Copyright	(c) Jonathan von Schroeder DFKI GmbH 2010
License	GPLv2 or higher, see LICENSE.txt
Maintainer	<jonathan.von_schroeder@dfki.de>
Stability	experimental
Portability	portable
Safe Haskell	Safe

QBF.Morphism

Description

Definition of morphisms for propositional logic copied to Temporal.Morphism Ref.

Till Mossakowski, Joseph Goguen, Razvan Diaconescu, Andrzej Tarlecki. What is a Logic?. In Jean-Yves Beziau (Ed.), Logica Universalis, pp. 113-133. Birkhaeuser. 2005.

Synopsis

data Morphism = Morphism {
- source :: Sign
- target :: Sign
- propMap :: Map Id Id
}
pretty :: Pretty a => a -> Doc
idMor :: Sign -> Morphism
isLegalMorphism :: Morphism -> Result ()
composeMor :: Morphism -> Morphism -> Result Morphism
inclusionMap :: Sign -> Sign -> Morphism
mapSentence :: Morphism -> FORMULA -> Result FORMULA
mapSentenceH :: Morphism -> FORMULA -> FORMULA
applyMap :: Map Id Id -> Id -> Id
applyMorphism :: Morphism -> Id -> Id
morphismUnion :: Morphism -> Morphism -> Result Morphism

Documentation

data Morphism Source #

The datatype for morphisms in propositional logic as maps of sets

Constructors

Morphism
Fields source :: Sign target :: Sign propMap :: Map Id Id

Instances

Instances details

Eq Morphism Source #
Instance details Defined in QBF.Morphism Methods (==) :: Morphism -> Morphism -> Bool (/=) :: Morphism -> Morphism -> Bool
Data Morphism Source #
Instance details Defined in QBF.Morphism Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Morphism -> c Morphism gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Morphism toConstr :: Morphism -> Constr dataTypeOf :: Morphism -> DataType dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Morphism) dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Morphism) gmapT :: (forall b. Data b => b -> b) -> Morphism -> Morphism gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Morphism -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Morphism -> r gmapQ :: (forall d. Data d => d -> u) -> Morphism -> [u] gmapQi :: Int -> (forall d. Data d => d -> u) -> Morphism -> u gmapM :: Monad m => (forall d. Data d => d -> m d) -> Morphism -> m Morphism gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Morphism -> m Morphism gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Morphism -> m Morphism
Ord Morphism Source #
Instance details Defined in QBF.Morphism Methods compare :: Morphism -> Morphism -> Ordering (<) :: Morphism -> Morphism -> Bool (<=) :: Morphism -> Morphism -> Bool (>) :: Morphism -> Morphism -> Bool (>=) :: Morphism -> Morphism -> Bool max :: Morphism -> Morphism -> Morphism min :: Morphism -> Morphism -> Morphism
Show Morphism Source #
Instance details Defined in QBF.Morphism Methods showsPrec :: Int -> Morphism -> ShowS show :: Morphism -> String showList :: [Morphism] -> ShowS
Generic Morphism
Instance details Defined in QBF.ATC_QBF Associated Types type Rep Morphism :: Type -> Type Methods from :: Morphism -> Rep Morphism x to :: Rep Morphism x -> Morphism
FromJSON Morphism
Instance details Defined in QBF.ATC_QBF Methods parseJSON :: Value -> Parser Morphism parseJSONList :: Value -> Parser [Morphism]
ToJSON Morphism
Instance details Defined in QBF.ATC_QBF Methods toJSON :: Morphism -> Value toEncoding :: Morphism -> Encoding toJSONList :: [Morphism] -> Value toEncodingList :: [Morphism] -> Encoding
ShATermConvertible Morphism
Instance details Defined in QBF.ATC_QBF Methods toShATermAux :: ATermTable -> Morphism -> IO (ATermTable, Int) toShATermList' :: ATermTable -> [Morphism] -> IO (ATermTable, Int) fromShATermAux :: Int -> ATermTable -> (ATermTable, Morphism) fromShATermList' :: Int -> ATermTable -> (ATermTable, [Morphism])
Pretty Morphism Source #
Instance details Defined in QBF.Morphism Methods pretty :: Morphism -> Doc Source # pretties :: [Morphism] -> Doc Source #
ProjectSublogic QBFSL Morphism Source #
Instance details Defined in QBF.Logic_QBF Methods projectSublogic :: QBFSL -> Morphism -> Morphism Source #
MinSublogic QBFSL Morphism Source #
Instance details Defined in QBF.Logic_QBF Methods minSublogic :: Morphism -> QBFSL Source #
Category Sign Morphism Source #	Instance of Category for propositional logic
Instance details Defined in QBF.Logic_QBF Methods ide :: Sign -> Morphism Source # composeMorphisms :: Morphism -> Morphism -> Result Morphism Source # dom :: Morphism -> Sign Source # cod :: Morphism -> Sign Source # inverse :: Morphism -> Result Morphism Source # isInclusion :: Morphism -> Bool Source # legal_mor :: Morphism -> Result () Source #
Sentences QBF FORMULA Sign Morphism Symbol Source #	Instance of Sentences for propositional logic
Instance details Defined in QBF.Logic_QBF Methods map_sen :: QBF -> Morphism -> FORMULA -> Result FORMULA Source # simplify_sen :: QBF -> Sign -> FORMULA -> FORMULA Source # negation :: QBF -> FORMULA -> Maybe FORMULA Source # print_sign :: QBF -> Sign -> Doc Source # print_named :: QBF -> Named FORMULA -> Doc Source # sym_of :: QBF -> Sign -> [Set Symbol] Source # mostSymsOf :: QBF -> Sign -> [Symbol] Source # symmap_of :: QBF -> Morphism -> EndoMap Symbol Source # sym_name :: QBF -> Symbol -> Id Source # sym_label :: QBF -> Symbol -> Maybe String Source # fullSymName :: QBF -> Symbol -> String Source # symKind :: QBF -> Symbol -> String Source # symsOfSen :: QBF -> Sign -> FORMULA -> [Symbol] Source # pair_symbols :: QBF -> Symbol -> Symbol -> Result Symbol Source #
StaticAnalysis QBF BASICSPEC FORMULA SYMBITEMS SYMBMAPITEMS Sign Morphism Symbol Symbol Source #	Static Analysis for propositional logic
Instance details Defined in QBF.Logic_QBF Methods basic_analysis :: QBF -> Maybe ((BASICSPEC, Sign, GlobalAnnos) -> Result (BASICSPEC, ExtSign Sign Symbol, [Named FORMULA])) Source # sen_analysis :: QBF -> Maybe ((BASICSPEC, Sign, FORMULA) -> Result FORMULA) Source # extBasicAnalysis :: QBF -> IRI -> LibName -> BASICSPEC -> Sign -> GlobalAnnos -> Result (BASICSPEC, ExtSign Sign Symbol, [Named FORMULA]) Source # stat_symb_map_items :: QBF -> Sign -> Maybe Sign -> [SYMBMAPITEMS] -> Result (EndoMap Symbol) Source # stat_symb_items :: QBF -> Sign -> [SYMBITEMS] -> Result [Symbol] Source # convertTheory :: QBF -> Maybe ((Sign, [Named FORMULA]) -> BASICSPEC) Source # ensures_amalgamability :: QBF -> ([CASLAmalgOpt], Gr Sign (Int, Morphism), [(Int, Morphism)], Gr String String) -> Result Amalgamates Source # quotient_term_algebra :: QBF -> Morphism -> [Named FORMULA] -> Result (Sign, [Named FORMULA]) Source # signature_colimit :: QBF -> Gr Sign (Int, Morphism) -> Result (Sign, Map Int Morphism) Source # qualify :: QBF -> SIMPLE_ID -> LibName -> Morphism -> Sign -> Result (Morphism, [Named FORMULA]) Source # symbol_to_raw :: QBF -> Symbol -> Symbol Source # id_to_raw :: QBF -> Id -> Symbol Source # matches :: QBF -> Symbol -> Symbol -> Bool Source # empty_signature :: QBF -> Sign Source # add_symb_to_sign :: QBF -> Sign -> Symbol -> Result Sign Source # signature_union :: QBF -> Sign -> Sign -> Result Sign Source # signatureDiff :: QBF -> Sign -> Sign -> Result Sign Source # intersection :: QBF -> Sign -> Sign -> Result Sign Source # final_union :: QBF -> Sign -> Sign -> Result Sign Source # morphism_union :: QBF -> Morphism -> Morphism -> Result Morphism Source # is_subsig :: QBF -> Sign -> Sign -> Bool Source # subsig_inclusion :: QBF -> Sign -> Sign -> Result Morphism Source # generated_sign :: QBF -> Set Symbol -> Sign -> Result Morphism Source # cogenerated_sign :: QBF -> Set Symbol -> Sign -> Result Morphism Source # induced_from_morphism :: QBF -> EndoMap Symbol -> Sign -> Result Morphism Source # induced_from_to_morphism :: QBF -> EndoMap Symbol -> ExtSign Sign Symbol -> ExtSign Sign Symbol -> Result Morphism Source # is_transportable :: QBF -> Morphism -> Bool Source # is_injective :: QBF -> Morphism -> Bool Source # theory_to_taxonomy :: QBF -> TaxoGraphKind -> MMiSSOntology -> Sign -> [Named FORMULA] -> Result MMiSSOntology Source # corresp2th :: QBF -> String -> Bool -> Sign -> Sign -> [SYMBITEMS] -> [SYMBITEMS] -> EndoMap Symbol -> EndoMap Symbol -> REL_REF -> Result (Sign, [Named FORMULA], Sign, Sign, EndoMap Symbol, EndoMap Symbol) Source # equiv2cospan :: QBF -> Sign -> Sign -> [SYMBITEMS] -> [SYMBITEMS] -> Result (Sign, Sign, Sign, EndoMap Symbol, EndoMap Symbol) Source # extract_module :: QBF -> [IRI] -> (Sign, [Named FORMULA]) -> Result (Sign, [Named FORMULA]) Source #
Logic QBF QBFSL BASICSPEC FORMULA SYMBITEMS SYMBMAPITEMS Sign Morphism Symbol Symbol ProofTree Source #	Instance of Logic for propositional logc
Instance details Defined in QBF.Logic_QBF Methods parse_basic_sen :: QBF -> Maybe (BASICSPEC -> AParser st FORMULA) Source # stability :: QBF -> Stability Source # data_logic :: QBF -> Maybe AnyLogic Source # top_sublogic :: QBF -> QBFSL Source # all_sublogics :: QBF -> [QBFSL] Source # bottomSublogic :: QBF -> Maybe QBFSL Source # sublogicDimensions :: QBF -> [[QBFSL]] Source # parseSublogic :: QBF -> String -> Maybe QBFSL Source # proj_sublogic_epsilon :: QBF -> QBFSL -> Sign -> Morphism Source # provers :: QBF -> [Prover Sign FORMULA Morphism QBFSL ProofTree] Source # default_prover :: QBF -> String Source # cons_checkers :: QBF -> [ConsChecker Sign FORMULA QBFSL Morphism ProofTree] Source # conservativityCheck :: QBF -> [ConservativityChecker Sign FORMULA Morphism] Source # empty_proof_tree :: QBF -> ProofTree Source # syntaxTable :: QBF -> Sign -> Maybe SyntaxTable Source # omdoc_metatheory :: QBF -> Maybe OMCD Source # export_symToOmdoc :: QBF -> NameMap Symbol -> Symbol -> String -> Result TCElement Source # export_senToOmdoc :: QBF -> NameMap Symbol -> FORMULA -> Result TCorOMElement Source # export_theoryToOmdoc :: QBF -> SigMap Symbol -> Sign -> [Named FORMULA] -> Result [TCElement] Source # omdocToSym :: QBF -> SigMapI Symbol -> TCElement -> String -> Result Symbol Source # omdocToSen :: QBF -> SigMapI Symbol -> TCElement -> String -> Result (Maybe (Named FORMULA)) Source # addOMadtToTheory :: QBF -> SigMapI Symbol -> (Sign, [Named FORMULA]) -> [[OmdADT]] -> Result (Sign, [Named FORMULA]) Source # addOmdocToTheory :: QBF -> SigMapI Symbol -> (Sign, [Named FORMULA]) -> [TCElement] -> Result (Sign, [Named FORMULA]) Source # sublogicOfTheo :: QBF -> (Sign, [FORMULA]) -> QBFSL Source #
Comorphism QBF2Prop QBF QBFSL BASICSPEC FORMULA SYMBITEMS SYMBMAPITEMS Sign Morphism Symbol Symbol ProofTree Propositional PropSL BASIC_SPEC FORMULA SYMB_ITEMS SYMB_MAP_ITEMS Sign Morphism Symbol Symbol ProofTree Source #
Instance details Defined in Comorphisms.QBF2Prop Methods sourceLogic :: QBF2Prop -> QBF Source # sourceSublogic :: QBF2Prop -> QBFSL Source # sourceSublogicLossy :: QBF2Prop -> QBFSL Source # minSourceTheory :: QBF2Prop -> Maybe (LibName, String) Source # targetLogic :: QBF2Prop -> Propositional Source # mapSublogic :: QBF2Prop -> QBFSL -> Maybe PropSL Source # map_theory :: QBF2Prop -> (Sign, [Named FORMULA]) -> Result (Sign, [Named FORMULA0]) Source # mapMarkedTheory :: QBF2Prop -> (Sign, [Named FORMULA]) -> Result (Sign, [Named FORMULA0]) Source # map_morphism :: QBF2Prop -> Morphism -> Result Morphism0 Source # map_sentence :: QBF2Prop -> Sign -> FORMULA -> Result FORMULA0 Source # map_symbol :: QBF2Prop -> Sign -> Symbol -> Set Symbol0 Source # extractModel :: QBF2Prop -> Sign -> ProofTree -> Result (Sign, [Named FORMULA]) Source # is_model_transportable :: QBF2Prop -> Bool Source # has_model_expansion :: QBF2Prop -> Bool Source # is_weakly_amalgamable :: QBF2Prop -> Bool Source # constituents :: QBF2Prop -> [String] Source # isInclusionComorphism :: QBF2Prop -> Bool Source # rps :: QBF2Prop -> Bool Source # eps :: QBF2Prop -> Bool Source # isGTC :: QBF2Prop -> Bool Source #
Comorphism Prop2QBF Propositional PropSL BASIC_SPEC FORMULA SYMB_ITEMS SYMB_MAP_ITEMS Sign Morphism Symbol Symbol ProofTree QBF QBFSL BASICSPEC FORMULA SYMBITEMS SYMBMAPITEMS Sign Morphism Symbol Symbol ProofTree Source #
Instance details Defined in Comorphisms.Prop2QBF Methods sourceLogic :: Prop2QBF -> Propositional Source # sourceSublogic :: Prop2QBF -> PropSL Source # sourceSublogicLossy :: Prop2QBF -> PropSL Source # minSourceTheory :: Prop2QBF -> Maybe (LibName, String) Source # targetLogic :: Prop2QBF -> QBF Source # mapSublogic :: Prop2QBF -> PropSL -> Maybe QBFSL Source # map_theory :: Prop2QBF -> (Sign, [Named FORMULA0]) -> Result (Sign, [Named FORMULA]) Source # mapMarkedTheory :: Prop2QBF -> (Sign, [Named FORMULA0]) -> Result (Sign, [Named FORMULA]) Source # map_morphism :: Prop2QBF -> Morphism0 -> Result Morphism Source # map_sentence :: Prop2QBF -> Sign -> FORMULA0 -> Result FORMULA Source # map_symbol :: Prop2QBF -> Sign -> Symbol0 -> Set Symbol Source # extractModel :: Prop2QBF -> Sign -> ProofTree -> Result (Sign, [Named FORMULA0]) Source # is_model_transportable :: Prop2QBF -> Bool Source # has_model_expansion :: Prop2QBF -> Bool Source # is_weakly_amalgamable :: Prop2QBF -> Bool Source # constituents :: Prop2QBF -> [String] Source # isInclusionComorphism :: Prop2QBF -> Bool Source # rps :: Prop2QBF -> Bool Source # eps :: Prop2QBF -> Bool Source # isGTC :: Prop2QBF -> Bool Source #
type Rep Morphism
Instance details Defined in QBF.ATC_QBF type Rep Morphism = D1 ('MetaData "Morphism" "QBF.Morphism" "main" 'False) (C1 ('MetaCons "Morphism" 'PrefixI 'True) (S1 ('MetaSel ('Just "source") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Sign) :: (S1 ('MetaSel ('Just "target") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Sign) :: S1 ('MetaSel ('Just "propMap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Map Id Id)))))

pretty :: Pretty a => a -> Doc Source #

idMor :: Sign -> Morphism Source #

Constructs an id-morphism

isLegalMorphism :: Morphism -> Result () Source #

Determines whether a morphism is valid

composeMor :: Morphism -> Morphism -> Result Morphism Source #

Composition of morphisms in propositional Logic

inclusionMap :: Sign -> Sign -> Morphism Source #

Inclusion map of a subsig into a supersig

mapSentence :: Morphism -> FORMULA -> Result FORMULA Source #

sentence translation along signature morphism here just the renaming of formulae

mapSentenceH :: Morphism -> FORMULA -> FORMULA Source #

applyMap :: Map Id Id -> Id -> Id Source #

Application function for propMaps

applyMorphism :: Morphism -> Id -> Id Source #

Application funtion for morphisms

morphismUnion :: Morphism -> Morphism -> Result Morphism Source #