{-|

Module : $Header$

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

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

Maintainer : hets@tzi.de

Stability : provisional

Portability : non-portable (via Logic)

Provides data structures for institution comorphisms.

These are just collections of

functions between (some of) the types of logics.

-}

{- References: see Logic.hs

Todo:

Weak amalgamability, also for comorphisms

comorphism modifications

comorphisms out of sublogic relationships

restrictions of comorphisms to sublogics

morphisms and other translations via spans

-}

module Logic.Comorphism where

import Logic.Logic

import qualified Common.Lib.Set as Set

import Common.Result

import Common.AS_Annotation

import Data.Maybe

class (Language cid,

Logic lid1 sublogics1

basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1,

Logic 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

| cid -> lid1, cid -> lid2

where

-- source and target logic and sublogic

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

-- the target sublogic is the resulting one

sourceLogic :: cid -> lid1

sourceSublogic :: cid -> sublogics1

targetLogic :: cid -> lid2

targetSublogic :: cid -> sublogics2

-- finer information of target sublogics corresponding to source sublogics

mapSublogic :: cid -> sublogics1 -> sublogics2

-- default implementation

mapSublogic cid _ = targetSublogic cid

-- the translation functions are partial

-- because the target may be a sublanguage

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

-- cover theoroidal comorphisms as well

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

-> Result (sign2,[Named sentence2])

map_morphism :: cid -> morphism1 -> Result morphism2

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

-- also covers semi-comorphisms

-- with no sentence translation

-- - but these are spans!

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

constituents :: cid -> [String]

-- default implementation

constituents cid = [language_name cid]

map_sign :: 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

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

map_sign cid sign = map_theory cid (sign,[])

simpleTheoryMapping :: (sign1 -> sign2) -> (sentence1 -> sentence2)

-> (sign1, [Named sentence1])

-> (sign2, [Named sentence2])

simpleTheoryMapping mapSig mapSen (sign,sens) =

(mapSig sign, map (mapNamed mapSen) sens)

mkTheoryMapping :: (Monad m) => (sign1 -> m (sign2, [Named sentence2]))

-> (sign1 -> sentence1 -> m sentence2)

-> (sign1, [Named sentence1])

-> m (sign2, [Named sentence2])

mkTheoryMapping mapSig mapSen (sign,sens) = do

(sign',sens') <- mapSig sign

sens'' <- mapM (mapNamedM $ mapSen sign) sens

return (sign',sens'++sens'')

data IdComorphism lid sublogics =

IdComorphism lid sublogics

instance Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

Show (IdComorphism lid sublogics)

where

show = language_name

instance Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

Language (IdComorphism lid sublogics) where

language_name (IdComorphism lid sub) =

case sublogic_names lid sub of

[] -> error "language_name IdComorphism"

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

instance Logic lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree =>

Comorphism (IdComorphism lid sublogics)

lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree

lid sublogics

basic_spec sentence symb_items symb_map_items

sign morphism symbol raw_symbol proof_tree

where

sourceLogic (IdComorphism lid _sub) = lid

targetLogic (IdComorphism lid _sub) = lid

sourceSublogic (IdComorphism _lid sub) = sub

targetSublogic (IdComorphism _lid sub) = sub

mapSublogic _ = id

map_theory _ = return

map_morphism _ = return

map_sentence _ = \_ -> return

map_symbol _ = Set.singleton

constituents _ = []

data CompComorphism cid1 cid2 = CompComorphism cid1 cid2 deriving Show

instance (Language cid1, Language cid2)

=> Language (CompComorphism cid1 cid2) where

language_name (CompComorphism cid1 cid2) =

language_name cid1++ ";" ++language_name cid2

instance (Comorphism cid1

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 cid2

lid4 sublogics4 basic_spec4 sentence4 symb_items4 symb_map_items4

sign4 morphism4 symbol4 raw_symbol4 proof_tree4

lid3 sublogics3 basic_spec3 sentence3 symb_items3 symb_map_items3

sign3 morphism3 symbol3 raw_symbol3 proof_tree3)

=> Comorphism (CompComorphism cid1 cid2)

lid1 sublogics1 basic_spec1 sentence1 symb_items1 symb_map_items1

sign1 morphism1 symbol1 raw_symbol1 proof_tree1

lid3 sublogics3 basic_spec3 sentence3 symb_items3 symb_map_items3

sign3 morphism3 symbol3 raw_symbol3 proof_tree3 where

sourceLogic (CompComorphism cid1 _) =

sourceLogic cid1

targetLogic (CompComorphism _ cid2) =

targetLogic cid2

sourceSublogic (CompComorphism cid1 _) =

sourceSublogic cid1

targetSublogic (CompComorphism cid1 cid2) =

mapSublogic cid2

(idcoerce (targetLogic cid1) (sourceLogic cid2)

(targetSublogic cid1))

mapSublogic (CompComorphism cid1 cid2) =

mapSublogic cid2

. idcoerce (targetLogic cid1) (sourceLogic cid2)

. mapSublogic cid1

map_sentence (CompComorphism cid1 cid2) =

\si1 se1 ->

do (si2,_) <- map_sign cid1 si1

se2 <- map_sentence cid1 si1 se1

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

"Mapping sentence along comorphism" (si2, se2)

map_sentence cid2 si2' se2'

map_theory (CompComorphism cid1 cid2) =

\ti1 ->

do ti2 <- map_theory cid1 ti1

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

"Mapping theory along comorphism" ti2

map_theory cid2 ti2'

map_morphism (CompComorphism cid1 cid2) = \ m1 ->

do m2 <- map_morphism cid1 m1

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

"Mapping signature morphism along comorphism"m2

map_morphism cid2 m3

map_symbol (CompComorphism cid1 cid2) = \ s1 ->

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

"Mapping symbol along comorphism"

in Set.unions

(map (map_symbol cid2 . mycast)

(Set.toList (map_symbol cid1 s1)))

constituents (CompComorphism cid1 cid2) =

constituents cid1 ++ constituents cid2