{-# OPTIONS -fallow-overlapping-instances -fallow-incoherent-instances #-}

{- |

Module : $Header$

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

License : similar to LGPL, see HetCATS/LICENSE.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.

This module heavily works with existential types, see

<http://haskell.org/hawiki/ExistentialTypes> and chapter 7 of /Heterogeneous

specification and the heterogeneous tool set/

(<http://www.tzi.de/~till/papers/habil.ps>).

References:

R. Diaconescu:

Grothendieck institutions

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

T. Mossakowski:

Comorphism-based Grothendieck institutions.

In K. Diks, W. Rytter (Eds.), Mathematical foundations of computer science,

LNCS 2420, pp. 593-604

T. Mossakowski:

Heterogeneous specification and the heterogeneous tool set.

Todo:

compComorphism: cancellation of id comorphisms if target sublogic is

not increased

gWeaklyAmalgamableCocone

Transportability for heterogeneous morphisms

-}

module Logic.Grothendieck where

import Logic.Logic

import Logic.Prover

import Logic.Comorphism

import Logic.Morphism

import Logic.Coerce

import Common.PrettyPrint

import Common.Lib.Pretty

import qualified Data.Graph.Inductive.Tree as Tree

import qualified Common.Lib.Map as Map

import qualified Common.Lib.Set as Set

import Common.Result

import Common.DynamicUtils

import Data.Dynamic

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 PrettyPrint G_basic_spec where

printText0 ga (G_basic_spec _ s) = printText0 ga s

-- | 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) =

coerceSign i1 i2 "Eq G_sign" 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) $ coerceSign i2 i1 "is_subgsign" sigma2

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)

-- | 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 PrettyPrint G_symbol where

printText0 ga (G_symbol _ s) = printText0 ga s

instance Eq G_symbol where

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

language_name i1 == language_name i2 && coerceSymbol i1 i2 s1 == 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 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) =

coerceSymbItemsList i1 i2 "Eq G_symb_items_list" 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 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) =

coerceSymbMapItemsList i1 i2 "Eq G_symb_map_items_list" 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 (Tree.Gr 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) =

language_name lid1 == language_name lid2

&& coerceSublogic lid1 lid2 l1 == l2

instance Ord G_sublogics where

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

compare (coerceSublogic lid1 lid2 l1) l2

-- | 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

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

-- Existential types for the logic graph

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

--- Comorphisms ----

-- | 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 []

-- | compute the identity comorphism for a logic

idComorphism :: AnyLogic -> AnyComorphism

idComorphism (Logic lid) = Comorphism (IdComorphism lid (top_sublogic lid))

-- | 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 (Comorphism cid1) (Comorphism cid2) =

let l1 = targetLogic cid1

l2 = sourceLogic cid2 in

if language_name l1 == language_name l2 then

if coerceSublogic l1 l2 (targetSublogic cid1) <= 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)

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

" and "++language_name cid2)

--- Morphisms ---

-- | Existential type for morphisms

data AnyMorphism = 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 .

Morphism 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 =>

Morphism cid

{-

instance Eq AnyMorphism where

Morphism cid1 == Morphism cid2 =

constituents cid1 == constituents cid2

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

instance Show AnyMorphism where

show (Morphism cid) =

language_name cid

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

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

-}

tyconAnyMorphism :: TyCon

tyconAnyMorphism = mkTyCon "Logic.Grothendieck.AnyMorphism"

instance Typeable AnyMorphism where

typeOf _ = mkTyConApp tyconAnyMorphism []

-- | Logic graph

data LogicGraph = LogicGraph {

logics :: Map.Map String AnyLogic,

comorphisms :: Map.Map String AnyComorphism,

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

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

}

emptyLogicGraph :: LogicGraph

emptyLogicGraph = LogicGraph Map.empty 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

-- | union to two logics

logicUnion :: LogicGraph -> AnyLogic -> AnyLogic -> Result (AnyComorphism,AnyComorphism)

logicUnion lg l1@(Logic lid1) l2@(Logic lid2) =

case logicInclusion lg l1 l2 of

Result _ (Just c) -> return (c,idComorphism l2)

_ -> case logicInclusion lg l2 l1 of

Result _ (Just c) -> return (idComorphism l1,c)

_ -> case Map.lookup (ln1,ln2) (unions lg) of

Just u -> return u

Nothing -> case Map.lookup (ln2,ln1) (unions lg) of

Just (c2,c1) -> return (c1,c2)

Nothing -> fail ("Union of logics "++ln1++" and "++ln2++" does not exist")

where ln1 = language_name lid1

ln2 = language_name lid2

-- | split list at separator elements, avoid empty sublists

splitBy :: Eq a => a -> [a] -> [[a]]

splitBy x xs = let (l, r) = break (==x) xs in

(if null l then [] else [l]) ++ (if null r then [] else splitBy x $ tail r)

-- suffix "By" usually indicates a (a -> a -> Bool) argument instead of Eq

-- | 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)

return $ idComorphism l

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

$ Map.lookup name (comorphisms logicGraph)

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

-- 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

&& coerceSign (sourceLogic cid1) (sourceLogic cid2)

"Eq GMorphism.coerceSign" sigma1 == Just sigma2

&& coerceMorphism (targetLogic cid1) (targetLogic cid2)

"Eq GMorphism.coerceMorphism" mor1 == Just mor2

isHomogeneous :: GMorphism -> Bool

isHomogeneous (GMorphism cid _ _) =

isIdComorphism (Comorphism cid)

data Grothendieck = Grothendieck deriving Show

instance Language Grothendieck

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 lid2 = targetLogic r1

lid3 = sourceLogic r2

lid4 = targetLogic r2

mor1' <- coerceMorphism lid2 lid3 "Grothendieck.comp" 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 maybeResult $ 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

-- | Embedding of comorphisms as Grothendieck sig mors

gEmbedComorphism :: AnyComorphism -> G_sign -> Result GMorphism

gEmbedComorphism (Comorphism cid) (G_sign lid sig) = do

sig' <- coerceSign lid (sourceLogic cid) "gEmbedComorphism" sig

(sigTar,_) <- map_sign cid sig'

let lidTar = targetLogic cid

return (GMorphism cid sig'(ide lidTar sigTar))

-- | heterogeneous union of two Grothendieck signatures

gsigUnion :: LogicGraph -> G_sign -> G_sign -> Result G_sign

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

if language_name lid1 == language_name lid2

then homogeneousGsigUnion gsig1 gsig2

else do

(Comorphism cid1,Comorphism cid2) <- logicUnion lg (Logic lid1) (Logic lid2)

let lidS1 = sourceLogic cid1

lidS2 = sourceLogic cid2

lidT1 = targetLogic cid1

lidT2 = targetLogic cid2

sigma1' <- coerceSign lid1 lidS1 "Union of signaturesa" sigma1

sigma2' <- coerceSign lid2 lidS2 "Union of signaturesb" sigma2

(sigma1'',_) <- map_sign cid1 sigma1' -- where to put axioms???

(sigma2'',_) <- map_sign cid2 sigma2' -- where to put axioms???

sigma2''' <- coerceSign lidT2 lidT1 "Union of signaturesc" sigma2''

sigma3 <- signature_union lidT1 sigma1'' sigma2'''

return (G_sign lidT1 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' <- coerceSign lid2 lid1 "Union of signaturesd" sigma2

sigma3 <- signature_union lid1 sigma1 sigma2'

return (G_sign lid1 sigma3)

-- | union of a list of Grothendieck signatures

gsigManyUnion :: LogicGraph -> [G_sign] -> Result G_sign

gsigManyUnion _ [] =

fail "union of emtpy list of signatures"

gsigManyUnion lg (gsigma : gsigmas) =

foldM (gsigUnion lg) gsigma gsigmas

-- | homogeneous Union of a list of morphisms

homogeneousMorManyUnion :: [G_morphism] -> Result G_morphism

homogeneousMorManyUnion [] =

fail "homogeneous union of emtpy list of morphisms"

homogeneousMorManyUnion (gmor : gmors) =

foldM ( \ (G_morphism lid2 mor2) (G_morphism lid1 mor1) -> do

mor1' <- coerceMorphism lid1 lid2 "homogeneousMorManyUnion" mor1

mor <- morphism_union lid2 mor1' mor2

return (G_morphism lid2 mor)) gmor gmors

-- | inclusion between two logics

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

logicInclusion logicGraph l1@(Logic lid1) (Logic lid2) =

let ln1 = language_name lid1

ln2 = language_name lid2 in

if ln1==ln2 then

return (idComorphism l1)

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' <- coerceSign lid1 (sourceLogic i) "Inclusion of signatures" sigma1

(sigma1'',_) <- map_sign i sigma1'

sigma2' <- coerceSign lid2 (targetLogic i) "Inclusion of signatures" 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 <- comp Grothendieck mor1 incl

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

-- | 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 3

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

if n>3 || 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) =

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

-- | check transpotability of Grothendieck signature morphisms

-- | (currently returns false for heterogeneous morphisms)

isTransportable :: GMorphism -> Bool

isTransportable (GMorphism cid _ mor) =

isIdComorphism (Comorphism cid) && is_transportable (targetLogic cid) mor

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

-- Provers

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

-- | provers and consistency checkers for specific logics

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)

coerceProver ::

(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,

Monad m) => lid1 -> lid2 -> String -> Prover sign1 sentence1 proof_tree1

-> m (Prover sign2 sentence2 proof_tree2)

coerceProver l1 l2 msg m1 = primCoerce l1 l2 msg m1

data G_cons_checker = 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_cons_checker lid (ConsChecker sign sentence morphism proof_tree)

coerceConsChecker ::

(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,

Monad m) => lid1 -> lid2 -> String

-> ConsChecker sign1 sentence1 morphism1 proof_tree1

-> m (ConsChecker sign2 sentence2 morphism2 proof_tree2)

coerceConsChecker l1 l2 msg m1 = primCoerce l1 l2 msg m1