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)
24 var start
: State is noinit
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
.as(not null).first
256 var tl
= t
.symbol
.as(not null).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
.to_a
do t
.delete
364 for t
in s
.outs
.to_a
do t
.delete
367 # Keep only the good stuff
369 states
.add_all
(goods
)
373 # Generate a minimal DFA
374 # REQUIRE: self is a DFA
375 fun to_minimal_dfa
: Automaton
381 # Graph of known distinct states.
382 var distincts
= new HashMap[State, Set[State]]
384 distincts
[s
] = new HashSet[State]
387 # split accept states.
388 # An accept state is distinct with a non accept state.
391 if distincts
[s1
].has
(s2
) then continue
392 if not accept
.has
(s2
) then
393 distincts
[s1
].add
(s2
)
394 distincts
[s2
].add
(s1
)
397 if tags
.get_or_null
(s1
) != tags
.get_or_null
(s2
) then
398 distincts
[s1
].add
(s2
)
399 distincts
[s2
].add
(s1
)
405 # Fixed point algorithm.
406 # * Get 2 states s1 and s2 not yet distinguished.
408 # * If s1.trans(w) and s2.trans(w) are distinguished, then
409 # distinguish s1 and s2.
411 var ints
= new Array[Int] # List of symbols to check
414 for s1
in states
do for s2
in states
do
415 if distincts
[s1
].has
(s2
) then continue
417 # The transitions use intervals. Therefore, for the states s1 and s2,
418 # we need to check only the meaningful symbols. They are the `first`
419 # symbol of each interval and the first one after the interval (`last+1`).
421 # Check only `s1`; `s2` will be checked later when s1 and s2 are switched.
427 if l
!= null then ints
.add l
+ 1
432 var ds1
= s1
.trans
(i
)
433 var ds2
= s2
.trans
(i
)
434 if ds1
== ds2
then continue
435 if ds1
!= null and ds2
!= null and not distincts
[ds1
].has
(ds2
) then continue
436 distincts
[s1
].add
(s2
)
437 distincts
[s2
].add
(s1
)
444 # We need to unify not-distinguished states.
445 # Just add an epsilon-transition and DFAize the automaton.
446 for s1
in states
do for s2
in states
do
447 if distincts
[s1
].has
(s2
) then continue
448 s1
.add_trans
(s2
, null)
454 # Assert that `self` is a valid automaton or abort
457 assert states
.has
(start
)
458 assert states
.has_all
(accept
)
460 for t
in s
.outs
do assert states
.has
(t
.to
)
461 for t
in s
.ins
do assert states
.has
(t
.from
)
463 assert states
.has_all
(tags
.keys
)
464 for t
, ss
in retrotags
do
465 assert states
.has_all
(ss
)
469 # Produce a graphviz string from the automatom
471 # Set `merge_transitions = false` to generate one edge by transition (default true).
472 fun to_dot
(merge_transitions
: nullable Bool): Writable
474 var names
= new HashMap[State, String]
482 f
.append
("digraph g \{\n")
483 f
.append
("rankdir=LR;")
487 f
.append
("s{names[s]}[shape=circle")
488 #f.write("label=\"\",")
489 if accept
.has
(s
) then
490 f
.append
(",shape=doublecircle")
492 if tags
.has_key
(s
) then
493 f
.append
(",label=\"")
494 for token in tags[s] do
495 f.append("{token.name.escape_to_dot}\\n
")
499 f
.append
(",label=\"{state_nb}\
"")
502 var outs
= new HashMap[State, Array[nullable TSymbol]]
507 if outs
.has_key
(s2
) then
510 a
= new Array[nullable TSymbol]
518 if merge_transitions
== false then labe
= ""
519 if not labe
.is_empty
then labe
+= "\n"
525 if merge_transitions
== false then
526 f
.append
("s{names[s]}->s{names[s2]} [label=\"{labe.escape_to_dot}\
"];\n")
529 if merge_transitions
or else true then
530 f
.append
("s{names[s]}->s{names[s2]} [label=\"{labe.escape_to_c}\
"];\n")
535 f
.append
("empty->s{names[start]}; empty[label=\"\
",shape=none];\n")
540 # Transform a NFA to a DFA.
541 # note: the DFA is not minimized.
542 fun to_dfa
: Automaton
548 var dfa
= new Automaton.empty
549 var n2d
= new ArrayMap[Set[State], State]
550 var seen
= new ArraySet[Set[State]]
551 var alphabet
= new HashSet[Int]
552 var st
= eclosure
([start
])
556 while not todo
.is_empty
do
557 var nfa_states
= todo
.pop
558 #print "* work on {nfa_states.inspect}={nfa_states} (remains {todo.length}/{seen.length})"
559 var dfa_state
= n2d
[nfa_states
]
561 for s
in nfa_states
do
562 # Collect important values to build the alphabet
565 if sym
== null then continue
566 alphabet
.add
(sym
.first
)
568 if l
!= null then alphabet
.add
(l
)
571 # Mark accept and tags
572 if accept
.has
(s
) then
573 if tags
.has_key
(s
) then
575 dfa
.add_tag
(dfa_state
, t
)
578 dfa
.accept
.add
(dfa_state
)
582 # From the important values, build a sequence of TSymbols
583 var a
= alphabet
.to_a
584 default_comparator
.sort
(a
)
585 var tsyms
= new Array[TSymbol]
588 if last
> 0 and last
<= i-1
then
589 tsyms
.add
(new TSymbol(last
,i-1
))
591 tsyms
.add
(new TSymbol(i
,i
))
595 tsyms
.add
(new TSymbol(last
,null))
597 #print "Alphabet: {tsyms.join(", ")}"
599 var lastst
: nullable Transition = null
601 var nfa_dest
= eclosure
(trans
(nfa_states
, sym
.first
))
602 if nfa_dest
.is_empty
then
606 #print "{nfa_states} -> {sym} -> {nfa_dest}"
608 if seen
.has
(nfa_dest
) then
609 #print "* reuse {nfa_dest.inspect}={nfa_dest}"
610 dfa_dest
= n2d
[nfa_dest
]
612 #print "* new {nfa_dest.inspect}={nfa_dest}"
614 dfa
.states
.add
(dfa_dest
)
615 n2d
[nfa_dest
] = dfa_dest
619 if lastst
!= null and lastst
.to
== dfa_dest
then
620 lastst
.symbol
.as(not null).last
= sym
.last
622 lastst
= dfa_state
.add_trans
(dfa_dest
, sym
)
629 # Transform a NFA to a epsilonless NFA.
630 fun to_nfa_noe
: Automaton
636 var dfa
= new Automaton.empty
637 var n2d
= new ArrayMap[Set[State], State]
638 var seen
= new ArraySet[Set[State]]
639 var st
= eclosure
([start
])
643 while not todo
.is_empty
do
644 var nfa_states
= todo
.pop
645 #print "* work on {nfa_states.inspect}={nfa_states} (remains {todo.length}/{seen.length})"
646 var dfa_state
= n2d
[nfa_states
]
647 for s
in nfa_states
do
649 if t
.symbol
== null then continue
650 var nfa_dest
= eclosure
([t
.to
])
651 #print "{nfa_states} -> {sym} -> {nfa_dest}"
653 if seen
.has
(nfa_dest
) then
654 #print "* reuse {nfa_dest.inspect}={nfa_dest}"
655 dfa_dest
= n2d
[nfa_dest
]
657 #print "* new {nfa_dest.inspect}={nfa_dest}"
659 dfa
.states
.add
(dfa_dest
)
660 n2d
[nfa_dest
] = dfa_dest
664 dfa_state
.add_trans
(dfa_dest
, t
.symbol
)
667 # Mark accept and tags
668 if accept
.has
(s
) then
669 if tags
.has_key
(s
) then
671 dfa
.add_tag
(dfa_state
, t
)
674 dfa
.accept
.add
(dfa_state
)
681 # Epsilon-closure on a state of states.
683 private fun eclosure
(states
: Collection[State]): Set[State]
685 var res
= new ArraySet[State]
687 var todo
= states
.to_a
688 while not todo
.is_empty
do
691 if t
.symbol
!= null then continue
693 if res
.has
(to
) then continue
701 # Trans on a set of states.
703 fun trans
(states
: Collection[State], symbol
: Int): Set[State]
705 var res
= new ArraySet[State]
709 if sym
== null then continue
710 if sym
.first
> symbol
then continue
712 if l
!= null and l
< symbol
then continue
714 if res
.has
(to
) then continue
721 # Generate the Nit source code of the lexer.
722 # `filepath` is the name of the output file.
723 # `parser` is the name of the parser module (used to import the token classes).
724 fun gen_to_nit
(filepath
: String, name
: String, parser
: nullable String)
726 var gen
= new DFAGenerator(filepath
, name
, self, parser
)
731 # Generate the Nit source code of the lexer
732 private class DFAGenerator
735 var automaton
: Automaton
736 var parser
: nullable String
738 var out
: Writer is noinit
741 self.out
= new FileWriter.open
(filepath
)
744 fun add
(s
: String) do out
.write
(s
)
748 var names
= new HashMap[State, String]
750 for s
in automaton
.states
do
755 add
"# Lexer generated by nitcc for the grammar {name}\n"
756 add
"module {name}_lexer is generated, no_warning \"missing-doc\
"\n"
757 add
("import nitcc_runtime\n")
760 if p
!= null then add
("import {p}\n")
762 add
("class Lexer_{name}\n")
763 add
("\tsuper Lexer\n")
764 add
("\tredef fun start_state do return dfastate_{names[automaton.start]}\n")
767 for s
in automaton
.states
do
769 add
("private fun dfastate_{n}: DFAState{n} do return once new DFAState{n}\n")
772 add
("class MyNToken\n")
773 add
("\tsuper NToken\n")
776 for s
in automaton
.states
do
778 add
("private class DFAState{n}\n")
779 add
("\tsuper DFAState\n")
780 if automaton
.accept
.has
(s
) then
782 if automaton
.tags
.has_key
(s
) then
783 token
= automaton
.tags
[s
].first
787 add
("\tredef fun is_accept do return true\n")
788 var is_ignored
= false
789 if token
!= null and token
.name
== "Ignored" then
791 add
("\tredef fun is_ignored do return true\n")
793 add
("\tredef fun make_token(position, source) do\n")
795 add
("\t\treturn null\n")
797 if token
== null then
798 add
("\t\tvar t = new MyNToken\n")
799 add
("\t\tt.text = position.extract(source)\n")
801 add
("\t\tvar t = new {token.cname}\n")
802 var ttext
= token
.text
803 if ttext
== null then
804 add
("\t\tt.text = position.extract(source)\n")
806 add
("\t\tt.text = \"{ttext.escape_to_nit}\
"\n")
809 add
("\t\tt.position = position\n")
810 add
("\t\treturn t\n")
814 var trans
= new ArrayMap[TSymbol, State]
820 if trans
.is_empty
then
821 # Do nothing, inherit the trans
823 add
("\tredef fun trans(char) do\n")
825 # Collect the sequence of tests in the dispatch sequence
826 # The point here is that for each transition, there is a first and a last
827 # So holes have to be identified
828 var dispatch
= new HashMap[Int, nullable State]
829 var haslast
: nullable State = null
832 for sym
, next
in trans
do
833 assert haslast
== null
834 assert sym
.first
> last
835 if sym
.first
> last
+ 1 then
836 dispatch
[sym
.first-1
] = null
847 if dispatch
.is_empty
and haslast
!= null then
848 # Only one transition that accepts everything (quite rare)
851 add
("\t\tvar c = char.code_point\n")
854 # Generate a sequence of `if` for the dispatch
855 if haslast
!= null and last
>= 0 then
856 # Special case: handle up-bound first if not an error
857 add
("\t\tif c > {last} then return dfastate_{names[haslast]}\n")
858 # previous become the new last case
859 haslast
= dispatch
[last
]
860 dispatch
.keys
.remove
(last
)
862 for c
, next
in dispatch
do
864 add
("\t\tif c <= {c} then return null\n")
866 add
("\t\tif c <= {c} then return dfastate_{names[next]}\n")
869 if haslast
== null then
870 add
("\t\treturn null\n")
872 add
("\t\treturn dfastate_{names[haslast]}\n")
885 # The associated text (if any, ie defined in the parser part)
886 var text
: nullable String is noautoinit
, writable
889 # A state in a finite automaton
891 # Outgoing transitions
892 var outs
= new Array[Transition]
894 # Ingoing transitions
895 var ins
= new Array[Transition]
897 # Add a transitions to `to` on `symbol` (null means epsilon)
898 fun add_trans
(to
: State, symbol
: nullable TSymbol): Transition
900 var t
= new Transition(self, to
, symbol
)
906 # Get the first state following the transition `i`.
907 # Null if no transition for `i`.
908 fun trans
(i
: Int): nullable State
915 if i
< f
then continue
916 if l
!= null and i
> l
then continue
923 # A range of symbols on a transition
925 # The first symbol in the range
928 # The last symbol if any.
930 # `null` means infinity.
931 var last
: nullable Int
940 res
= f
.code_point
.to_s
943 if f
== l
then return res
945 if l
== null then return res
946 if l
<= 32 or l
>= 127 then return res
+ "#{l}"
947 return res
+ l
.code_point
.to_s
951 # A transition in a finite automaton
955 # The destination state
957 # The symbol on the transition (null means epsilon)
958 var symbol
: nullable TSymbol
960 # Remove the transition from the automaton.
961 # Detach from `from` and `to`.
964 from
.outs
.remove
(self)