakC

else NormalC

unifyType :: Type -> Constraint -> Result [(Token, Type)]

unifyType tp1 tp2_ =

let (weak, (s, r, tp2)) = constraintToType tp2_

c t = toConstraint weak (s, r, t)

in case (tp1, tp2) of

(ParType tp1', _) ->

unifyType tp1' (c tp2)

(_, ParType tp2') ->

unifyType tp1 (c tp2')

(VType t1, VType t2) -> return $

if t1 == t2 then [] else [(t1, tp2)]

(VType t1, _) -> if occursType t1 tp2

then fatal_error ("Occurs check failed! - "

++ s) r

else return [(t1, tp2)]

(_, VType t2) -> if occursType t2 tp1

then fatal_error ("Occurs check failed! - "

++ s) r

else return [(t2, tp1)]

(MapType tp1_1 tp1_2,

MapType tp2_1 tp2_2) -> do

u1 <- unifyType tp1_1 (c tp2_1)

u2 <- unifyType tp1_2 (c tp2_2)

return $ u1 ++ u2

(MapType _ _, _) ->

fatal_error ("Different type constructors! " ++

" - " ++ s) r

(_, MapType _ _) ->

fatal_error ("Different type constructor! " ++

" - " ++ s) r

(ProdType tps1, ProdType tps2) ->

if length tps1 == length tps2 ||

weak then

liftM concat $

mapR (\ (tp1', tp2') -> unifyType tp1' (c tp2'))

(zip tps1 tps2)

else fatal_error ("Products of different size! - " ++ s) r

(ProdType _, _) ->

fatal_error ("Different type constructors! - " ++ s) r

(CType c1, CType c2) -> if c1 == c2

then return [] else fatal_error ("Cannot unify different kinds!" ++ s) r

(CType _, _) -> fatal_error ("Unification not possible! - " ++ s) r

(_, CType _) -> fatal_error ("Unification not possible! - " ++ s) r

(_, ProdType _) ->

fatal_error ("Different type constructors! - " ++ s) r

(TType, TType) -> return []

(OType, OType) -> return []

(IType, IType) -> return []

(TType, _) -> fatal_error ("Cannot unify TType with "

++ show tp2 ++ "! - " ++ s) r

(_, TType) -> fatal_error ("Cannot unify TType with "

++ show tp1 ++ "! - " ++ s) r

(OType, _) -> fatal_error ("Cannot unify OType with "

++ show tp2 ++ "! - " ++ s) r

(_, OType) -> fatal_error ("Cannot unify OType with "

++ show tp1 ++ "! - " ++ s) r

(IType, _) -> fatal_error ("Cannot unify IType with "

++ show tp2 ++ "! - " ++ s) r

(_, IType) -> fatal_error ("Cannot unify IType with "

++ show tp1 ++ "! - " ++ s) r

_ -> return []

applyType :: [(Token, Type)] -> Token -> Maybe Type

applyType us t = case us of

(t', tp) : _ | t' == t -> Just tp

_ : us' -> applyType us' t

_ -> Nothing

apply :: [(Token, Type)] -> Type -> Type

apply us t = case t of

ParType t' -> ParType $ apply us t'

MapType t1 t2 -> MapType (apply us t1)

(apply us t2)

ProdType tps -> ProdType $ map (apply us) tps

VType tok -> case applyType us tok of

Just t' -> apply us t'

Nothing -> t

_ -> t

unify' :: [(Type, Constraint)] -> Result [(Token, Type)]

unify' ts = case ts of

[] -> return []

(t1, t2) : ts' -> do

r1 <- unify' ts'

let t1' = apply r1 t1

let (weak, (msg, rg, t2'')) = constraintToType t2

let t2' = apply r1 t2''

r2 <- unifyType t1' (toConstraint weak (msg, rg, t2'))

return (r1 ++ r2)

tmpV :: Token

tmpV = mkSimpleId "tmpV"

type Constraints = UniqueT Result (Type, [(Type, Constraint)])

not_supported :: (Show a, GetRange a) => a -> Constraints

not_supported f = lift $ fatal_error

("Formula " ++ show f ++ " not supported!")

(getRange f)

getTypeC :: ConstMap -> THFFormula -> Constraints

getTypeC cm f = case f of

TF_THF_Logic_Formula lf -> getTypeCLF cm lf

_ -> not_supported f

getTypeCLF :: ConstMap -> THFLogicFormula -> Constraints

getTypeCLF cm lf = case lf of

TLF_THF_Binary_Formula bf -> getTypeCBF cm bf

TLF_THF_Unitary_Formula uf -> getTypeCUF cm uf

_ -> not_supported lf

getTypeCBF :: ConstMap -> THFBinaryFormula -> Constraints

getTypeCBF cm bf = case bf of

TBF_THF_Binary_Pair uf1 c uf2 -> if (case c of

Infix_Equality -> True

Infix_Inequality -> True

_ -> False) then do

(t1, cs1) <- getTypeCUF cm uf1

(t2, cs2) <- getTypeCUF cm uf2

let errMsg = "(In-)Equality requires (" ++

sh uf1 ++ ") : (" ++ sh t1

++ ") and (" ++ sh uf2 ++ ") : ("

++ sh t2 ++ " to have the same type"

return (OType,

cs1 ++ cs2 ++ [(t1, NormalC (errMsg, getRangeSpan bf, t2))])

else do

(t1, cs1) <- getTypeCUF cm uf1

(t2, cs2) <- getTypeCUF cm uf2

let errMsg1 = "Infix operator " ++ sh c

++ " requires (" ++ sh uf1 ++ ") : ("

++ sh t1 ++ ") to have type OType"

let errMsg2 = "Infix operator " ++ sh c

++ " requires (" ++ sh uf2 ++ ") : ("

++ sh t2 ++ ") to have type OType"

return (OType,

cs1 ++ cs2 ++ [(t1, NormalC (errMsg1, getRangeSpan uf1, OType)),

(t2, NormalC (errMsg2, getRangeSpan uf2, OType))])

TBF_THF_Binary_Tuple bt ->

let ufs = case bt of

TBT_THF_Or_Formula ufs' -> ufs'

TBT_THF_And_Formula ufs' -> ufs'

TBT_THF_Apply_Formula ufs' -> ufs'

in case bt of

TBT_THF_Apply_Formula _ -> do

ufs' <- mapM (getTypeCUF cm) ufs

case ufs' of

[] -> lift $ fatal_error ("Invalid Application: "

++ show bt) (getRange bt)

_ : [] -> lift $ fatal_error ("Invalid Application: "

++ show bt) (getRange bt)

u : ufs'' -> do

let (t1, cs1) = u

tps = map fst ufs''

cs2 = map snd ufs''

{- try to do a best-effort beta-reduction

* either t1 is a "function type" we

can recognize

* or we simply assign a new type variable

and hope that further constraints

will determine the type variable -}

t <- applyResult (length ufs'') t1

let errMsg = "Application is not well typed"

return (t, cs1 ++ concat cs2

++ [(t1, WeakC (errMsg, getRangeSpan bt, genFn $ tps ++ [t]))])

_ -> do

ufs' <- mapM (getTypeCUF cm) ufs

case ufs' of

[] -> lift $ fatal_error ("Empty boolean connective: "

++ show bt) (getRange bt)

(t, cs) : [] -> return (t, cs ++ [(t, NormalC (

"Boolean connective requires all " ++

"arguments to be of type OType", getRangeSpan ufs, OType))])

_ -> do

let (ts, cs) = unzip ufs'

let errMsg = "Boolean connective requires all " ++

"arguments to be of type OType"

return (OType, concat cs ++ map (\ t ->

(t, NormalC (errMsg, getRangeSpan bt, OType))) ts)

_ -> not_supported bf

applyResult :: Int -> Type -> UniqueT Result Type

applyResult 0 t = return t

applyResult i t = case t of

MapType _ t' -> applyResult (i - 1) t'

_ -> do

v <- numberedTok tmpV

return (VType v)

getTypeCUF :: ConstMap -> THFUnitaryFormula -> Constraints

getTypeCUF cm uf = case uf of

TUF_THF_Quantified_Formula qf -> case qf of

TQF_THF_Quantified_Formula _ vs uf' -> getTypeCQF vs uf'

T0QF_THF_Quantified_Var _ vs uf' -> getTypeCQF vs uf'

_ -> not_supported uf

where getTypeCQF vs uf' = do

cm' <- foldM (\ cm' v ->

case v of

TV_THF_Typed_Variable t tp -> case thfTopLevelTypeToType tp of

Just tp' -> return $ ins t tp' cm'

Nothing ->

lift $ fatal_error ("Failed to analyze type " ++ show tp)

(getRange tp)

TV_Variable t -> do

v' <- numberedTok tmpV

return $ ins t (VType v') cm') cm vs

(t, cs) <- getTypeCUF cm' uf'

let errMsg = "Quantified Formula (" ++ sh uf' ++ ") : ("

++ sh t ++ ") is expected to be of type OType"

return (t, cs ++ [(t, NormalC (errMsg, getRangeSpan uf', OType))])

c = A_Single_Quoted

ins t tp = Data.Map.insert (c t)

ConstInfo {

constId = c t,

constName = N_Atomic_Word $ c t,

constType = tp,

constAnno = Null}

TUF_THF_Unary_Formula _ lf -> do

(lf', cs) <- getTypeCLF cm lf

let errMsg = "Unary Formula (" ++ sh lf ++ ") : ("

++ sh lf' ++ ") is expected to be of type OType"

return (lf', cs ++ [(lf', NormalC (errMsg, getRangeSpan lf, OType))])

TUF_THF_Atom a -> case a of

TA_THF_Conn_Term _ -> not_supported a

T0A_Constant c -> case Data.Map.lookup c cm of

Just ti -> return (constType ti, [])

Nothing -> case show $ toToken c of

'p' : 'r' : '_' : i' -> do

let i = read i' :: Int

vs <- replicateM i $ liftM VType $ numberedTok tmpV

return (MapType (ProdType vs) $ last vs, [])

_ -> do

v <- numberedTok tmpV

return (VType v, [])

-- fixme - add types for internal constants

T0A_Defined_Constant _ -> not_supported a

T0A_System_Constant _ -> not_supported a

T0A_Variable v -> case Data.Map.lookup (A_Single_Quoted v) cm of

Just ti -> return (constType ti, [])

Nothing -> do

v' <- numberedTok tmpV

return (VType v', [])

_ -> not_supported a

TUF_THF_Tuple lfs -> do

lfs' <- mapM (getTypeCLF cm) lfs

let (tps, cs) = unzip lfs'

return (ProdType tps, concat cs)

TUF_THF_Logic_Formula_Par lf -> getTypeCLF cm lf

T0UF_THF_Abstraction vs uf' -> do

(vst, cm') <- foldM (\ (l, cm') v ->

case v of

TV_THF_Typed_Variable t tp ->

case thfTopLevelTypeToType tp of

Just tp' -> return (tp' : l, ins t tp' cm')

Nothing ->

lift $ fatal_error ("Failed to analyze type " ++ show tp)

(getRange tp)

TV_Variable t -> do

v' <- numberedTok tmpV

return (VType v' : l, ins t (VType v') cm')) ([], cm) vs

(uf'', cs) <- getTypeCUF cm' uf'

case vst of

[] -> lift $ fatal_error ("Invalid Abstraction: "

++ show uf) (getRange uf)

_ -> return (genFn (vst ++ [uf'']), cs)

where c = A_Single_Quoted

ins t tp = Data.Map.insert (c t)

ConstInfo {

constId = c t,

constName = N_Atomic_Word $ c t,

constType = tp,

constAnno = Null }

_ -> not_supported uf

genFn :: [Type] -> Type

genFn (tp : []) = tp

genFn (tp : tps) = MapType tp (genFn tps)

genFn _ = error "This shouldn't happen!"

insertAndIdx :: (Ord a, Eq b) => Data.Map.Map a [b] -> a -> b

-> (Data.Map.Map a [b], Maybe Int)

insertAndIdx m k v = case Data.Map.lookup k m of

Just l -> case Data.List.elemIndex v l of

Just i -> (m, Just i)

Nothing -> (Data.Map.insert k (l ++ [v]) m,

Just $ length l)

Nothing -> (Data.Map.insert k [v] m, Just 0)

intToStr :: Int -> String

intToStr 0 = ""

intToStr i = '_' : show i

flattenMap :: Data.Map.Map Constant [a] -> Data.Map.Map Constant a

flattenMap = Data.Map.foldWithKey

(\ k v new_m ->

let ks = evalUnique $ replicateM (length v) $ do

f <- fresh

let s = intToStr $ fromIntegral (f - 1)

return $ addSuffix s k

in foldl (\ new_m' (k', v') -> Data.Map.insert k' v' new_m')

new_m (zip ks v)) Data.Map.empty

type RewriteArg = Data.Map.Map Constant (Maybe Int)

rewriteVariableList' :: (RewriteFuns RewriteArg, RewriteArg) ->

[THFVariable] -> Result [THFVariable]

rewriteVariableList' (_, cm) vs = return $

map (\ v -> let t = case v of

TV_THF_Typed_Variable t' _ -> t'

TV_Variable t' -> t'

in case Data.Map.lookup (A_Single_Quoted t) cm of

Just (Just i) -> TV_Variable $

t { tokStr = tokStr t ++ intToStr i }

_ -> v) vs

rewriteConst' :: (RewriteFuns RewriteArg, RewriteArg) ->

Constant -> Result THFUnitaryFormula

rewriteConst' (_, cm) c = return . TUF_THF_Atom . T0A_Constant $

case Data.Map.lookup c cm of

Just (Just i) -> addSuffix (intToStr i) c

_ -> c

rewriteConst4needsConst :: (RewriteFuns Constant, Constant) ->

Constant -> Result THFUnitaryFormula

rewriteConst4needsConst (_, c1) c2 =

if c1 == c2 then mkError "" nullRange

else return . TUF_THF_Atom . T0A_Constant $ c2

needsConst :: Constant -> Named THFFormula -> Bool

needsConst c f =

let r = rewriteTHF0 {rewriteConst = rewriteConst4needsConst}

res = rewriteSenFun (r, c) f

in case resultToMaybe res of

Nothing -> True

_ -> False

infer :: ConstMap -> [Named THFFormula]

-> Result (ConstMap, [Named THFFormula])

infer cm fs =

let constraints' = mapM (evalUniqueT . getTypeC cm

. sentence) fs

errMsg = "Sentences have to be of type OType"

constraints =

liftM (map (\ (t, cs) -> (OType, NormalC

(errMsg, getRangeSpan cs, t)) : cs)) constraints'

in do

unis' <- liftM (map unify') constraints

sequence unis' >>= \ unis ->

let (cm', instances) = Data.List.mapAccumL

(\ cm'_ (f, u) ->

let (cm'', m1) = Data.Map.mapAccumWithKey

(\ cm''' c ci -> if needsConst c f

then insertAndIdx cm''' c

(apply u (constType ci))

else (cm''', Nothing)) cm'_ cm

in (cm'', m1))

Data.Map.empty (zip fs unis)

new_cm = Data.Map.mapWithKey (\ k v ->

ConstInfo { constId = k,

constName = N_Atomic_Word k,

constType = v,

constAnno = Null}) $ flattenMap cm'

in do

let r = rewriteTHF0 {

rewriteVariableList = rewriteVariableList',

rewriteConst = rewriteConst'

}

fs' <- mapM (\ (f, i) -> rewriteSenFun (r, i) f)

(zip fs instances)

return (new_cm, fs')

type_check :: TypeMap -> ConstMap -> [Named THFFormula]

-> Result [[(Token, Type)]]

type_check _ cm sens = do

let constraints' = mapM (evalUniqueT .

getTypeC cm . sentence) sens

let errMsg = "Every formula is expected to be of type OType"

let constraints =

liftM (map (\ (t, cs) -> (OType, NormalC (errMsg, nullRange, t)) : cs))

constraints'

unifications <- liftM (map unify') constraints

sequence unifications