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require "set"
require "lrama/counterexamples/derivation"
require "lrama/counterexamples/example"
require "lrama/counterexamples/path"
require "lrama/counterexamples/production_path"
require "lrama/counterexamples/start_path"
require "lrama/counterexamples/state_item"
require "lrama/counterexamples/transition_path"
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)
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
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
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