PopulationProtocol.hs 9.38 KB
Newer Older
1
2
3
4
{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-}
{-# OPTIONS_GHC -fno-warn-name-shadowing #-}

module PopulationProtocol
5
6
    (PopulationProtocol,State(..),Transition(..),
     Configuration,FlowVector,RConfiguration,RFlowVector,
7
     renameState,renameTransition,renameStatesAndTransitions,
8
     name,showNetName,states,transitions,initialStates,trueStates,falseStates,
9
10
     pre,lpre,post,lpost,mpre,mpost,context,
     makePopulationProtocol,makePopulationProtocolWithTrans,
11
12
     makePopulationProtocolFromStrings,makePopulationProtocolWithTransFromStrings,
     Trap,Siphon,Invariant(..))
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
where

import qualified Data.Map as M
import qualified Data.Set as S
import Control.Arrow (first,(***))
import Data.List (sort,(\\))

import Util

newtype State = State String deriving (Ord,Eq)
newtype Transition = Transition String deriving (Ord,Eq)

instance Show State where
        show (State q) = q
instance Show Transition where
        show (Transition t) = t

type ContextMap a b = M.Map a ([(b, Integer)],[(b, Integer)])

class (Ord a, Ord b) => Nodes a b | a -> b where
        lpre :: PopulationProtocol -> a -> [(b, Integer)]
        lpre pp = fst . context pp
        lpost :: PopulationProtocol -> a -> [(b, Integer)]
        lpost pp = snd . context pp
        pre :: PopulationProtocol -> a -> [b]
        pre pp = map fst . lpre pp
        post :: PopulationProtocol -> a -> [b]
        post pp = map fst . lpost pp
        lmpre :: PopulationProtocol -> [a] -> [(b, Integer)]
        lmpre pp = listMap . concatMap (lpre pp)
        lmpost :: PopulationProtocol -> [a] -> [(b, Integer)]
        lmpost pp = listMap . concatMap (lpost pp)
        mpre :: PopulationProtocol -> [a] -> [b]
        mpre pp = map fst . lmpre pp
        mpost :: PopulationProtocol -> [a] -> [b]
        mpost pp = map fst . lmpost pp
        context :: PopulationProtocol -> a -> ([(b, Integer)], [(b, Integer)])
        context pp x = M.findWithDefault ([],[]) x (contextMap pp)
        contextMap :: PopulationProtocol -> ContextMap a b

instance Nodes State Transition where
        contextMap = adjacencyQ
instance Nodes Transition State where
        contextMap = adjacencyT

58
type Configuration = IVector State
59
type FlowVector = IVector Transition
60

61
type RConfiguration = RVector State
62
type RFlowVector = RVector Transition
63
64
65
66
67
68
69
70
71
72
73
74

type Trap = [State]
type Siphon = [State]

class Invariant a where
        invariantSize :: a -> Int

data PopulationProtocol = PopulationProtocol {
        name :: String,
        states :: [State],
        transitions :: [Transition],
        initialStates :: [State],
75
76
        trueStates :: [State],
        falseStates :: [State],
77
78
79
80
81
82
83
84
85
86
        adjacencyQ :: M.Map State ([(Transition,Integer)], [(Transition,Integer)]),
        adjacencyT :: M.Map Transition ([(State,Integer)], [(State,Integer)])
}

showNetName :: PopulationProtocol -> String
showNetName pp = "Population protocol" ++
               (if null (name pp) then "" else " " ++ show (name pp))

instance Show PopulationProtocol where
        show pp = showNetName pp ++
87
88
89
90
91
92
                   "\nStates         : " ++ show (states pp) ++
                   "\nTransitions    : " ++ show (transitions pp) ++
                   "\nInitial states : " ++ show (initialStates pp) ++
                   "\nTrue states    : " ++ show (trueStates pp) ++
                   "\nFalse states   : " ++ show (falseStates pp) ++
                   "\nState arcs     :\n" ++ unlines
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
                        (map showContext (M.toList (adjacencyQ pp))) ++
                   "\nTransition arcs:\n" ++ unlines
                        (map showContext (M.toList (adjacencyT pp)))
                where showContext (s,(l,r)) =
                          show l ++ " -> " ++ show s ++ " -> " ++ show r

renameState :: (String -> String) -> State -> State
renameState f (State q) = State (f q)

renameTransition :: (String -> String) -> Transition -> Transition
renameTransition f (Transition t) = Transition (f t)

renameStatesAndTransitions :: (String -> String) -> PopulationProtocol -> PopulationProtocol
renameStatesAndTransitions f pp =
            PopulationProtocol {
                name = name pp,
                states      =
                    listSet $ map (renameState f) $ states pp,
                transitions =
                    listSet $ map (renameTransition f) $ transitions pp,
                initialStates =
                    listSet $ map (renameState f) $ initialStates pp,
115
116
117
118
                trueStates =
                    listSet $ map (renameState f) $ trueStates pp,
                falseStates =
                    listSet $ map (renameState f) $ falseStates pp,
119
120
121
122
123
124
125
126
127
128
129
130
131
                adjacencyQ  = mapAdjacency (renameState f) (renameTransition f) $
                    adjacencyQ pp,
                adjacencyT  = mapAdjacency (renameTransition f) (renameState f) $
                    adjacencyT pp
            }
        where mapAdjacency f g m = M.mapKeys f (M.map (mapContext g) m)
              mapContext f (pre, post) =
                  (listMap (map (first f) pre), listMap (map (first f) post))

makePopulationProtocol :: String -> [State] -> [Transition] ->
        [State] -> [State] -> [State] ->
        [Either (Transition, State, Integer) (State, Transition, Integer)] ->
        PopulationProtocol
132
makePopulationProtocol name states transitions initialStates trueStates falseStates arcs =
133
134
135
136
137
            PopulationProtocol {
                name = name,
                states = listSet states,
                transitions = listSet transitions,
                initialStates = listSet initialStates,
138
139
                trueStates = listSet trueStates,
                falseStates = listSet falseStates,
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
                adjacencyQ = M.map (listMap *** listMap) adQ,
                adjacencyT = M.map (listMap *** listMap) adT
            }
        where
            (adQ, adT) = foldl buildMaps (M.empty, M.empty) arcs
            buildMaps (mq,mt) (Left (_,_,0)) = (mq,mt)
            buildMaps (mq,mt) (Right (_,_,0)) = (mq,mt)
            buildMaps (mq,mt) (Right (q,t,w)) =
                       let mq' = M.insertWith addArc
                                    q ([],[(t,w)]) mq
                           mt' = M.insertWith addArc
                                    t ([(q,w)],[]) mt
                       in  (mq',mt')
            buildMaps (mq,mt) (Left (t,q,w)) =
                       let mt' = M.insertWith addArc
                                    t ([],[(q,w)]) mt
                           mq' = M.insertWith addArc
                                    q ([(t,w)],[]) mq
                       in  (mq',mt')
            addArc (lNew,rNew) (lOld,rOld) = (lNew ++ lOld,rNew ++ rOld)

makePopulationProtocolFromStrings :: String -> [String] -> [String] -> [String] -> [String] -> [String] ->
        [(String, String, Integer)] -> PopulationProtocol
163
makePopulationProtocolFromStrings name states transitions initialStates trueStates falseStates arcs =
164
165
166
167
168
            makePopulationProtocol
                name
                (map State (S.toAscList stateSet))
                (map Transition (S.toAscList transitionSet))
                (map State initialStates)
169
170
                (map State trueStates)
                (map State falseStates)
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
                (map toEitherArc arcs)
        where
            stateSet = S.fromList states
            transitionSet = S.fromList transitions
            toEitherArc (l,r,w) =
                let lq = l `S.member` stateSet
                    lt = l `S.member` transitionSet
                    rq = r `S.member` stateSet
                    rt = r `S.member` transitionSet
                in  case (lq,lt,rq,rt) of
                        (True,False,False,True) ->
                            Right (State l, Transition r, w)
                        (False,True,True,False) ->
                            Left (Transition l, State r, w)
                        (False,False,_,_) ->
                            error $ l ++ " not a declared state or transition "
                        (_,_,False,False) ->
                            error $ r ++ " not a declared state or transition "
                        (True,_,True,_) ->
                            error $ l ++ " and " ++ r ++ " both states"
                        (_,True,_,True) ->
                            error $ l ++ " and " ++ r ++ " both transitions"

makePopulationProtocolWithTrans :: String -> [State] -> [State] -> [State] -> [State] ->
        [(Transition, ([(State, Integer)], [(State, Integer)]))] ->
        PopulationProtocol
197
198
makePopulationProtocolWithTrans name states initialStates trueStates falseStates ts =
            makePopulationProtocol name states (map fst ts) initialStates trueStates falseStates arcs
199
200
201
202
203
204
205
        where
            arcs = [ Right (q,t,w) | (t,(is,_)) <- ts, (q,w) <- is ] ++
                   [ Left  (t,q,w) | (t,(_,os)) <- ts, (q,w) <- os ]

makePopulationProtocolWithTransFromStrings :: String -> [String] -> [String] -> [String] -> [String] ->
        [(String, ([(String, Integer)], [(String, Integer)]))] ->
        PopulationProtocol
206
makePopulationProtocolWithTransFromStrings name states initialStates trueStates falseStates arcs =
207
208
209
210
            makePopulationProtocolWithTrans
                name
                (map State states)
                (map State initialStates)
211
212
                (map State trueStates)
                (map State falseStates)
213
214
215
216
                (map toTArc arcs)
        where
            toTArc (t, (iq, oq)) =
                (Transition t, (map (first State) iq, map (first State) oq))