-- -----------------------------------------------------------------------------
--
-- DFA.hs, part of Alex
--
-- (c) Chris Dornan 1995-2000, Simon Marlow 2003
--
-- This module generates a DFA from a scanner by first converting it
-- to an NFA and then converting the NFA with the subset construction.
--
-- See the chapter on `Finite Automata and Lexical Analysis' in the
-- dragon book for an excellent overview of the algorithms in this
-- module.
--
-- ----------------------------------------------------------------------------}
module DFA(scanner2dfa) where
import AbsSyn
import qualified Map
import qualified Data.IntMap as IntMap
import NFA
import Sort ( msort, nub' )
import CharSet
import Data.Array ( (!) )
import Data.Maybe ( fromJust )
{- Defined in the Scan Module
-- (This section should logically belong to the DFA module but it has been
-- placed here to make this module self-contained.)
--
-- `DFA' provides an alternative to `Scanner' (described in the RExp module);
-- it can be used directly to scan text efficiently. Additionally it has an
-- extra place holder for holding action functions for generating
-- application-specific tokens. When this place holder is not being used, the
-- unit type will be used.
--
-- Each state in the automaton consist of a list of `Accept' values, descending
-- in priority, and an array mapping characters to new states. As the array
-- may only cover a sub-range of the characters, a default state number is
-- given in the third field. By convention, all transitions to the -1 state
-- represent invalid transitions.
--
-- A list of accept states is provided for as the original specification may
-- have been ambiguous, in which case the highest priority token should be
-- taken (the one appearing earliest in the specification); this can not be
-- calculated when the DFA is generated in all cases as some of the tokens may
-- be associated with leading or trailing context or start codes.
--
-- `scan_token' (see above) can deal with unconditional accept states more
-- efficiently than those associated with context; to save it testing each time
-- whether the list of accept states contains an unconditional state, the flag
-- in the first field of `St' is set to true whenever the list contains an
-- unconditional state.
--
-- The `Accept' structure contains the priority of the token being accepted
-- (lower numbers => higher priorities), the name of the token, a place holder
-- that can be used for storing the `action' function for constructing the
-- token from the input text and thge scanner's state, a list of start codes
-- (listing the start codes that the scanner must be in for the token to be
-- accepted; empty => no restriction), the leading and trailing context (both
-- `Nothing' if there is none).
--
-- The leading context consists simply of a character predicate that will
-- return true if the last character read is acceptable. The trailing context
-- consists of an alternative starting state within the DFA; if this `sub-dfa'
-- turns up any accepting state when applied to the residual input then the
-- trailing context is acceptable (see `scan_token' above).
type DFA a = Array SNum (State a)
type SNum = Int
data State a = St Bool [Accept a] SNum (Array Char SNum)
data Accept a = Acc Int String a [StartCode] (MB(Char->Bool)) (MB SNum)
type StartCode = Int
-}
-- Scanners are converted to DFAs by converting them to NFAs first. Converting
-- an NFA to a DFA works by identifying the states of the DFA with subsets of
-- the NFA. The PartDFA is used to construct the DFA; it is essentially a DFA
-- in which the states are represented directly by state sets of the NFA.
-- `nfa2pdfa' constructs the partial DFA from the NFA by searching for all the
-- transitions from a given list of state sets, initially containing the start
-- state of the partial DFA, until all possible state sets have been considered
-- The final DFA is then constructed with a `mk_dfa'.
scanner2dfa:: Encoding -> Scanner -> [StartCode] -> DFA SNum Code
scanner2dfa enc scanner scs = nfa2dfa scs (scanner2nfa enc scanner scs)
nfa2dfa:: [StartCode] -> NFA -> DFA SNum Code
nfa2dfa scs nfa = mk_int_dfa nfa (nfa2pdfa nfa pdfa (dfa_start_states pdfa))
where
pdfa = new_pdfa n_starts nfa
n_starts = length scs -- number of start states
-- `nfa2pdfa' works by taking the next outstanding state set to be considered
-- and and ignoring it if the state is already in the partial DFA, otherwise
-- generating all possible transitions from it, adding the new state to the
-- partial DFA and continuing the closure with the extra states. Note the way
-- it incorporates the trailing context references into the search (by
-- including `rctx_ss' in the search).
nfa2pdfa:: NFA -> DFA StateSet Code -> [StateSet] -> DFA StateSet Code
nfa2pdfa _ pdfa [] = pdfa
nfa2pdfa nfa pdfa (ss:umkd)
| ss `in_pdfa` pdfa = nfa2pdfa nfa pdfa umkd
| otherwise = nfa2pdfa nfa pdfa' umkd'
where
pdfa' = add_pdfa ss (State accs (IntMap.fromList ss_outs)) pdfa
umkd' = rctx_sss ++ map snd ss_outs ++ umkd
-- for each character, the set of states that character would take
-- us to from the current set of states in the NFA.
ss_outs :: [(Int, StateSet)]
ss_outs = [ (fromIntegral ch, mk_ss nfa ss')
| ch <- byteSetElems $ setUnions [p | (p,_) <- outs],
let ss' = [ s' | (p,s') <- outs, byteSetElem p ch ],
not (null ss')
]
rctx_sss = [ mk_ss nfa [s]
| Acc _ _ _ (RightContextRExp s) <- accs ]
outs :: [(ByteSet,SNum)]
outs = [ out | s <- ss, out <- nst_outs (nfa!s) ]
accs = sort_accs [acc| s<-ss, acc<-nst_accs (nfa!s)]
-- `sort_accs' sorts a list of accept values into decending order of priority,
-- eliminating any elements that follow an unconditional accept value.
sort_accs:: [Accept a] -> [Accept a]
sort_accs accs = foldr chk [] (msort le accs)
where
chk acc@(Acc _ _ Nothing NoRightContext) _ = [acc]
chk acc rst = acc:rst
le (Acc{accPrio = n}) (Acc{accPrio=n'}) = n<=n'
{------------------------------------------------------------------------------
State Sets and Partial DFAs
------------------------------------------------------------------------------}
-- A `PartDFA' is a partially constructed DFA in which the states are
-- represented by sets of states of the original NFA. It is represented by a
-- triple consisting of the start state of the partial DFA, the NFA from which
-- it is derived and a map from state sets to states of the partial DFA. The
-- state set for a given list of NFA states is calculated by taking the epsilon
-- closure of all the states, sorting the result with duplicates eliminated.
type StateSet = [SNum]
new_pdfa:: Int -> NFA -> DFA StateSet a
new_pdfa starts nfa
= DFA { dfa_start_states = start_ss,
dfa_states = Map.empty
}
where
start_ss = [ msort (<=) (nst_cl(nfa!n)) | n <- [0..(starts-1)]]
-- starts is the number of start states
-- constructs the epsilon-closure of a set of NFA states
mk_ss:: NFA -> [SNum] -> StateSet
mk_ss nfa l = nub' (<=) [s'| s<-l, s'<-nst_cl(nfa!s)]
add_pdfa:: StateSet -> State StateSet a -> DFA StateSet a -> DFA StateSet a
add_pdfa ss pst (DFA st mp) = DFA st (Map.insert ss pst mp)
in_pdfa:: StateSet -> DFA StateSet a -> Bool
in_pdfa ss (DFA _ mp) = ss `Map.member` mp
-- Construct a DFA with numbered states, from a DFA whose states are
-- sets of states from the original NFA.
mk_int_dfa:: NFA -> DFA StateSet a -> DFA SNum a
mk_int_dfa nfa (DFA start_states mp)
= DFA [0 .. length start_states-1]
(Map.fromList [ (lookup' st, cnv pds) | (st, pds) <- Map.toAscList mp ])
where
mp' = Map.fromList (zip (start_states ++
(map fst . Map.toAscList) (foldr Map.delete mp start_states)) [0..])
lookup' = fromJust . flip Map.lookup mp'
cnv :: State StateSet a -> State SNum a
cnv (State accs as) = State accs' as'
where
as' = IntMap.mapWithKey (\_ch s -> lookup' s) as
accs' = map cnv_acc accs
cnv_acc (Acc p a lctx rctx) = Acc p a lctx rctx'
where rctx' =
case rctx of
RightContextRExp s ->
RightContextRExp (lookup' (mk_ss nfa [s]))
other -> other
{-
-- `mk_st' constructs a state node from the list of accept values and a list of
-- transitions. The transitions list all the valid transitions out of the
-- node; all invalid transitions should be represented in the array by state
-- -1. `mk_st' has to work out whether the accept states contain an
-- unconditional entry, in which case the first field of `St' should be true,
-- and which default state to use in constructing the array (the array may span
-- a sub-range of the character set, the state number given the third argument
-- of `St' being taken as the default if an input character lies outside the
-- range). The default values is chosen to minimise the bounds of the array
-- and so there are two candidates: the value that 0 maps to (in which case
-- some initial segment of the array may be omitted) or the value that 255 maps
-- to (in which case a final segment of the array may be omitted), hence the
-- calculation of `(df,bds)'.
--
-- Note that empty arrays are avoided as they can cause severe problems for
-- some popular Haskell compilers.
mk_st:: [Accept Code] -> [(Char,Int)] -> State Code
mk_st accs as =
if null as
then St accs (-1) (listArray ('0','0') [-1])
else St accs df (listArray bds [arr!c| c<-range bds])
where
bds = if sz==0 then ('0','0') else bds0
(sz,df,bds0) | sz1 < sz2 = (sz1,df1,bds1)
| otherwise = (sz2,df2,bds2)
(sz1,df1,bds1) = mk_bds(arr!chr 0)
(sz2,df2,bds2) = mk_bds(arr!chr 255)
mk_bds df = (t-b, df, (chr b, chr (255-t)))
where
b = length (takeWhile id [arr!c==df| c<-['\0'..'\xff']])
t = length (takeWhile id [arr!c==df| c<-['\xff','\xfe'..'\0']])
arr = listArray ('\0','\xff') (take 256 (repeat (-1))) // as
-}