306763c67bb99228487345b32ab8c5c6cd41f23cChristian Maeder{-|

306763c67bb99228487345b32ab8c5c6cd41f23cChristian Maeder

306763c67bb99228487345b32ab8c5c6cd41f23cChristian MaederModule : $Header$

306763c67bb99228487345b32ab8c5c6cd41f23cChristian MaederCopyright : (c) Till Mossakowski, Uni Bremen 2002-2004

306763c67bb99228487345b32ab8c5c6cd41f23cChristian MaederLicense : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

306763c67bb99228487345b32ab8c5c6cd41f23cChristian MaederMaintainer : till@tzi.de

306763c67bb99228487345b32ab8c5c6cd41f23cChristian MaederStability : provisional

306763c67bb99228487345b32ab8c5c6cd41f23cChristian MaederPortability : non-portable (via Logic)

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

44fb55f639914f4f531641f32dd4904f15c510a4Till MossakowskiProvides data structures for institution comorphisms.

44fb55f639914f4f531641f32dd4904f15c510a4Till Mossakowski These are just collections of

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski functions between (some of) the types of logics.

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

306763c67bb99228487345b32ab8c5c6cd41f23cChristian Maeder-}

306763c67bb99228487345b32ab8c5c6cd41f23cChristian Maeder

306763c67bb99228487345b32ab8c5c6cd41f23cChristian Maeder{- References: see Logic.hs

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski Todo:

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski Weak amalgamability, also for comorphisms

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski comorphism modifications

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski comorphisms out of sublogic relationships

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski restrictions of comorphisms to sublogics

ae7058143db9e9993b5eff70bd6b7aede7cec658Till Mossakowski morphisms and other translations via spans

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski-}

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowskimodule Logic.Comorphism where

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowskiimport Logic.Logic

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowskiimport qualified Common.Lib.Set as Set

a89e661aad28f1b39f4fc9f9f9a4d46074234123Christian Maederimport Common.Result

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maederimport Common.AS_Annotation

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowskiimport Data.Maybe

9e2e744c6b967c3f5f581acf01c13769b6769285Till Mossakowski

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maederclass (Language cid,

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski Logic lid1 sublogics1

59fa9b1349ae1e001d996da732c4ac805c2938e2Christian Maeder basic_spec1 sentence1 symb_items1 symb_map_items1

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign1 morphism1 symbol1 raw_symbol1 proof_tree1,

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski Logic lid2 sublogics2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski basic_spec2 sentence2 symb_items2 symb_map_items2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign2 morphism2 symbol2 raw_symbol2 proof_tree2) =>

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski Comorphism cid

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign1 morphism1 symbol1 raw_symbol1 proof_tree1

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign2 morphism2 symbol2 raw_symbol2 proof_tree2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski | cid -> lid1, cid -> lid2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder where

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder -- source and target logic and sublogic

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski -- the source sublogic is the maximal one for which the comorphism works

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski -- the target sublogic is the resulting one

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski sourceLogic :: cid -> lid1

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski sourceSublogic :: cid -> sublogics1

4184cb191a9081cb2a9cf3ef5f060f56f0ca5922Till Mossakowski targetLogic :: cid -> lid2

8731f7b93b26083dc34a2c0937cd6493b42f2c2cTill Mossakowski targetSublogic :: cid -> sublogics2

4184cb191a9081cb2a9cf3ef5f060f56f0ca5922Till Mossakowski -- finer information of target sublogics corresponding to source sublogics

8731f7b93b26083dc34a2c0937cd6493b42f2c2cTill Mossakowski mapSublogic :: cid -> sublogics1 -> sublogics2

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski -- default implementation

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski mapSublogic cid _ = targetSublogic cid

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski -- the translation functions are partial

2ecf6cfb90e84d40f224cda5d92c191182c976d2Till Mossakowski -- because the target may be a sublanguage

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski -- map_basic_spec :: cid -> basic_spec1 -> Result basic_spec2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski -- cover theoroidal comorphisms as well

a89e661aad28f1b39f4fc9f9f9a4d46074234123Christian Maeder map_theory :: cid -> (sign1,[Named sentence1])

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski -> Result (sign2,[Named sentence2])

5d6e7ea3bd14fc987436cff0f542393ea9ba34bbTill Mossakowski map_morphism :: cid -> morphism1 -> Result morphism2

a89e661aad28f1b39f4fc9f9f9a4d46074234123Christian Maeder map_sentence :: cid -> sign1 -> sentence1 -> Result sentence2

a89e661aad28f1b39f4fc9f9f9a4d46074234123Christian Maeder -- also covers semi-comorphisms

a89e661aad28f1b39f4fc9f9f9a4d46074234123Christian Maeder -- with no sentence translation

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski -- - but these are spans!

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski map_symbol :: cid -> symbol1 -> Set.Set symbol2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski constituents :: cid -> [String]

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski -- default implementation

0e51a998b1b213654c7a9eca451562041971f100Till Mossakowski constituents cid = [language_name cid]

0e51a998b1b213654c7a9eca451562041971f100Till Mossakowski

0e51a998b1b213654c7a9eca451562041971f100Till Mossakowskimap_sign :: Comorphism cid

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder sign1 morphism1 symbol1 raw_symbol1 proof_tree1

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder sign2 morphism2 symbol2 raw_symbol2 proof_tree2

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder => cid -> sign1 -> Result (sign2,[Named sentence2])

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maedermap_sign cid sign = map_theory cid (sign,[])

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder

19298cbfd6ee2abd904f3181af7760b965b822c3Christian MaedersimpleTheoryMapping :: (sign1 -> sign2) -> (sentence1 -> sentence2)

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder -> (sign1, [Named sentence1])

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder -> (sign2, [Named sentence2])

19298cbfd6ee2abd904f3181af7760b965b822c3Christian MaedersimpleTheoryMapping mapSig mapSen (sign,sens) =

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder (mapSig sign, map (mapNamed mapSen) sens)

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder

19298cbfd6ee2abd904f3181af7760b965b822c3Christian MaedermkTheoryMapping :: (Monad m) => (sign1 -> m (sign2, [Named sentence2]))

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder -> (sign1 -> sentence1 -> m sentence2)

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder -> (sign1, [Named sentence1])

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder -> m (sign2, [Named sentence2])

19298cbfd6ee2abd904f3181af7760b965b822c3Christian MaedermkTheoryMapping mapSig mapSen (sign,sens) = do

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder (sign',sens') <- mapSig sign

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder sens'' <- mapM (mapNamedM $ mapSen sign) sens

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder return (sign',sens'++sens'')

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maederdata IdComorphism lid sublogics =

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder IdComorphism lid sublogics

586af0e9490a14dd3075095692b584c652584875Till Mossakowski

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowskiinstance Logic lid sublogics

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowski basic_spec sentence symb_items symb_map_items

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowski sign morphism symbol raw_symbol proof_tree =>

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowski Show (IdComorphism lid sublogics)

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowski where

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowski show = language_name

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowski

797595aad6dfd626bc1c9df52616f1ac4235c669Till Mossakowskiinstance Logic lid sublogics

933baca0720dae81434de384b32a93b47e754d09Christian Maeder basic_spec sentence symb_items symb_map_items

8db2d2c5a8df6dd6d7302bc59577150b87237940Till Mossakowski sign morphism symbol raw_symbol proof_tree =>

8db2d2c5a8df6dd6d7302bc59577150b87237940Till Mossakowski Language (IdComorphism lid sublogics) where

933baca0720dae81434de384b32a93b47e754d09Christian Maeder language_name (IdComorphism lid sub) =

586af0e9490a14dd3075095692b584c652584875Till Mossakowski case sublogic_names lid sub of

59fa9b1349ae1e001d996da732c4ac805c2938e2Christian Maeder [] -> error "language_name IdComorphism"

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski h : _ -> "id_" ++ language_name lid ++ "." ++ h

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowskiinstance Logic lid sublogics

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski basic_spec sentence symb_items symb_map_items

586af0e9490a14dd3075095692b584c652584875Till Mossakowski sign morphism symbol raw_symbol proof_tree =>

586af0e9490a14dd3075095692b584c652584875Till Mossakowski Comorphism (IdComorphism lid sublogics)

933baca0720dae81434de384b32a93b47e754d09Christian Maeder lid sublogics

933baca0720dae81434de384b32a93b47e754d09Christian Maeder basic_spec sentence symb_items symb_map_items

933baca0720dae81434de384b32a93b47e754d09Christian Maeder sign morphism symbol raw_symbol proof_tree

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski lid sublogics

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski basic_spec sentence symb_items symb_map_items

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign morphism symbol raw_symbol proof_tree

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski where

586af0e9490a14dd3075095692b584c652584875Till Mossakowski sourceLogic (IdComorphism lid _sub) = lid

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski targetLogic (IdComorphism lid _sub) = lid

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sourceSublogic (IdComorphism _lid sub) = sub

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski targetSublogic (IdComorphism _lid sub) = sub

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski mapSublogic _ = id

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski map_theory _ = return

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski map_morphism _ = return

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski map_sentence _ = \_ -> return

933baca0720dae81434de384b32a93b47e754d09Christian Maeder map_symbol _ = Set.singleton

933baca0720dae81434de384b32a93b47e754d09Christian Maeder constituents _ = []

933baca0720dae81434de384b32a93b47e754d09Christian Maeder

933baca0720dae81434de384b32a93b47e754d09Christian Maederdata CompComorphism cid1 cid2 = CompComorphism cid1 cid2 deriving Show

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maederinstance (Language cid1, Language cid2)

a89e661aad28f1b39f4fc9f9f9a4d46074234123Christian Maeder => Language (CompComorphism cid1 cid2) where

a89e661aad28f1b39f4fc9f9f9a4d46074234123Christian Maeder language_name (CompComorphism cid1 cid2) =

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski language_name cid1++ ";" ++language_name cid2

0e51a998b1b213654c7a9eca451562041971f100Till Mossakowski

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maederinstance (Comorphism cid1

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign1 morphism1 symbol1 raw_symbol1 proof_tree1

8db2d2c5a8df6dd6d7302bc59577150b87237940Till Mossakowski lid2 sublogics2 basic_spec2 sentence2 symb_items2 symb_map_items2

933baca0720dae81434de384b32a93b47e754d09Christian Maeder sign2 morphism2 symbol2 raw_symbol2 proof_tree2,

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder Comorphism cid2

59fa9b1349ae1e001d996da732c4ac805c2938e2Christian Maeder lid4 sublogics4 basic_spec4 sentence4 symb_items4 symb_map_items4

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign4 morphism4 symbol4 raw_symbol4 proof_tree4

ca8550c6d47234042130bdc10a152806ecbc9832Christian Maeder lid3 sublogics3 basic_spec3 sentence3 symb_items3 symb_map_items3

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder sign3 morphism3 symbol3 raw_symbol3 proof_tree3)

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski => Comorphism (CompComorphism cid1 cid2)

ca8550c6d47234042130bdc10a152806ecbc9832Christian Maeder lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign1 morphism1 symbol1 raw_symbol1 proof_tree1

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder lid3 sublogics3 basic_spec3 sentence3 symb_items3 symb_map_items3

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sign3 morphism3 symbol3 raw_symbol3 proof_tree3 where

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sourceLogic (CompComorphism cid1 _) =

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sourceLogic cid1

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski targetLogic (CompComorphism _ cid2) =

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski targetLogic cid2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski sourceSublogic (CompComorphism cid1 _) =

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder sourceSublogic cid1

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder targetSublogic (CompComorphism cid1 cid2) =

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski mapSublogic cid2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski (idcoerce (targetLogic cid1) (sourceLogic cid2)

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder (targetSublogic cid1))

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski mapSublogic (CompComorphism cid1 cid2) =

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski mapSublogic cid2

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski . idcoerce (targetLogic cid1) (sourceLogic cid2)

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder . mapSublogic cid1

f7819aa9d183836144a98c70d4fa7d65e31cb513Till Mossakowski map_sentence (CompComorphism cid1 cid2) =

f7819aa9d183836144a98c70d4fa7d65e31cb513Till Mossakowski \si1 se1 ->

f7819aa9d183836144a98c70d4fa7d65e31cb513Till Mossakowski do (si2,_) <- map_sign cid1 si1

f7819aa9d183836144a98c70d4fa7d65e31cb513Till Mossakowski se2 <- map_sentence cid1 si1 se1

8731f7b93b26083dc34a2c0937cd6493b42f2c2cTill Mossakowski (si2', se2') <- mcoerce (targetLogic cid1) (sourceLogic cid2)

8731f7b93b26083dc34a2c0937cd6493b42f2c2cTill Mossakowski "Mapping sentence along comorphism" (si2, se2)

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski map_sentence cid2 si2' se2'

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski map_theory (CompComorphism cid1 cid2) =

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski \ti1 ->

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski do ti2 <- map_theory cid1 ti1

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski ti2' <- mcoerce (targetLogic cid1) (sourceLogic cid2)

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski "Mapping theory along comorphism" ti2

f2a87c712ea3cd13f86a95cae738f861f6c4a908Till Mossakowski map_theory cid2 ti2'

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski map_morphism (CompComorphism cid1 cid2) = \ m1 ->

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski do m2 <- map_morphism cid1 m1

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski m3 <- mcoerce (targetLogic cid1) (sourceLogic cid2)

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder "Mapping signature morphism along comorphism"m2

19298cbfd6ee2abd904f3181af7760b965b822c3Christian Maeder map_morphism cid2 m3

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder

e9249d3ecd51a2b6a966a58669953e58d703adc6Till Mossakowski map_symbol (CompComorphism cid1 cid2) = \ s1 ->

5bb3727ef464d9f08ab0decb2d4a59c1352a389eChristian Maeder let mycast = fromJust . mcoerce (targetLogic cid1) (sourceLogic cid2)

5bb3727ef464d9f08ab0decb2d4a59c1352a389eChristian Maeder "Mapping symbol along comorphism"

5bb3727ef464d9f08ab0decb2d4a59c1352a389eChristian Maeder in Set.unions

9d34a8049237647d0188ee2ec88db2dc45f1f848Till Mossakowski (map (map_symbol cid2 . mycast)

9d34a8049237647d0188ee2ec88db2dc45f1f848Till Mossakowski (Set.toList (map_symbol cid1 s1)))

5bb3727ef464d9f08ab0decb2d4a59c1352a389eChristian Maeder constituents (CompComorphism cid1 cid2) =

5bb3727ef464d9f08ab0decb2d4a59c1352a389eChristian Maeder constituents cid1 ++ constituents cid2

d85e3f253f6af237c4b70bbfacb1bfecb5cfa678Christian Maeder