{-# LANGUAGE MultiParamTypeClasses, TypeSynonymInstances #-}

{- |

Module : $Header$

Description : Static analysis for THF

Copyright : (c) A. Tsogias, DFKI Bremen 2011

License : GPLv2 or higher, see LICENSE.txt

Maintainer : Alexis.Tsogias@dfki.de

Stability : provisional

Portability : portable

Static analysis for THF.

NOTE: This implementation covers only THF0!

-}

module THF.StaticAnalysisTHF (basicAnalysis) where

import THF.As as As

import THF.Cons

import THF.Print ()

import THF.Sign

import Common.Id hiding (typeId)

import Common.AS_Annotation

import Common.GlobalAnnotations

import Common.Result

import Common.ExtSign

import Common.Lib.State

import Common.DocUtils

import Control.Monad

import Data.Maybe

import qualified Data.Map as Map

import qualified Data.Set as Set

--------------------------------------------------------------------------------

-- Questions:

-- * how to handle SysType in isTypeConsistent?

-- Todo:

-- * find out what fi_domain, fi_predicates and fi_functors are and try

-- to somehow support them

--------------------------------------------------------------------------------

-- The main method for the static analysis

basicAnalysis :: (BasicSpecTHF, SignTHF, GlobalAnnos) ->

Result (BasicSpecTHF, ExtSign SignTHF SymbolTHF, [Named SentenceTHF])

basicAnalysis (bs@(BasicSpecTHF bs1), sig1, _) =

let (diag1, bs2) = filterBS [] bs1

(diag2, sig2, syms) = execState (fillSig bs2) (diag1, sig1, Set.empty)

(diag3, ns) = getSentences bs2 (diag2, [])

in Result (reverse diag3) $ Just (bs, ExtSign sig2 syms, ns)

-- This functions delets all Comments and Includes because they are not needed

-- for the static analysis

-- The diagnosis list has a reverted order!

filterBS :: [Diagnosis] -> [TPTP_THF] -> ([Diagnosis], [TPTP_THF])

filterBS d [] = (d, [])

filterBS d (t : rt) = case t of

TPTP_Include i -> let ds = (mkDiag Warning

"Include will be ignored." i)

in filterBS (ds : d) rt

TPTP_Comment _ -> filterBS d rt

TPTP_Defined_Comment _ -> filterBS d rt

TPTP_System_Comment _ -> filterBS d rt

TPTP_Header _ -> filterBS d rt

_ -> let (diag, thf) = filterBS d rt

in (diag, t : thf)

-- Append the Signature by the Types and Constants given inside the basic spec

fillSig :: [TPTP_THF] -> State ([Diagnosis], SignTHF, Set.Set SymbolTHF) ()

fillSig [] = return ()

fillSig bs = mapM_ fillSingleType bs >> mapM_ fillSingleConst bs

where

fillSingleType t = case t of

TPTP_THF_Annotated_Formula n fr tf a -> case fr of

Type ->

when (isType tf) $ case makeKind tf of

Right d -> appandDiag d

Left (k, c) -> insertType c n k a

_ -> return ()

_ -> return ()

fillSingleConst t = case t of

TPTP_THF_Annotated_Formula n fr tf a -> case fr of

Type ->

unless (isType tf) $ case makeType tf of

Right d -> appandDiag d

Left (ty, c) -> insertConst c n ty a

_ -> return ()

_ -> return ()

-- Append the Diagnosis-List by the given Diagnosis

-- The new diag will be put on top of the existing list.

appandDiag :: Diagnosis -> State ([Diagnosis], SignTHF, Set.Set SymbolTHF) ()

appandDiag d = modify (\ (diag, s, syms) -> (d : diag, s, syms))

-- insert the given type into the Signature

insertType :: Constant -> As.Name -> Kind -> Annotations

-> State ([Diagnosis], SignTHF, Set.Set SymbolTHF) ()

insertType c n k a = do

(diag, sig, syms) <- get

if sigHasConstSymbol c sig then appandDiag $ mkDiag Error

"Duplicate definition a symbol as Type an Constant. Symbol: " c

else

if sigHasTypeSymbol c sig then

unless (sigHasSameKind c k sig) $ appandDiag $

mkDiag Error ("A Type with the same identifier"

++ "but another Kind is already inside the signature") c

else do -- everythign is fine

let ti = TypeInfo { typeId = c, typeName = n, typeKind = k

, typeAnno = a }

sym = Symbol { symId = c, symName = n, symType = ST_Type k }

put (diag, sig { types = Map.insert c ti (types sig)

, symbols = Map.insert c sym (symbols sig) }

, Set.insert sym syms)

-- insert the given constant into the Signature

insertConst :: Constant -> As.Name -> Type -> Annotations

-> State ([Diagnosis], SignTHF, Set.Set SymbolTHF) ()

insertConst c n t a = do

(diag, sig, syms) <- get

if sigHasTypeSymbol c sig then appandDiag $ mkDiag Error

"Duplicate definition a symbol as Type an Constant. Symbol: " c

else case isTypeConsistent t sig of

Just d -> appandDiag d

_ ->

if sigHasConstSymbol c sig then

unless (sigHasSameType c t sig) $ appandDiag $ mkDiag Error

("A Constant with the same identifier but another " ++

"Type is already inside the signature") c

else do -- everything is fine

let ci = ConstInfo { constId = c, constName = n, constType = t

, constAnno = a }

sym = Symbol { symId = c, symName = n

, symType = ST_Const t }

put (diag, sig { consts = Map.insert c ci (consts sig)

, symbols = Map.insert c sym (symbols sig) }

, Set.insert sym syms)

-- Check if a type symbol is already inside the sig

sigHasTypeSymbol :: Constant -> SignTHF -> Bool

sigHasTypeSymbol c sig = Map.member c (types sig)

-- This Method is ment to be used after sigHasTypeSymbol

-- Check if a type symbol with the same kind is inside the Sig

-- If this is not the case me have a problem!

sigHasSameKind :: Constant -> Kind -> SignTHF -> Bool

sigHasSameKind c k sig = typeKind (types sig Map.! c) == k

-- Check if a const symbol is already inside the sig

sigHasConstSymbol :: Constant -> SignTHF -> Bool

sigHasConstSymbol c sig = Map.member c (consts sig)

-- This Method is ment to be used after sigHasConstSymbol

-- Check if a const symbol with the same type is inside the Sig

-- If this is not the case me have a problem!

sigHasSameType :: Constant -> Type -> SignTHF -> Bool

sigHasSameType c t sig = constType (consts sig Map.! c) == t

-- check if all cTypes inside the given Type are elements of the signaure.

-- Nothing means that everything is fine, otherwise Just diag will be returned.

isTypeConsistent :: Type -> SignTHF -> Maybe Diagnosis

isTypeConsistent t sig = case t of

MapType t1 t2 ->

let tc1 = isTypeConsistent t1 sig

tc2 = isTypeConsistent t2 sig

in if isNothing tc1 then tc2 else tc1

ParType t1 -> isTypeConsistent t1 sig

CType c -> if sigHasTypeSymbol c sig then Nothing

else Just $ mkDiag Error "Unknown type: " c

ProdType ts -> let ds = map (\tp -> isTypeConsistent tp sig) ts

in case catMaybes ds of

[] -> Nothing

m : _ -> Just m

SType _ -> Nothing -- how to handle these?

_ -> Nothing

--------------------------------------------------------------------------------

-- Extract the sentences from the basic spec

--------------------------------------------------------------------------------

-- Get all sentences from the content of the BasicSpecTH

-- The diag list has a reverted order.

getSentences :: [TPTP_THF] -> ([Diagnosis], [Named SentenceTHF])

-> ([Diagnosis], [Named SentenceTHF])

getSentences [] dn = dn

getSentences (t : rt) dn@(d, ns) = case t of

TPTP_THF_Annotated_Formula _ fr _ _ -> case fr of

Type -> getSentences rt dn

Unknown ->

let diag = (mkDiag Warning

"THFFormula with role \'unknown\' will be ignored." t)

in getSentences rt (diag : d, ns)

Plain ->

let diag = (mkDiag Warning

"THFFormula with role \'plain\' will be ignored." t)

in getSentences rt (diag : d, ns)

Fi_Domain ->

let diag = (mkDiag Warning

"THFFormula with role \'fi_domain\' will be ignored." t)

in getSentences rt (diag : d, ns)

Fi_Functors ->

let diag = (mkDiag Warning

"THFFormula with role \'fi_functors\' will be ignored." t)

in getSentences rt (diag : d, ns)

Fi_Predicates ->

let diag = (mkDiag Warning

"THFFormula with role \'fi_predicates\' will be ignored." t)

in getSentences rt (diag : d, ns)

Assumption ->

let diag = (mkDiag Warning

"THFFormula with role \'assumption\' will be ignored." t)

in getSentences rt (diag : d, ns)

_ ->

let (d1, ns1) = getSentences rt dn

in (d1, tptpthfToNS t : ns1)

_ -> getSentences rt dn

-- Precondition: The formulaRole must not be Type, Unknown, Plain, Fi_Domain

-- Fi_Functors, Fi_Predicates or Assumption

-- (They are filtered out in getSentences)

tptpthfToNS :: TPTP_THF -> Named SentenceTHF

tptpthfToNS t = case formulaRoleAF t of

Definition ->

let sen = Sentence (formulaRoleAF t) (thfFormulaAF t) (annotationsAF t)

in SenAttr { senAttr = show $ pretty $ nameAF t , isAxiom = True

, isDef = True, wasTheorem = False, simpAnno = Nothing

, attrOrigin = Nothing, sentence = sen }

Conjecture ->

let sen = Sentence (formulaRoleAF t) (thfFormulaAF t) (annotationsAF t)

in SenAttr { senAttr = show $ pretty $ nameAF t, isAxiom = False

, isDef = False, wasTheorem = False, simpAnno = Nothing

, attrOrigin = Nothing, sentence = sen }

Negated_Conjecture ->

let sen = Sentence (formulaRoleAF t) (thfFormulaAF t) (annotationsAF t)

in SenAttr { senAttr = show $ pretty $ nameAF t, isAxiom = False

, isDef = False, wasTheorem = False, simpAnno = Nothing

, attrOrigin = Nothing, sentence = sen }

Theorem ->

let sen = Sentence (formulaRoleAF t) (thfFormulaAF t) (annotationsAF t)

in SenAttr { senAttr = show $ pretty $ nameAF t , isAxiom = True

, isDef = False, wasTheorem = True, simpAnno = Nothing

, attrOrigin = Nothing, sentence = sen }

Lemma ->

let sen = Sentence (formulaRoleAF t) (thfFormulaAF t) (annotationsAF t)

in SenAttr { senAttr = show $ pretty $ nameAF t , isAxiom = True

, isDef = False, wasTheorem = True, simpAnno = Nothing

, attrOrigin = Nothing, sentence = sen }

Hypothesis -> --isAxiom = false

let sen = Sentence (formulaRoleAF t) (thfFormulaAF t) (annotationsAF t)

in SenAttr { senAttr = show $ pretty $ nameAF t , isAxiom = False

, isDef = False, wasTheorem = False, simpAnno = Nothing

, attrOrigin = Nothing, sentence = sen }

_ -> -- Axiom

let sen = Sentence (formulaRoleAF t) (thfFormulaAF t) (annotationsAF t)

in makeNamed (show $ pretty $ nameAF t) sen

--------------------------------------------------------------------------------

-- Get the Kind of a type

--------------------------------------------------------------------------------

makeKind :: THFFormula -> Either (Kind, Constant) Diagnosis

makeKind t = maybe (Right $ mkDiag Error "Error while parsing the Kind of:" t)

Left (thfFormulaToKind t)

thfFormulaToKind :: THFFormula -> Maybe (Kind, Constant)

thfFormulaToKind (T0F_THF_Typed_Const tc) = thfTypedConstToKind tc

thfFormulaToKind _ = Nothing

thfTypedConstToKind :: THFTypedConst -> Maybe (Kind, Constant)

thfTypedConstToKind (T0TC_THF_TypedConst_Par tcp) = thfTypedConstToKind tcp

thfTypedConstToKind (T0TC_Typed_Const c tlt) =

maybe Nothing (\ k -> Just (k, c))

(thfTopLevelTypeToKind tlt)

thfTopLevelTypeToKind :: THFTopLevelType -> Maybe Kind

thfTopLevelTypeToKind tlt = case tlt of

T0TLT_THF_Binary_Type bt -> thfBinaryTypeToKind bt

T0TLT_Defined_Type _ -> Just Kind

T0TLT_System_Type st -> Just $ SysType st

T0TLT_Variable v -> Just $ VKind v

_ -> Nothing

thfBinaryTypeToKind :: THFBinaryType -> Maybe Kind

thfBinaryTypeToKind bt = case bt of

TBT_THF_Mapping_Type [] -> Nothing

TBT_THF_Mapping_Type (_ : []) -> Nothing

TBT_THF_Mapping_Type mt -> thfMappingTypeToKind mt

T0BT_THF_Binary_Type_Par btp -> fmap ParKind (thfBinaryTypeToKind btp)

_ -> Nothing

thfMappingTypeToKind :: [THFUnitaryType] -> Maybe Kind

thfMappingTypeToKind [] = Nothing

thfMappingTypeToKind (u : []) = thfUnitaryTypeToKind u

thfMappingTypeToKind (u : ru) =

let k1 = thfUnitaryTypeToKind u

k2 = thfMappingTypeToKind ru

in if isJust k1 && isJust k2

then Just $ MapKind (fromJust k1) (fromJust k2) nullRange

else Nothing

thfUnitaryTypeToKind :: THFUnitaryType -> Maybe Kind

thfUnitaryTypeToKind ut = case ut of

T0UT_THF_Binary_Type_Par bt -> fmap ParKind (thfBinaryTypeToKind bt)

T0UT_Defined_Type _ -> Just Kind

T0UT_System_Type st -> Just $ SysType st

T0UT_Variable v -> Just $ VKind v

_ -> Nothing

--------------------------------------------------------------------------------

-- Get the Type of a constant

--------------------------------------------------------------------------------

makeType :: THFFormula -> Either (Type, Constant) Diagnosis

makeType t = maybe (Right $ mkDiag Error "Error while parsing the Type of:" t)

Left (thfFormulaToType t)

thfFormulaToType :: THFFormula -> Maybe (Type, Constant)

thfFormulaToType (T0F_THF_Typed_Const tc) = thfTypedConstToType tc

thfFormulaToType _ = Nothing

thfTypedConstToType :: THFTypedConst -> Maybe (Type, Constant)

thfTypedConstToType (T0TC_THF_TypedConst_Par tcp) = thfTypedConstToType tcp

thfTypedConstToType (T0TC_Typed_Const c tlt) =

maybe Nothing (\ t -> Just (t, c))

(thfTopLevelTypeToType tlt)

thfTopLevelTypeToType :: THFTopLevelType -> Maybe Type

thfTopLevelTypeToType tlt = case tlt of

T0TLT_Defined_Type dt -> thfDefinedTypeToType dt

T0TLT_THF_Binary_Type bt -> thfBinaryTypeToType bt

T0TLT_Constant c -> Just $ CType c

T0TLT_System_Type st -> Just $ SType st

T0TLT_Variable v -> Just $ VType v

_ -> Nothing

thfDefinedTypeToType :: DefinedType -> Maybe Type

thfDefinedTypeToType dt = case dt of

DT_oType -> Just OType

DT_o -> Just OType

DT_iType -> Just TType

DT_i -> Just IType

DT_tType -> Just TType

_ -> Nothing

thfBinaryTypeToType :: THFBinaryType -> Maybe Type

thfBinaryTypeToType bt = case bt of

TBT_THF_Mapping_Type [] -> Nothing

TBT_THF_Mapping_Type (_ : []) -> Nothing

TBT_THF_Mapping_Type mt -> thfMappingTypeToType mt

T0BT_THF_Binary_Type_Par btp -> fmap ParType (thfBinaryTypeToType btp)

TBT_THF_Xprod_Type [] -> Nothing

TBT_THF_Xprod_Type (u : []) -> thfUnitaryTypeToType u

TBT_THF_Xprod_Type us -> let us' = map thfUnitaryTypeToType us

in if all isJust us' then

(Just . ProdType) $ map fromJust us'

else Nothing

_ -> Nothing

thfMappingTypeToType :: [THFUnitaryType] -> Maybe Type

thfMappingTypeToType [] = Nothing

thfMappingTypeToType (u : []) = thfUnitaryTypeToType u

thfMappingTypeToType (u : ru) =

let k1 = thfUnitaryTypeToType u

k2 = thfMappingTypeToType ru

in if isJust k1 && isJust k2

then Just $ MapType (fromJust k1) (fromJust k2)

else Nothing

thfUnitaryTypeToType :: THFUnitaryType -> Maybe Type

thfUnitaryTypeToType ut = case ut of

T0UT_THF_Binary_Type_Par bt -> fmap ParType (thfBinaryTypeToType bt)

T0UT_Defined_Type dt -> thfDefinedTypeToType dt

T0UT_Constant c -> Just $ CType c

T0UT_System_Type st -> Just $ SType st

T0UT_Variable v -> Just $ VType v

_ -> Nothing

--------------------------------------------------------------------------------

-- Check if a THFFormula is a Type definition

--------------------------------------------------------------------------------

isType :: THFFormula -> Bool

isType tf = case tf of

T0F_THF_Typed_Const tc -> thfTypedConstIsType tc

_ -> False

thfTypedConstIsType :: THFTypedConst -> Bool

thfTypedConstIsType tc = case tc of

T0TC_THF_TypedConst_Par tcp -> thfTypedConstIsType tcp

T0TC_Typed_Const _ tlt -> thfTopLevelTypeIsType tlt

thfTopLevelTypeIsType :: THFTopLevelType -> Bool

thfTopLevelTypeIsType tlt = case tlt of

T0TLT_Defined_Type dt -> thfDefinedTypeIsType dt

T0TLT_THF_Binary_Type bt -> thfBinaryTypeIsType bt

T0TLT_System_Type _ -> True

_ -> False

thfDefinedTypeIsType :: DefinedType -> Bool

thfDefinedTypeIsType dt = case dt of

DT_tType -> True

_ -> False

thfBinaryTypeIsType :: THFBinaryType -> Bool

thfBinaryTypeIsType bt = case bt of

TBT_THF_Mapping_Type [] -> False

TBT_THF_Mapping_Type (_ : []) -> False

TBT_THF_Mapping_Type mt -> thfMappingTypeIsType mt

T0BT_THF_Binary_Type_Par btp -> thfBinaryTypeIsType btp

_ -> False

thfMappingTypeIsType :: [THFUnitaryType] -> Bool

thfMappingTypeIsType mt = case mt of

[] -> False

(u : []) -> thfUnitaryTypeIsType u

(u : ru) -> thfUnitaryTypeIsType u && thfMappingTypeIsType ru

thfUnitaryTypeIsType :: THFUnitaryType -> Bool

thfUnitaryTypeIsType ut = case ut of

T0UT_Defined_Type dt -> thfDefinedTypeIsType dt

T0UT_THF_Binary_Type_Par bt -> thfBinaryTypeIsType bt

T0UT_System_Type _ -> True

_ -> False