[nit.git] / contrib / nitcc / src / autom.nit

# This file is part of NIT ( http://www.nitlanguage.org ).
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# Finite automaton (NFA & DFA)
module autom

# For the class Token
import grammar

# A finite automaton
class Automaton
        # The start state
        var start: State is noinit

        # State that are accept states
        var accept = new Array[State]

        # All states
        var states = new Array[State]

        # Tokens associated on accept states.
        # Use `add_tag` to update
        var tags = new HashMap[State, Set[Token]]

        # Accept states associated on tokens.
        # Use `add_tag` to update
        var retrotags = new HashMap[Token, Set[State]]

        # Tag all accept states
        fun tag_accept(t: Token)
        do
                for s in accept do add_tag(s, t)
        end

        # Add a token to a state
        fun add_tag(s: State, t: Token)
        do
                if not tags.has_key(s) then
                        var set = new ArraySet[Token]
                        tags[s] = set
                        set.add t
                else
                        tags[s].add t
                end

                if not retrotags.has_key(t) then
                        var set = new ArraySet[State]
                        retrotags[t] = set
                        set.add s
                else
                        retrotags[t].add s
                end

                assert tags[s].has(t)
                assert retrotags[t].has(s)
        end

        # Remove all occurrences of a tag in an automaton
        fun clear_tag(t: Token)
        do
                if not retrotags.has_key(t) then return
                for s in retrotags[t] do
                        if not tags.has_key(s) then continue
                        tags[s].remove(t)
                        if tags[s].is_empty then tags.keys.remove(s)
                end
                retrotags.keys.remove(t)
        end

        # Remove tokens from conflicting state according the inclusion of language.
        # REQUIRE: self isa DFA automaton
        fun solve_token_inclusion
        do
                for s, ts in tags do
                        if ts.length <= 1 then continue
                        var losers = new Array[Token]
                        for t1 in ts do
                                for t2 in ts do
                                        if t1 == t2 then continue
                                        if retrotags[t1].length > retrotags[t2].length and retrotags[t1].has_all(retrotags[t2]) then
                                                losers.add(t1)
                                                break
                                        end
                                end
                        end
                        for t in losers do
                                ts.remove(t)
                                retrotags[t].remove s
                        end
                end
        end

        # Initialize a new automaton for the empty language.
        # One state, no accept, no transition.
        init empty
        do
                var state = new State
                start = state
                states.add state
        end

        # Initialize a new automaton for the empty-string language.
        # One state, is accept, no transition.
        init epsilon
        do
                var state = new State
                start = state
                accept.add state
                states.add state
        end

        # Initialize a new automation for the language that accepts only a single symbol.
        # Two state, the second is accept, one transition on `symbol`.
        init atom(symbol: Int)
        do
                var s = new State
                var a = new State
                var sym = new TSymbol(symbol, symbol)
                s.add_trans(a, sym)
                start = s
                accept.add a
                states.add s
                states.add a
        end

        # Initialize a new automation for the language that accepts only a range of symbols
        # Two state, the second is accept, one transition for `from` to `to`
        init cla(first: Int, last: nullable Int)
        do
                var s = new State
                var a = new State
                var sym = new TSymbol(first, last)
                s.add_trans(a, sym)
                start = s
                accept.add a
                states.add s
                states.add a
        end

        # Concatenate `other` to `self`.
        # Other is modified and invalidated.
        fun concat(other: Automaton)
        do
                var s2 = other.start
                for a1 in accept do
                        a1.add_trans(s2, null)
                end
                accept = other.accept
                states.add_all other.states
        end

        # `self` become the alternation of `self` and `other`.
        # `other` is modified and invalidated.
        fun alternate(other: Automaton)
        do
                var s = new State
                var a = new State
                s.add_trans(start, null)
                for a1 in accept do
                        a1.add_trans(a, null)
                end
                s.add_trans(other.start, null)
                for a2 in other.accept do
                        a2.add_trans(a, null)
                        accept.add(a2)
                end

                start = s
                accept = [a]

                states.add s
                states.add a
                states.add_all other.states
        end

        # Return a new automaton that recognize `self` but not `other`.
        # For a theoretical POV, this is the subtraction of languages.
        # Note: the implementation use `to_dfa` internally, so the theoretical complexity is not cheap.
        fun except(other: Automaton): Automaton
        do
                var ta = new Token("1")
                self.tag_accept(ta)
                var tb = new Token("2")
                other.tag_accept(tb)

                var c = new Automaton.empty
                c.absorb(self)
                c.absorb(other)
                c = c.to_dfa
                c.accept.clear
                for s in c.retrotags[ta] do
                        if not c.tags[s].has(tb) then
                                c.accept.add(s)
                        end
                end
                c.clear_tag(ta)
                c.clear_tag(tb)
                return c
        end

        # `self` absorbs all states, transitions, tags, and acceptations of `other`.
        # An epsilon transition is added between `self.start` and `other.start`.
        fun absorb(other: Automaton)
        do
                states.add_all other.states
                start.add_trans(other.start, null)
                for s, ts in other.tags do for t in ts do add_tag(s, t)
                accept.add_all other.accept
        end

        # Do the Kleene closure (*) on self
        fun close
        do
                for a1 in accept do
                        a1.add_trans(start, null)
                        start.add_trans(a1, null)
                end
        end

        # Do the + on self
        fun plus
        do
                for a1 in accept do
                        a1.add_trans(start, null)
                end
        end

        # Do the ? on self
        fun optionnal
        do
                alternate(new Automaton.epsilon)
        end

        # Remove all transitions on a given symbol
        fun minus_sym(symbol: TSymbol)
        do
                var f = symbol.first
                var l = symbol.last
                for s in states do
                        for t in s.outs.to_a do
                                if t.symbol == null then continue

                                # Check overlaps
                                var tf = t.symbol.as(not null).first
                                var tl = t.symbol.as(not null).last
                                if l != null and tf > l then continue
                                if tl != null and f > tl then continue

                                t.delete

                                # Add left and right part if non empty
                                if tf < f then
                                        var sym = new TSymbol(tf,f-1)
                                        s.add_trans(t.to, sym)
                                end
                                if l != null then
                                        if tl == null then
                                                var sym = new TSymbol(l+1, null)
                                                s.add_trans(t.to, sym)
                                        else if tl > l then
                                                var sym = new TSymbol(l+1, tl)
                                                s.add_trans(t.to, sym)
                                        end
                                end
                        end
                end
        end

        # Fully duplicate an automaton
        fun dup: Automaton
        do
                var res = new Automaton.empty
                var map = new HashMap[State, State]
                map[start] = res.start
                for s in states do
                        if s == start then continue
                        var s2 = new State
                        map[s] = s2
                        res.states.add(s2)
                end
                for s in accept do
                        res.accept.add map[s]
                end
                for s, ts in tags do for t in ts do
                        res.add_tag(map[s], t)
                end
                for s in states do
                        for t in s.outs do
                                map[s].add_trans(map[t.to], t.symbol)
                        end
                end
                return res
        end

        # Reverse an automaton in place
        fun reverse
        do
                for s in states do
                        var tmp = s.ins
                        s.ins = s.outs
                        s.outs = tmp
                        for t in s.outs do
                                var tmp2 = t.from
                                t.from = t.to
                                t.to = tmp2
                        end
                end
                var st = start
                if accept.length == 1 then
                        start = accept.first
                else
                        var st2 = new State
                        start = st2
                        states.add(st2)

                        for s in accept do
                                st2.add_trans(s, null)
                        end
                end
                accept.clear
                accept.add(st)
        end

        # Remove states (and transitions) that does not reach an accept state
        fun trim
        do
                # Good states are those we want to keep
                var goods = new HashSet[State]
                goods.add_all(accept)

                var todo = accept.to_a

                # Propagate goodness
                while not todo.is_empty do
                        var s = todo.pop
                        for t in s.ins do
                                var s2 = t.from
                                if goods.has(s2) then continue
                                goods.add(s2)
                                todo.add(s2)
                        end
                end

                # What are the bad state then?
                var bads = new Array[State]
                for s in states do
                        if not goods.has(s) then bads.add(s)
                end

                # Remove their transitions
                for s in bads do
                        for t in s.ins.to_a do t.delete
                        for t in s.outs.to_a do t.delete
                end

                # Keep only the good stuff
                states.clear
                states.add_all(goods)
                states.add(start)
        end

        # Generate a minimal DFA
        # REQUIRE: self is a DFA
        fun to_minimal_dfa: Automaton
        do
                assert_valid

                trim

                # Graph of known distinct states.
                var distincts = new HashMap[State, Set[State]]
                for s in states do
                        distincts[s] = new HashSet[State]
                end

                # split accept states.
                # An accept state is distinct with a non accept state.
                for s1 in accept do
                        for s2 in states do
                                if distincts[s1].has(s2) then continue
                                if not accept.has(s2) then
                                        distincts[s1].add(s2)
                                        distincts[s2].add(s1)
                                        continue
                                end
                                if tags.get_or_null(s1) != tags.get_or_null(s2) then
                                        distincts[s1].add(s2)
                                        distincts[s2].add(s1)
                                        continue
                                end
                        end
                end

                # Fixed point algorithm.
                # * Get 2 states s1 and s2 not yet distinguished.
                # * Get a symbol w.
                # * If s1.trans(w) and s2.trans(w) are distinguished, then
                #   distinguish s1 and s2.
                var changed = true
                var ints = new Array[Int] # List of symbols to check
                while changed do
                        changed = false
                        for s1 in states do for s2 in states do
                                if distincts[s1].has(s2) then continue

                                # The transitions use intervals. Therefore, for the states s1 and s2,
                                # we need to check only the meaningful symbols. They are the `first`
                                # symbol of each interval and the first one after the interval (`last+1`).
                                ints.clear
                                # Check only `s1`; `s2` will be checked later when s1 and s2 are switched.
                                for t in s1.outs do
                                        var sym = t.symbol
                                        assert sym != null
                                        ints.add sym.first
                                        var l = sym.last
                                        if l != null then ints.add l + 1
                                end

                                # Check each symbol
                                for i in ints do
                                        var ds1 = s1.trans(i)
                                        var ds2 = s2.trans(i)
                                        if ds1 == ds2 then continue
                                        if ds1 != null and ds2 != null and not distincts[ds1].has(ds2) then continue
                                        distincts[s1].add(s2)
                                        distincts[s2].add(s1)
                                        changed = true
                                        break
                                end
                        end
                end

                # We need to unify not-distinguished states.
                # Just add an epsilon-transition and DFAize the automaton.
                for s1 in states do for s2 in states do
                        if distincts[s1].has(s2) then continue
                        s1.add_trans(s2, null)
                end

                return to_dfa
        end

        # Assert that `self` is a valid automaton or abort
        fun assert_valid
        do
                assert states.has(start)
                assert states.has_all(accept)
                for s in states do
                        for t in s.outs do assert states.has(t.to)
                        for t in s.ins do assert states.has(t.from)
                end
                assert states.has_all(tags.keys)
                for t, ss in retrotags do
                        assert states.has_all(ss)
                end
        end

        # Produce a graphviz string from the automatom
        #
        # Set `merge_transitions = false` to generate one edge by transition (default true).
        fun to_dot(merge_transitions: nullable Bool): Writable
        do
                var names = new HashMap[State, String]
                var ni = 0
                for s in states do
                        names[s] = ni.to_s
                        ni += 1
                end

                var f = new Buffer
                f.append("digraph g \{\n")
                f.append("rankdir=LR;")

                var state_nb = 0
                for s in states do
                        f.append("s{names[s]}[shape=circle")
                        #f.write("label=\"\",")
                        if accept.has(s) then
                                f.append(",shape=doublecircle")
                        end
                        if tags.has_key(s) then
                                f.append(",label=\"")
                                for token in tags[s] do
                                        f.append("{token.name.escape_to_dot}\\n")
                                end
                                f.append("\"")
                        else
                                f.append(",label=\"{state_nb}\"")
                        end
                        f.append("];\n")
                        var outs = new HashMap[State, Array[nullable TSymbol]]
                        for t in s.outs do
                                var a
                                var s2 = t.to
                                var c = t.symbol
                                if outs.has_key(s2) then
                                        a = outs[s2]
                                else
                                        a = new Array[nullable TSymbol]
                                        outs[s2] = a
                                end
                                a.add(c)
                        end
                        for s2, a in outs do
                                var labe = ""
                                for c in a do
                                        if merge_transitions == false then labe = ""
                                        if not labe.is_empty then labe += "\n"
                                        if c == null then
                                                labe += "ε"
                                        else
                                                labe += c.to_s
                                        end
                                        if merge_transitions == false then
                                                f.append("s{names[s]}->s{names[s2]} [label=\"{labe.escape_to_dot}\"];\n")
                                        end
                                end
                                if merge_transitions or else true then
                                        f.append("s{names[s]}->s{names[s2]} [label=\"{labe.escape_to_c}\"];\n")
                                end
                        end
                        state_nb += 1
                end
                f.append("empty->s{names[start]}; empty[label=\"\",shape=none];\n")
                f.append("\}\n")
                return f
        end

        # Transform a NFA to a DFA.
        # note: the DFA is not minimized.
        fun to_dfa: Automaton
        do
                assert_valid

                trim

                var dfa = new Automaton.empty
                var n2d = new ArrayMap[Set[State], State]
                var seen = new ArraySet[Set[State]]
                var alphabet = new HashSet[Int]
                var st = eclosure([start])
                var todo = [st]
                n2d[st] = dfa.start
                seen.add(st)
                while not todo.is_empty do
                        var nfa_states = todo.pop
                        #print "* work on {nfa_states.inspect}={nfa_states} (remains {todo.length}/{seen.length})"
                        var dfa_state = n2d[nfa_states]
                        alphabet.clear
                        for s in nfa_states do
                                # Collect important values to build the alphabet
                                for t in s.outs do
                                        var sym = t.symbol
                                        if sym == null then continue
                                        alphabet.add(sym.first)
                                        var l = sym.last
                                        if l != null then alphabet.add(l)
                                end

                                # Mark accept and tags
                                if accept.has(s) then
                                        if tags.has_key(s) then
                                                for t in tags[s] do
                                                        dfa.add_tag(dfa_state, t)
                                                end
                                        end
                                        dfa.accept.add(dfa_state)
                                end
                        end

                        # From the important values, build a sequence of TSymbols
                        var a = alphabet.to_a
                        default_comparator.sort(a)
                        var tsyms = new Array[TSymbol]
                        var last = 0
                        for i in a do
                                if last > 0 and last <= i-1 then
                                        tsyms.add(new TSymbol(last,i-1))
                                end
                                tsyms.add(new TSymbol(i,i))
                                last = i+1
                        end
                        if last > 0 then
                                tsyms.add(new TSymbol(last,null))
                        end
                        #print "Alphabet: {tsyms.join(", ")}"

                        var lastst: nullable Transition = null
                        for sym in tsyms do
                                var nfa_dest = eclosure(trans(nfa_states, sym.first))
                                if nfa_dest.is_empty then
                                        lastst = null
                                        continue
                                end
                                #print "{nfa_states} -> {sym} -> {nfa_dest}"
                                var dfa_dest
                                if seen.has(nfa_dest) then
                                        #print "* reuse {nfa_dest.inspect}={nfa_dest}"
                                        dfa_dest = n2d[nfa_dest]
                                else
                                        #print "* new {nfa_dest.inspect}={nfa_dest}"
                                        dfa_dest = new State
                                        dfa.states.add(dfa_dest)
                                        n2d[nfa_dest] = dfa_dest
                                        todo.add(nfa_dest)
                                        seen.add(nfa_dest)
                                end
                                if lastst != null and lastst.to == dfa_dest then
                                        lastst.symbol.as(not null).last = sym.last
                                else
                                        lastst = dfa_state.add_trans(dfa_dest, sym)
                                end
                        end
                end
                return dfa
        end

        # Transform a NFA to a epsilonless NFA.
        fun to_nfa_noe: Automaton
        do
                assert_valid

                trim

                var dfa = new Automaton.empty
                var n2d = new ArrayMap[Set[State], State]
                var seen = new ArraySet[Set[State]]
                var st = eclosure([start])
                var todo = [st]
                n2d[st] = dfa.start
                seen.add(st)
                while not todo.is_empty do
                        var nfa_states = todo.pop
                        #print "* work on {nfa_states.inspect}={nfa_states} (remains {todo.length}/{seen.length})"
                        var dfa_state = n2d[nfa_states]
                        for s in nfa_states do
                                for t in s.outs do
                                        if t.symbol == null then continue
                                        var nfa_dest = eclosure([t.to])
                                        #print "{nfa_states} -> {sym} -> {nfa_dest}"
                                        var dfa_dest
                                        if seen.has(nfa_dest) then
                                                #print "* reuse {nfa_dest.inspect}={nfa_dest}"
                                                dfa_dest = n2d[nfa_dest]
                                        else
                                                #print "* new {nfa_dest.inspect}={nfa_dest}"
                                                dfa_dest = new State
                                                dfa.states.add(dfa_dest)
                                                n2d[nfa_dest] = dfa_dest
                                                todo.add(nfa_dest)
                                                seen.add(nfa_dest)
                                        end
                                        dfa_state.add_trans(dfa_dest, t.symbol)
                                end

                                # Mark accept and tags
                                if accept.has(s) then
                                        if tags.has_key(s) then
                                                for t in tags[s] do
                                                        dfa.add_tag(dfa_state, t)
                                                end
                                        end
                                        dfa.accept.add(dfa_state)
                                end
                        end
                end
                return dfa
        end

        # Epsilon-closure on a state of states.
        # Used by `to_dfa`.
        private fun eclosure(states: Collection[State]): Set[State]
        do
                var res = new ArraySet[State]
                res.add_all(states)
                var todo = states.to_a
                while not todo.is_empty do
                        var s = todo.pop
                        for t in s.outs do
                                if t.symbol != null then continue
                                var to = t.to
                                if res.has(to) then continue
                                res.add(to)
                                todo.add(to)
                        end
                end
                return res
        end

        # Trans on a set of states.
        # Used by `to_dfa`.
        fun trans(states: Collection[State], symbol: Int): Set[State]
        do
                var res = new ArraySet[State]
                for s in states do
                        for t in s.outs do
                                var sym = t.symbol
                                if sym == null then continue
                                if sym.first > symbol then continue
                                var l = sym.last
                                if l != null and l < symbol then continue
                                var to = t.to
                                if res.has(to) then continue
                                res.add(to)
                        end
                end
                return res
        end

        # Generate the Nit source code of the lexer.
        # `filepath` is the name of the output file.
        # `parser` is the name of the parser module (used to import the token classes).
        fun gen_to_nit(filepath: String, name: String, parser: nullable String)
        do
                var gen = new DFAGenerator(filepath, name, self, parser)
                gen.gen_to_nit
        end
end

# Generate the Nit source code of the lexer
private class DFAGenerator
        var filepath: String
        var name: String
        var automaton: Automaton
        var parser: nullable String

        var out: Writer is noinit

        init do
                self.out = new FileWriter.open(filepath)
        end

        fun add(s: String) do out.write(s)

        fun gen_to_nit
        do
                var names = new HashMap[State, String]
                var i = 0
                for s in automaton.states do
                        names[s] = i.to_s
                        i += 1
                end

                add "# Lexer generated by nitcc for the grammar {name}\n"
                add "module {name}_lexer is generated, no_warning \"missing-doc\"\n"
                add("import nitcc_runtime\n")

                var p = parser
                if p != null then add("import {p}\n")

                add("class Lexer_{name}\n")
                add("\tsuper Lexer\n")
                add("\tredef fun start_state do return dfastate_{names[automaton.start]}\n")
                add("end\n")

                for s in automaton.states do
                        var n = names[s]
                        add("private fun dfastate_{n}: DFAState{n} do return once new DFAState{n}\n")
                end

                add("class MyNToken\n")
                add("\tsuper NToken\n")
                add("end\n")

                for s in automaton.states do
                        var  n = names[s]
                        add("private class DFAState{n}\n")
                        add("\tsuper DFAState\n")
                        if automaton.accept.has(s) then
                                var token
                                if automaton.tags.has_key(s) then
                                        token = automaton.tags[s].first
                                else
                                        token = null
                                end
                                add("\tredef fun is_accept do return true\n")
                                var is_ignored = false
                                if token != null and token.name == "Ignored" then
                                        is_ignored = true
                                        add("\tredef fun is_ignored do return true\n")
                                end
                                add("\tredef fun make_token(position, source) do\n")
                                if is_ignored then
                                        add("\t\treturn null\n")
                                else
                                        if token == null then
                                                add("\t\tvar t = new MyNToken\n")
                                                add("\t\tt.text = position.extract(source)\n")
                                        else
                                                add("\t\tvar t = new {token.cname}\n")
                                                var ttext = token.text
                                                if ttext == null then
                                                        add("\t\tt.text = position.extract(source)\n")
                                                else
                                                        add("\t\tt.text = \"{ttext.escape_to_nit}\"\n")
                                                end
                                        end
                                        add("\t\tt.position = position\n")
                                        add("\t\treturn t\n")
                                end
                                add("\tend\n")
                        end
                        var trans = new ArrayMap[TSymbol, State]
                        for t in s.outs do
                                var sym = t.symbol
                                assert sym != null
                                trans[sym] = t.to
                        end
                        if trans.is_empty then
                                # Do nothing, inherit the trans
                        else
                                add("\tredef fun trans(char) do\n")

                                # Collect the sequence of tests in the dispatch sequence
                                # The point here is that for each transition, there is a first and a last
                                # So holes have to be identified
                                var dispatch = new HashMap[Int, nullable State]
                                var haslast: nullable State = null

                                var last = -1
                                for sym, next in trans do
                                        assert haslast == null
                                        assert sym.first > last
                                        if sym.first > last + 1 then
                                                dispatch[sym.first-1] = null
                                        end
                                        var l = sym.last
                                        if l == null then
                                                haslast = next
                                        else
                                                dispatch[l] = next
                                                last = l
                                        end
                                end

                                if dispatch.is_empty and haslast != null then
                                        # Only one transition that accepts everything (quite rare)
                                else
                                        # We need to check
                                        add("\t\tvar c = char.code_point\n")
                                end

                                # Generate a sequence of `if` for the dispatch
                                if haslast != null and last >= 0 then
                                        # Special case: handle up-bound first if not an error
                                        add("\t\tif c > {last} then return dfastate_{names[haslast]}\n")
                                        # previous become the new last case
                                        haslast = dispatch[last]
                                        dispatch.keys.remove(last)
                                end
                                for c, next in dispatch do
                                        if next == null then
                                                add("\t\tif c <= {c} then return null\n")
                                        else
                                                add("\t\tif c <= {c} then return dfastate_{names[next]}\n")
                                        end
                                end
                                if haslast == null then
                                        add("\t\treturn null\n")
                                else
                                        add("\t\treturn dfastate_{names[haslast]}\n")
                                end

                                add("\tend\n")
                        end
                        add("end\n")
                end

                self.out.close
        end
end

redef class Token
        # The associated text (if any, ie defined in the parser part)
        var text: nullable String is noautoinit, writable
end

# A state in a finite automaton
class State
        # Outgoing transitions
        var outs = new Array[Transition]

        # Ingoing transitions
        var ins = new Array[Transition]

        # Add a transitions to `to` on `symbol` (null means epsilon)
        fun add_trans(to: State, symbol: nullable TSymbol): Transition
        do
                var t = new Transition(self, to, symbol)
                outs.add(t)
                to.ins.add(t)
                return t
        end

        # Get the first state following the transition `i`.
        # Null if no transition for `i`.
        fun trans(i: Int): nullable State
        do
                for t in outs do
                        var sym = t.symbol
                        assert sym != null
                        var f = sym.first
                        var l = sym.last
                        if i < f then continue
                        if l != null and i > l then continue
                        return t.to
                end
                return null
        end
end

# A range of symbols on a transition
class TSymbol
        # The first symbol in the range
        var first: Int

        # The last symbol if any.
        #
        # `null` means infinity.
        var last: nullable Int

        redef fun to_s
        do
                var res
                var f = first
                if f <= 32 then
                        res = "#{f}"
                else
                        res = f.code_point.to_s
                end
                var l = last
                if f == l then return res
                res += " .. "
                if l == null then return res
                if l <= 32 or l >= 127 then return res + "#{l}"
                return res + l.code_point.to_s
        end
end

# A transition in a finite automaton
class Transition
        # The source state
        var from: State
        # The destination state
        var to: State
        # The symbol on the transition (null means epsilon)
        var symbol: nullable TSymbol

        # Remove the transition from the automaton.
        # Detach from `from` and `to`.
        fun delete
        do
                from.outs.remove(self)
                to.ins.remove(self)
        end
end