Class: Prover

Inherits:
Object
  • Object
show all
Defined in:
lib/rover_prover/prover/prover.rb

Instance Method Summary collapse

Instance Method Details

#derivation_left(old, left) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 61

def derivation_left(old, left)
  return derivation_left_not(old, left) if left.is_a?(Not)
  return derivation_left_and(old, left) if left.is_a?(And)
  return derivation_left_or(old, left) if left.is_a?(Or)
  return derivation_left_implies(old, left) if left.is_a?(Implies)
  return derivation_left_for_all(old, left) if left.is_a?(ForAll)
  return derivation_left_there_exists(old, left) if left.is_a?(ThereExists)
  []
end

#derivation_left_and(sequent, left) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 92

def derivation_left_and(sequent, left)
  new = sequent.deepen
  new.left_remove(left)
  left_depth = sequent.left_get_depth(left)
  new.left_add(left.formula_a)
  new.left_set_depth(left.formula_a, left_depth + 1)
  new.left_add(left.formula_b)
  new.left_set_depth(left.formula_b, left_depth + 1)
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_left_for_all(sequent, left) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 144

def derivation_left_for_all(sequent, left)
  new = sequent.deepen(enable_siblings: true)
  left_depth = sequent.left_get_depth(left)
  new.left_set_depth(left, left_depth + 1)
  t = UnificationTerm.new(sequent.get_variable_name('t'))
  t.set_instantiation_time(sequent.depth + 1)
  formula = left.formula.replace(
    left.variable,
    t
  )
  unless new.left.include?(formula)
    new.left_add(formula)
    new.left_set_depth(formula, left_depth + 1)
  end
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_left_implies(sequent, left) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 125

def derivation_left_implies(sequent, left)
  new_a = sequent.deepen
  new_b = sequent.deepen
  new_a.left_remove(left)
  new_b.left_remove(left)
  left_depth = sequent.left_get_depth(left)
  new_a.right_add(left.formula_a)
  new_a.right_set_depth(left.formula_a, left_depth + 1)
  new_b.left_add(left.formula_b)
  new_b.left_set_depth(left.formula_b, left_depth + 1)
  unless new_a.siblings.nil?
    new_a.siblings.push(new_a)
  end
  unless new_b.siblings.nil?
    new_b.siblings.push(new_b)
  end
  [new_a, new_b]
end

#derivation_left_not(sequent, left) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 81

def derivation_left_not(sequent, left)
  new = sequent.deepen
  new.left_remove(left)
  new.right_add(left.formula)
  new.right_set_depth(left.formula, (sequent.left_get_depth(left) + 1))
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_left_or(sequent, left) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 106

def derivation_left_or(sequent, left)
  new_a = sequent.deepen
  new_b = sequent.deepen
  new_a.left_remove(left)
  new_b.left_remove(left)
  left_depth = sequent.left_get_depth(left)
  new_a.left_add(left.formula_a)
  new_a.left_set_depth(left.formula_a, left_depth + 1)
  new_b.left_add(left.formula_b)
  new_b.left_set_depth(left.formula_b, left_depth + 1)
  unless new_a.siblings.nil?
    new_a.siblings.push(new_a)
  end
  unless new_b.siblings.nil?
    new_b.siblings.push(new_b)
  end
  [new_a, new_b]
end

#derivation_left_there_exists(sequent, left) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 164

def derivation_left_there_exists(sequent, left)
  new = sequent.deepen
  new.left_remove(left)
  left_depth = sequent.left_get_depth(left)
  variable = Variable.new(sequent.get_variable_name('v'))
  variable.set_instantiation_time(sequent.depth + 1)
  formula = left.formula.replace(left.variable, variable)
  new.left_add(formula)
  new.left_set_depth(formula, left_depth + 1)
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_right(old, right) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 71

def derivation_right(old, right)
  return derivation_right_not(old, right) if right.is_a?(Not)
  return derivation_right_and(old, right) if right.is_a?(And)
  return derivation_right_or(old, right) if right.is_a?(Or)
  return derivation_right_implies(old, right) if right.is_a?(Implies)
  return derivation_right_for_all(old, right) if right.is_a?(ForAll)
  return derivation_right_there_exists(old, right) if right.is_a?(ThereExists)
  []
end

#derivation_right_and(sequent, right) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 190

def derivation_right_and(sequent, right)
  new_a = sequent.deepen
  new_b = sequent.deepen
  new_a.right_remove(right)
  new_b.right_remove(right)
  right_depth = sequent.right_get_depth(right)
  new_a.right_add(right.formula_a)
  new_a.right_set_depth(right.formula_a, right_depth + 1)
  new_b.right_add(right.formula_b)
  new_b.right_set_depth(right.formula_b, right_depth + 1)
  unless new_a.siblings.nil?
    new_a.siblings.push(new_a)
  end
  unless new_b.siblings.nil?
    new_b.siblings.push(new_b)
  end
  [new_a, new_b]
end

#derivation_right_for_all(sequent, right) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 237

def derivation_right_for_all(sequent, right)
  new = sequent.deepen
  new.right_remove(right)
  right_depth = sequent.right_get_depth(right)
  variable = Variable.new(sequent.get_variable_name('v'))
  variable.set_instantiation_time(sequent.depth + 1)
  formula = right.formula.replace(right.variable, variable)
  new.right_add(formula)
  new.right_set_depth(formula, right_depth + 1)
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_right_implies(sequent, right) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 223

def derivation_right_implies(sequent, right)
  new = sequent.deepen
  new.right_remove(right)
  right_depth = sequent.right_get_depth(right)
  new.left_add(right.formula_a)
  new.left_set_depth(right.formula_a, right_depth + 1)
  new.right_add(right.formula_b)
  new.right_set_depth(right.formula_b, right_depth + 1)
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_right_not(sequent, right) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 179

def derivation_right_not(sequent, right)
  new = sequent.deepen
  new.right_remove(right)
  new.left_add(right.formula)
  new.left_set_depth(right.formula, (sequent.right_get_depth(right) + 1))
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_right_or(sequent, right) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 209

def derivation_right_or(sequent, right)
  new = sequent.deepen
  new.right_remove(right)
  right_depth = sequent.right_get_depth(right)
  new.right_add(right.formula_a)
  new.right_set_depth(right.formula_a, right_depth + 1)
  new.right_add(right.formula_b)
  new.right_set_depth(right.formula_b, right_depth + 1)
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#derivation_right_there_exists(sequent, right) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 252

def derivation_right_there_exists(sequent, right)
  new = sequent.deepen(enable_siblings: true)
  right_depth = sequent.right_get_depth(right)
  new.right_set_depth(right, right_depth + 1)
  t = UnificationTerm.new(sequent.get_variable_name('t'))
  t.set_instantiation_time(sequent.depth + 1)
  formula = right.formula.replace(
    right.variable,
    t
  )
  unless new.right.include?(formula)
    new.right_add(formula)
  end
  new.right_set_depth(formula, right_depth + 1)
  unless new.siblings.nil?
    new.siblings.push(new)
  end
  [new]
end

#prove(sequent) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 16

def prove(sequent)
  sequent.set_default_instantiation_time(0)
  unifier = Unifier.new

  frontier = [sequent]
  proven = []
  while true do
    frontier = frontier - proven
    old = frontier.pop
    break if old.nil?
    puts "#{old.depth}. #{old.to_s}"

    if old.trivial?
      proven.push(old)
      next
    end

    unless old.siblings.nil?
      pairs_list = old.siblings.map(&:get_unifiable_pairs)
      if pairs_list.all? { |list| !list.empty? }
        subst = unifier.unify_all(pairs_list)
        unless subst.nil?
          subst.each { |k, v| puts "#{k.to_s} = #{v.to_s}" }
          proven = proven | old.siblings
          frontier = frontier - proven
          next
        end
      else
        old.siblings.delete(old)
      end
    end

    left = old.left_formula
    right = old.right_formula
    return false if left.nil? && right.nil?

    if apply_left?(old, left, right)
      frontier.push(*derivation_left(old, left))
    else
      frontier.push(*derivation_right(old, right))
    end
  end
  true
end

#prove_formula(axioms, formula) ⇒ Object 



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# File 'lib/rover_prover/prover/prover.rb', line 5

def prove_formula(axioms, formula)
  prove(
    Sequent.new(
      axioms,
      [formula],
      nil,
      0
    )
  )
end