{- |

Module : $Header$

Copyright : (c) Till Mossakowski, and Uni Bremen 2002-2004

Licence : similar to LGPL, see HetCATS/LICENCE.txt or LIZENZ.txt

Maintainer : till@tzi.de

Stability : provisional

Portability : non-portable (overlapping instances, dynamics, existentials)

The Grothendieck logic is defined to be the

heterogeneous logic over the logic graph.

This will be the logic over which the data

structures and algorithms for specification in-the-large

are built.

References:

R. Diaconescu:

Grothendieck institutions

J. applied categorical structures 10, 2002, p. 383-402.

T. Mossakowski:

Heterogeneous development graphs and heterogeneous borrowing

Fossacs 2002, LNCS 2303, p. 326-341

T. Mossakowski: Foundations of heterogeneous specification

Submitted

T. Mossakowski:

Relating CASL with Other Specification Languages:

the Institution Level

Theoretical Computer Science 286, 2002, p. 367-475

Todo:

-}

module Logic.Grothendieck where

import Logic.Logic

import Logic.Prover

import Logic.Comorphism

import Common.PrettyPrint

import Common.Lib.Pretty

import qualified Common.Lib.Map as Map

import qualified Common.Lib.Set as Set

import Common.Result

import Common.Id

import Common.AS_Annotation

import Common.ListUtils

import Data.Dynamic

import Common.DynamicUtils

import qualified Data.List as List

import Data.Maybe

import Control.Monad

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

--"Grothendieck" versions of the various parts of type class Logic

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

-- | Grothendieck basic specifications

data G_basic_spec = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_basic_spec lid basic_spec

instance Show G_basic_spec where

show (G_basic_spec _ s) = show s

instance PrettyPrint G_basic_spec where

printText0 ga (G_basic_spec _ s) = printText0 ga s

-- | Grothendieck sentences

data G_sentence = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_sentence lid sentence

instance Show G_sentence where

show (G_sentence _ s) = show s

-- | Grothendieck sentence lists

data G_l_sentence_list = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_l_sentence_list lid [Named sentence]

instance Show G_l_sentence_list where

show (G_l_sentence_list _ s) = show s

instance Eq G_l_sentence_list where

(G_l_sentence_list i1 nl1) == (G_l_sentence_list i2 nl2) =

coerce i1 i2 nl1 == Just nl2

eq_G_l_sentence_set :: G_l_sentence_list -> G_l_sentence_list -> Bool

eq_G_l_sentence_set (G_l_sentence_list i1 nl1) (G_l_sentence_list i2 nl2) =

case coerce i1 i2 nl1 of

Just nl1' -> Set.fromList nl1' == Set.fromList nl2

Nothing -> False

-- | Grothendieck signatures

data G_sign = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_sign lid sign

tyconG_sign :: TyCon

tyconG_sign = mkTyCon "Logic.Grothendieck.G_sign"

instance Typeable G_sign where

typeOf _ = mkTyConApp tyconG_sign []

instance Eq G_sign where

(G_sign i1 sigma1) == (G_sign i2 sigma2) =

coerce i1 i2 sigma1 == Just sigma2

-- | prefer a faster subsignature test if possible

is_subgsign :: G_sign -> G_sign -> Bool

is_subgsign (G_sign i1 sigma1) (G_sign i2 sigma2) =

maybe False (is_subsig i1 sigma1) $ coerce i2 i1 sigma2

instance Show G_sign where

show (G_sign _ s) = show s

instance PrettyPrint G_sign where

printText0 ga (G_sign _ s) = printText0 ga s

langNameSig :: G_sign -> String

langNameSig (G_sign lid _) = language_name lid

-- | Grothendieck signature lists

data G_sign_list = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_sign_list lid [sign]

-- | Grothendieck extended signatures

data G_ext_sign = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_ext_sign lid sign (Set.Set symbol)

tyconG_ext_sign :: TyCon

tyconG_ext_sign = mkTyCon "Logic.Grothendieck.G_ext_sign"

instance Typeable G_ext_sign where

typeOf _ = mkTyConApp tyconG_ext_sign []

instance Eq G_ext_sign where

(G_ext_sign i1 sigma1 sys1) == (G_ext_sign i2 sigma2 sys2) =

coerce i1 i2 sigma1 == Just sigma2

&& coerce i1 i2 sys1 == Just sys2

instance Show G_ext_sign where

show (G_ext_sign _ s _) = show s

instance PrettyPrint G_ext_sign where

printText0 ga (G_ext_sign _ s _) = printText0 ga s

langNameExtSig :: G_ext_sign -> String

langNameExtSig (G_ext_sign lid _ _) = language_name lid

-- | Grothendieck theories

data G_theory = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_theory lid sign [Named sentence]

-- | compute sublogic of a theory

sublogicOfTh :: G_theory -> G_sublogics

sublogicOfTh (G_theory lid sigma sens) =

let sub = foldr Logic.Logic.join

(min_sublogic_sign lid sigma)

(map (min_sublogic_sentence lid . sentence) sens)

in G_sublogics lid sub

-- | simplify a theory (throw away qualifications)

simplifyTh :: G_theory -> G_theory

simplifyTh (G_theory lid sigma sens) =

G_theory lid sigma (map (mapNamed (simplify_sen lid sigma)) sens)

-- | Grothendieck symbols

data G_symbol = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_symbol lid symbol

instance Show G_symbol where

show (G_symbol _ s) = show s

instance Eq G_symbol where

(G_symbol i1 s1) == (G_symbol i2 s2) =

coerce i1 i2 s1 == Just s2

-- | Grothendieck symbol lists

data G_symb_items_list = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_symb_items_list lid [symb_items]

instance Show G_symb_items_list where

show (G_symb_items_list _ l) = show l

instance PrettyPrint G_symb_items_list where

printText0 ga (G_symb_items_list _ l) =

fsep $ punctuate comma $ map (printText0 ga) l

instance Eq G_symb_items_list where

(G_symb_items_list i1 s1) == (G_symb_items_list i2 s2) =

coerce i1 i2 s1 == Just s2

-- | Grothendieck symbol maps

data G_symb_map_items_list = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_symb_map_items_list lid [symb_map_items]

instance Show G_symb_map_items_list where

show (G_symb_map_items_list _ l) = show l

instance PrettyPrint G_symb_map_items_list where

printText0 ga (G_symb_map_items_list _ l) =

fsep $ punctuate comma $ map (printText0 ga) l

instance Eq G_symb_map_items_list where

(G_symb_map_items_list i1 s1) == (G_symb_map_items_list i2 s2) =

coerce i1 i2 s1 == Just s2

-- | Grothendieck diagrams

data G_diagram = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_diagram lid (Diagram sign morphism)

-- | Grothendieck sublogics

data G_sublogics = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_sublogics lid sublogics

tyconG_sublogics :: TyCon

tyconG_sublogics = mkTyCon "Logic.Grothendieck.G_sublogics"

instance Typeable G_sublogics where

typeOf _ = mkTyConApp tyconG_sublogics []

instance Show G_sublogics where

show (G_sublogics lid sub) = case sublogic_names lid sub of

[] -> error "show G_sublogics"

h : _ -> show lid ++ "." ++ h

instance Eq G_sublogics where

(G_sublogics lid1 l1) == (G_sublogics lid2 l2) =

coerce lid1 lid2 l1 == Just l2

instance Ord G_sublogics where

compare (G_sublogics lid1 l1) (G_sublogics lid2 l2) =

case coerce lid1 lid2 l2 of

Just l2' -> compare l1 l2' {-if l1==l2' then EQ

else if l1 <<= l2' then LT

else GT-}

Nothing -> error "Attempt to compare sublogics of different logics"

-- | Homogeneous Grothendieck signature morphisms

data G_morphism = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_morphism lid morphism

instance Show G_morphism where

show (G_morphism _ l) = show l

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

-- Existential types for the logic graph

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

-- | Existential type for comorphisms

data AnyComorphism = forall cid lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 .

Comorphism cid

lid1 sublogics1 basic_spec1 sentence1

symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2

symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 =>

Comorphism cid

instance Eq AnyComorphism where

Comorphism cid1 == Comorphism cid2 =

constituents cid1 == constituents cid2

-- need to be refined, using comorphism translations !!!

instance Show AnyComorphism where

show (Comorphism cid) =

language_name cid

++" : "++language_name (sourceLogic cid)

++" -> "++language_name (targetLogic cid)

tyconAnyComorphism :: TyCon

tyconAnyComorphism = mkTyCon "Logic.Grothendieck.AnyComorphism"

instance Typeable AnyComorphism where

typeOf _ = mkTyConApp tyconAnyComorphism []

-- | Test whether a comporphism is the identity

isIdComorphism :: AnyComorphism -> Bool

isIdComorphism (Comorphism cid) =

constituents cid == []

-- | Compose comorphisms

compComorphism :: Monad m => AnyComorphism -> AnyComorphism -> m AnyComorphism

compComorphism cm1@(Comorphism cid1) cm2@(Comorphism cid2) =

case coerce (targetLogic cid1) (sourceLogic cid2) (targetSublogic cid1) of

Just sl1 ->

if sl1 <= sourceSublogic cid2

then case (isIdComorphism cm1,isIdComorphism cm2) of

(True,_) -> return cm2

(_,True) -> return cm1

_ -> return $ Comorphism (CompComorphism cid1 cid2)

else fail ("Sublogic mismatch in composition of "++language_name cid1++

" and "++language_name cid2)

Nothing -> fail ("Logic mismatch in composition of "++language_name cid1++

" and "++language_name cid2)

-- | Logic graph

data LogicGraph = LogicGraph {

logics :: Map.Map String AnyLogic,

comorphisms :: Map.Map String AnyComorphism,

inclusions :: Map.Map (String,String) AnyComorphism

}

emptyLogicGraph :: LogicGraph

emptyLogicGraph = LogicGraph Map.empty Map.empty Map.empty

-- | find a logic in a logic graph

lookupLogic :: Monad m => String -> String -> LogicGraph -> m AnyLogic

lookupLogic error_prefix logname logicGraph =

case Map.lookup logname (logics logicGraph) of

Nothing -> fail (error_prefix++" in LogicGraph logic \""

++logname++"\" unknown")

Just lid -> return lid

-- | find a comorphism in a logic graph

lookupComorphism :: Monad m => String -> LogicGraph -> m AnyComorphism

lookupComorphism coname logicGraph = do

let nameList = splitBy ';' coname

cs <- sequence $ map lookupN nameList

case cs of

c:cs1 -> foldM compComorphism c cs1

_ -> fail ("Illgegal comorphism name: "++coname)

where

lookupN name =

case name of

'i':'d':'_':logic -> do

let mainLogic = takeWhile (/= '.') logic

l <- maybe (fail ("Cannot find Logic "++mainLogic)) return

$ Map.lookup mainLogic (logics logicGraph)

case l of

Logic lid ->

return $ Comorphism $ IdComorphism lid (top_sublogic lid)

_ -> maybe (fail ("Cannot find logic comorphism "++name)) return

$ Map.lookup name (comorphisms logicGraph)

-- | auxiliary existential type needed for composition of comorphisms

data AnyComorphismAux lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 =

forall cid .

Comorphism cid

lid1 sublogics1 basic_spec1 sentence1

symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2

symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 =>

ComorphismAux cid lid1 lid2 sign1 morphism2

tyconAnyComorphismAux :: TyCon

tyconAnyComorphismAux = mkTyCon "Logic.Grothendieck.AnyComorphismAux"

instance Typeable (AnyComorphismAux lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2)

where typeOf _ = mkTyConApp tyconG_sign []

instance Show (AnyComorphismAux lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2)

where show _ = "<AnyComorphismAux>"

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

-- The Grothendieck signature category

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

-- | Grothendieck signature morphisms

data GMorphism = forall cid lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2

basic_spec2 sentence2 symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 .

Comorphism cid

lid1 sublogics1 basic_spec1 sentence1

symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid2 sublogics2 basic_spec2 sentence2

symb_items2 symb_map_items2

sign2 morphism2 symbol2 raw_symbol2 proof_tree2 =>

GMorphism cid sign1 morphism2

instance Eq GMorphism where

GMorphism cid1 sigma1 mor1 == GMorphism cid2 sigma2 mor2

= Comorphism cid1 == Comorphism cid2 &&

coerce cid1 cid1 (sigma1, mor1) == Just (sigma2, mor2)

data Grothendieck = Grothendieck deriving Show

instance Language Grothendieck

instance Show GMorphism where

show (GMorphism cid s m) = show cid ++ "(" ++ show s ++ ")" ++ show m

instance PrettyPrint GMorphism where

printText0 ga (GMorphism cid s m) =

ptext (show cid)

<+> -- ptext ":" <+> ptext (show (sourceLogic cid)) <+>

-- ptext "->" <+> ptext (show (targetLogic cid)) <+>

ptext "(" <+> printText0 ga s <+> ptext ")"

$$

printText0 ga m

instance Category Grothendieck G_sign GMorphism where

ide _ (G_sign lid sigma) =

GMorphism (IdComorphism lid (top_sublogic lid)) sigma (ide lid sigma)

comp _

(GMorphism r1 sigma1 mor1)

(GMorphism r2 _sigma2 mor2) =

do let lid1 = sourceLogic r1

lid2 = targetLogic r1

lid3 = sourceLogic r2

lid4 = targetLogic r2

ComorphismAux r1' _ _ sigma1' mor1' <-

(coerce lid2 lid3 $ ComorphismAux r1 lid1 lid2 sigma1 mor1)

mor1'' <- map_morphism r2 mor1'

mor <- comp lid4 mor1'' mor2

return (GMorphism (CompComorphism r1' r2) sigma1' mor)

dom _ (GMorphism r sigma _mor) =

G_sign (sourceLogic r) sigma

cod _ (GMorphism r _sigma mor) =

G_sign lid2 (cod lid2 mor)

where lid2 = targetLogic r

legal_obj _ (G_sign lid sigma) = legal_obj lid sigma

legal_mor _ (GMorphism r sigma mor) =

legal_mor lid2 mor &&

case map_sign r sigma of

Just (sigma',_) -> sigma' == cod lid2 mor

Nothing -> False

where lid2 = targetLogic r

-- | Embedding of homogeneous signature morphisms as Grothendieck sig mors

gEmbed :: G_morphism -> GMorphism

gEmbed (G_morphism lid mor) =

GMorphism (IdComorphism lid (top_sublogic lid)) (dom lid mor) mor

-- | heterogeneous union of two Grothendieck signatures

-- the left signature determines the result logic

gsigLeftUnion :: LogicGraph -> G_sign -> G_sign -> Result G_sign

gsigLeftUnion lg gsig1@(G_sign lid1 sigma1) gsig2@(G_sign lid2 sigma2) =

if language_name lid1 == language_name lid2

then homogeneousGsigUnion gsig1 gsig2

else do

GMorphism incl _ _ <- ginclusion lg

(G_sign lid2 (empty_signature lid2))

(G_sign lid1 (empty_signature lid1))

let lid1' = targetLogic incl

lid2' = sourceLogic incl

sigma1' <- coerce lid1 lid1' sigma1

sigma2' <- coerce lid2 lid2' sigma2

(sigma2'',_) <- maybeToMonad "gsigLeftUnion: signature mapping failed"

(map_sign incl sigma2') -- where to put axioms???

sigma3 <- signature_union lid1' sigma1' sigma2''

return (G_sign lid1' sigma3)

-- | homogeneous Union of two Grothendieck signatures

homogeneousGsigUnion :: G_sign -> G_sign -> Result G_sign

homogeneousGsigUnion (G_sign lid1 sigma1) (G_sign lid2 sigma2) = do

sigma2' <- coerce lid2 lid1 sigma2

sigma3 <- signature_union lid1 sigma1 sigma2'

return (G_sign lid1 sigma3)

-- | homogeneous Union of a list of Grothendieck signatures

homogeneousGsigManyUnion :: [G_sign] -> Result G_sign

homogeneousGsigManyUnion [] =

fail "homogeneous union of emtpy list of signatures"

homogeneousGsigManyUnion (G_sign lid sigma : gsigmas) = do

sigmas <- let coerce_lid (G_sign lid1 sigma1) =

coerce lid lid1 sigma1

in sequence (map coerce_lid gsigmas)

bigSigma <- let sig_union s1 s2 = do

s1' <- s1

signature_union lid s1' s2

in foldl sig_union (return sigma) sigmas

return (G_sign lid bigSigma)

-- | homogeneous Union of a list of morphisms

homogeneousMorManyUnion :: [G_morphism] -> Result G_morphism

homogeneousMorManyUnion [] =

fail "homogeneous union of emtpy list of morphisms"

homogeneousMorManyUnion (G_morphism lid mor : gmors) = do

mors <- let coerce_lid (G_morphism lid1 mor1) =

coerce lid lid1 mor1

in sequence (map coerce_lid gmors)

bigMor <- let mor_union s1 s2 = do

s1' <- s1

morphism_union lid s1' s2

in foldl mor_union (return mor) mors

return (G_morphism lid bigMor)

-- | inclusion between two logics

logicInclusion :: LogicGraph -> AnyLogic -> AnyLogic -> Result AnyComorphism

logicInclusion logicGraph (Logic lid1) (Logic lid2) =

let ln1 = language_name lid1

ln2 = language_name lid2 in

if ln1==ln2 then

return (Comorphism (IdComorphism lid1 (top_sublogic lid1)))

else case Map.lookup (ln1,ln2) (inclusions logicGraph) of

Just (Comorphism i) ->

return (Comorphism i)

Nothing ->

fail ("No inclusion from "++ln1++" to "++ln2++" found")

-- | inclusion morphism between two Grothendieck signatures

ginclusion :: LogicGraph -> G_sign -> G_sign -> Result GMorphism

ginclusion logicGraph (G_sign lid1 sigma1) (G_sign lid2 sigma2) = do

Comorphism i <- logicInclusion logicGraph (Logic lid1) (Logic lid2)

sigma1' <- rcoerce lid1 (sourceLogic i) (newPos "u" 0 0) sigma1

(sigma1'',_) <- maybeToResult (newPos "w" 0 0)

"ginclusion: signature map failed"

(map_sign i sigma1')

sigma2' <- rcoerce lid2 (targetLogic i) (newPos "v" 0 0) sigma2

mor <- inclusion (targetLogic i) sigma1'' sigma2'

return (GMorphism i sigma1' mor)

-- | Composition of two Grothendieck signature morphisms

-- | with itermediate inclusion

compInclusion :: LogicGraph -> GMorphism -> GMorphism -> Result GMorphism

compInclusion lg mor1 mor2 = do

incl <- ginclusion lg (cod Grothendieck mor1) (dom Grothendieck mor2)

mor <- maybeToResult nullPos

"compInclusion: composition falied" $ comp Grothendieck mor1 incl

maybeToResult nullPos

"compInclusion: composition falied" $ comp Grothendieck mor mor2

-- | Composition of two Grothendieck signature morphisms

-- | with itermediate homogeneous inclusion

compHomInclusion :: GMorphism -> GMorphism -> Result GMorphism

compHomInclusion mor1 mor2 = compInclusion emptyLogicGraph mor1 mor2

-- | Translation of a G_l_sentence_list along a GMorphism

translateG_l_sentence_list :: GMorphism -> G_l_sentence_list

-> Result G_l_sentence_list

translateG_l_sentence_list (GMorphism cid sign1 morphism2)

(G_l_sentence_list lid sens) = do

let tlid = targetLogic cid

--(sigma2,_) <- map_sign cid sign1

sens' <- coerce lid (sourceLogic cid) sens

let sens'' = mapMaybe (mapNamedM (map_sentence cid sign1)) $ sens'

sens''' <- sequence $ map (mapNamedM (map_sen tlid morphism2)) $ sens''

return (G_l_sentence_list tlid sens''')

-- | Join two G_l_sentence_list's

joinG_l_sentence_list :: G_l_sentence_list -> G_l_sentence_list

-> Maybe G_l_sentence_list

joinG_l_sentence_list (G_l_sentence_list lid1 sens1)

(G_l_sentence_list lid2 sens2) = do

sens2' <- coerce lid1 lid2 sens2

return (G_l_sentence_list lid1 (sens1++sens2'))

-- | Flatten a list of G_l_sentence_list's

flatG_l_sentence_list :: [G_l_sentence_list] -> Maybe G_l_sentence_list

flatG_l_sentence_list [] = Nothing

flatG_l_sentence_list (gl:gls) = foldM joinG_l_sentence_list gl gls

-- | Find all (composites of) comorphisms starting from a given logic

findComorphismPaths :: LogicGraph -> G_sublogics -> [AnyComorphism]

findComorphismPaths lg (G_sublogics lid sub) =

List.nub $ map fst $ iterateComp (0::Int) [(idc,[idc])]

where

idc = Comorphism (IdComorphism lid sub)

coMors = Map.elems $ comorphisms lg

-- compute possible compositions, but only up to depth 5

iterateComp n (l::[(AnyComorphism,[AnyComorphism])]) =

if n>5 || l==newL then newL else iterateComp (n+1) newL

where

newL = List.nub (l ++ (concat (map extend l)))

-- extend comorphism list in all directions, but no cylces

extend (coMor,comps::[AnyComorphism]) =

let addCoMor c =

case compComorphism coMor c of

Nothing -> Nothing

Just c1 -> Just (c1,c:comps)

in catMaybes $ map addCoMor $ filter (not . (`elem` comps)) $ coMors

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

-- Provers

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

-- | Grothendieck sublogics

data G_prover = forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

G_prover lid (Prover sign sentence proof_tree symbol)

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

-- Coercion

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

-- | coerce a theory into a "different" logic

coerceTheory :: forall lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree .

Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

lid -> G_theory -> Result (sign, [Named sentence])

coerceTheory lid (G_theory lid2 sign2 sens2)

= rcoerce lid lid2 nullPos (sign2,sens2)