lr1 parser, unstable

Cargo.toml

@@ -13,3 +13,6 @@ path = "src/main.rs"
 
 [[bin]]
 name = "book"
+
+[[bin]]
+name = "g10"

src/bin/g10.rs

@@ -0,0 +1,87 @@
+use rcompiler::prelude::*;
+use regex::Match;
+use std::collections::HashMap;
+
+double_enum!(
+    BareTokens, Tokens {
+        WhiteSpace,
+        Assign,
+        Add,
+        LBrace,
+        RBrace,
+        Ident(String),
+    }
+);
+
+token_scanner!(
+    Tokens,
+    r"^\s|\t|\n|\r" : |_,_| {
+        Some(WhiteSpace)
+    }
+    r"^\+" : |_,_| {
+        Some(Add)
+    }
+    r"^=" : |_,_| {
+        Some(Assign)
+    }
+    r"^\(" : |_,_| {
+        Some(LBrace)
+    }
+    r"^\)" : |_,_| {
+        Some(RBrace)
+    }
+    r"^[a-zA-Z](\w)*" : |_, m: Match<'_>| {
+        Some(Ident(String::from(m.as_str())))
+    }
+);
+
+#[derive(Debug, PartialEq, Eq, Hash, Clone, PartialOrd, Ord)]
+enum NoneTerminals {
+    E,
+    P,
+    T,
+}
+
+impl<N> From<NoneTerminals> for Sentential<NoneTerminals, N> {
+    fn from(value: NoneTerminals) -> Self {
+        Sentential::NoneTerminal(value)
+    }
+}
+
+impl<T> From<BareTokens> for Sentential<T, BareTokens> {
+    fn from(value: BareTokens) -> Self {
+        Sentential::Terminal(value)
+    }
+}
+
+fn grammer() -> Grammar<NoneTerminals, BareTokens> {
+    use BareTokens::*;
+    use NoneTerminals::*;
+    cfg_grammar![
+        start: P;
+        P -> E;
+        E -> E, Add, T;
+        E -> T;
+        T -> Ident, LBrace, E, RBrace;
+        T -> Ident;
+    ]
+}
+
+fn main() {
+    let code = String::from("b(f)+c");
+    let mut m = Scanner::<Tokens>::new(code).with_skipping(Tokens::WhiteSpace);
+
+    let mut grammar = grammer();
+    grammar.gen_follow();
+    println!("first: {:?}", grammar.first);
+    println!("follow: {:?}", grammar.follow);
+    grammar.gen_lr1_automaton();
+    println!("automaton: {:?}", grammar.lr1_automaton);
+    println!("conflict: {}", grammar.gen_slr_parse_table());
+    println!("conflict: {}", grammar.gen_lr1_parse_table());
+    println!("parse_table: {:?}", grammar.lr1_automaton);
+    println!(
+        "parsed: {:?}",
+        grammar.slr_parser(&mut m.iter_mut()).parse()
+    )
+}

src/cfg/ll_grammar.rs

@@ -2,7 +2,7 @@ use std::{collections::HashMap, fmt::Debug, hash::Hash};
 
 use super::{Grammar, NodeChild, ParseTree, Sentential};
 
-impl<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone> Grammar<N, T> {
+impl<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone + Ord> Grammar<N, T> {
     pub fn gen_ll_parse_table(&mut self) -> bool {
         if self.first.is_none() {
             self.gen_first();
@@ -10,9 +10,6 @@ impl<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone> Grammar
         if self.follow.is_none() {
             self.gen_follow();
         }
-        if self.ll_parse_table.is_some() {
-            return false;
-        }
         let mut conflict = false;
         // left derivation
         // when hiding N and T is next (None = e)
@@ -88,7 +85,7 @@ impl<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone> Grammar
 pub struct LLTabelParser<'a, N, T, S>
 where
     N: PartialEq + Eq + Hash + Clone,
-    T: PartialEq + Eq + Hash + Clone,
+    T: PartialEq + Eq + Hash + Clone + Ord,
     S: Into<T> + PartialEq<T> + Clone,
 {
     grammar: &'a Grammar<N, T>,
@@ -98,7 +95,7 @@ where
 impl<'a, N, T, S> LLTabelParser<'a, N, T, S>
 where
     N: PartialEq + Eq + Hash + Clone + Debug,
-    T: PartialEq + Eq + Hash + Clone + Debug,
+    T: PartialEq + Eq + Hash + Clone + Debug + Ord,
     S: Into<T> + PartialEq<T> + Clone + Debug,
 {
     pub fn parse(&mut self) -> Result<ParseTree<N, S>, String> {

src/cfg/lr0_grammar.rs

@@ -5,13 +5,20 @@ use std::{
     rc::{Rc, Weak},
 };
 
-use super::{Grammar, NodeChild, ParseTree, RuleIndex, Sentential};
+use super::{
+    lr_parser::{LRTabelParser, LrAction, LrActionTable, LrGotoTable},
+    Grammar, RuleIndex, Sentential,
+};
 
 pub type RL0Automaton<N, T> =
     HashMap<Rc<LR0State<N>>, HashMap<Sentential<N, T>, Weak<LR0State<N>>>>;
 
 #[derive(Debug, Eq, PartialEq)]
+/// general state of lr0 automaton
+/// rule and reading point
 pub struct LR0State<N: Hash + Eq>(HashSet<(RuleIndex<N>, usize)>);
+
+/// start state of lr0 automaton
 pub type LR0Start<N> = Weak<LR0State<N>>;
 
 impl<N: Hash + Eq + Ord> Hash for LR0State<N> {
@@ -23,23 +30,13 @@ impl<N: Hash + Eq + Ord> Hash for LR0State<N> {
         }
     }
 }
-#[derive(Debug)]
-pub enum SlrAction<Shift, Reduce> {
-    Shift(Shift),
-    Reduce(Reduce),
-}
-
-/// None is $
-pub type SlrActionTable<N, T> = HashMap<(usize, Option<T>), SlrAction<usize, RuleIndex<N>>>;
-pub type SlrGotoTable<N> = HashMap<(usize, N), usize>;
-pub type SlrParseTable<N, T> = (SlrActionTable<N, T>, SlrGotoTable<N>, usize);
 
 impl<N, T> Grammar<N, T>
 where
     N: PartialEq + Eq + Hash + Clone + Ord,
     T: PartialEq + Eq + Hash + Clone + Ord,
 {
-    pub fn next_kernel(&self, state: &LR0State<N>, read: &Sentential<N, T>) -> LR0State<N> {
+    pub fn lr0_next_kernel(&self, state: &LR0State<N>, read: &Sentential<N, T>) -> LR0State<N> {
         let mut next_state: LR0State<N> = LR0State(HashSet::new());
         for ((from, rule_id), dot) in state.0.iter() {
             let Some(to) = self.rules.get(from).and_then(|v| v.get(*rule_id)) else {
@@ -51,7 +48,7 @@ where
         }
         next_state
     }
-    pub fn readable(&self, state: &LR0State<N>) -> HashSet<Sentential<N, T>> {
+    pub fn lr0_readable(&self, state: &LR0State<N>) -> HashSet<Sentential<N, T>> {
         let mut readables = HashSet::new();
         for ((from, rule_id), dot) in state.0.iter() {
             let Some(to) = self.rules.get(from).and_then(|v| v.get(*rule_id)) else {
@@ -114,8 +111,8 @@ where
                 let mut vec = Vec::new();
 
                 // add clozures from the kernels from all readable symbols
-                for none_terminal in self.readable(&state) {
+                for none_terminal in self.lr0_readable(&state) {
-                    let next_state = self.lr0_clozure(self.next_kernel(&state, &none_terminal));
+                    let next_state = self.lr0_clozure(self.lr0_next_kernel(&state, &none_terminal));
                     let rc = Rc::new(next_state);
                     if let Some((k, _)) = out.get_key_value(&rc) {
                         vec.push((none_terminal, Rc::downgrade(k)));
@@ -136,6 +133,9 @@ where
     }
 
     pub fn gen_slr_parse_table(&mut self) -> bool {
+        if self.first.is_none() {
+            self.gen_first();
+        }
         if self.follow.is_none() {
             self.gen_follow();
         }
@@ -158,15 +158,15 @@ where
             .upgrade()
             .and_then(|rc| ids.get(&rc))
             .expect("Found broken state in slr parse table gen.");
-        let mut action: SlrActionTable<N, T> = HashMap::new();
+        let mut action: LrActionTable<N, T> = HashMap::new();
-        let mut goto: SlrGotoTable<N> = HashMap::new();
+        let mut goto: LrGotoTable<N> = HashMap::new();
         let mut conflict = false;
         for (state, to) in lr0_automaton.0.iter() {
             let id = ids
                 .get(state)
                 .expect("Found broken state in slr parse table gen.");
 
-            for go in self.readable(state) {
+            for go in self.lr0_readable(state) {
                 let Some(to) = to.get(&go).and_then(|to| to.upgrade()) else {
                     continue;
                 };
@@ -178,7 +178,7 @@ where
                 match go {
                     Sentential::Terminal(t) => {
                         conflict |= action
-                            .insert((*id, Some(t)), SlrAction::Shift(*to_id))
+                            .insert((*id, Some(t)), LrAction::Shift(*to_id))
                             .is_some();
                     }
                     Sentential::NoneTerminal(nt) => {
@@ -194,7 +194,7 @@ where
                 if to.len() <= *dot {
                     for follow in self.follow(from) {
                         conflict |= action
-                            .insert((*id, follow), SlrAction::Reduce((from.clone(), *rule_id)))
+                            .insert((*id, follow), LrAction::Reduce((from.clone(), *rule_id)))
                             .is_some();
                     }
                 }
@@ -207,137 +207,16 @@ where
     pub fn slr_parser<'a, S: Into<T> + PartialEq<T> + Clone>(
         &'a self,
         iter: &'a mut dyn Iterator<Item = Result<S, String>>,
-    ) -> SLRTabelParser<N, T, S> {
+    ) -> LRTabelParser<N, T, S> {
         assert!(
             self.slr_parse_table.is_some(),
             "Please call gen_slr_parse_table before this!"
         );
-        SLRTabelParser {
+        LRTabelParser {
             input: iter,
-            grammar: self,
+            start_rule: &self.start,
-        }
+            rules: &self.rules,
-    }
+            parse_table: self.slr_parse_table.as_ref().unwrap(),
-    pub fn get_slr_action(
-        &self,
-        state: &usize,
-        next: &Option<T>,
-    ) -> Option<&SlrAction<usize, (N, usize)>> {
-        assert!(
-            self.slr_parse_table.is_some(),
-            "Please call gen_slr_parse_table before this!"
-        );
-        self.slr_parse_table
-            .as_ref()
-            .unwrap()
-            .0
-            .get(&(*state, next.clone()))
-    }
-    pub fn get_slr_goto(&self, state: &usize, next: &N) -> Option<&usize> {
-        assert!(
-            self.slr_parse_table.is_some(),
-            "Please call gen_slr_parse_table before this!"
-        );
-        self.slr_parse_table
-            .as_ref()
-            .unwrap()
-            .1
-            .get(&(*state, next.clone()))
-    }
-}
-
-pub struct SLRTabelParser<'a, N, T, S>
-where
-    N: PartialEq + Eq + Hash + Clone,
-    T: PartialEq + Eq + Hash + Clone,
-    S: Into<T> + PartialEq<T> + Clone,
-{
-    grammar: &'a Grammar<N, T>,
-    input: &'a mut dyn Iterator<Item = Result<S, String>>,
-}
-
-impl<'a, N, T, S> SLRTabelParser<'a, N, T, S>
-where
-    N: PartialEq + Eq + Hash + Clone + Debug + Ord,
-    T: PartialEq + Eq + Hash + Clone + Debug + Ord,
-    S: Into<T> + PartialEq<T> + Clone + Debug,
-{
-    pub fn parse(&mut self) -> Result<ParseTree<N, S>, String> {
-        let mut stack: Vec<(NodeChild<N, S>, usize)> = Vec::new();
-
-        let mut next = match self.input.next() {
-            Some(Ok(d)) => Some(d),
-            Some(Err(err)) => return Err(format!("Invalid token: {}", err)),
-            None => None,
-        };
-        let mut first = true;
-        loop {
-            let state = if first {
-                self.grammar.slr_parse_table.as_ref().unwrap().2
-            } else {
-                let Some(state) = stack.last() else {
-                    return Err("Unexpected EOS".into());
-                };
-                state.1
-            };
-            first = false;
-            let Some(current_state) = self
-                .grammar
-                .get_slr_action(&state, &next.as_ref().map(|f| f.clone().into()))
-            else {
-                return Err(format!(
-                    "Unexpected Token: {}",
-                    next.map(|f| format!("{f:?}"))
-                        .unwrap_or("end of file".to_string())
-                ));
-            };
-
-            match current_state {
-                SlrAction::Shift(to) => {
-                    stack.push((NodeChild::Data(next.expect("Can not shift on EOF.")), *to));
-                    next = match self.input.next() {
-                        Some(Ok(d)) => Some(d),
-                        Some(Err(err)) => return Err(format!("Invalid token: {}", err)),
-                        None => None,
-                    };
-                }
-                SlrAction::Reduce((rule, ind)) => {
-                    let Some(r) = self.grammar.rules.get(rule).and_then(|e| e.get(*ind)) else {
-                        return Err(format!("Invalid rule: {:?}-{}", rule, ind));
-                    };
-                    let mut childs = Vec::new();
-                    for elem in r.iter().rev() {
-                        let Some(last) = stack.pop() else {
-                            return Err("Unexpected EOF".into());
-                        };
-                        if last.0 != *elem {
-                            return Err(format!("Broken Stack: {:?} and {:?}", last.0, elem));
-                        }
-                        childs.push(last);
-                    }
-                    if self.grammar.start == *rule {
-                        return Ok(ParseTree {
-                            rule: Some((rule.clone(), *ind)),
-                            childs: childs.into_iter().rev().map(|(a, _)| a.clone()).collect(),
-                        });
-                    }
-                    let Some(state) = stack.last() else {
-                        return Err("Unexpected EOS".into());
-                    };
-                    let Some(next) = self.grammar.get_slr_goto(&state.1, rule) else {
-                        return Err(format!(
-                            "Invalid reduction: state: {} rule: {:?}",
-                            state.1, rule
-                        ));
-                    };
-                    stack.push((
-                        NodeChild::Child(ParseTree {
-                            rule: Some((rule.clone(), *ind)),
-                            childs: childs.into_iter().rev().map(|(d, _)| d).collect(),
-                        }),
-                        *next,
-                    ));
-                }
-            }
         }
     }
 }

src/cfg/lr1_grammar.rs

@@ -0,0 +1,299 @@
+use super::{
+    lr_parser::{LRTabelParser, LrAction, LrActionTable, LrGotoTable},
+    Grammar, RuleIndex, Sentential,
+};
+use std::{
+    cmp::Ordering,
+    collections::{HashMap, HashSet},
+    hash::{Hash, Hasher},
+    rc::{Rc, Weak},
+};
+
+/// lookahead table of lr1 state, None is $
+#[derive(Debug, Clone, Eq, PartialEq)]
+pub struct LR1Lookahead<T: Hash + Eq>(HashSet<Option<T>>);
+
+impl<T: Hash + Eq> Default for LR1Lookahead<T> {
+    fn default() -> Self {
+        Self(HashSet::new())
+    }
+}
+
+impl<T: Hash + Eq + Ord> Ord for LR1Lookahead<T> {
+    fn cmp(&self, other: &Self) -> Ordering {
+        let mut a: Vec<&Option<T>> = self.0.iter().collect();
+        let mut b: Vec<&Option<T>> = other.0.iter().collect();
+        a.sort();
+        b.sort();
+        a.cmp(&b)
+    }
+}
+
+impl<T: Hash + Eq + Ord> PartialOrd for LR1Lookahead<T> {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl<T: Hash + Eq + Ord> Hash for LR1Lookahead<T> {
+    fn hash<H: Hasher>(&self, state: &mut H) {
+        let mut a: Vec<&Option<T>> = self.0.iter().collect();
+        a.sort();
+        for s in a.iter() {
+            s.hash(state);
+        }
+    }
+}
+
+#[derive(Debug, Eq, PartialEq)]
+/// general state of lr1 automaton
+pub struct LR1State<N: Hash + Eq, T: Hash + Eq + Ord>(
+    HashSet<(RuleIndex<N>, LR1Lookahead<T>, usize)>,
+);
+
+impl<N: Hash + Eq + Ord, T: Hash + Eq + Ord> Hash for LR1State<N, T> {
+    fn hash<H: Hasher>(&self, state: &mut H) {
+        let mut a: Vec<&(RuleIndex<N>, LR1Lookahead<T>, usize)> = self.0.iter().collect();
+        a.sort();
+        for s in a.iter() {
+            s.hash(state);
+        }
+    }
+}
+
+/// start state of lr1 automaton
+pub type LR1Start<N, T> = Weak<LR1State<N, T>>;
+
+pub type RL1Automaton<N, T> =
+    HashMap<Rc<LR1State<N, T>>, HashMap<Sentential<N, T>, Weak<LR1State<N, T>>>>;
+
+impl<N, T> Grammar<N, T>
+where
+    N: PartialEq + Eq + Hash + Clone + Ord,
+    T: PartialEq + Eq + Hash + Clone + Ord,
+{
+    pub fn lr1_next_kernel(
+        &self,
+        state: &LR1State<N, T>,
+        read: &Sentential<N, T>,
+    ) -> LR1State<N, T> {
+        let mut next_state: LR1State<N, T> = LR1State(HashSet::new());
+        for ((from, rule_id), lookahead, dot) in state.0.iter() {
+            let Some(to) = self.rules.get(from).and_then(|v| v.get(*rule_id)) else {
+                continue;
+            };
+            if to.get(*dot).map(|elem| *elem == *read).unwrap_or(false) {
+                next_state
+                    .0
+                    .insert(((from.clone(), *rule_id), lookahead.clone(), dot + 1));
+            }
+        }
+        next_state
+    }
+
+    pub fn lr1_readable(&self, state: &LR1State<N, T>) -> HashSet<Sentential<N, T>> {
+        let mut readables = HashSet::new();
+        for ((from, rule_id), _, dot) in state.0.iter() {
+            let Some(to) = self.rules.get(from).and_then(|v| v.get(*rule_id)) else {
+                continue;
+            };
+            if let Some(l) = to.get(*dot) {
+                readables.insert(l.clone());
+            }
+        }
+        readables
+    }
+
+    pub fn lr1_clozure(&self, mut state: LR1State<N, T>) -> LR1State<N, T> {
+        assert!(self.first.is_some(), "Please call gen_first before this!");
+        assert!(
+            self.produces_epsilon.is_some(),
+            "Please call gen_produces_epsilon before this!"
+        );
+        loop {
+            let mut change = false;
+
+            let relevant = state
+                .0
+                .iter()
+                .filter_map(|((from, rule_id), lookahead, dot)| {
+                    self.rules
+                        .get(from)
+                        .and_then(|v| v.get(*rule_id))
+                        .and_then(|to| match to.get(*dot) {
+                            Some(Sentential::NoneTerminal(b)) => {
+                                Some((b.clone(), to[dot + 1..].to_vec(), lookahead.clone()))
+                            }
+                            Some(Sentential::Terminal(_)) | None => None,
+                        })
+                })
+                .collect::<Vec<_>>();
+            for (nt, rest, lookahead) in relevant {
+                if let Some(rule) = self.rules.get(&nt) {
+                    let mut lookahead = if self.can_produce_epsilon_sen(&rest) {
+                        lookahead
+                    } else {
+                        LR1Lookahead::default()
+                    };
+                    lookahead.0.extend(
+                        // extend with first set of rest, except e
+                        self.first(&rest)
+                            .iter()
+                            .filter_map(|t| t.as_ref().map(|elem| Some(elem.clone()))),
+                    );
+                    for to in 0..rule.len() {
+                        change |= state.0.insert(((nt.clone(), to), lookahead.clone(), 0));
+                    }
+                }
+            }
+
+            if !change {
+                return state;
+            }
+        }
+    }
+
+    pub fn gen_lr1_automaton(&mut self) {
+        if self.first.is_none() {
+            self.gen_first();
+        }
+        if self.produces_epsilon.is_none() {
+            self.gen_produces_epsilon();
+        }
+        let mut out: RL1Automaton<N, T> = HashMap::new();
+        // add state zero
+        let mut start_state = LR1State(HashSet::new());
+        if let Some(rule) = self.rules.get(&self.start) {
+            for to in 0..rule.len() {
+                start_state.0.insert((
+                    (self.start.clone(), to),
+                    LR1Lookahead(HashSet::from([None])),
+                    0,
+                ));
+            }
+        }
+        // add state to graph and mark for todo
+        let rc = Rc::new(self.lr1_clozure(start_state));
+        let start = Rc::downgrade(&rc);
+        let mut todo = vec![Rc::downgrade(&rc)];
+        out.insert(rc, HashMap::new());
+
+        // add states while marked states exists
+        while let Some(state) = todo.pop() {
+            if let Some(state) = state.upgrade() {
+                // new adjacent list
+                let mut vec = Vec::new();
+
+                // add clozures from the kernels from all readable symbols
+                for none_terminal in self.lr1_readable(&state) {
+                    let next_state = self.lr1_clozure(self.lr1_next_kernel(&state, &none_terminal));
+                    let rc = Rc::new(next_state);
+                    if let Some((k, _)) = out.get_key_value(&rc) {
+                        vec.push((none_terminal, Rc::downgrade(k)));
+                    } else {
+                        todo.push(Rc::downgrade(&rc));
+                        vec.push((none_terminal, Rc::downgrade(&rc)));
+                        out.insert(rc, HashMap::new());
+                    }
+                }
+                // write adjacent list to state
+                // does not check duplicates. Is not needed, because `readable` returns a set
+                out.entry(state).and_modify(|elem| {
+                    elem.extend(vec);
+                });
+            }
+        }
+        self.lr1_automaton = Some((out, start));
+    }
+
+    pub fn gen_lr1_parse_table(&mut self) -> bool {
+        if self.first.is_none() {
+            self.gen_first();
+        }
+        if self.follow.is_none() {
+            self.gen_follow();
+        }
+        if self.lr1_automaton.is_none() {
+            self.gen_lr1_automaton();
+        }
+
+        let lr1_automaton = self.lr1_automaton.as_ref().unwrap();
+
+        let ids: HashMap<Rc<LR1State<N, T>>, usize> = HashMap::from_iter(
+            lr1_automaton
+                .0
+                .iter()
+                .enumerate()
+                .map(|(id, (a, _))| (a.clone(), id)),
+        );
+
+        let start = *lr1_automaton
+            .1
+            .upgrade()
+            .and_then(|rc| ids.get(&rc))
+            .expect("Found broken state in slr parse table gen.");
+        let mut action: LrActionTable<N, T> = HashMap::new();
+        let mut goto: LrGotoTable<N> = HashMap::new();
+        let mut conflict = false;
+        for (state, to) in lr1_automaton.0.iter() {
+            let id = ids
+                .get(state)
+                .expect("Found broken state in slr parse table gen.");
+
+            for go in self.lr1_readable(state) {
+                let Some(to) = to.get(&go).and_then(|to| to.upgrade()) else {
+                    continue;
+                };
+
+                let to_id = ids
+                    .get(&to)
+                    .expect("Found broken state in slr parse table gen.");
+
+                match go {
+                    Sentential::Terminal(t) => {
+                        conflict |= action
+                            .insert((*id, Some(t)), LrAction::Shift(*to_id))
+                            .is_some();
+                    }
+                    Sentential::NoneTerminal(nt) => {
+                        conflict |= goto.insert((*id, nt), *to_id).is_some();
+                    }
+                };
+            }
+
+            for ((from, rule_id), lookahead, dot) in state.0.iter() {
+                let Some(to) = self.rules.get(from).and_then(|v| v.get(*rule_id)) else {
+                    continue;
+                };
+                if to.len() <= *dot {
+                    for follow in lookahead.0.iter() {
+                        conflict |= action
+                            .insert(
+                                (*id, follow.clone()),
+                                LrAction::Reduce((from.clone(), *rule_id)),
+                            )
+                            .is_some();
+                    }
+                }
+            }
+        }
+        self.lr1_parse_table = Some((action, goto, start));
+        conflict
+    }
+
+    pub fn lr1_parser<'a, S: Into<T> + PartialEq<T> + Clone>(
+        &'a self,
+        iter: &'a mut dyn Iterator<Item = Result<S, String>>,
+    ) -> LRTabelParser<N, T, S> {
+        assert!(
+            self.lr1_parse_table.is_some(),
+            "Please call gen_lr1_parse_table before this!"
+        );
+        LRTabelParser {
+            input: iter,
+            start_rule: &self.start,
+            rules: &self.rules,
+            parse_table: self.lr1_parse_table.as_ref().unwrap(),
+        }
+    }
+}

src/cfg/lr_parser.rs

@@ -0,0 +1,133 @@
+use std::{collections::HashMap, fmt::Debug, hash::Hash};
+
+use super::{NodeChild, ParseTree, RuleIndex, Sentential};
+
+#[derive(Debug)]
+pub enum LrAction<Shift, Reduce> {
+    Shift(Shift),
+    Reduce(Reduce),
+}
+
+/// None is $
+pub type LrActionTable<N, T> = HashMap<(usize, Option<T>), LrAction<usize, RuleIndex<N>>>;
+pub type LrGotoTable<N> = HashMap<(usize, N), usize>;
+pub type LrParseTable<N, T> = (LrActionTable<N, T>, LrGotoTable<N>, usize);
+
+pub struct LRTabelParser<'a, N, T, S>
+where
+    N: Eq + Hash + Clone,
+    T: Eq + Hash + Clone + Ord,
+    S: Into<T> + PartialEq<T> + Clone,
+{
+    pub start_rule: &'a N,
+    pub rules: &'a HashMap<N, Vec<Vec<Sentential<N, T>>>>,
+    pub parse_table: &'a LrParseTable<N, T>,
+    pub input: &'a mut dyn Iterator<Item = Result<S, String>>,
+}
+
+impl<'a, N, T, S> LRTabelParser<'a, N, T, S>
+where
+    N: Eq + Hash + Clone,
+    T: Eq + Hash + Clone + Ord,
+    S: Into<T> + PartialEq<T> + Clone,
+{
+    pub fn get_action(
+        &self,
+        state: &usize,
+        next: &Option<T>,
+    ) -> Option<&LrAction<usize, (N, usize)>> {
+        self.parse_table.0.get(&(*state, next.clone()))
+    }
+    pub fn get_goto(&self, state: &usize, next: &N) -> Option<&usize> {
+        self.parse_table.1.get(&(*state, next.clone()))
+    }
+}
+
+impl<'a, N, T, S> LRTabelParser<'a, N, T, S>
+where
+    N: Eq + Hash + Clone + Debug + Ord,
+    T: Eq + Hash + Clone + Debug + Ord,
+    S: Into<T> + PartialEq<T> + Clone + Debug,
+{
+    pub fn parse(&mut self) -> Result<ParseTree<N, S>, String> {
+        let mut stack: Vec<(NodeChild<N, S>, usize)> = Vec::new();
+
+        let mut next = match self.input.next() {
+            Some(Ok(d)) => Some(d),
+            Some(Err(err)) => return Err(format!("Invalid token: {}", err)),
+            None => None,
+        };
+        let mut first = true;
+        loop {
+            let state = if first {
+                // start with first state
+                self.parse_table.2
+            } else {
+                let Some(state) = stack.last() else {
+                    return Err("Unexpected EOS 1".into());
+                };
+                state.1
+            };
+            first = false;
+            let Some(current_state) =
+                self.get_action(&state, &next.as_ref().map(|f| f.clone().into()))
+            else {
+                return Err(format!(
+                    "Unexpected Token: {}",
+                    next.map(|f| format!("{f:?}"))
+                        .unwrap_or("end of file".to_string())
+                ));
+            };
+
+            println!("next: {next:?}, state: {current_state:?}, stack: {stack:?}");
+
+            match current_state {
+                LrAction::Shift(to) => {
+                    stack.push((NodeChild::Data(next.expect("Can not shift on EOF.")), *to));
+                    next = match self.input.next() {
+                        Some(Ok(d)) => Some(d),
+                        Some(Err(err)) => return Err(format!("Invalid token: {}", err)),
+                        None => None,
+                    };
+                }
+                LrAction::Reduce((rule, ind)) => {
+                    let Some(r) = self.rules.get(rule).and_then(|e| e.get(*ind)) else {
+                        return Err(format!("Invalid rule: {:?}-{}", rule, ind));
+                    };
+                    let mut childs = Vec::new();
+                    for elem in r.iter().rev() {
+                        let Some(last) = stack.pop() else {
+                            return Err("Unexpected EOF".into());
+                        };
+                        if last.0 != *elem {
+                            return Err(format!("Broken Stack: {:?} and {:?}", last.0, elem));
+                        }
+                        childs.push(last);
+                    }
+                    if *self.start_rule == *rule {
+                        return Ok(ParseTree {
+                            rule: Some((rule.clone(), *ind)),
+                            childs: childs.into_iter().rev().map(|(a, _)| a.clone()).collect(),
+                        });
+                    }
+                    let Some(state) = stack.last() else {
+                        return Err("Unexpected EOS 2".into());
+                    };
+                    let Some(next) = self.get_goto(&state.1, rule) else {
+                        return Err(format!(
+                            "Invalid reduction: state: {} rule: {:?}",
+                            state.1, rule
+                        ));
+                    };
+                    stack.push((
+                        NodeChild::Child(ParseTree {
+                            rule: Some((rule.clone(), *ind)),
+                            childs: childs.into_iter().rev().map(|(d, _)| d).collect(),
+                        }),
+                        *next,
+                    ));
+                }
+            }
+        }
+    }
+}

src/cfg/mod.rs

@@ -4,10 +4,14 @@ use std::{
     hash::Hash,
 };
 
-use lr0_grammar::{LR0Start, RL0Automaton, SlrParseTable};
+use lr0_grammar::{LR0Start, RL0Automaton};
+use lr1_grammar::{LR1Start, RL1Automaton};
+use lr_parser::LrParseTable;
 
 pub mod ll_grammar;
 pub mod lr0_grammar;
+pub mod lr1_grammar;
+pub mod lr_parser;
 
 #[macro_export]
 macro_rules! cfg_grammar {
@@ -27,15 +31,7 @@ macro_rules! cfg_grammar {
                 }
                 map.get_mut(&$left).unwrap().push(vec![$($right.into()),*]);
             })*
-            $crate::cfg::Grammar {
+            $crate::cfg::Grammar::new($start, map)
-                start: $start,
-                rules: map,
-                first: None,
-                follow: None,
-                ll_parse_table: None,
-                lr0_automaton: None,
-                slr_parse_table: None,
-            }
         }
     };
 }
@@ -70,9 +66,14 @@ impl<T: Ord, N: Ord> Ord for Sentential<N, T> {
 
 pub type RuleIndex<N> = (N, usize);
 
-pub struct Grammar<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone> {
+pub struct Grammar<N, T>
+where
+    N: PartialEq + Eq + Hash + Clone,
+    T: PartialEq + Eq + Hash + Clone + Ord,
+{
     pub start: N,
     pub rules: HashMap<N, Vec<Vec<Sentential<N, T>>>>,
+    pub produces_epsilon: Option<HashSet<N>>,
     /// none is epsilon
     pub first: Option<HashMap<N, HashSet<Option<T>>>>,
     /// none is $
@@ -89,22 +90,73 @@ pub struct Grammar<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash +
     pub lr0_automaton: Option<(RL0Automaton<N, T>, LR0Start<N>)>,
 
     ///
-    pub slr_parse_table: Option<SlrParseTable<N, T>>,
+    pub slr_parse_table: Option<LrParseTable<N, T>>,
+
+    ///
+    pub lr1_automaton: Option<(RL1Automaton<N, T>, LR1Start<N, T>)>,
+
+    ///
+    pub lr1_parse_table: Option<LrParseTable<N, T>>,
 }
 
-impl<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone> Grammar<N, T> {
+impl<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone + Ord> Grammar<N, T> {
+    pub fn new(start: N, rules: HashMap<N, Vec<Vec<Sentential<N, T>>>>) -> Self {
+        Self {
+            start,
+            rules,
+            produces_epsilon: None,
+            first: None,
+            follow: None,
+            ll_parse_table: None,
+            lr0_automaton: None,
+            slr_parse_table: None,
+            lr1_automaton: None,
+            lr1_parse_table: None,
+        }
+    }
+
+    pub fn gen_produces_epsilon(&mut self) {
+        let mut out: HashSet<N> = HashSet::new();
+        loop {
+            let mut change = false;
+            for (from, to) in self.rules.iter() {
+                for to in to.iter() {
+                    if to.iter().all(|sen| match sen {
+                        Sentential::Terminal(_) => false,
+                        Sentential::NoneTerminal(a) => out.contains(a),
+                    }) {
+                        change |= out.insert(from.clone());
+                    }
+                }
+            }
+            if !change {
+                break;
+            }
+        }
+        self.produces_epsilon = Some(out);
+    }
+
     pub fn can_produce_epsilon(&self, rule: &Sentential<N, T>) -> bool {
+        assert!(
+            self.produces_epsilon.is_some(),
+            "Please call gen_produces_epsilon before this!"
+        );
+
         match rule {
             Sentential::Terminal(_) => false,
-            Sentential::NoneTerminal(nt) => self
+            Sentential::NoneTerminal(nt) => self.produces_epsilon.as_ref().unwrap().contains(nt),
-                .rules
-                .get(nt)
-                .map(|f| f.iter().any(|v| v.is_empty()))
-                .unwrap_or(false),
         }
     }
 
+    pub fn can_produce_epsilon_sen(&self, rule: &Vec<Sentential<N, T>>) -> bool {
+        rule.iter()
+            .all(|s: &Sentential<N, T>| self.can_produce_epsilon(s))
+    }
+
     pub fn gen_first(&mut self) {
+        if self.produces_epsilon.is_none() {
+            self.gen_produces_epsilon();
+        }
         let mut first: HashMap<N, HashSet<Option<T>>> = HashMap::new();
         loop {
             let mut change = false;
@@ -165,6 +217,8 @@ impl<N: PartialEq + Eq + Hash + Clone, T: PartialEq + Eq + Hash + Clone> Grammar
         self.first = Some(first);
     }
 
+    /// get first of sentential
+    /// None is e
     pub fn first(&self, sent: &Vec<Sentential<N, T>>) -> HashSet<Option<T>> {
         assert!(self.first.is_some(), "Please call gen_first before this!");
         let mut out = HashSet::<Option<T>>::new();

src/main.rs

@@ -104,7 +104,7 @@ token_scanner!(
     }
 );
 
-#[derive(Debug, PartialEq, Eq, Hash, Clone)]
+#[derive(Debug, PartialEq, Eq, Hash, Clone, PartialOrd, Ord)]
 enum NoneTerminals {
     P,   // Program, ; separated
     L,   // Line of code
@@ -193,9 +193,11 @@ fn main() {
 
     let mut grammar = grammer();
     grammar.gen_follow();
-    println!("first: {:?}", grammar.first);
+    //println!("first: {:?}", grammar.first);
-    println!("follow: {:?}", grammar.follow);
+    //println!("follow: {:?}", grammar.follow);
-    let conflict = grammar.gen_ll_parse_table();
+    grammar.gen_lr1_automaton();
+    println!("conflict: {:?}", grammar.lr1_automaton); 
+    /* let conflict = grammar.gen_ll_parse_table();
     println!("conflict: {conflict}");
     println!("prase table: {:?}", grammar.ll_parse_table);
     println!("parse\n\n");
@@ -205,5 +207,5 @@ fn main() {
             .ll_parser(&mut m.iter_mut())
             .parse()
             .map(|tree| tree.clean())
-    )
+    ) */
 }