Implement Counterexamples

Implement Nonunifying Counterexamples.
See https://www.cs.cornell.edu/andru/papers/cupex/cupex.pdf

These examples are rendered for conflicts.

```
Shift Conflict:
0:  stmt                                                           "end of file"
    3:  expr                                         '?' stmt stmt
        6:  expr                            '+' expr
            6: expr '+' expr
                        6: expr  • '+' expr

Reduce Conflict:
0:  stmt                                                "end of file"
    3:  expr                              '?' stmt stmt
        6:  expr                 '+' expr
            6: expr '+' expr  •
```

doc/TODO.md

@@ -44,6 +44,10 @@
 * Reporting
   * [ ] Bison style
     * [ ] Wrap not selected reduce with "[]". See basic.output file generated by Bison.
+* Counterexamples
+  * [x] Nonunifying Counterexamples
+  * [ ] Unifying Counterexamples
+  * [ ] Performance improvement using reverse_transitions and reverse_productions
 * Error Tolerance
   * [x] Corchuelo et al. algorithm with N = 1 (this means the next token when error is raised)
   * [x] Add new decl for error token semantic value initialization (%error-token)

lib/lrama.rb

@@ -1,6 +1,7 @@
 require "lrama/bitmap"
 require "lrama/command"
 require "lrama/context"
+require "lrama/counterexamples"
 require "lrama/digraph"
 require "lrama/grammar"
 require "lrama/lexer"

lib/lrama/command.rb

@@ -67,7 +67,7 @@ def validate_report(report)
       bison_list = %w[states itemsets lookaheads solved counterexamples cex all none]
       others = %w[verbose]
       list = bison_list + others
-      not_supported = %w[counterexamples cex none]
+      not_supported = %w[cex none]
       h = { grammar: true }
 
       report.each do |r|

lib/lrama/counterexamples.rb

@@ -0,0 +1,285 @@
+require "set"
+
+require "lrama/counterexamples/derivation"
+require "lrama/counterexamples/example"
+require "lrama/counterexamples/path"
+require "lrama/counterexamples/state_item"
+require "lrama/counterexamples/triple"
+
+module Lrama
+  # See: https://www.cs.cornell.edu/andru/papers/cupex/cupex.pdf
+  #      4. Constructing Nonunifying Counterexamples
+  class Counterexamples
+    attr_reader :transitions, :productions
+
+    def initialize(states)
+      @states = states
+      setup_transitions
+      setup_productions
+    end
+
+    def to_s
+      "#<Counterexamples>"
+    end
+    alias :inspect :to_s
+
+    def compute(conflict_state)
+      conflict_state.conflicts.flat_map do |conflict|
+        case conflict.type
+        when :shift_reduce
+          shift_reduce_example(conflict_state, conflict)
+        when :reduce_reduce
+          reduce_reduce_examples(conflict_state, conflict)
+        end
+      end.compact
+    end
+
+    private
+
+    def setup_transitions
+      # Hash [StateItem, Symbol] => StateItem
+      @transitions = {}
+      # Hash [StateItem, Symbol] => Set(StateItem)
+      @reverse_transitions = {}
+
+      @states.states.each do |src_state|
+        trans = {}
+
+        src_state.transitions.each do |shift, next_state|
+          trans[shift.next_sym] = next_state
+        end
+
+        src_state.items.each do |src_item|
+          next if src_item.end_of_rule?
+          sym = src_item.next_sym
+          dest_state = trans[sym]
+
+          dest_state.kernels.each do |dest_item|
+            next unless (src_item.rule == dest_item.rule) && (src_item.position + 1 == dest_item.position)
+            src_state_item = StateItem.new(src_state, src_item)
+            dest_state_item = StateItem.new(dest_state, dest_item)
+
+            @transitions[[src_state_item, sym]] = dest_state_item
+
+            key = [dest_state_item, sym]
+            @reverse_transitions[key] ||= Set.new
+            @reverse_transitions[key] << src_state_item
+          end
+        end
+      end
+    end
+
+    def setup_productions
+      # Hash [StateItem] => Set(Item)
+      @productions = {}
+      # Hash [State, Symbol] => Set(Item). Symbol is nterm
+      @reverse_productions = {}
+
+      @states.states.each do |state|
+        # LHS => Set(Item)
+        h = {}
+
+        state.closure.each do |item|
+          sym = item.lhs
+
+          h[sym] ||= Set.new
+          h[sym] << item
+        end
+
+        state.items.each do |item|
+          next if item.end_of_rule?
+          next if item.next_sym.term?
+
+          sym = item.next_sym
+          state_item = StateItem.new(state, item)
+          key = [state, sym]
+
+          @productions[state_item] = h[sym]
+
+          @reverse_productions[key] ||= Set.new
+          @reverse_productions[key] << item
+        end
+      end
+    end
+
+    def shift_reduce_example(conflict_state, conflict)
+      conflict_symbol = conflict.symbols.first
+      shift_conflict_item = conflict_state.items.find { |item| item.next_sym == conflict_symbol }
+      path2 = shortest_path(conflict_state, conflict.reduce.item, conflict_symbol)
+      path1 = find_shift_conflict_shortest_path(path2, conflict_state, shift_conflict_item)
+
+      Example.new(path1, path2, conflict, conflict_symbol, self)
+    end
+
+    def reduce_reduce_examples(conflict_state, conflict)
+      conflict_symbol = conflict.symbols.first
+      path1 = shortest_path(conflict_state, conflict.reduce1.item, conflict_symbol)
+      path2 = shortest_path(conflict_state, conflict.reduce2.item, conflict_symbol)
+
+      Example.new(path1, path2, conflict, conflict_symbol, self)
+    end
+
+    def find_shift_conflict_shortest_path(reduce_path, conflict_state, conflict_item)
+      state_items = find_shift_conflict_shortest_state_items(reduce_path, conflict_state, conflict_item)
+      build_paths_from_state_items(state_items)
+    end
+
+    def find_shift_conflict_shortest_state_items(reduce_path, conflict_state, conflict_item)
+      target_state_item = StateItem.new(conflict_state, conflict_item)
+      result = [target_state_item]
+      reversed_reduce_path = reduce_path.to_a.reverse
+      # Index for state_item
+      i = 0
+
+      while (path = reversed_reduce_path[i])
+        # Index for prev_state_item
+        j = i + 1
+        _j = j
+
+        while (prev_path = reversed_reduce_path[j])
+          if prev_path.production?
+            j += 1
+          else
+            break
+          end
+        end
+
+        state_item = path.to
+        prev_state_item = prev_path&.to
+
+        if target_state_item == state_item || target_state_item.item.start_item?
+          result.concat(reversed_reduce_path[_j..-1].map(&:to))
+          break
+        end
+
+        if target_state_item.item.beginning_of_rule?
+          queue = []
+          queue << [target_state_item]
+
+          # Find reverse production
+          while (sis = queue.shift)
+            si = sis.last
+
+            # Reach to start state
+            if si.item.start_item?
+              sis.shift
+              result.concat(sis)
+              target_state_item = si
+              break
+            end
+
+            if !si.item.beginning_of_rule?
+              key = [si, si.item.previous_sym]
+              @reverse_transitions[key].each do |prev_target_state_item|
+                next if prev_target_state_item.state != prev_state_item.state
+                sis.shift
+                result.concat(sis)
+                result << prev_target_state_item
+                target_state_item = prev_target_state_item
+                i = j
+                queue.clear
+                break
+              end
+            else
+              key = [si.state, si.item.lhs]
+              @reverse_productions[key].each do |item|
+                state_item = StateItem.new(si.state, item)
+                queue << (sis + [state_item])
+              end
+            end
+          end
+        else
+          # Find reverse transition
+          key = [target_state_item, target_state_item.item.previous_sym]
+          @reverse_transitions[key].each do |prev_target_state_item|
+            next if prev_target_state_item.state != prev_state_item.state
+            result << prev_target_state_item
+            target_state_item = prev_target_state_item
+            i = j
+            break
+          end
+        end
+      end
+
+      result.reverse
+    end
+
+    def build_paths_from_state_items(state_items)
+      paths = state_items.zip([nil] + state_items).map do |si, prev_si|
+        case
+        when prev_si.nil?
+          StartPath.new(si)
+        when si.item.beginning_of_rule?
+          ProductionPath.new(prev_si, si)
+        else
+          TransitionPath.new(prev_si, si)
+        end
+      end
+
+      paths
+    end
+
+    def shortest_path(conflict_state, conflict_reduce_item, conflict_term)
+      # queue: is an array of [Triple, [Path]]
+      queue = []
+      visited = {}
+      start_state = @states.states.first
+      raise "BUG: Start state should be just one kernel." if start_state.kernels.count != 1
+
+      start = Triple.new(start_state, start_state.kernels.first, Set.new([@states.eof_symbol]))
+
+      queue << [start, [StartPath.new(start.state_item)]]
+
+      while true
+        triple, paths = queue.shift
+
+        next if visited[triple]
+        visited[triple] = true
+
+        # Found
+        if triple.state == conflict_state && triple.item == conflict_reduce_item && triple.l.include?(conflict_term)
+          return paths
+        end
+
+        # transition
+        triple.state.transitions.each do |shift, next_state|
+          next unless triple.item.next_sym && triple.item.next_sym == shift.next_sym
+          next_state.kernels.each do |kernel|
+            next if kernel.rule != triple.item.rule
+            t = Triple.new(next_state, kernel, triple.l)
+            queue << [t, paths + [TransitionPath.new(triple.state_item, t.state_item)]]
+          end
+        end
+
+        # production step
+        triple.state.closure.each do |item|
+          next unless triple.item.next_sym && triple.item.next_sym == item.lhs
+          l = follow_l(triple.item, triple.l)
+          t = Triple.new(triple.state, item, l)
+          queue << [t, paths + [ProductionPath.new(triple.state_item, t.state_item)]]
+        end
+
+        break if queue.empty?
+      end
+
+      return nil
+    end
+
+    def follow_l(item, current_l)
+      # 1. follow_L (A -> X1 ... Xn-1 • Xn) = L
+      # 2. follow_L (A -> X1 ... Xk • Xk+1 Xk+2 ... Xn) = {Xk+2} if Xk+2 is a terminal
+      # 3. follow_L (A -> X1 ... Xk • Xk+1 Xk+2 ... Xn) = FIRST(Xk+2) if Xk+2 is a nonnullable nonterminal
+      # 4. follow_L (A -> X1 ... Xk • Xk+1 Xk+2 ... Xn) = FIRST(Xk+2) + follow_L (A -> X1 ... Xk+1 • Xk+2 ... Xn) if Xk+2 is a nullable nonterminal
+      case
+      when item.number_of_rest_symbols == 1
+        current_l
+      when item.next_next_sym.term?
+        Set.new([item.next_next_sym])
+      when !item.next_next_sym.nullable
+        item.next_next_sym.first_set
+      else
+        item.next_next_sym.first_set + follow_l(item.new_by_next_position, current_l)
+      end
+    end
+  end
+end

lib/lrama/counterexamples/derivation.rb

@@ -0,0 +1,63 @@
+module Lrama
+  class Counterexamples
+    class Derivation
+      attr_reader :item, :left, :right
+      attr_writer :right
+
+      def initialize(item, left, right = nil)
+        @item = item
+        @left = left
+        @right = right
+      end
+
+      def to_s
+        "#<Derivation(#{item.display_name})>"
+      end
+      alias :inspect :to_s
+
+      def render_strings_for_report
+        result = []
+        _render_for_report(self, 0, result, 0)
+        result.map(&:rstrip)
+      end
+
+      def render_for_report
+        render_strings_for_report.join("\n")
+      end
+
+      private
+
+      def _render_for_report(derivation, offset, strings, index)
+        item = derivation.item
+        if strings[index]
+          strings[index] << " " * (offset - strings[index].length)
+        else
+          strings[index] = " " * offset
+        end
+        str = strings[index]
+        str << "#{item.rule_id}: #{item.symbols_before_dot.map(&:display_name).join(" ")} "
+
+        if derivation.left
+          len = str.length
+          str << "#{item.next_sym.display_name}"
+          length = _render_for_report(derivation.left, len, strings, index + 1)
+          # I want String#ljust!
+          str << " " * (length - str.length)
+        else
+          str << " • #{item.symbols_after_dot.map(&:display_name).join(" ")} "
+          return str.length
+        end
+
+        if derivation.right&.left
+          length = _render_for_report(derivation.right.left, str.length, strings, index + 1)
+          str << "#{item.symbols_after_dot[1..-1].map(&:display_name).join(" ")} "
+          str << " " * (length - str.length) if length > str.length
+        elsif item.next_next_sym
+          str << "#{item.symbols_after_dot[1..-1].map(&:display_name).join(" ")} "
+        end
+
+        return str.length
+      end
+    end
+  end
+end