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implementation module DTMC
import StdArray
import StdBool
import StdClass
import StdFile
from StdFunc import o
import StdInt
import StdList
import StdString
import StdTuple
import Data.Error
from Data.Func import $, mapSt, seqSt
import Data.List
import qualified Data.Map as M
from Data.Map import :: Map, alter
import Data.Maybe
import System.File
import System.FilePath
import Text
paths :: !*DTMC -> *([[Int]], !*DTMC)
paths dtmc=:{nr_states,states}
# (inits,states) = getInitStates (nr_states-1) states
# (ps,states) = mapSt (paths` []) inits states
= (flatten ps, {dtmc & states=states})
where
getInitStates :: !Int !*{Maybe State} -> *(![Int], !*{Maybe State})
getInitStates i ss
| i < 0 = ([], ss)
# (s,ss) = ss![i]
| isNothing s = ([], ss)
# s = fromJust s
| s.init
# (inits,ss) = getInitStates (i-1) ss
= ([i:inits],ss)
= getInitStates (i-1) ss
paths` :: ![Int] !Int !*{Maybe State} -> *(![[Int]], !*{Maybe State})
paths` seen cur ss
| isMember cur seen = ([], ss)
# (s,ss) = ss![cur]
| isNothing s = ([], ss)
# s = fromJust s
| isAbsorbing s = ([[cur]], ss)
# succ = 'M'.keys s.transitions
# (pss,ss) = mapSt (paths` [cur:seen]) succ ss
= ([[cur:p] \\ ps <- pss, p <- ps], ss)
stateElimination :: !*DTMC -> *DTMC
stateElimination dtmc=:{nr_states}
# (ps,dtmc) = paths dtmc
= case [p \\ p=:[_:_:_:_] <- ps] of
[] -> {dtmc & states=prune (nr_states-1) dtmc.states}
[p:_] -> stateElimination {dtmc & states=uncurry elim (penultimate_trans p) dtmc.states}
with
penultimate_trans [x,y,_] = (x,y)
penultimate_trans [_:xs] = penultimate_trans xs
where
prune :: !Int !*{Maybe State} -> *{Maybe State}
prune i ss
| i < 0 = ss
# (Just s,ss) = ss![i]
| s.init || isAbsorbing s = prune (i-1) ss
| otherwise = prune (i-1) $ remove i (nr_states-1) ss
where
remove :: !Int !Int !*{Maybe State} -> *{Maybe State}
remove i j ss
| j < 0 = {ss & [i]=Nothing}
# (s,ss) = ss![j]
| isNothing s = remove i (j-1) ss
# s = fromJust s
= remove i (j-1) ss
elim :: !Int !Int !*{Maybe State} -> *{Maybe State}
elim s1 s ss
# (Just s1s,ss) = ss![s1]
# prob = 'M'.get s s1s.transitions
# (succ,ss) = ss![s]
| isNothing succ = ss
# succ = fromJust succ
| succ.init || isAbsorbing succ = ss
# succ = succ.transitions
# self_prob = fromMaybe "0" $ 'M'.get s succ
# succ = 'M'.toList succ
| s1 == s
# ss = seqSt (uncurry $ update_eq self_prob) succ ss
# (Just s1s,ss) = ss![s1]
# ss & [s1] = Just {s1s & transitions='M'.del s s1s.transitions}
= ss
| otherwise
# ss = seqSt (uncurry $ update_ne self_prob) succ ss
# (Just s1s,ss) = ss![s1]
# ss & [s1] = Just {s1s & transitions='M'.del s s1s.transitions}
= ss
where
update_eq :: !String !Int !String !*{Maybe State} -> *{Maybe State}
update_eq self_prob s2 prob2 ss
| s == s2 = ss
# (Just s1s,ss) = ss![s1]
# ss & [s1] = Just
{ s1s
& transitions = 'M'.put s2
("(" +++ prob2 +++ ")/(1-(" +++ self_prob +++ "))")
s1s.transitions
}
= ss
update_ne :: !String !Int !String !*{Maybe State} -> *{Maybe State}
update_ne self_prob s2 prob2 ss
| s == s2 = ss
# (Just s1s,ss) = ss![s1]
# ps1s2 = fromMaybe "0" $ 'M'.get s2 s1s.transitions
# ps1s = fromMaybe "0" $ 'M'.get s s1s.transitions
# ss & [s1] = Just
{ s1s
& transitions = 'M'.put s2
(ps1s2 +++ "+(" +++ ps1s +++ ")*(" +++ prob2 +++ ")/(1-(" +++ self_prob +++ "))")
s1s.transitions
}
= ss
isAbsorbing :: !State -> Bool
isAbsorbing s = all ((==) s.state_id) [to \\ (to,_) <- 'M'.toList s.transitions]
parseDTMC :: !FilePath !*World -> *(!DTMC, !*World)
parseDTMC fp w
# (lines,w) = readFileLines fp w
= (parseDTMCFromLines [s % (0,size s-2) \\ s <- fromOk lines], w)
parseDTMCFromLines :: ![String] -> DTMC
parseDTMCFromLines lines
# [nr_states:_:lines] = tl $ dropWhile ((<>) "@nr_states") lines
# states = map parseState $ groupLines "\t" [] lines
=
{ nr_states = toInt nr_states
, states = {Just s \\ s <- states}
}
where
parseState :: ![String] -> State
parseState [head:actions] =
{ state_id = toInt $ trim $ head % (5,size head-1)
, transitions = 'M'.unions $ map (snd o parseAction) $ groupLines "\t\t" [] actions
, init = endsWith "init" head
}
where
parseAction :: ![String] -> (!Int, !Map Int String)
parseAction [head:transitions] =
( toInt (head % (8, size head-1))
, 'M'.fromList $ map parseTransition transitions
)
where
parseTransition :: !String -> (!Int, !String)
parseTransition s = case split " : " (trim s) of
[id:prob:_] -> (toInt id, prob)
groupLines :: !String ![String] ![String] -> [[String]]
groupLines head current [] = [reverse current]
groupLines head current [line:lines]
| startsWith head line = groupLines head [line:current] lines
| isEmpty current = groupLines head [line] lines
| otherwise = [reverse current:groupLines head [line] lines]
addVars :: *DTMC -> *DTMC
addVars dtmc = {DTMC | nr_states = dtmc.nr_states, states = addVarsS 0 dtmc.nr_states dtmc.states}
where
addVarsS :: !Int !Int !*{Maybe State} -> *{Maybe State}
addVarsS i m ss
| i >= m = ss
| otherwise = addVarsS (i + 1) m {ss & [i]=addVarsT 0 m ss.[i]}
addVarsT :: Int Int (Maybe State) -> (Maybe State)
addVarsT _ _ Nothing = Nothing
addVarsT i m (Just s)
| i >= m = Just s
| otherwise = (addVarsT (i + 1) m (Just {s & transitions = alter (addVar i s.state_id) i s.transitions}))
addVar :: Int Int (Maybe String) -> Maybe String
addVar _ _ Nothing = Nothing
addVar f t (Just fn) = Just ("((" <+ fn <+ ") + " <+ f <+ "_" <+ t <+ ")")
Start w
# (dtmc,w) = parseDTMC "die.drn" w
= [(s.state_id, 'M'.toList s.transitions, '\n') \\ Just s <-: (stateElimination dtmc).states]
|
