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use std::collections::{BTreeMap, BTreeSet, VecDeque};
use proc_macro2::TokenStream;
use quote::{quote, ToTokens};
use super::nfa::{Range, NFA};
/// A nondeterministic finite automaton.
/// By convention, always starts in state 0.
pub struct DFA {
transition_table: BTreeMap<usize, BTreeMap<Range, usize>>,
accept_states: BTreeSet<usize>,
}
struct LabeledDFA<Label: Ord> {
start_state: Label,
transition_table: BTreeMap<Label, BTreeMap<Range, Label>>,
accept_states: BTreeSet<Label>,
}
impl From<NFA> for LabeledDFA<BTreeSet<usize>> {
fn from(nfa: NFA) -> Self {
type StateSet = BTreeSet<usize>;
let mut transition_table: BTreeMap<StateSet, BTreeMap<Range, StateSet>> = BTreeMap::new();
let mut queue: VecDeque<StateSet> = VecDeque::new();
let start_state = nfa.epsilon_closure(0);
queue.push_back(start_state.clone());
while let Some(state_set) = queue.pop_front() {
let state_set = nfa.epsilon_closure_all(state_set);
let mut next_table: BTreeMap<Range, StateSet> = BTreeMap::new();
for &state in &state_set {
let table_entry = nfa.transition_table.get(&state);
let non_epsilon_table_entries = table_entry
.iter()
.flat_map(|x| x.iter())
.filter_map(|(c, s)| c.as_ref().map(|c| (c.clone(), s)));
for (c, next_states) in non_epsilon_table_entries {
// TODO check for non-disjoint ranges
next_table
.entry(c)
.or_default()
.extend(nfa.epsilon_closure_all(next_states.iter().copied()))
}
}
for states in next_table.values() {
if !transition_table.contains_key(states) && !queue.contains(states) {
queue.push_back(states.clone());
}
}
transition_table.insert(state_set, next_table);
}
let accept_states = transition_table
.keys()
.chain(transition_table.values().flat_map(|v| v.values()))
.filter(|s| s.iter().any(|s| nfa.accept_states.contains(s)))
.cloned()
.collect();
Self {
start_state,
transition_table,
accept_states,
}
}
}
impl<Label: Ord> From<LabeledDFA<Label>> for DFA {
fn from(dfa: LabeledDFA<Label>) -> Self {
let mut state_names = BTreeMap::new();
state_names.insert(&dfa.start_state, 0usize);
let mut next_name = 1usize;
for reachable_state in dfa.transition_table.values().flat_map(|x| x.values()) {
state_names.entry(reachable_state).or_insert_with(|| {
let result = next_name;
next_name = next_name.saturating_add(1);
result
});
}
let transition_table = dfa
.transition_table
.iter()
.map(|(state, table)| {
(
state_names[&state],
table
.iter()
.map(|(c, s)| (c.clone(), state_names[&s]))
.collect(),
)
})
.collect();
let accept_states = state_names
.iter()
.filter(|(s, _)| dfa.accept_states.contains(s))
.map(|(_, n)| n)
.copied()
.collect();
Self {
transition_table,
accept_states,
}
}
}
impl From<NFA> for DFA {
fn from(a: NFA) -> Self {
let intermediate = LabeledDFA::from(a);
Self::from(intermediate)
}
}
impl ToTokens for Range {
fn to_tokens(&self, tokens: &mut TokenStream) {
let start = self.0.start();
let end = self.0.end();
let result = quote!(#start..=#end);
result.to_tokens(tokens);
}
}
impl ToTokens for DFA {
fn to_tokens(&self, tokens: &mut TokenStream) {
let transition = self
.transition_table
.iter()
.flat_map(|(current_state, table)| {
table
.iter()
.map(move |(ch, next_state)| quote!((#current_state, #ch) => #next_state,))
});
let accepts = self.accept_states.iter();
let result = quote! {
let mut state = 0usize;
for c in input.chars() {
state = match (state, c) {
#(#transition)*
_ => return false,
};
}
matches!(state, #(#accepts)|*)
};
result.to_tokens(tokens);
}
}
|
