1 # This file is part of NIT ( http://www.nitlanguage.org ).
3 # Licensed under the Apache License, Version 2.0 (the "License");
4 # you may not use this file except in compliance with the License.
5 # You may obtain a copy of the License at
7 # http://www.apache.org/licenses/LICENSE-2.0
9 # Unless required by applicable law or agreed to in writing, software
10 # distributed under the License is distributed on an "AS IS" BASIS,
11 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 # See the License for the specific language governing permissions and
13 # limitations under the License.
15 # Finite automaton (NFA & DFA)
26 # State that are accept states
27 var accept
= new Array[State]
30 var states
= new Array[State]
32 # Tokens associated on accept states.
33 # Use `add_tag` to update
34 var tags
= new HashMap[State, Set[Token]]
36 # Accept states associated on tokens.
37 # Use `add_tag` to update
38 var retrotags
= new HashMap[Token, Set[State]]
40 # Tag all accept states
41 fun tag_accept
(t
: Token)
43 for s
in accept
do add_tag
(s
, t
)
46 # Add a token to a state
47 fun add_tag
(s
: State, t
: Token)
49 if not tags
.has_key
(s
) then
50 var set
= new ArraySet[Token]
57 if not retrotags
.has_key
(t
) then
58 var set
= new ArraySet[State]
66 assert retrotags
[t
].has
(s
)
69 # Remove all occurrences of a tag in an automaton
70 fun clear_tag
(t
: Token)
72 if not retrotags
.has_key
(t
) then return
73 for s
in retrotags
[t
] do
74 if not tags
.has_key
(s
) then continue
76 if tags
[s
].is_empty
then tags
.keys
.remove
(s
)
78 retrotags
.keys
.remove
(t
)
81 # Remove tokens from conflicting state according the inclusion of language.
82 # REQUIRE: self isa DFA automaton
83 fun solve_token_inclusion
86 if ts
.length
<= 1 then continue
87 var losers
= new Array[Token]
90 if t1
== t2
then continue
91 if retrotags
[t1
].length
> retrotags
[t2
].length
and retrotags
[t1
].has_all
(retrotags
[t2
]) then
104 # Initialize a new automaton for the empty language.
105 # One state, no accept, no transition.
108 var state
= new State
113 # Initialize a new automaton for the empty-string language.
114 # One state, is accept, no transition.
117 var state
= new State
123 # Initialize a new automation for the language that accepts only a single symbol.
124 # Two state, the second is accept, one transition on `symbol`.
125 init atom
(symbol
: Int)
129 var sym
= new TSymbol(symbol
, symbol
)
137 # Initialize a new automation for the language that accepts only a range of symbols
138 # Two state, the second is accept, one transition for `from` to `to`
139 init cla
(first
: Int, last
: nullable Int)
143 var sym
= new TSymbol(first
, last
)
151 # Concatenate `other` to `self`.
152 # Other is modified and invalidated.
153 fun concat
(other
: Automaton)
157 a1
.add_trans
(s2
, null)
159 accept
= other
.accept
160 states
.add_all other
.states
163 # `self` become the alternation of `self` and `other`.
164 # `other` is modified and invalidated.
165 fun alternate
(other
: Automaton)
169 s
.add_trans
(start
, null)
171 a1
.add_trans
(a
, null)
173 s
.add_trans
(other
.start
, null)
174 for a2
in other
.accept
do
175 a2
.add_trans
(a
, null)
184 states
.add_all other
.states
187 # Return a new automaton that recognize `self` but not `other`.
188 # For a theoretical POV, this is the subtraction of languages.
189 # Note: the implementation use `to_dfa` internally, so the theoretical complexity is not cheap.
190 fun except
(other
: Automaton): Automaton
192 var ta
= new Token("1")
194 var tb
= new Token("2")
197 var c
= new Automaton.empty
202 for s
in c
.retrotags
[ta
] do
203 if not c
.tags
[s
].has
(tb
) then
212 # `self` absorbs all states, transitions, tags, and acceptations of `other`.
213 # An epsilon transition is added between `self.start` and `other.start`.
214 fun absorb
(other
: Automaton)
216 states
.add_all other
.states
217 start
.add_trans
(other
.start
, null)
218 for s
, ts
in other
.tags
do for t
in ts
do add_tag
(s
, t
)
219 accept
.add_all other
.accept
222 # Do the Kleene closure (*) on self
226 a1
.add_trans
(start
, null)
227 start
.add_trans
(a1
, null)
235 a1
.add_trans
(start
, null)
242 alternate
(new Automaton.epsilon
)
245 # Remove all transitions on a given symbol
246 fun minus_sym
(symbol
: TSymbol)
251 for t
in s
.outs
.to_a
do
252 if t
.symbol
== null then continue
255 var tf
= t
.symbol
.first
256 var tl
= t
.symbol
.last
257 if l
!= null and tf
> l
then continue
258 if tl
!= null and f
> tl
then continue
262 # Add left and right part if non empty
264 var sym
= new TSymbol(tf
,f-1
)
265 s
.add_trans
(t
.to
, sym
)
269 var sym
= new TSymbol(l
+1, null)
270 s
.add_trans
(t
.to
, sym
)
272 var sym
= new TSymbol(l
+1, tl
)
273 s
.add_trans
(t
.to
, sym
)
280 # Fully duplicate an automaton
283 var res
= new Automaton.empty
284 var map
= new HashMap[State, State]
285 map
[start
] = res
.start
287 if s
== start
then continue
293 res
.accept
.add map
[s
]
295 for s
, ts
in tags
do for t
in ts
do
296 res
.add_tag
(map
[s
], t
)
300 map
[s
].add_trans
(map
[t
.to
], t
.symbol
)
306 # Reverse an automaton in place
320 if accept
.length
== 1 then
328 st2
.add_trans
(s
, null)
335 # Remove states (and transitions) that does not reach an accept state
338 # Good states are those we want to keep
339 var goods
= new HashSet[State]
340 goods
.add_all
(accept
)
342 var todo
= accept
.to_a
345 while not todo
.is_empty
do
349 if goods
.has
(s2
) then continue
355 # What are the bad state then?
356 var bads
= new Array[State]
358 if not goods
.has
(s
) then bads
.add
(s
)
361 # Remove their transitions
363 for t
in s
.ins
do t
.delete
364 for t
in s
.outs
do t
.delete
367 # Keep only the good stuff
369 states
.add_all
(goods
)
372 # Generate a minimal DFA
373 # REQUIRE: self is a DFA
374 fun to_minimal_dfa
: Automaton
378 var distincts
= new HashMap[State, Set[State]]
380 distincts
[s
] = new HashSet[State]
383 # split accept states
386 if distincts
[s1
].has
(s2
) then continue
387 if not accept
.has
(s1
) then continue
388 if not accept
.has
(s2
) then
389 distincts
[s1
].add
(s2
)
390 distincts
[s2
].add
(s1
)
393 if tags
[s1
] != tags
[s2
] then
394 distincts
[s1
].add
(s2
)
395 distincts
[s2
].add
(s1
)
402 var ints
= new Array[Int]
405 for s1
in states
do for s2
in states
do
406 if distincts
[s1
].has
(s2
) then continue
413 if l
!= null then ints
.add l
416 var ds1
= s1
.trans
(i
)
417 var ds2
= s2
.trans
(i
)
418 if ds1
== null and ds2
== null then continue
419 if ds1
!= null and ds2
!= null and not distincts
[ds1
].has
(ds2
) then continue
420 distincts
[s1
].add
(s2
)
421 distincts
[s2
].add
(s1
)
428 for s1
in states
do for s2
in states
do
429 if distincts
[s1
].has
(s2
) then continue
430 s1
.add_trans
(s2
, null)
436 # Produce a graphvis file for the automaton
437 fun to_dot
(filepath
: String)
439 var names
= new HashMap[State, String]
446 var f
= new OFStream.open
(filepath
)
447 f
.write
("digraph g \{\n")
450 f
.write
("s{names[s]}[shape=oval")
451 #f.write("label=\"\",")
452 if accept
.has
(s
) then
453 f
.write
(",color=blue")
455 if tags
.has_key
(s
) then
457 for token in tags[s] do
458 f.write("{token.name.escape_to_c}\\n
")
462 f
.write
(",label=\"\
"")
465 var outs
= new HashMap[State, Array[nullable TSymbol]]
470 if outs
.has_key
(s2
) then
473 a
= new Array[nullable TSymbol]
481 if not labe
.is_empty
then labe
+= "\n"
488 f
.write
("s{names[s]}->s{names[s2]} [label=\"{labe.escape_to_c}\
"];\n")
491 f
.write
("empty->s{names[start]}; empty[label=\"\
",shape=none];\n")
497 # Transform a NFA to a DFA.
498 # note: the DFA is not minimized.
499 fun to_dfa
: Automaton
503 var dfa
= new Automaton.empty
504 var n2d
= new ArrayMap[Set[State], State]
505 var seen
= new ArraySet[Set[State]]
506 var alphabet
= new HashSet[Int]
507 var st
= eclosure
([start
])
511 while not todo
.is_empty
do
512 var nfa_states
= todo
.pop
513 #print "* work on {nfa_states.inspect}={nfa_states} (remains {todo.length}/{seen.length})"
514 var dfa_state
= n2d
[nfa_states
]
516 for s
in nfa_states
do
517 # Collect important values to build the alphabet
520 if sym
== null then continue
521 alphabet
.add
(sym
.first
)
523 if l
!= null then alphabet
.add
(l
)
526 # Mark accept and tags
527 if accept
.has
(s
) then
528 if tags
.has_key
(s
) then
530 dfa
.add_tag
(dfa_state
, t
)
533 dfa
.accept
.add
(dfa_state
)
537 # From the important values, build a sequence of TSymbols
538 var a
= alphabet
.to_a
539 default_comparator
.sort
(a
)
540 var tsyms
= new Array[TSymbol]
543 if last
> 0 and last
<= i-1
then
544 tsyms
.add
(new TSymbol(last
,i-1
))
546 tsyms
.add
(new TSymbol(i
,i
))
550 tsyms
.add
(new TSymbol(last
,null))
552 #print "Alphabet: {tsyms.join(", ")}"
554 var lastst
: nullable Transition = null
556 var nfa_dest
= eclosure
(trans
(nfa_states
, sym
.first
))
557 if nfa_dest
.is_empty
then
561 #print "{nfa_states} -> {sym} -> {nfa_dest}"
563 if seen
.has
(nfa_dest
) then
564 #print "* reuse {nfa_dest.inspect}={nfa_dest}"
565 dfa_dest
= n2d
[nfa_dest
]
567 #print "* new {nfa_dest.inspect}={nfa_dest}"
569 dfa
.states
.add
(dfa_dest
)
570 n2d
[nfa_dest
] = dfa_dest
574 if lastst
!= null and lastst
.to
== dfa_dest
then
575 lastst
.symbol
.last
= sym
.last
577 lastst
= dfa_state
.add_trans
(dfa_dest
, sym
)
584 # Epsilon-closure on a state of states.
586 private fun eclosure
(states
: Collection[State]): Set[State]
588 var res
= new ArraySet[State]
590 var todo
= states
.to_a
591 while not todo
.is_empty
do
594 if t
.symbol
!= null then continue
596 if res
.has
(to
) then continue
604 # Trans on a set of states.
606 fun trans
(states
: Collection[State], symbol
: Int): Set[State]
608 var res
= new ArraySet[State]
612 if sym
== null then continue
613 if sym
.first
> symbol
then continue
615 if l
!= null and l
< symbol
then continue
617 if res
.has
(to
) then continue
624 # Generate the Nit source code of the lexer.
625 # `filepath` is the name of the output file.
626 # `parser` is the name of the parser module (used to import the token classes).
627 fun gen_to_nit
(filepath
: String, name
: String, parser
: nullable String)
629 var gen
= new DFAGenerator(filepath
, name
, self, parser
)
634 # Generate the Nit source code of the lexer
635 private class DFAGenerator
638 var automaton
: Automaton
639 var parser
: nullable String
641 var out
: OStream is noinit
644 self.out
= new OFStream.open
(filepath
)
647 fun add
(s
: String) do out
.write
(s
)
651 var names
= new HashMap[State, String]
653 for s
in automaton
.states
do
658 add
"# Lexer generated by nitcc for the grammar {name}"
659 add
("import nitcc_runtime\n")
662 if p
!= null then add
("import {p}\n")
664 add
("class Lexer_{name}\n")
665 add
("\tsuper Lexer\n")
666 add
("\tredef fun start_state do return dfastate_{names[automaton.start]}\n")
669 add
("redef class Object\n")
670 for s
in automaton
.states
do
672 add
("\tprivate fun dfastate_{n}: DFAState{n} do return once new DFAState{n}\n")
676 add
("class MyNToken\n")
677 add
("\tsuper NToken\n")
680 for s
in automaton
.states
do
682 add
("private class DFAState{n}\n")
683 add
("\tsuper DFAState\n")
684 if automaton
.accept
.has
(s
) then
686 if automaton
.tags
.has_key
(s
) then
687 token
= automaton
.tags
[s
].first
691 add
("\tredef fun is_accept do return true\n")
692 add
("\tredef fun make_token(position, text) do\n")
693 if token
!= null and token
.name
== "Ignored" then
694 add
("\t\treturn null\n")
696 if token
== null then
697 add
("\t\tvar t = new MyNToken\n")
699 add
("\t\tvar t = new {token.cname}\n")
701 add
("\t\tt.position = position\n")
702 add
("\t\tt.text = text\n")
703 add
("\t\treturn t\n")
707 var trans
= new ArrayMap[TSymbol, State]
713 if trans
.is_empty
then
714 # Do nothing, inherit the trans
716 add
("\tredef fun trans(char) do\n")
718 add
("\t\tvar c = char.ascii\n")
721 for sym
, next
in trans
do
723 assert sym
.first
> last
724 if sym
.first
> last
+ 1 then add
("\t\tif c <= {sym.first-1} then return null\n")
727 add
("\t\treturn dfastate_{names[next]}\n")
730 add
("\t\tif c <= {l} then return dfastate_{names[next]}\n")
734 if not haslast
then add
("\t\treturn null\n")
744 # A state in a finite automaton
746 # Outgoing transitions
747 var outs
= new Array[Transition]
749 # Ingoing transitions
750 var ins
= new Array[Transition]
752 # Add a transitions to `to` on `symbol` (null means epsilon)
753 fun add_trans
(to
: State, symbol
: nullable TSymbol): Transition
755 var t
= new Transition(self, to
, symbol
)
761 # Get the first state following the transition `i`.
762 # Null if no transition for `i`.
763 fun trans
(i
: Int): nullable State
770 if i
< f
then continue
771 if l
!= null and i
> l
then continue
778 # A range of symbols on a transition
780 # The first symbol in the range
783 # The last symbol if any.
785 # `null` means infinity.
786 var last
: nullable Int
798 if f
== l
then return res
800 if l
== null then return res
801 if l
<= 32 or l
>= 127 then return res
+ "#{l}"
802 return res
+ l
.ascii
.to_s
806 # A transition in a finite automaton
810 # The destination state
812 # The symbol on the transition (null means epsilon)
813 var symbol
: nullable TSymbol
815 # Remove the transition from the automaton.
816 # Detach from `from` and `to`.
819 from
.outs
.remove
(self)