{- |

Module : $Header$

Description : static analysis of CASL (heterogeneous) structured specifications

Copyright : (c) Till Mossakowski and Uni Bremen 2003-2006

License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

Maintainer : till@tzi.de

Stability : provisional

Portability : non-portable (imports Logic.Grothendieck)

Static analysis of CASL (heterogeneous) structured specifications

Follows the verfication semantic rules in Chap. IV:4.7

of the CASL Reference Manual.

-}

{-

Todo:

analysis of basic specs: use union of sigs

analysis of instantiations:

if necessary, translate body along inclusion comorphism

Improve efficiency by storing local signature fragments only

Name views in devgraphs?

Issue warning for unions of non-disjoint signatures

(and offer tool for renaming?)

Check that translations and reductions do not effect local env

(Implement new semantics for revealing here)

Should we use institution independent analysis over the Grothendieck logic?

abstract syntax + devgraph would have to be changed to homogeneous case

logic translations are symbol maps in the Grothendieck logic

Problem with this approach: symbol functor goes into rel,

and induced_from_morphism gets difficult to implement

Unions need inclusion morphisms. Should these play a special role?

At least we need a function delivering the inclusion morphism

between two (sub)signatures.

In most logics, inclusions could be represented specially, such

that composition for them becomes fast.

Should we even identify an inclusion subcategory?

Then inclusions are represented by pair of signatures

(Non-inclusions could be specially displayed in the DG)

No optimization of heterogeneous unions!

(or use heterogeneous compInclusion in Proofs/Proof.hs)

(or perhaps abandon optimized unions at all and

replace compHomInclusion with comp Grothendieck? is this more efficient?)

Treatment of translations and reductions along logic translations

(see WADT 02 paper).

Open question:

may local env be translated, and even reduced, along logic translations?

if yes: how is local env linked to signature of resulting spec?

(important e.g. for checking that local env is not being renamed?)

does signature+comorphism suffice, such that c(local env)\subseteq sig?

if no: this means that only closed specs may be translated

Revealings without translations: just one arrow

Pushouts: only admissible within one logic?

Instantiations with formal parameter: add no new internal nodes

call extend_morphism

Optimizations:

Union nodes can be extended by a basic spec directly (no new node needed)

no new nodes for trivial translations

use foldM

Also: free, cofree nodes

Basic specs: if local env node is otherwise unused, overwrite it with

local sig+axioms

Ensure that just_struct option leads to disabling of various dg operations

(show sig, show mor, proving)

local: better error message for the following

spec GenCardinality [sort Subject,Object;

pred predicate : Subject * Object] =

%%Nat then

local {

Set [sort Object fit sort Elem |-> Object]

reveal Set[Object], #__, __eps__,

Nat,0,1,2,3,4,5,6,7,8,9,__@@__,__>=__,__<=__

then

op toSet : Subject -> Set [Object]

forall x : Subject; y : Object

. predicate (x,y) <=> y eps toSet(x)

} within

pred minCardinality(s: Subject;n: Nat) <=>

# toSet(s) >= n;

maxCardinality(s: Subject;n: Nat) <=>

# toSet(s) <= n;

cardinality(s: Subject;n: Nat) <=>

# toSet(s) = n

%%} hide Pos,toSet,Set[Object],#__,__eps__,__<=__,__>=__

end

-}

module Static.AnalysisStructured (ana_SPEC, ana_GENERICITY,

ana_VIEW_TYPE, ana_err, isStructured,

ana_RENAMING, ana_RESTRICTION,

homogenizeGM, extendMorphism)

where

import Driver.Options

import Logic.Logic

import Logic.Coerce

import Logic.Comorphism

import Logic.Grothendieck

import Logic.Prover

import Static.DevGraph

import Syntax.AS_Structured

import Common.Result

import Common.Id

import Common.AS_Annotation hiding (isAxiom,isDef)

import qualified Data.Set as Set

import qualified Data.Map as Map

import qualified Common.Lib.Rel as Rel(image, setInsert)

import Common.DocUtils

import Data.Graph.Inductive.Graph

import Data.Maybe

import Data.List hiding (union)

import Control.Monad

getMapAndMaxIndex :: (GlobalContext -> Map.Map Int a) -> GlobalContext

-> (Map.Map Int a, Int)

getMapAndMaxIndex f gctx = let m = f gctx in

(m, if Map.null m then 0 else fst $ Map.findMax m)

sigMapI :: GlobalContext -> (Map.Map Int G_sign, Int)

sigMapI = getMapAndMaxIndex sigMap

morMapI :: GlobalContext -> (Map.Map Int G_morphism, Int)

morMapI = getMapAndMaxIndex morMap

thMapI :: GlobalContext -> (Map.Map Int G_theory, Int)

thMapI = getMapAndMaxIndex thMap

insEdgeNub :: LEdge DGLinkLab -> DGraph -> DGraph

insEdgeNub (v, w, l) g =

if (l, w) `elem` s then g

else (p, v, l', (l, w) : s) & g'

where (Just (p, _, l', s), g') = match v g

-- | analyze a SPEC

-- Parameters: global context, local environment,

-- the SIMPLE_ID may be a name if the specification shall be named,

-- options: here we need the info: shall only the structure be analysed?

ana_SPEC :: LogicGraph -> GlobalContext -> MaybeNode -> NODE_NAME ->

HetcatsOpts -> SPEC -> Result (SPEC, NodeSig, GlobalContext)

ana_SPEC lg gctx nsig name opts sp =

let dg = devGraph gctx

in case sp of

Basic_spec (G_basic_spec lid bspec) ->

do G_sign lid' sigma' i1 <- return (getMaybeSig nsig)

sigma <- coerceSign lid' lid "Analysis of basic spec" sigma'

(bspec', sigma_complete, ax) <-

if isStructured opts

then return (bspec, empty_signature lid, [])

else do b <- maybeToMonad

("no basic analysis for logic "

++ language_name lid)

(basic_analysis lid)

b (bspec, sigma, globalAnnos gctx)

let (sgMap, s) = sigMapI gctx

(mrMap, m) = morMapI gctx

(tMap, t) = thMapI gctx

gsig = G_sign lid sigma_complete (s+1)

incl <- ginclusion lg (G_sign lid sigma i1) gsig

let gTh = G_theory lid sigma_complete (s+1) (toThSens ax) (t+1)

node_contents =

DGNode {

dgn_name = name,

dgn_theory = gTh,

-- no, not only the delta

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGBasic,

dgn_cons = None,

dgn_cons_status = LeftOpen }

node = getNewNode dg

dg' = insNode (node,node_contents) dg

incl' = updateMorIndex (m+1) incl

link = DGLink {

dgl_morphism = incl',

dgl_type = GlobalDef,

dgl_origin = DGExtension }

dg'' = case nsig of

EmptyNode _ -> dg'

JustNode (NodeSig n _) -> insEdgeNub (n,node,link) dg'

return (Basic_spec (G_basic_spec lid bspec'),

NodeSig node gsig,

gctx { devGraph = dg''

, sigMap = Map.insert (s+1) gsig sgMap

, thMap = Map.insert (t+1) gTh tMap

, morMap = Map.insert (m+1) (toG_morphism incl') mrMap})

Translation asp ren ->

do let sp1 = item asp

(sp1', NodeSig n' gsigma, gctx') <-

ana_SPEC lg gctx nsig (inc name) opts sp1

let (mrMap, m) = morMapI gctx'

mor <- ana_RENAMING lg nsig gsigma opts ren

-- ??? check that mor is identity on local env

let gsigma' = cod Grothendieck mor

-- ??? too simplistic for non-comorphism inter-logic translations

G_sign lid' gsig ind <- return gsigma'

let node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid' gsig ind noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGTranslation,

dgn_cons = None,

dgn_cons_status = LeftOpen }

dg' = devGraph gctx'

node = getNewNode dg'

mor' = updateMorIndex (m+1) mor

link = (n',node,DGLink {

dgl_morphism = mor',

dgl_type = GlobalDef,

dgl_origin = DGTranslation })

dg'' = insNode (node,node_contents) dg'

return (Translation (replaceAnnoted sp1' asp) ren,

NodeSig node gsigma',

gctx' { devGraph = insEdgeNub link dg''

, morMap = Map.insert (m+1) (toG_morphism mor') mrMap})

Reduction asp restr ->

do let sp1 = item asp

(sp1', NodeSig n' gsigma', gctx') <-

ana_SPEC lg gctx nsig (inc name) opts sp1

let gsigma = getMaybeSig nsig

dg' = devGraph gctx'

(mrMap, m) = morMapI gctx'

(hmor,tmor) <- ana_RESTRICTION dg gsigma gsigma' opts restr

-- we treat hiding and revealing differently

-- in order to keep the dg as simple as possible

let hmor' = updateMorIndex (m+1) hmor

case tmor of

Nothing ->

do let gsigma'' = dom Grothendieck hmor

-- ??? too simplistic for non-comorphism inter-logic reductions

G_sign lid' gsig ind <- return gsigma''

let node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid' gsig ind noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGHiding,

dgn_cons = None,

dgn_cons_status = LeftOpen }

node = getNewNode dg'

link = (n',node,DGLink {

dgl_morphism = hmor',

dgl_type = HidingDef,

dgl_origin = DGHiding })

dg'' = insNode (node,node_contents) dg'

return (Reduction (replaceAnnoted sp1' asp) restr,

NodeSig node gsigma'',

gctx' { devGraph = insEdgeNub link dg''

, morMap = Map.insert (m+1) (toG_morphism hmor')

mrMap

})

Just tmor' -> do

let gsigma1 = dom Grothendieck tmor'

gsigma'' = cod Grothendieck tmor'

-- ??? too simplistic for non-comorphism inter-logic reductions

G_sign lid1 gsig ind <- return gsigma1

G_sign lid'' gsig'' ind'' <- return gsigma''

-- the case with identity translation leads to a simpler dg

if tmor' == ide Grothendieck (dom Grothendieck tmor')

then do

let node1 = getNewNode dg'

node_contents1 = DGNode {

dgn_name = name,

dgn_theory = G_theory lid1 gsig ind noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGRevealing,

dgn_cons = None,

dgn_cons_status = LeftOpen }

link1 = (n',node1,DGLink {

dgl_morphism = hmor',

dgl_type = HidingDef,

dgl_origin = DGRevealing })

dg'' = insNode (node1,node_contents1) dg'

return (Reduction (replaceAnnoted sp1' asp) restr,

NodeSig node1 gsigma1,

gctx' { devGraph = insEdgeNub link1 dg''

, morMap = Map.insert (m+1) (toG_morphism hmor')

mrMap

})

else do

let [node1,node''] = newNodes 2 dg'

node_contents1 = DGNode {

dgn_name = extName "T" name,

dgn_theory = G_theory lid1 gsig ind noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGRevealing,

dgn_cons = None,

dgn_cons_status = LeftOpen }

link1 = (n',node1,DGLink {

dgl_morphism = hmor',

dgl_type = HidingDef,

dgl_origin = DGRevealing })

node_contents'' = DGNode {

dgn_name = name,

dgn_theory = G_theory lid'' gsig'' ind'' noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGRevealTranslation,

dgn_cons = None,

dgn_cons_status = LeftOpen }

link'' = (node1,node'',DGLink {

dgl_morphism = tmor',

dgl_type = GlobalDef,

dgl_origin = DGRevealTranslation })

return (Reduction (replaceAnnoted sp1' asp) restr,

NodeSig node'' gsigma'',

gctx' { devGraph = insEdgeNub link'' $

insNode (node'',node_contents'') $

insEdgeNub link1 $

insNode (node1,node_contents1) dg'

, morMap = Map.insert (m+1) (toG_morphism hmor')

mrMap

})

Union [] pos -> adjustPos pos $ fail $ "empty union"

Union asps pos ->

do let sps = map item asps

(sps', nsigs, gctx', _) <-

let ana r sp' = do

(sps1,nsigs,dg',n) <- r

(sp1,nsig',dg1) <- ana_SPEC lg dg' nsig n opts sp'

return (sp1:sps1,nsig':nsigs,dg1,inc n)

in foldl ana (return ([], [], gctx, extName "U" name)) sps

let nsigs' = reverse nsigs

dg' = devGraph gctx'

adj = adjustPos pos

(sgMap, s) = sigMapI gctx'

gbigSigma <- adj $ gsigManyUnion lg (map getSig nsigs')

G_sign lid' gsig _ <- return gbigSigma

gbigSigma' <- return $ G_sign lid' gsig (s+1)

let node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid' gsig (s+1) noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGUnion,

dgn_cons = None,

dgn_cons_status = LeftOpen }

node = getNewNode dg'

dg1 = insNode (node, node_contents) dg'

gctx1 = gctx' { devGraph = dg1

, sigMap = Map.insert (s+1) gbigSigma' sgMap }

insE gctxres (NodeSig n gsigma) = do

gctxl <- gctxres

let (mrMapl, ml) = morMapI gctxl

dgl = devGraph gctxl

incl <- adj $ ginclusion lg gsigma gbigSigma

let incl' = updateMorIndex (ml+1) incl

link = DGLink {

dgl_morphism = incl',

dgl_type = GlobalDef,

dgl_origin = DGUnion }

return (gctxl { devGraph = insEdgeNub (n,node,link) dgl

, morMap = Map.insert (ml+1)

(toG_morphism incl') mrMapl})

gctx2 <- foldl insE (return gctx1) nsigs'

return (Union (map (uncurry replaceAnnoted)

(zip (reverse sps') asps))

pos,

NodeSig node gbigSigma', gctx2)

Extension asps pos -> do

(sps',nsig1',dg1, _, _, _) <-

foldl ana_Extension (return ([], nsig, gctx, lg, opts, pos)) namedSps

case nsig1' of

EmptyNode _ -> fail "empty extension"

JustNode nsig1 -> return (Extension (map (uncurry replaceAnnoted)

(zip (reverse sps') asps))

pos, nsig1,dg1)

where

namedSps = zip (reverse (name: tail (take (length asps)

(iterate inc (extName "E" name)))))

asps

Free_spec asp poss ->

do let sp1 = item asp

(sp', NodeSig n' gsigma'@(G_sign lid' gsig ind), gctx') <-

ana_SPEC lg gctx nsig (inc name) opts sp1

let pos = poss

dg' = devGraph gctx'

(mrMap, m) = morMapI gctx'

incl <- adjustPos pos $ ginclusion lg (getMaybeSig nsig) gsigma'

let incl' = updateMorIndex (m+1) incl

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid' gsig ind noSens 0, -- delta is empty

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGFree,

dgn_cons = None,

dgn_cons_status = LeftOpen }

node = getNewNode dg'

link = (n',node,DGLink {

dgl_morphism = incl',

dgl_type = FreeDef nsig,

dgl_origin = DGFree })

return (Free_spec (replaceAnnoted sp' asp) poss,

NodeSig node gsigma',

gctx' { devGraph = insEdgeNub link $

insNode (node,node_contents) dg'

, morMap = Map.insert (m+1) (toG_morphism incl') mrMap})

Cofree_spec asp poss ->

do let sp1 = item asp

(sp', NodeSig n' gsigma'@(G_sign lid' gsig ind), gctx') <-

ana_SPEC lg gctx nsig (inc name) opts sp1

let pos = poss

dg' = devGraph gctx'

(mrMap, m) = morMapI gctx'

incl <- adjustPos pos $ ginclusion lg (getMaybeSig nsig) gsigma'

let incl' = updateMorIndex (m+1) incl

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid' gsig ind noSens 0, -- delta is empty

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGCofree,

dgn_cons = None,

dgn_cons_status = LeftOpen }

node = getNewNode dg'

link = (n',node,DGLink {

dgl_morphism = incl',

dgl_type = CofreeDef nsig,

dgl_origin = DGCofree })

return (Cofree_spec (replaceAnnoted sp' asp) poss,

NodeSig node gsigma',

gctx' { devGraph = insEdgeNub link $

insNode (node,node_contents) dg'

, morMap = Map.insert (m+1) (toG_morphism incl') mrMap})

Local_spec asp asp' poss ->

do let sp1 = item asp

sp1' = item asp'

(sp2, nsig'@(NodeSig _ (G_sign lid' sigma' _)), dg') <-

ana_SPEC lg gctx nsig (extName "L" name) opts sp1

(sp2', NodeSig n'' (G_sign lid'' sigma'' _), gctx'') <-

ana_SPEC lg dg' (JustNode nsig') (inc name) opts sp1'

let gsigma = getMaybeSig nsig

dg'' = devGraph gctx''

(sgMap, s) = sigMapI gctx''

(mrMap, m) = morMapI gctx''

G_sign lid sigma _<- return gsigma

sigma1 <- coerceSign lid' lid "Analysis of local spec" sigma'

sigma2 <- coerceSign lid'' lid "Analysis of local spec" sigma''

let sys = sym_of lid sigma

sys1 = sym_of lid sigma1

sys2 = sym_of lid sigma2

pos = poss

mor3 <- if isStructured opts then return (ide lid sigma2)

else adjustPos pos $ cogenerated_sign lid

(sys1 `Set.difference` sys) sigma2

let sigma3 = dom lid mor3

-- gsigma2 = G_sign lid sigma2

gsigma3 = G_sign lid sigma3 (s+1)

sys3 = sym_of lid sigma3

when (not( isStructured opts ||

sys2 `Set.difference` sys1 `Set.isSubsetOf` sys3))

$ plain_error () (

"attempt to hide the following symbols from the local environment:\n"

++ showDoc ((sys2 `Set.difference` sys1) `Set.difference` sys3) "")

pos

let node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid sigma3 (s+1) noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGLocal,

dgn_cons = None,

dgn_cons_status = LeftOpen }

node = getNewNode dg''

link = (n'', node, DGLink {

dgl_morphism = gEmbed2 gsigma3 (G_morphism lid mor3 (m+1)),

dgl_type = HidingDef,

dgl_origin = DGLocal })

return (Local_spec (replaceAnnoted sp2 asp)

(replaceAnnoted sp2' asp')

poss,

NodeSig node gsigma3,

gctx'' { devGraph = insEdgeNub link $

insNode (node,node_contents) dg''

, sigMap = Map.insert (s+1) gsigma3 sgMap

, morMap = Map.insert (m+1) (G_morphism lid mor3 (m+1))

mrMap

})

Closed_spec asp pos ->

do let sp1 = item asp

l = getLogic nsig

-- analyse spec with empty local env

(sp', NodeSig n' gsigma', gctx') <-

ana_SPEC lg gctx (EmptyNode l) (inc name) opts sp1

let gsigma = getMaybeSig nsig

adj = adjustPos pos

dg' = devGraph gctx'

(sgMap, s) = sigMapI gctx'

(mrMap, m) = morMapI gctx'

gsigma'' <- adj $ gsigUnion lg gsigma gsigma'

G_sign lid'' gsig'' _ <- return gsigma''

gsigma2 <- return $ G_sign lid'' gsig'' (s+1)

incl1 <- adj $ ginclusion lg gsigma gsigma2

incl2 <- adj $ ginclusion lg gsigma' gsigma2

let incl1' = updateMorIndex (m+1) incl1

incl2' = updateMorIndex (m+2) incl2

node = getNewNode dg'

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid'' gsig'' (s+1) noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGClosed,

dgn_cons = None,

dgn_cons_status = LeftOpen }

link1 = DGLink {

dgl_morphism = incl1',

dgl_type = GlobalDef,

dgl_origin = DGClosedLenv }

link2 = (n',node,DGLink {

dgl_morphism = incl2',

dgl_type = GlobalDef,

dgl_origin = DGClosed })

insLink1 = case nsig of

EmptyNode _ -> id

JustNode (NodeSig n _) -> insEdgeNub (n, node, link1)

morMap1 = Map.insert (m+1) (toG_morphism incl1') mrMap

morMap2 = Map.insert (m+2) (toG_morphism incl2') morMap1

return (Closed_spec (replaceAnnoted sp' asp) pos,

NodeSig node gsigma2,

gctx' { devGraph = insLink1 $

insEdgeNub link2 $

insNode (node,node_contents) dg'

, sigMap = Map.insert (s+1) gsigma2 sgMap

, morMap = morMap2})

Qualified_spec (Logic_name ln sublog) asp pos -> do

l <- lookupLogic "Static analysis: " (tokStr ln) lg

-- analyse spec with empty local env

(sp', NodeSig n' gsigma', gctx') <-

ana_SPEC lg gctx (EmptyNode l) (inc name) opts (item asp)

-- construct union with local env

let gsigma = getMaybeSig nsig

dg' = devGraph gctx'

adj = adjustPos pos

(sgMap, s) = sigMapI gctx'

(mrMap, m) = morMapI gctx'

gsigma'' <- adj $ gsigUnion lg gsigma gsigma'

G_sign lid'' gsig'' _ <- return gsigma''

gsigma2 <- return $ G_sign lid'' gsig'' (s+1)

incl1 <- adj $ ginclusion lg gsigma gsigma2

incl2 <- adj $ ginclusion lg gsigma' gsigma2

let incl1' = updateMorIndex (m+1) incl1

incl2' = updateMorIndex (m+2) incl2

node = getNewNode dg'

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid'' gsig'' (s+1) noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGLogicQual,

dgn_cons = None,

dgn_cons_status = LeftOpen }

link1 = DGLink {

dgl_morphism = incl1',

dgl_type = GlobalDef,

dgl_origin = DGLogicQualLenv }

link2 = (n',node,DGLink {

dgl_morphism = incl2',

dgl_type = GlobalDef,

dgl_origin = DGLogicQual })

insLink1 = case nsig of

EmptyNode _ -> id

JustNode (NodeSig n _) -> insEdgeNub (n, node, link1)

morMap1 = Map.insert (m+1) (toG_morphism incl1') mrMap

morMap2 = Map.insert (m+2) (toG_morphism incl2') morMap1

return (Qualified_spec (Logic_name ln sublog)

(replaceAnnoted sp' asp) pos,

NodeSig node gsigma2,

gctx' { devGraph = insLink1 $ insEdgeNub link2 $

insNode (node,node_contents) dg'

, sigMap = Map.insert (s+1) gsigma2 sgMap

, morMap = morMap2})

Group asp pos -> do

(sp',nsig',dg') <- ana_SPEC lg gctx nsig name opts (item asp)

return (Group (replaceAnnoted sp' asp) pos,nsig',dg')

Spec_inst spname afitargs pos -> do

let adj = adjustPos pos

spstr = tokStr spname

(sgMap, s) = sigMapI gctx

(mrMap, m) = morMapI gctx

case Map.lookup spname $ globalEnv gctx of

Nothing -> fatal_error

("Specification " ++ spstr ++ " not found") pos

Just (ViewEntry _) ->

fatal_error

(spstr ++ " is a view, not a specification") pos

Just (ArchEntry _) ->

fatal_error

(spstr ++

" is an architectural, not a structured specification") pos

Just (UnitEntry _) ->

fatal_error

(spstr ++

" is a unit specification, not a structured specification") pos

Just (RefEntry) ->

fatal_error

(spstr ++

" is a refinement specification, not a structured specification") pos

Just (SpecEntry gs@(imps,params,_,body@(NodeSig nB gsigmaB))) ->

case (\x y -> (x,x-y)) (length afitargs) (length params) of

-- the case without parameters leads to a simpler dg

(0,0) -> do

G_sign lid gsig _ <-

adj $ gsigUnion lg (getMaybeSig nsig) gsigmaB

let gsigma' = G_sign lid gsig (s+1)

case nsig of

-- the subcase with empty local env leads to an even simpler dg

EmptyNode _ ->

-- if the node shall not be named and the logic does not change,

if isInternal name && langNameSig gsigma'==langNameSig gsigmaB

-- then just return the body

then return (sp, body, gctx)

-- otherwise, we need to create a new one

else do

incl <- adj $ ginclusion lg gsigmaB gsigma'

let incl' = updateMorIndex (m+1) incl

node = getNewNode dg

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid gsig (s+1) noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGSpecInst spname,

dgn_cons = None,

dgn_cons_status = LeftOpen}

link = (nB,node,DGLink {

dgl_morphism = incl',

dgl_type = GlobalDef,

dgl_origin = DGSpecInst spname})

return (sp,

NodeSig node gsigma',

gctx { devGraph = insEdgeNub link $

insNode (node,node_contents) dg

, sigMap = Map.insert (s+1) gsigma' sgMap

, morMap = Map.insert (m+1) (toG_morphism incl')

mrMap})

-- the subcase with nonempty local env

JustNode (NodeSig n sigma) -> do

incl1 <- adj $ ginclusion lg sigma gsigma'

incl2 <- adj $ ginclusion lg gsigmaB gsigma'

let incl1' = updateMorIndex (m+1) incl1

incl2' = updateMorIndex (m+2) incl2

node = getNewNode dg

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lid gsig (s+1) noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGSpecInst spname,

dgn_cons = None,

dgn_cons_status = LeftOpen}

link1 = (n,node,DGLink {

dgl_morphism = incl1',

dgl_type = GlobalDef,

dgl_origin = DGSpecInst spname})

link2 = (nB,node,DGLink {

dgl_morphism = incl2',

dgl_type = GlobalDef,

dgl_origin = DGSpecInst spname})

morMap1 = Map.insert (m+1) (toG_morphism incl1') mrMap

morMap2 = Map.insert (m+2) (toG_morphism incl2') morMap1

return (sp,

NodeSig node gsigma',

gctx { devGraph = insEdgeNub link1 $

insEdgeNub link2 $

insNode (node,node_contents) dg

, sigMap = Map.insert (s+1) gsigma' sgMap

, morMap = morMap2})

-- now the case with parameters

(_,0) -> do

let fitargs = map item afitargs

(fitargs', gctx', args, _) <-

foldl anaFitArg (return ([], gctx, [], extName "A" name))

(zip params fitargs)

let actualargs = reverse args

dg' = devGraph gctx'

(gsigma',morDelta) <- adj $ apply_GS lg gs actualargs

gsigmaRes <- adj $ gsigUnion lg (getMaybeSig nsig) gsigma'

G_sign lidRes gsigRes _ <- return gsigmaRes

gsigmaRes' <- return $ G_sign lidRes gsigRes (s+1)

incl1 <- adj $ ginclusion lg (getMaybeSig nsig) gsigmaRes'

incl2 <- adj $ ginclusion lg gsigma' gsigmaRes'

let incl1' = updateMorIndex (m+1) incl1

incl2' = updateMorIndex (m+2) incl2

morDelta' <- comp Grothendieck (gEmbed morDelta) incl2'

let node = getNewNode dg'

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lidRes gsigRes (s+1) noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGSpecInst spname,

dgn_cons = None,

dgn_cons_status = LeftOpen}

link1 = DGLink {

dgl_morphism = incl1',

dgl_type = GlobalDef,

dgl_origin = DGSpecInst spname}

insLink1 = case nsig of

EmptyNode _ -> id

JustNode (NodeSig n _) -> insEdgeNub (n, node, link1)

link2 = (nB,node,DGLink {

dgl_morphism = morDelta',

dgl_type = GlobalDef,

dgl_origin = DGSpecInst spname})

parLinks = catMaybes (map (parLink gsigmaRes' node) actualargs)

morMap1 = Map.insert (m+1) (toG_morphism incl1') mrMap

morMap2 = Map.insert (m+2) (toG_morphism incl2') morMap1

return (Spec_inst spname

(map (uncurry replaceAnnoted)

(zip (reverse fitargs') afitargs))

pos,

NodeSig node gsigmaRes',

gctx' { devGraph = foldr insEdgeNub

(insLink1 $ insEdgeNub link2 $

insNode (node,node_contents) dg')

parLinks

, sigMap = Map.insert (s+1) gsigmaRes' sgMap

, morMap = morMap2})

where

anaFitArg res (nsig', fa) = do

(fas', dg1, args, name') <- res

(fa', dg', arg) <- ana_FIT_ARG lg dg1 spname imps nsig' opts name' fa

return (fa' : fas', dg', arg : args , inc name')

parLink gsigma' node (_mor_i, NodeSig nA_i sigA_i) = do

incl <- maybeResult $ ginclusion lg sigA_i gsigma'

let link = DGLink {

dgl_morphism = incl,

dgl_type = GlobalDef,

dgl_origin = DGFitSpec }

return (nA_i,node,link)

-- finally the case with conflicting numbers of formal and actual parameters

_ ->

fatal_error

(spstr ++ " expects " ++ show (length params) ++ " arguments"

++ " but was given " ++ show (length afitargs)) pos

Data (Logic lidD) (Logic lidP) asp1 asp2 pos ->

do let sp1 = item asp1

sp2 = item asp2

adj = adjustPos pos

Comorphism cid <- adj $ logicInclusion lg (Logic lidD) (Logic lidP)

let lidD' = sourceLogic cid

lidP' = targetLogic cid

(sp1', NodeSig n' (G_sign lid' sigma' _), gctx1) <-

ana_SPEC lg gctx (EmptyNode (Logic lidD)) (inc name) opts sp1

sigmaD <- adj $ coerceSign lid' lidD' "Analysis of data spec" sigma'

(sigmaD',sensD') <- adj $ map_sign cid sigmaD

let gsigmaD' = G_sign lidP' sigmaD' 0

dg1 = devGraph gctx1

node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lidP' sigmaD' 0 (toThSens sensD') 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGData,

dgn_cons = None,

dgn_cons_status = LeftOpen }

node = getNewNode dg1

link = (n',node,DGLink {

dgl_morphism = GMorphism cid sigmaD 0 (ide lidP' sigmaD') 0,

dgl_type = GlobalDef,

dgl_origin = DGData })

dg2 = insEdgeNub link $

insNode (node,node_contents) dg1

nsig2 = NodeSig node gsigmaD'

(sp2',nsig3,dg3) <-

ana_SPEC lg gctx1 { devGraph = dg2 } (JustNode nsig2) name opts sp2

return (Data (Logic lidD) (Logic lidP)

(replaceAnnoted sp1' asp1)

(replaceAnnoted sp2' asp2)

pos,

nsig3, dg3)

-- analysis of renamings

ana_ren1 :: LogicGraph -> MaybeNode -> Range -> GMorphism -> G_mapping

-> Result GMorphism

ana_ren1 _ lenv _pos (GMorphism r sigma ind1 mor _)

(G_symb_map (G_symb_map_items_list lid sis)) = do

let lid2 = targetLogic r

sis1 <- coerceSymbMapItemsList lid lid2 "Analysis of renaming" sis

rmap <- stat_symb_map_items lid2 sis1

mor1 <- induced_from_morphism lid2 rmap (cod lid2 mor)

case lenv of

EmptyNode _ -> return ()

JustNode (NodeSig _ (G_sign lidLenv sigmaLenv _)) -> do

-- needs to be changed for logic translations

sigmaLenv' <- coerceSign lidLenv lid2

"Analysis of renaming: logic translations not yet properly handeled"

sigmaLenv

let sysLenv = sym_of lid2 sigmaLenv'

m = symmap_of lid2 mor1

isChanged sy = case Map.lookup sy m of

Just sy' -> sy /= sy'

Nothing -> False

_forbiddenSys = Set.filter isChanged sysLenv

return ()

{- when (not (forbiddenSys == Set.empty)) $ plain_error () (

"attempt to rename the following symbols from the local environment:\n"

++ showDoc forbiddenSys "") pos

-}

mor2 <- comp lid2 mor mor1

return $ GMorphism r sigma ind1 mor2 0

ana_ren1 lg _ _ mor (G_logic_translation (Logic_code tok src tar pos1)) = do

let adj = adjustPos pos1

G_sign srcLid srcSig ind<- return (cod Grothendieck mor)

c <- adj $ case tok of

Just ctok -> do

Comorphism cid <- lookupComorphism (tokStr ctok) lg

when (isJust src && getLogicStr (fromJust src) /=

language_name (sourceLogic cid))

(fail (getLogicStr (fromJust src) ++

"is not the source logic of "

++ language_name cid))

when (isJust tar && getLogicStr (fromJust tar) /=

language_name (targetLogic cid))

(fail (getLogicStr (fromJust tar) ++

"is not the target logic of "

++ language_name cid))

return (Comorphism cid)

Nothing -> case tar of

Just (Logic_name l _) -> do

tarL <- lookupLogic "with logic: " (tokStr l) lg

logicInclusion lg (Logic srcLid) tarL

Nothing -> fail "with logic: cannot determine comorphism"

mor1 <- adj $ gEmbedComorphism c (G_sign srcLid srcSig ind)

adj $ comp Grothendieck mor mor1

where getLogicStr (Logic_name l _) = tokStr l

ana_ren :: LogicGraph -> MaybeNode -> Range -> Result GMorphism -> G_mapping

-> Result GMorphism

ana_ren lg lenv pos mor_res ren =

do mor <- mor_res

ana_ren1 lg lenv pos mor ren

ana_RENAMING :: LogicGraph -> MaybeNode -> G_sign -> HetcatsOpts -> RENAMING

-> Result GMorphism

ana_RENAMING lg lenv gSigma opts (Renaming ren pos) =

if isStructured opts

then return (ide Grothendieck gSigma)

else foldl (ana_ren lg lenv pos) (return (ide Grothendieck gSigma)) ren

-- analysis of restrictions

ana_restr1 :: DGraph -> G_sign -> Range -> GMorphism -> G_hiding

-> Result GMorphism

ana_restr1 _ (G_sign lidLenv sigmaLenv _) pos

(GMorphism cid sigma1 _ mor _)

(G_symb_list (G_symb_items_list lid' sis')) = do

let lid1 = sourceLogic cid

lid2 = targetLogic cid

sis1 <- coerceSymbItemsList lid' lid1 "Analysis of restriction" sis'

rsys <- stat_symb_items lid1 sis1

let sys = sym_of lid1 sigma1

sys' = Set.filter (\sy -> any (\rsy -> matches lid1 sy rsy) rsys)

sys

-- needs to be changed when logic projections are implemented

sigmaLenv' <- coerceSign lidLenv lid1

"Analysis of restriction: logic projections not yet properly handeled"

sigmaLenv

let sysLenv = sym_of lid1 sigmaLenv'

forbiddenSys = sys' `Set.intersection` sysLenv

when (not (forbiddenSys == Set.empty))

$ plain_error () (

"attempt to hide the following symbols from the local environment:\n"

++ showDoc forbiddenSys "") pos

mor1 <- cogenerated_sign lid1 sys' sigma1

mor1' <- map_morphism cid mor1

mor2 <- comp lid2 mor1' mor

return $ GMorphism cid (dom lid1 mor1) 0 mor2 0

ana_restr1 _dg _gSigma _mor _pos

(G_logic_projection (Logic_code _tok _src _tar pos1)) =

fatal_error "no analysis of logic projections yet" pos1

ana_restr :: DGraph -> G_sign -> Range -> Result GMorphism -> G_hiding

-> Result GMorphism

ana_restr dg gSigma pos mor_res restr =

do mor <- mor_res

ana_restr1 dg gSigma pos mor restr

ana_RESTRICTION :: DGraph -> G_sign -> G_sign -> HetcatsOpts -> RESTRICTION

-> Result (GMorphism, Maybe GMorphism)

ana_RESTRICTION dg gSigma gSigma' opts restr =

ana_RESTRICTION' dg gSigma gSigma' (isStructured opts) restr

ana_RESTRICTION' :: DGraph -> G_sign -> G_sign -> Bool -> RESTRICTION

-> Result (GMorphism, Maybe GMorphism)

ana_RESTRICTION' _ _ gSigma True _ =

return (ide Grothendieck gSigma,Nothing)

ana_RESTRICTION' dg gSigma gSigma' False (Hidden restr pos) =

do mor <- foldl (ana_restr dg gSigma pos)

(return (ide Grothendieck gSigma'))

restr

return (mor,Nothing)

-- ??? Need to check that local env is not affected !

ana_RESTRICTION' _ (G_sign lid sigma _) (G_sign lid' sigma' _)

False (Revealed (G_symb_map_items_list lid1 sis) pos) =

do let sys = sym_of lid sigma -- local env

sys' = sym_of lid' sigma' -- "big" signature

adj = adjustPos pos

sis' <- adj $ coerceSymbMapItemsList lid1 lid'

"Analysis of restriction" sis

rmap <- adj $ stat_symb_map_items lid' sis'

let sys'' =

Set.fromList

[sy | sy <- Set.toList sys', rsy <-

Map.keys rmap, matches lid' sy rsy]

-- domain of rmap intersected with sys'

-- domain of rmap should be checked to match symbols from sys' ???

sys1 <- adj $ coerceSymbolSet lid lid' "Analysis of restriction" sys

-- ??? this is too simple in case that local env is translated

-- to a different logic

mor1 <- adj $ generated_sign lid' (sys1 `Set.union` sys'') sigma'

mor2 <- adj $ induced_from_morphism lid' rmap (dom lid' mor1)

return (gEmbed (G_morphism lid' mor1 0),

Just (gEmbed (G_morphism lid' mor2 0)))

ana_FIT_ARG :: LogicGraph -> GlobalContext -> SPEC_NAME -> MaybeNode

-> NodeSig -> HetcatsOpts -> NODE_NAME -> FIT_ARG

-> Result (FIT_ARG, GlobalContext, (G_morphism,NodeSig))

ana_FIT_ARG lg gctx spname nsigI

(NodeSig nP (G_sign lidP sigmaP _)) opts name

(Fit_spec asp gsis pos) = do

let adj = adjustPos pos

(sp', nsigA@(NodeSig nA (G_sign lidA sigmaA _)), dg') <-

ana_SPEC lg gctx nsigI name opts (item asp)

G_symb_map_items_list lid sis <- homogenizeGM (Logic lidP) gsis

sigmaA' <- adj $ coerceSign lidA lidP "Analysis of fitting argument" sigmaA

mor <- adj $ if isStructured opts then return (ide lidP sigmaP)

else do

rmap <- stat_symb_map_items lid sis

rmap' <- if null sis then return Map.empty

else coerceRawSymbolMap lid lidP

"Analysis of fitting argument" rmap

induced_from_to_morphism lidP rmap' sigmaP sigmaA'

{-

let symI = sym_of lidP sigmaI'

symmap_mor = symmap_of lidP mor

-- are symbols of the imports left untouched?

if Set.all (\sy -> lookupFM symmap_mor sy == Just sy) symI

then return ()

else plain_error () "Fitting morphism must not affect import" pos

-} -- ??? does not work

-- ??? also output some symbol that is affected

let link = (nP,nA,DGLink {

dgl_morphism = gEmbed (G_morphism lidP mor 0),

dgl_type = GlobalThm LeftOpen None LeftOpen,

dgl_origin = DGSpecInst spname})

return (Fit_spec (replaceAnnoted sp' asp) gsis pos,

gctx { devGraph = insEdgeNub link $ devGraph dg' },

(G_morphism lidP mor 0,nsigA)

)

ana_FIT_ARG lg gctx spname nsigI (NodeSig nP gsigmaP)

opts name fv@(Fit_view vn afitargs pos) = do

let adj = adjustPos pos

dg = devGraph gctx

spstr = tokStr spname

case Map.lookup vn $ globalEnv gctx of

Nothing -> fatal_error

("View " ++ tokStr vn ++ " not found") pos

Just (SpecEntry _) ->

fatal_error

(spstr ++ " is a specification, not a view") pos

Just (ArchEntry _) ->

fatal_error

(spstr ++

" is an architectural specification, not a view ") pos

Just (UnitEntry _) ->

fatal_error

(spstr ++

" is a unit specification, not a view") pos

Just (RefEntry) ->

fatal_error

(spstr ++

" is a refinement specification, not a view") pos

Just (ViewEntry (src,mor,gs@(imps,params,_,target))) -> do

let nSrc = getNode src

nTar = getNode target

gsigmaS = getSig src

gsigmaT = getSig target

gsigmaI = getMaybeSig nsigI

GMorphism cid _ _ morHom ind<- return mor

let lid = targetLogic cid

when (not (language_name (sourceLogic cid) == language_name lid))

(fatal_error

"heterogeneous fitting views not yet implemented"

pos)

case (\x y -> (x,x-y)) (length afitargs) (length params) of

-- the case without parameters leads to a simpler dg

(0,0) -> case nsigI of

-- the subcase with empty import leads to a simpler dg

EmptyNode _ -> do

let link = (nP,nSrc,DGLink {

dgl_morphism = ide Grothendieck gsigmaP,

dgl_type = GlobalThm LeftOpen None LeftOpen,

dgl_origin = DGFitView spname})

return (fv, gctx { devGraph = insEdgeNub link dg },

(G_morphism lid morHom ind, target))

-- the subcase with nonempty import

JustNode (NodeSig nI _) -> do

gsigmaIS <- adj $ gsigUnion lg gsigmaI gsigmaS

when (not (isSubGsign lg gsigmaP gsigmaIS))

(plain_error ()

("Parameter does not match source of fittig view. "

++ "Parameter signature:\n"

++ showDoc gsigmaP

"\nSource signature of fitting view (united with import):\n"

++ showDoc gsigmaIS "") pos)

G_sign lidI sigI1 _<- return gsigmaI

sigI <- adj $ coerceSign lidI lid

"Analysis of instantiation with import" sigI1

mor_I <- adj $ morphism_union lid morHom $ ide lid sigI

gsigmaA <- adj $ gsigUnion lg gsigmaI gsigmaT

G_sign lidA gsigA indA <- return gsigmaA

G_sign lidP gsigP indP <- return gsigmaP

incl1 <- adj $ ginclusion lg gsigmaI gsigmaA

incl2 <- adj $ ginclusion lg gsigmaT gsigmaA

incl3 <- adj $ ginclusion lg gsigmaI gsigmaP

incl4 <- adj $ ginclusion lg gsigmaS gsigmaP

let [nA,n'] = newNodes 2 dg

node_contentsA = DGNode {

dgn_name = name,

dgn_theory = G_theory lidA gsigA indA noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGFitViewA spname,

dgn_cons = None,

dgn_cons_status = LeftOpen}

node_contents' = DGNode {

dgn_name = inc name,

dgn_theory = G_theory lidP gsigP indP noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGFitView spname,

dgn_cons = None,

dgn_cons_status = LeftOpen}

link = (nP,n',DGLink {

dgl_morphism = ide Grothendieck gsigmaP,

dgl_type = GlobalThm LeftOpen None LeftOpen,

dgl_origin = DGFitView spname})

link1 = (nSrc,n',DGLink {

dgl_morphism = incl4,

dgl_type = GlobalDef,

dgl_origin = DGFitView spname})

link2 = (nTar,nA,DGLink {

dgl_morphism = incl2,

dgl_type = GlobalDef,

dgl_origin = DGFitViewA spname})

link3 = (nI,n',DGLink {

dgl_morphism = incl3,

dgl_type = GlobalDef,

dgl_origin = DGFitViewImp spname})

link4 = (nI,nA,DGLink {

dgl_morphism = incl1,

dgl_type = GlobalDef,

dgl_origin = DGFitViewAImp spname})

return (fv, gctx { devGraph =

insEdgeNub link $

insEdgeNub link1 $

insEdgeNub link2 $

insEdgeNub link3 $

insEdgeNub link4 $

insNode (nA,node_contentsA) $

insNode (n',node_contents') dg },

(G_morphism lid mor_I 0, NodeSig nA gsigmaA))

-- now the case with parameters

(_,0) -> do

let fitargs = map item afitargs

(fitargs', gctx', args,_) <-

foldl anaFitArg (return ([], gctx, [], extName "A" name))

(zip params fitargs)

let actualargs = reverse args

(gsigmaA,mor_f) <- adj $ apply_GS lg gs actualargs

let gmor_f = gEmbed mor_f

gsigmaRes <- adj $ gsigUnion lg gsigmaI gsigmaA

G_sign lidRes gsigRes indRes<- return gsigmaRes

mor1 <- adj $ comp Grothendieck mor gmor_f

incl1 <- adj $ ginclusion lg gsigmaA gsigmaRes

mor' <- adj $ comp Grothendieck gmor_f incl1

GMorphism cid1 _ _ mor1Hom _<- return mor1

let lid1 = targetLogic cid1

when (not (language_name (sourceLogic cid1) == language_name lid1))

(fatal_error

("heterogeneous fitting views not yet implemented")

pos)

G_sign lidI sigI1 _<- return gsigmaI

sigI <- adj $ coerceSign lidI lid1

"Analysis of instantiation with parameters" sigI1

theta <- adj $ morphism_union lid1 mor1Hom (ide lid1 sigI)

incl2 <- adj $ ginclusion lg gsigmaI gsigmaRes

incl3 <- adj $ ginclusion lg gsigmaI gsigmaP

incl4 <- adj $ ginclusion lg gsigmaS gsigmaP

G_sign lidP gsigP indP <- return gsigmaP

let dg' = devGraph gctx'

[nA,n'] = newNodes 2 dg'

node_contentsA = DGNode {

dgn_name = name,

dgn_theory = G_theory lidRes gsigRes indRes noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGFitViewA spname,

dgn_cons = None,

dgn_cons_status = LeftOpen}

node_contents' = DGNode {

dgn_name = extName "V" name,

dgn_theory = G_theory lidP gsigP indP noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGFitView spname,

dgn_cons = None,

dgn_cons_status = LeftOpen}

link = (nP,n',DGLink {

dgl_morphism = ide Grothendieck gsigmaP,

dgl_type = GlobalThm LeftOpen None LeftOpen,

dgl_origin = DGFitView spname})

link1 = (nSrc,n',DGLink {

dgl_morphism = incl4,

dgl_type = GlobalDef,

dgl_origin = DGFitView spname})

link2 = (nTar,nA,DGLink {

dgl_morphism = mor',

dgl_type = GlobalDef,

dgl_origin = DGFitViewA spname})

fitLinks = [link,link1,link2] ++ case nsigI of

EmptyNode _ -> []

JustNode (NodeSig nI _) -> let

link3 = (nI,n',DGLink {

dgl_morphism = incl3,

dgl_type = GlobalDef,

dgl_origin = DGFitViewImp spname})

link4 = (nI,nA,DGLink {

dgl_morphism = incl2,

dgl_type = GlobalDef,

dgl_origin = DGFitViewAImp spname})

in [link3,link4]

parLinks = catMaybes (map (parLink gsigmaRes nA) actualargs)

return (Fit_view vn

(map (uncurry replaceAnnoted)

(zip (reverse fitargs') afitargs))

pos,

gctx' { devGraph = foldr insEdgeNub

(insNode (nA,node_contentsA) $

insNode (n',node_contents') dg')

(fitLinks ++ parLinks) },

(G_morphism lid1 theta 0, NodeSig nA gsigmaRes))

where

anaFitArg res (nsig',fa) = do

(fas',dg1,args,name') <- res

(fa',dg',arg) <- ana_FIT_ARG lg dg1

spname imps nsig' opts name' fa

return (fa':fas',dg',arg:args,inc name')

parLink gsigmaRes node (_mor_i,nsigA_i) = do

let nA_i = getNode nsigA_i

incl <- maybeResult $ ginclusion lg (getSig nsigA_i) gsigmaRes

let link = DGLink {

dgl_morphism = incl,

dgl_type = GlobalDef,

dgl_origin = DGFitView spname }

return (nA_i,node,link)

-- finally the case with conflicting numbers of formal and actual parameters

_ ->

fatal_error

(spstr ++ " expects " ++ show (length params) ++ " arguments"

++ " but was given " ++ show (length afitargs)) pos

-- Extension of signature morphisms (for instantitations)

-- first some auxiliary functions

mapID :: Map.Map Id (Set.Set Id) -> Id -> Result Id

mapID idmap i@(Id toks comps pos1) =

case Map.lookup i idmap of

Nothing -> do

compsnew <- sequence $ map (mapID idmap) comps

return (Id toks compsnew pos1)

Just ids -> if Set.null ids then return i else

if Set.null $ Set.deleteMin ids then return $ Set.findMin ids else

plain_error i

("Identifier component " ++ showId i

" can be mapped in various ways:\n"

++ showDoc ids "") $ getRange i

extID1 :: Map.Map Id (Set.Set Id) -> Id

-> Result (EndoMap Id) -> Result (EndoMap Id)

extID1 idmap i@(Id toks comps pos1) m = do

m1 <- m

compsnew <- sequence $ map (mapID idmap) comps

if comps==compsnew

then return m1

else return (Map.insert i (Id toks compsnew pos1) m1)

extID :: Set.Set Id -> Map.Map Id (Set.Set Id) -> Result (EndoMap Id)

extID ids idmap = Set.fold (extID1 idmap) (return Map.empty) ids

extendMorphism :: G_sign -- ^ formal parameter

-> G_sign -- ^ body

-> G_sign -- ^ actual parameter

-> G_morphism -- ^ fitting morphism

-> Result(G_sign,G_morphism)

extendMorphism (G_sign lid sigmaP _) (G_sign lidB sigmaB1 _)

(G_sign lidA sigmaA1 _) (G_morphism lidM fittingMor1 _) = do

-- for now, only homogeneous instantiations....

sigmaB <- coerceSign lidB lid "Extension of symbol map" sigmaB1

sigmaA <- coerceSign lidA lid "Extension of symbol map" sigmaA1

fittingMor <- coerceMorphism lidM lid "Extension of symbol map" fittingMor1

let symsP = sym_of lid sigmaP

symsB = sym_of lid sigmaB

idsB = Set.map (sym_name lid) symsB

h = symmap_of lid fittingMor

symbMapToRawSymbMap =

Map.foldWithKey (\sy1 sy2 -> Map.insert (symbol_to_raw lid sy1)

(symbol_to_raw lid sy2))

Map.empty

rh = symbMapToRawSymbMap h

idh = Map.foldWithKey

(\sy1 sy2 -> Rel.setInsert (sym_name lid sy1) (sym_name lid sy2))

Map.empty h

idhExt <- extID idsB idh

let rIdExt = Map.foldWithKey (\id1 id2 -> Map.insert

(id_to_raw lid id1) (id_to_raw lid id2))

Map.empty

(foldr (\i -> Map.delete i) idhExt $ Map.keys idh)

r = rh `Map.union` rIdExt

-- do we need combining function catching the clashes???

mor <- induced_from_morphism lid r sigmaB

let hmor = symmap_of lid mor

sigmaAD = cod lid mor

sigma <- final_union lid sigmaA sigmaAD

let illShared = (sym_of lid sigmaA `Set.intersection` sym_of lid sigmaAD )

Set.\\ Rel.image h symsP

when (not (Set.null illShared))

(plain_error () ("Symbols shared between actual parameter and body"

++ "\nmust be in formal parameter:\n"

++ showDoc illShared "") nullRange)

let myKernel m = Set.fromDistinctAscList $ comb1 $ Map.toList m

comb1 [] = []

comb1 (p : qs) =

comb2 p qs [] ++ comb1 qs

comb2 _ [] rs = rs

comb2 p@(a, b) ((c, d) : qs) rs =

comb2 p qs $ if b == d then (a, c) : rs else rs

newIdentifications = myKernel hmor Set.\\ myKernel h

when (not (Set.null newIdentifications))

(plain_error () (

"Fitting morphism leads to forbidden identifications:\n"

++ showDoc newIdentifications "") nullRange)

incl <- inclusion lid sigmaAD sigma

mor1 <- comp lid mor incl

return (G_sign lid sigma 0, G_morphism lid mor1 0)

apply_GS :: LogicGraph -> ExtGenSig -> [(G_morphism,NodeSig)]

-> Result(G_sign,G_morphism)

apply_GS lg (nsigI,_params,gsigmaP,nsigB) args = do

let mor_i = map fst args

gsigmaA_i = map (getSig . snd) args

gsigmaB = getSig nsigB

gsigmaI = getMaybeSig nsigI

G_sign lidI sigmaI _<- return gsigmaI

let idI = ide lidI sigmaI

gsigmaA <- gsigManyUnion lg gsigmaA_i

mor_f <- homogeneousMorManyUnion (G_morphism lidI idI 0:mor_i)

extendMorphism gsigmaP gsigmaB gsigmaA mor_f

-- | analyze a GENERICITY

-- Parameters: global context, current logic, just-structure-flag, GENERICITY

ana_GENERICITY :: LogicGraph -> GlobalContext -> AnyLogic -> HetcatsOpts

-> NODE_NAME -> GENERICITY

-> Result (GENERICITY, GenericitySig, GlobalContext)

-- zero parameters,

ana_GENERICITY _ gctx l _ _

gen@(Genericity (Params []) (Imported imps) pos) = do

when (not (null imps))

(plain_error () "Parameterless specifications must not have imports"

pos)

return (gen,(EmptyNode l, [], EmptyNode l), gctx)

-- one parameter ...

ana_GENERICITY lg gctx l opts name

(Genericity (Params [asp]) imps pos) = do

(imps',nsigI,dg') <- ana_IMPORTS lg gctx l opts (extName "I" name) imps

(sp',nsigP,dg'') <- ana_SPEC lg dg' nsigI

name opts (item asp)

return (Genericity (Params [replaceAnnoted sp' asp]) imps' pos,

(nsigI, [nsigP], JustNode nsigP), dg'')

-- ... and more parameters

ana_GENERICITY lg gctx l opts name

(Genericity params imps pos) = do

let adj = adjustPos pos

(imps',nsigI,dg') <- ana_IMPORTS lg gctx l opts (extName "I" name) imps

(params',nsigPs,gctx'') <-

ana_PARAMS lg dg' l nsigI opts (inc name) params

gsigmaP <- adj $ gsigManyUnion lg (map getSig nsigPs)

G_sign lidP gsigP indP <- return gsigmaP

let node_contents = DGNode {

dgn_name = name,

dgn_theory = G_theory lidP gsigP indP noSens 0,

dgn_nf = Nothing,

dgn_sigma = Nothing,

dgn_origin = DGFormalParams,

dgn_cons = None,

dgn_cons_status = LeftOpen }

dg'' = devGraph gctx''

node = getNewNode dg''

dg''' = insNode (node,node_contents) dg''

inslink dgres (NodeSig n sigma) = do

dg <- dgres

incl <- adj $ ginclusion lg sigma gsigmaP

return (insEdgeNub (n,node,DGLink {

dgl_morphism = incl,

dgl_type = GlobalDef,

dgl_origin = DGFormalParams }) dg)

dg4 <- foldl inslink (return dg''') nsigPs

return (Genericity params' imps' pos,

(nsigI, nsigPs, JustNode $ NodeSig node gsigmaP),

gctx { devGraph = dg4 })

ana_PARAMS :: LogicGraph -> GlobalContext -> AnyLogic -> MaybeNode

-> HetcatsOpts -> NODE_NAME -> PARAMS

-> Result (PARAMS, [NodeSig], GlobalContext)

ana_PARAMS lg gctx _ nsigI opts name (Params asps) = do

(sps',pars,dg',_) <- foldl ana (return ([], [], gctx, name))

$ map item asps

return (Params (map (uncurry replaceAnnoted)

(zip (reverse sps') asps)),

reverse pars, dg')

where

ana res sp = do

(sps',pars,dg1,n) <- res

(sp',par,dg') <- ana_SPEC lg dg1 nsigI n opts sp

return (sp':sps',par:pars,dg',inc n)

ana_IMPORTS :: LogicGraph -> GlobalContext -> AnyLogic -> HetcatsOpts

-> NODE_NAME -> IMPORTED

-> Result (IMPORTED, MaybeNode, GlobalContext)

ana_IMPORTS lg gctx l opts name imps@(Imported asps) =

case asps of

[] -> return (imps, EmptyNode l, gctx)

_ -> do

let sp = Union asps nullRange

(Union asps' _, nsig', dg') <-

ana_SPEC lg gctx (EmptyNode l) name opts sp

return (Imported asps', JustNode nsig', dg')

-- ??? emptyExplicit stuff needs to be added here

-- | analyze a VIEW_TYPE

-- The first three arguments give the global context

-- The AnyLogic is the current logic

-- The NodeSig is the signature of the parameter of the view

-- flag, whether just the structure shall be analysed

ana_VIEW_TYPE :: LogicGraph -> GlobalContext -> AnyLogic

-> MaybeNode -> HetcatsOpts -> NODE_NAME -> VIEW_TYPE

-> Result (VIEW_TYPE, (NodeSig, NodeSig), GlobalContext)

ana_VIEW_TYPE lg gctx l parSig opts name

(View_type aspSrc aspTar pos) = do

(spSrc',srcNsig,dg') <-

ana_SPEC lg gctx (EmptyNode l) (extName "S" name) opts (item aspSrc)

(spTar',tarNsig,dg'') <-

ana_SPEC lg dg' parSig

(extName "T" name) opts (item aspTar)

return (View_type (replaceAnnoted spSrc' aspSrc)

(replaceAnnoted spTar' aspTar)

pos,

(srcNsig, tarNsig), dg'')

homogenizeGM :: AnyLogic -> [Syntax.AS_Structured.G_mapping]

-> Result G_symb_map_items_list

homogenizeGM (Logic lid) gsis =

foldl homogenize1 (return (G_symb_map_items_list lid [])) gsis

where

homogenize1 res

(Syntax.AS_Structured.G_symb_map (G_symb_map_items_list lid1 sis1)) = do

(G_symb_map_items_list lid2 sis) <- res

sis1' <- coerceSymbMapItemsList lid1 lid2 "" sis1

return $ G_symb_map_items_list lid2 $ sis ++ sis1'

homogenize1 res _ = res

-- | check if structured analysis should be performed

isStructured :: HetcatsOpts -> Bool

isStructured a = case analysis a of

Structured -> True

_ -> False

-- | Auxiliary function for not yet implemented features

ana_err :: String -> a

ana_err f = error $ "*** Analysis of " ++ f ++ " is not yet implemented!"

ana_Extension :: Result ([SPEC],MaybeNode, GlobalContext,

LogicGraph, HetcatsOpts, Range)

-> (NODE_NAME, Annoted SPEC) ->

Result ([SPEC], MaybeNode, GlobalContext,

LogicGraph, HetcatsOpts, Range)

ana_Extension res (name',asp') = do

(sps', nsig', dg',lg,opts, pos) <- res

(sp1', nsig1@(NodeSig n1 sig1), gctx1) <-

ana_SPEC lg dg' nsig' name' opts (item asp')

let anno = find isSemanticAnno $ l_annos asp'

dg1 = devGraph gctx1

mrMapl = morMap gctx1

ml = if Map.null mrMapl then 0 else fst $ Map.findMax mrMapl

-- is the extension going between real nodes?

gctx2 <- case (anno, nsig') of

(Just anno0@(Semantic_anno anno1 _), JustNode (NodeSig n' sig')) -> do

-- any other semantic annotation? that's an error

when (any (\an -> isSemanticAnno an && an/=anno0) $ l_annos asp')

(plain_error () "Conflicting semantic annotations"

pos)

-- %implied should not occur here

when (anno1==SA_implied)

(plain_error ()

"Annotation %implied should come after a BASIC-ITEM"

pos)

if anno1==SA_implies then do

when (not (isHomSubGsign sig1 sig')) (plain_error ()

"Signature must not be extended in presence of %implies"

pos)

-- insert a theorem link according to p. 319 of the CASL Reference Manual

return gctx1 { devGraph = insEdgeNub (n1, n', DGLink

{ dgl_morphism = ide Grothendieck sig1,

dgl_type = GlobalThm LeftOpen None LeftOpen,

dgl_origin = DGExtension }) dg1 }

else do

let anno2 = case anno1 of

SA_cons -> Cons

SA_def -> Def

SA_mono -> Mono

_ -> error "Static.AnalysisStructured: this cannot happen"

-- insert a theorem link according to p. 319 of the CASL Reference Manual

-- the theorem link is trivally proved by the parallel definition link,

-- but for clarity, we leave it open here

-- the interesting open proof obligation is anno2, of course

incl <- ginclusion lg sig' sig1

let incl' = updateMorIndex (ml+1) incl

return gctx1 { devGraph = insEdgeNub (n', n1, DGLink

{ dgl_morphism = incl'

, dgl_type = GlobalThm LeftOpen anno2 LeftOpen

, dgl_origin = DGExtension }) dg1

, morMap = Map.insert (ml+1) (toG_morphism incl')

mrMapl }

_ -> return gctx1

return (sp1' : sps', JustNode nsig1, gctx2, lg, opts, pos)