Module: Porolog

Defined in:
lib/porolog.rb,
lib/porolog/goal.rb,
lib/porolog/rule.rb,
lib/porolog/tail.rb,
lib/porolog/error.rb,
lib/porolog/scope.rb,
lib/porolog/value.rb,
lib/porolog/variable.rb,
lib/porolog/arguments.rb,
lib/porolog/predicate.rb,
lib/porolog/instantiation.rb,
lib/porolog/predicate/builtin.rb

Overview

lib/porolog/predicate/builtin.rb - Plain Old Ruby Objects Prolog Engine – Builtin Predicates

Luis Esteban   29 July 2020
  created

Defined Under Namespace

Classes: Arguments, Goal, Instantiation, NoGoalError, NonVariableError, PorologError, Predicate, Rule, Scope, Tail, Value, Variable

Constant Summary collapse

VERSION =

The most recent version of the Porolog gem.

'1.0.1'.freeze
VERSION_DATE =

The most recent date of when the VERSION changed.

'2020-08-06'.freeze
UNKNOWN_TAIL =

Represents an unknown tail of a list.

Object.new
UNKNOWN_ARRAY =

Represents a list where all elements are unknown.

[UNKNOWN_TAIL].freeze
ANONYMOUS =

Stores the next unique anonymous variable name.

['_a']

Instance Method Summary collapse

Instance Method Details

#anonymous ⇒ Symbol Also known as: _

Returns a unique variable name.

Returns:

  • (Symbol) —

    a unique variable name.



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# File 'lib/porolog.rb', line 128

def anonymous
  anonymous = ANONYMOUS[0].to_sym
  ANONYMOUS[0].succ!
  anonymous
end

#builtin(*names, class_base: Object) ⇒ Porolog::Predicate+

A method to declare use of a standard / builtin Predicate, along with a method that returns an Arguments based on the arguments provided to the method.

Examples:

builtin :is, :member, :append
member(:e,:l)       # --> Porolog::Arguments

Parameters:

  • names (Array<#to_sym>) —

    names of the Predicates to declare.

  • class_base (Class) —

    class to define the method in.

Returns:



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# File 'lib/porolog.rb', line 89

def builtin(*names, class_base: Object)
  names = [names].flatten
  
  predicates = names.map{|name|
    method     = name.to_sym
    raise NameError, "Undefined builtin predicate #{name.inspect}" unless Predicate::Builtin.instance_methods.include?(method)
    predicate  = Predicate.new(name, builtin: true)
    if class_base == Object
      # -- Add Global Method --
      class_base.class_eval{
        remove_method(method) if method_defined?(method)
        define_method(method){|*args, &block|
          predicate.(*args, &block)
        }
      }
    else
      # -- Add Instance Method --
      class_base.class_eval{
        remove_method(method) if methods(false).include?(method)
        define_method(method){|*args, &block|
          predicate.(*args, &block)
        }
      }
      
      # -- Add Class Method --
      (class << class_base; self; end).instance_eval {
        remove_method(method) if methods(false).include?(method)
        define_method(method){|*args, &block|
          predicate.(*args, &block)
        }
      }
    end
    predicate
  }
  
  predicates.size > 1 && predicates || predicates.first
end

#expand_splat(array) ⇒ Array

Expands a superfluous splat.

Parameters:

  • array (Array) —

    the given Array.

Returns:

  • (Array) —

    the given Array with any superfluous splats expanded.



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# File 'lib/porolog.rb', line 464

def expand_splat(array)
  array = array.first.value if array.is_a?(Array) && array.length == 1 && array.first.is_a?(Tail)
  
  if array.is_a?(Array) && array.last.is_a?(Tail) && array.last.value.is_a?(Array)
    array = [*array[0...-1], *array.last.value]
  end
  
  if array.is_a?(Array)
    array = array.map{|element|
      expand_splat(element)
    }
  end
  
  array
end

#has_tail?(value, apply_value = true) ⇒ Boolean

Returns whether the provided value has a Tail.

Parameters:

  • value (Object) —

    the provided value.

Returns:

  • (Boolean) —

    whether the provided value has a Tail.



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# File 'lib/porolog.rb', line 451

def has_tail?(value, apply_value = true)
  value = value.value if value.respond_to?(:value) && apply_value
  
  if value.is_a?(Array)
    value.last == UNKNOWN_TAIL || value.last.is_a?(Tail)
  else
    false
  end
end

#instantiate_unifications(unifications) ⇒ Boolean

Instantiates the unifications from an attempt to unify.

Parameters:

  • unifications (Array) —

    unifications to instantiate.

Returns:

  • (Boolean) —

    whether the instantiations could be made.



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# File 'lib/porolog.rb', line 164

def instantiate_unifications(unifications)
  # -- Gather Unifications --
  goals_variables = {}
  
  return_false = false
  unifications.each do |unification|
    left, right, left_goal, right_goal = unification
    
    goals_variables[left_goal]       ||= {}
    goals_variables[left_goal][left] ||= []
    goals_variables[left_goal][left] << [right_goal,right]
    
    # -- Check Consistency --
    goals_variables[left_goal][left].map(&:last).map(&:value)
    values = goals_variables[left_goal][left].map{|value|
      value.last.value.value
    }
    next if values.size < 2
    
    arrays = values.any?{|value| value.is_a?(Array) }
    if arrays && !values.variables.empty?
      zipped_values = values[0].zip(*values[1..-1])
      zipped_values.each do |zipped_value|
        vars, atomics = zipped_value.partition{|v| v.type == :variable }
        return_false = true if atomics.uniq.size > 1
        vars.each do |var|
          goals_variables[var.goal]      ||= {}
          goals_variables[var.goal][var] ||= []
          goals_variables[var.goal][var] << [([left_goal,right_goal]-[var.goal]).first,atomics.first]
        end
      end
    else
      return_false = values.reject{|value|
        value.is_a?(Variable) || value.is_a?(Symbol)
      }.uniq.size > 1
    end
    
    return false if return_false
  end
  
  # -- Make Instantiations --
  instantiations = []
  consistent     = true
  
  goals_variables.each do |goal, variables|
    variables.each do |name, others|
      others.each do |other_goal, other|
        instantiation = goal.instantiate(name, other, other_goal)
        if instantiation
          instantiations << instantiation
        else
          consistent = false
        end
      end
    end
  end
  
  # -- Revert if inconsistent --
  if consistent
    instantiations
  else
    instantiations.each(&:remove)
    nil
  end
end

#predicate(*names, class_base: Object) ⇒ Porolog::Predicate+

A convenience method to create a Predicate, along with a method that returns an Arguments based on the arguments provided to the method.

Examples:

predicate :combobulator
combobulator(:x,:y)       # --> Porolog::Arguments

Parameters:

  • names (Array<#to_sym>) —

    names of the Predicates to create.

  • class_base (Class) —

    class to define the method in.

Returns:



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# File 'lib/porolog.rb', line 55

def predicate(*names, class_base: Object)
  names = [names].flatten
  
  predicates = names.map{|name|
    method     = name.to_sym
    predicate  = Predicate.new(name)
    class_base.class_eval{
      remove_method(method) if public_method_defined?(method)
      define_method(method){|*args|
        predicate.(*args)
      }
    }
    (class << class_base; self; end).instance_eval {
      remove_method(method) if public_method_defined?(method)
      define_method(method){|*args|
        predicate.(*args)
      }
    } unless class_base == Object
    predicate
  }
  
  predicates.size > 1 && predicates || predicates.first
end

#unify(left, right, left_goal, right_goal = left_goal, visited = []) ⇒ Array?

Attempt to unify two entities of two goals.

Parameters:

  • left (Object) —

    left hand side entity.

  • right (Object) —

    right hand side entity.

  • left_goal (Porolog::Goal) —

    goal of left hand side entity.

  • right_goal (Porolog::Goal) (defaults to: left_goal) —

    goal of right hand side entity.

  • visited (Array) (defaults to: []) —

    prevents infinite recursion.

Returns:

  • (Array) —

    an Array of unifications when the left hand side can be unified with the right hand.

  • (nil) —

    nil if they cannot be unified.



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# File 'lib/porolog.rb', line 238

def unify(left, right, left_goal, right_goal = left_goal, visited = [])
  right_goal ||= left_goal
  goals     = [left_goal, right_goal].uniq
  signature = [left.type, right.type]
  
  # -- Nil is Uninstantiated (can always unify) --
  return [] unless left && right
  
  # -- Set HeadTail Goals --
  case signature
    when [:atomic, :atomic]
      if left == right
        []
      else
        msg = "Cannot unify because #{left.inspect} != #{right.inspect} (atomic != atomic)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:array, :array], [:tail, :tail]
      _merged, unifications = unify_arrays(left, right, left_goal, right_goal, visited)
      if unifications
        unifications
      else
        msg = "Cannot unify because #{left.inspect} != #{right.inspect} (array != array)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:array, :tail]
      _merged, unifications = unify_arrays([left], right.value, left_goal, right_goal, visited)
      if unifications
        unifications
      else
        msg = "Cannot unify because #{left.inspect} != #{right.inspect} (array != tail)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:tail, :array]
      _merged, unifications = unify_arrays(left.value, [right], left_goal, right_goal, visited)
      if unifications
        unifications
      else
        msg = "Cannot unify because #{left.inspect} != #{right.inspect} (tail != array)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:variable, :atomic]
      left_value  = left_goal.value_of(left, nil, visited)
      right_value = right
      if left_value == right_value || left_value.is_a?(Variable) || left_value.nil?
        [[left, right, left_goal, right_goal]]
      else
        msg = "Cannot unify because #{left_value.inspect} != #{right_value.inspect} (variable != atomic)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:atomic, :variable]
      left_value  = left
      right_value = right_goal.value_of(right, nil, visited)
      if left == right_value || right_value.is_a?(Variable) || right_value.nil?
        [[right,left,right_goal,left_goal]]
      else
        msg = "Cannot unify because #{left_value.inspect} != #{right_value.inspect} (atomic != variable)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:variable, :variable]
      left_value  = left_goal.value_of(left, nil, visited).value
      right_value = right_goal.value_of(right, nil, visited).value
      if left_value == right_value || left_value.is_a?(Variable) || right_value.is_a?(Variable) || left_value.nil? || right_value.nil?
        [[left, right, left_goal, right_goal]]
      elsif left_value == UNKNOWN_ARRAY && (right_value.is_a?(Variable) || right_value.nil? || right_value.is_a?(Array))
        [[left, right, left_goal, right_goal]]
      elsif right_value == UNKNOWN_ARRAY && (left_value.is_a?(Variable) || left_value.nil? || left_value.is_a?(Array))
        [[left, right, left_goal, right_goal]]
      else
        msg = "Cannot unify because #{left_value.inspect} != #{right_value.inspect} (variable != variable)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:variable, :array], [:variable, :tail]
      left_value  = left_goal.value_of(left, nil, visited)
      right_value = right
      if left_value == right_value || left_value.is_a?(Variable) || left_value == UNKNOWN_ARRAY || left_value.nil?
        [[left, right, left_goal, right_goal]]
      elsif left_value.type == :array
        _merged, unifications = unify_arrays(left_value, right, left_goal, right_goal, visited)
        if unifications
          unifications
        else
          msg = "Cannot unify because #{left_value.inspect} != #{right.inspect} (variable/array != array)"
          goals.each{|goal| goal.log << msg }
          nil
        end
      else
        msg = "Cannot unify because #{left_value.inspect} != #{right_value.inspect} (variable != array)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:array, :variable], [:tail, :variable]
      left_value  = left
      right_value = right_goal.value_of(right, nil, visited)
      if left_value == right_value || right_value.is_a?(Variable) || right_value == UNKNOWN_ARRAY || right_value.nil?
        [[right, left, right_goal, left_goal]]
      elsif right_value.type == :array
        _merged, unifications = unify_arrays(left, right_value, left_goal, right_goal, visited)
        if unifications
          unifications
        else
          msg = "Cannot unify because #{left.inspect} != #{right_value.inspect} (variable/array != array)"
          goals.each{|goal| goal.log << msg }
          nil
        end
      else
        msg = "Cannot unify because #{left_value.inspect} != #{right_value.inspect} (array != variable)"
        goals.each{|goal| goal.log << msg }
        nil
      end
    
    when [:array, :atomic], [:atomic, :array], [:tail, :atomic], [:atomic, :tail]
      msg = "Cannot unify #{left.inspect} with #{right.inspect} (#{signature.join(' != ')})"
      goals.each{|goal| goal.log << msg }
      nil
    
    else
      # :nocov:
      raise UnknownUnificationSignature, "UNKNOWN UNIFICATION SIGNATURE: #{signature.inspect}"
      # :nocov:
  end
end

#unify_arrays(left, right, left_goal, right_goal = left_goal, visited = []) ⇒ Array<Array, Array>?

Attempt to unify two Arrays.

Parameters:

  • left (Array) —

    left hand side Array.

  • right (Array) —

    right hand side Array.

  • left_goal (Porolog::Goal) —

    goal of left hand side Array.

  • right_goal (Porolog::Goal) (defaults to: left_goal) —

    goal of right hand side Array.

  • visited (Array) (defaults to: []) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 384

def unify_arrays(left, right, left_goal, right_goal = left_goal, visited = [])
  arrays        = [left,       right]
  arrays_goals  = [left_goal,  right_goal]
  arrays_values = arrays.map{|array| array.value(visited) }
  
  # -- Trivial Unifications --
  return [left_goal. variablise(left),  []] if right == UNKNOWN_ARRAY
  return [right_goal.variablise(right), []] if left  == UNKNOWN_ARRAY
  
  # -- Validate Arrays --
  unless arrays_values.all?{|array| array.is_a?(Array) || array == UNKNOWN_TAIL }
    msg = "Cannot unify a non-array with an array: #{left.inspect} with #{right.inspect}"
    arrays_goals.uniq.each{|goal| goal.log  << msg }
    return nil
  end
  
  # -- Count Tails --
  number_of_arrays = arrays.size
  number_of_tails  = arrays.count{|array| has_tail?(array) }
  
  # -- Handle Tails --
  if number_of_tails.zero?
    unify_arrays_with_no_tails(arrays, arrays_goals, visited)
  elsif number_of_tails == number_of_arrays
    unify_arrays_with_all_tails(arrays, arrays_goals, visited)
  else
    unify_arrays_with_some_tails(arrays, arrays_goals, visited)
  end
end

#unify_arrays_with_all_tails(arrays, arrays_goals, visited) ⇒ Array<Array, Array>?

Unifies Arrays where each Array has a Tail.

Parameters:

  • arrays (Array<Array>) —

    the Arrays to be unified.

  • arrays_goals (Array<Porolog::Goal>) —

    the Goals of the Arrays to be unified.

  • visited (Array) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 656

def unify_arrays_with_all_tails(arrays, arrays_goals, visited)
  # -- All tails --
  arrays = arrays.map{|array|
    expand_splat(array.headtail? ? array : array.value)
  }
  
  # -- Unify Embedded Arrays --
  if arrays.any?{|array| array.type == :variable }
    unifications = unify(*arrays[0...2], *arrays_goals[0...2], visited)
    if unifications
      merged = arrays.reject{|value| value.type == :variable }.first || nil
      return [merged, unifications]
    else
      msg = "Cannot unify embedded arrays: #{arrays[0...2].map(&:value).map(&:inspect).join(' with ')}"
      arrays_goals.uniq.each do |goal|
        goal.log << msg
      end
      return nil
    end
  end
  
  signature = arrays.map(&:headtail?)
  unifications = []
  merged       = []
  
  if signature.all?
    merged, unifications = unify_headtail_with_headtail(arrays, arrays_goals, visited)
  elsif signature.map(&:!).all?
    merged, unifications = unify_tail_with_tail(arrays, arrays_goals, visited)
  else
    merged, unifications = unify_headtail_with_tail(arrays, arrays_goals, visited)
  end
  
  if unifications
    [merged, unifications]
  else
    nil
  end
end

#unify_arrays_with_no_tails(arrays, arrays_goals, visited) ⇒ Array<Array, Array>?

Unifies Arrays where no Array has a Tail.

Parameters:

  • arrays (Array<Array>) —

    the Arrays to be unified.

  • arrays_goals (Array<Porolog::Goal>) —

    the Goals of the Arrays to be unified.

  • visited (Array) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 486

def unify_arrays_with_no_tails(arrays, arrays_goals, visited)
  # -- Validate Arrays --
  if arrays.any?{|array| has_tail?(array) }
    msg = "Wrong unification method called: no_tails but one or more of #{arrays.inspect} has a tail"
    arrays_goals.uniq.each do |goal|
      goal.log << msg
    end
    return nil
  end
  
  # -- Trivial Unifications --
  return [[],[]] if arrays.empty?
  
  # -- Ensure Arrays elements have Goals --
  arrays_values = arrays.dup
  arrays_goals  = arrays_goals.dup
  
  arrays.each_with_index do |array, index|
    if array.is_a?(Value)
      arrays_goals[index] ||= array.goal
      arrays_values[index]  = array.value
    end
    
    if arrays_goals[index].nil?
      value_with_goal = array.find{|element| element.respond_to?(:goal) }
      arrays_goals[index] = value_with_goal.goal if value_with_goal&.goal
    end
    
    if arrays_goals[index].nil?
      # :nocov:
      raise NoGoalError, "Array #{array.inspect} has no goal for unification"
      # :nocov:
    end
    
    arrays_values[index] = expand_splat(arrays_values[index])
  end
  
  # -- Check whether all arrays are an Array --
  unless arrays_values.all?{|array| array.is_a?(Array) }
    merged, unifications = unify_many_arrays(arrays.map{|array| [array] }, arrays_goals, visited)
    return [merged] + [unifications]
  end
  
  arrays_variables = arrays_goals.zip(arrays)
  
  # -- Remap Arrays so that they are variablised and valuised with their Goals --
  new_arrays = []
  arrays_variables.each do |goal, variables|
    new_array = variables.map{|variable|
      value = goal.value_of(variable, nil, visited).value
      value = variable if [UNKNOWN_TAIL, UNKNOWN_ARRAY].include?(value)
      
      if value.type == :variable
        value = goal.variable(value)
      elsif value.is_a?(Array)
        value = value.map{|element|
          if element.type == :variable
            goal.variable(element)
          elsif element.is_a?(Value)
            element
          elsif element.is_a?(Tail)
            element
          else
            goal.value(element)
          end
        }
      elsif !value.is_a?(Value)
        value = goal.value(value)
      end
      value
    }
    new_arrays << new_array
  end
  arrays = new_arrays
  
  # -- Unify All Elements --
  sizes = arrays.map(&:length).uniq
  if sizes.size <= 1
    # -- Arrays are the same length --
    zipped       = arrays[0].zip(*arrays[1..-1]).map(&:uniq).map(&:compact).uniq
    unifications = []
    merged       = []
    
    # TODO: Change these names
    zipped.each{|values_to_unify|
      values_to_unify_values = values_to_unify.map{|value|
        value_value = value.value
        if [UNKNOWN_TAIL, UNKNOWN_ARRAY].include?(value_value)
          value
        else
          value_value
        end
      }.compact.uniq
      
      if values_to_unify_values.size <= 1
        # -- One Value --
        value = values_to_unify_values.first
        if value.type == :variable
          merged << nil
        else
          merged << value.value
        end
      else
        if values_to_unify_values.all?{|value| value.is_a?(Array) }
          submerged, subunifications = unify_many_arrays(values_to_unify_values, arrays_goals)
          if subunifications
            merged << submerged
            unifications += subunifications
          else
            msg = "Cannot unify: #{values_to_unify_values.map(&:inspect).join(' with ')}"
            arrays_goals.uniq.each{|goal| goal.log << msg }
            return nil
          end
        elsif values_to_unify.variables.empty?
          # -- Incompatible Values --
          incompatible_values = values_to_unify.map(&:value)
          msg = "Cannot unify incompatible values: #{incompatible_values.compact.map(&:inspect).join(' with ')}"
          arrays_goals.uniq.each{|goal| goal.log << msg }
          return nil
        else
          # -- Potentially Compatible Values/Variables --
          nonvariables = values_to_unify.map(&:value).compact.reject{|value| value.type == :variable }
          
          values_to_unify.reject{|value| value.value.nil? }.combination(2).each do |vl, vr|
            subunifications = unify(vl, vr, vl.goal, vr.goal, visited)
            if subunifications
              unifications += subunifications
            else
              msg = "Cannot unify: #{vl.inspect} with #{vr.inspect}"
              [vl.goal, vr.goal].uniq.each{|goal| goal.log << msg }
              return nil
            end
          end
          
          if nonvariables.size > 1
            subgoals = arrays_goals.dup
            nonvariables.each_with_index do |nonvariable, index|
              if nonvariable.respond_to?(:goal)
                subgoal = nonvariable.goal
                subgoals[index] = subgoal if subgoal
              end
            end
            subgoals = subgoals[0...nonvariables.size]
            merged_nonvariables, _nonvariable_unifications = unify_many_arrays(nonvariables, subgoals, visited)
          else
            merged_nonvariables      = nonvariables
          end
          
          merged_value = merged_nonvariables
          merged_value = [nonvariables.first.value] if merged_value.nil? || merged_value == []
          merged += merged_value
        end
      end
    }
    
    [merged, unifications]
  else
    # -- Arrays are different lengths --
    msg = "Cannot unify arrays of different lengths: #{arrays_values.map(&:inspect).join(' with ')}"
    arrays_goals.uniq.each{|goal| goal.log << msg }
    nil
  end
end

#unify_arrays_with_some_tails(arrays, arrays_goals, visited) ⇒ Array<Array, Array>?

Unifies Arrays where Arrays with a Tail are unified with Arrays without a Tail.

Parameters:

  • arrays (Array<Array>) —

    the Arrays to be unified.

  • arrays_goals (Array<Porolog::Goal>) —

    the Goals of the Arrays to be unified.

  • visited (Array) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 1051

def unify_arrays_with_some_tails(arrays, arrays_goals, visited)
  # -- Variablise Arrays --
  arrays = arrays_goals.zip(arrays).map{|goal,array|
    if goal.nil?
      goal = array.goal        if array.is_a?(Value)
      if goal.nil? && array.is_a?(Array)
        v = array.find{|element| element.respond_to?(:goal) }
        goal = v&.goal
      end
    end
    goal = arrays_goals.compact.last if goal.nil?
    raise NoGoalError, "#{array.inspect} has no associated goal!  Cannot variablise!" if goal.nil? || !goal.is_a?(Goal)
    goal.variablise(array)
  }
  
  # -- Some unknown tails --
  tailed_arrays, finite_arrays = arrays.partition{|array| has_tail?(array) }
  
  finite_sizes = finite_arrays.reject{|finite_array| finite_array.type == :variable }.map(&:size).uniq
  
  unless finite_sizes.size == 1
    msg = "Cannot unify different sizes of arrays: #{arrays.map(&:inspect).join(' with ')}"
    arrays_goals.uniq.each do |goal|
      goal.log << msg
    end
    return nil
  end
  
  exact_size = finite_sizes.first
  
  tails         = tailed_arrays.map{|array| [array[0...-1].size,array.last,arrays_goals[arrays.index(array)]] }
  tailed_arrays = tailed_arrays.map{|array| array[0...-1] }
  
  # -- Fail --
  #   [nil,nil,nil,nil,...]
  #   [1,  2,  3]
  min_tailed_size = tailed_arrays.map(&:size).max
  
  if min_tailed_size > exact_size
    msg = "Cannot unify enough elements: #{arrays.map(&:inspect).join(' with ')}"
    arrays_goals.uniq.each do |goal|
      goal.log << msg
    end
    return nil
  end
  
  # -- Succeed --
  #   [nil,nil,...]
  #   [1,  2,  3]
  arrays = tailed_arrays + finite_arrays
  
  zip_arrays = arrays.map{|array|
    if array.is_a?(Value) && array.value.is_a?(Array)
      array.value.map{|v|
        if v.type == :variable
          array.goal.variable(v)
        else
          array.goal.value(v)
        end
      }
    elsif array.type == :variable
      array.goal.value_of(array)
    else
      array
    end
  }.select{|array| array.is_a?(Array) }
  
  zipped       = ([nil] * exact_size).zip(*zip_arrays).map(&:uniq).map(&:compact)
  merged       = []
  unifications = []
  
  zipped.each{|zipped_values|
    values = zipped_values
    value = values.reject{|v| v.value(visited).nil? }.compact.uniq
    value_values = value.map(&:value).compact.uniq
    if value_values.size <= 1
      m = value.first.value
      merged << m
    else
      if values.variables.empty?
        msg = "Cannot unify enough elements: #{values.map(&:inspect).join(' with ')}"
        arrays_goals.uniq.each do |goal|
          goal.log << msg
        end
        return nil
      else
        _variables, nonvariables = values.reject{|v| v.value.nil? }.partition{|element| element.type == :variable }
        if nonvariables.value.uniq.size <= 1
          m = nonvariables.first.value
          merged << m
          
          value.combination(2).each do |vl, vr|
            if vl.type == :variable
              unifications << [vl, vr, vl.goal, vr.goal]
            elsif vr.type == :variable
              unifications << [vr, vl, vr.goal, vl.goal]
            end
          end
        else
          msg = "Cannot unify non-variables: #{nonvariables.value.uniq.map(&:inspect).join(' with ')}"
          arrays_goals.uniq.each do |goal|
            goal.log << msg
          end
          return nil
        end
      end
    end
  }
  
  # -- Unify Tails --
  tails.each do |head_size,tail,goal|
    next if tail == UNKNOWN_TAIL
    merged_goals = arrays_goals - [goal] + [goal]
    unifications << [tail.value(visited).value(visited), merged[head_size..-1], goal, merged_goals.compact.first]
  end
  
  [merged, unifications]
end

#unify_goals(goal, subgoal) ⇒ Array<Porolog::Instantiation>, ...

Unify the Arguments of a Goal and a sub-Goal.

Parameters:

  • goal (Porolog::Goal) —

    a Goal to solve a Predicate for specific Arguments.

  • subgoal (Porolog::Goal) —

    a sub-Goal to solve the Goal following the Rules of the Predicate.

Returns:

  • (Array<Porolog::Instantiation>) —

    the instantiations if the goals can be unified and instantiated.

  • (false) —

    if they cannot be unified.

  • (nil) —

    if they can be unified but the instantiations are inconsistent.



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# File 'lib/porolog.rb', line 142

def unify_goals(goal, subgoal)
  if goal.arguments.predicate == subgoal.arguments.predicate
    unifications = unify(goal.arguments.arguments, subgoal.arguments.arguments, goal, subgoal)
    if unifications
      instantiate_unifications(unifications)
    else
      msg = "Could not unify goals: #{goal.arguments.arguments.inspect} !~ #{subgoal.arguments.arguments.inspect}"
      goal.log << msg
      subgoal.log << msg
      false
    end
  else
    msg = "Cannot unify goals because they are for different predicates: #{goal.arguments.predicate.name.inspect} and #{subgoal.arguments.predicate.name.inspect}"
    goal.log << msg
    subgoal.log << msg
    false
  end
end

#unify_headtail_with_headtail(arrays, arrays_goals, visited) ⇒ Array<Array, Array>?

Unifies Arrays where each Array is a Head/Tail array.

Parameters:

  • arrays (Array<Array>) —

    the Arrays to be unified.

  • arrays_goals (Array<Porolog::Goal>) —

    the Goals of the Arrays to be unified.

  • visited (Array) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 990

def unify_headtail_with_headtail(arrays, arrays_goals, visited)
  unless arrays.all?(&:headtail?)
    msg = "Wrong method called to unify #{arrays.inspect}"
    arrays_goals.uniq.each do |goal|
      goal.log << msg
    end
    return nil
  end
  
  unifications = []
  
  arrays.combination(2).each do |pair|
    # -- Collect Goals --
    pair_goals = pair.map{|array| arrays_goals[arrays.index(array)] }
    
    # -- Unify Heads --
    heads = pair.map(&:first)
    subunifications = unify(*heads, *pair_goals, visited)
    if subunifications
      unifications += subunifications
    else
      unifications = nil
      msg = "Cannot unify headtail heads: #{heads.map(&:inspect).join(' with ').inspect}"
      pair_goals.uniq.each do |goal|
        goal.log  << msg
      end

      return nil
    end
    
    # -- Unify Tails --
    tails = pair.map(&:last).map{|tail| tail.value(visited) }
    subunifications = unify(*tails, *pair_goals, visited)
    if subunifications
      unifications += subunifications
    else
      unifications = nil
      msg = "Cannot unify headtail tails: #{tails.map(&:inspect).join(' with ')}"
      pair_goals.uniq.each do |goal|
        goal.log  << msg
      end

      return nil
    end
  end
  
  # -- Determine Merged --
  merged = [
    arrays.map(&:first).map{|head| head.value(visited) }.reject{|head| head.type == :variable }.first,
    *arrays.map(&:last).map{|tail| tail.value(visited) }.reject{|tail| tail.type == :variable || tail == UNKNOWN_TAIL }.first || UNKNOWN_TAIL,
  ]
  
  [merged, unifications]
end

#unify_headtail_with_tail(arrays, arrays_goals, visited) ⇒ Array<Array, Array>?

Unifies Arrays where the Arrays are a mixture of Head/Tail and non-Head/Tail arrays.

Parameters:

  • arrays (Array<Array>) —

    the Arrays to be unified.

  • arrays_goals (Array<Porolog::Goal>) —

    the Goals of the Arrays to be unified.

  • visited (Array) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 790

def unify_headtail_with_tail(arrays, arrays_goals, visited)
  # -- Validate Arrays --
  unless arrays.all?{|array| has_tail?(array, false) }
    msg = "Wrong method called to unify #{arrays.inspect}"
    arrays_goals.uniq.each do |goal|
      goal.log << msg
    end
    return nil
  end
  
  merged       = []
  unifications = []
  
  # -- Variablise Arrays --
  arrays = arrays_goals.zip(arrays).map do |goal, array|
    if array == UNKNOWN_ARRAY
      array
    else
      goal.variablise(array)
    end
  end
  
  # -- Determine the fixed length (if any) --
  fixed_length = nil
  arrays.each do |array|
    next if has_tail?(array)
    
    array_length = array.value.size
    fixed_length ||= array_length
    unless fixed_length == array_length
      array.goal.log << "Cannot unify #{array.value.inspect} because it has a different length from #{fixed_length}"
      return nil
    end
  end
  
  # -- Partition Arrays --
  headtail_arrays, tail_arrays = arrays.partition(&:headtail?)
  
  # -- Unify All HeadTail Arrays --
  if headtail_arrays.size > 1
    headtail_goals = headtail_arrays.map(&:goal)
    merged_headtails, headtail_unifications = unify_headtail_with_headtail(headtail_arrays, headtail_goals, visited)
    unless merged_headtails
      msg = "Could not unify headtail arrays: #{headtail_arrays.map(&:value).map(&:inspect).join(' with ')}"
      headtail_goals.uniq.each do |goal|
        goal.log << msg
      end
      return nil
    end
    unifications += headtail_unifications
    
    if merged_headtails.length > merged.length
      merged += [[]] * (merged_headtails.length - merged.length)
    end
    
    # TODO: Remove flatten
    merged = merged.zip(merged_headtails).map(&:flatten)
  end
  
  # -- Unify All Tail Arrays --
  if tail_arrays.size > 1
    tail_goals = tail_arrays.map(&:goal)
    merged_tails, tail_unifications = unify_tail_with_tail(tail_arrays, tail_goals, visited)
    return nil unless merged_tails
    unifications += tail_unifications
    
    if merged_tails.length > merged.length
      merged += [[]] * (merged_tails.length - merged.length)
    end
    
    # TODO: Remove flatten
    merged = merged.zip(merged_tails).map(&:flatten).map{|merge_values|
      merge_values.map{|value|
        if value == UNKNOWN_TAIL
          nil
        else
          value
        end
      }
    }.map(&:compact)
  end
  
  # -- Combine HeadTail Arrays and Tail Arrays --
  headtail_arrays.product(tail_arrays).each do |pair|
    # == :head/:tail ~~ [1,2,3]/:tail ==
    # -- Extract Elements --
    left       = expand_splat(pair.first)
    left_head  = left.head
    left_tail  = left.tail
    
    right      = expand_splat(pair.last)
    right_head = right.head
    right_tail = right.tail
    
    # -- Expand Tail --
    left_tail  = expand_splat(left_tail)
    right_tail = expand_splat(right_tail)
    
    # -- Determine Goals --
    left_goal  = pair.first.goal
    right_goal = pair.last.goal
    
    # -- Unify Heads --
    head_unifications = unify(left_head, right_head, left_goal, right_goal, visited)
    if head_unifications.nil?
      msg = "Cannot unify heads: #{left_head.inspect} with #{right_head.inspect}"
      left_goal.log  << msg
      right_goal.log << msg unless right_goal == left_goal
      return nil
    end
    unifications += head_unifications
    
    # -- Unify Tails --
    tail_unifications = unify(left_tail, right_tail, left_goal, right_goal, visited)
    if tail_unifications.nil?
      msg = "Cannot unify tails: #{left_tail.inspect} with #{right_tail.inspect}"
      left_goal.log  << msg
      right_goal.log << msg unless right_goal == left_goal
      return nil
    end
    unifications += tail_unifications
    
    # -- Determine Merged and Unifications --
    left_reassembled  = [left_head,  *left_tail ]
    right_reassembled = [right_head, *right_tail]
    max_length = [left_reassembled.length, right_reassembled.length].max
    
    if max_length > merged.length
      merged += [[]] * (max_length - merged.length)
    end
    
    merged = merged.zip(left_reassembled ).map(&:flatten)
    merged = merged.zip(right_reassembled).map(&:flatten)
  end
  
  merged = merged.value
  merged = merged.map(&:value)
  
  # TODO: Cleanup names
  # TODO: Flatten out tails
  #   E.g.  [nil, [2, 3], ...] should be [nil, 2, 3, ...]
  is_tails = []
  merged = merged.value.map{|elements|
    sorted_elements = elements.reject{|element|
      element.is_a?(Variable)
    }.uniq.compact.sort_by{|element|
      case element.type
        when :atomic
          0
        when :array, :tail
          if [UNKNOWN_TAIL, UNKNOWN_ARRAY].include?(element)
            3
          else
            1
          end
        else
          # :nocov:
          # There are only 3 types and variables have already been filtered.
          2
          # :nocov:
      end
    }
    
    is_tails << sorted_elements.any?{|element| element.is_a?(Tail) || element == UNKNOWN_TAIL }
    
    merged_value = sorted_elements.first
    
    if merged_value.is_a?(Tail) && merged_value.value.is_a?(Variable)
      UNKNOWN_TAIL
    else
      merged_value
    end
  }
  merged[0...-1] = merged[0...-1].map{|value|
    if value == UNKNOWN_TAIL
      nil
    else
      value
    end
  }
  
  merged = merged.map{|value|
    if is_tails.shift
      value
    else
      [value]
    end
  }
  merged = merged.flatten(1)
  merged = merged[0...fixed_length] if fixed_length
  
  [merged, unifications]
end

#unify_many_arrays(arrays, arrays_goals, visited = []) ⇒ Array<Array, Array>?

Attempt to unify multiple Arrays.

Parameters:

  • arrays (Array<Array>) —

    the Arrays to be unified.

  • arrays_goals (Array<Porolog::Goal>) —

    the Goals of the Arrays.

  • visited (Array) (defaults to: []) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 420

def unify_many_arrays(arrays, arrays_goals, visited = [])
  arrays_values = arrays.
    map{|array| expand_splat(array) }.
    map{|array| array.is_a?(Array) ? array.map(&:value) : array.value }
  
  unless arrays_values.all?{|array_values| [:array,:variable].include?(array_values.type) }
    msg = "Cannot unify: #{arrays.map(&:inspect).join(' with ')}"
    arrays_goals.uniq.each{|goal| goal.log << msg }
    return nil
  end
  
  # TODO: Fix / improve
  if arrays_values.size == 2 && arrays_values.any?{|array| array == UNKNOWN_ARRAY }
    merged = arrays_values.reject{|array| array == UNKNOWN_ARRAY }.first
    return [merged,[]]
  end
  
  number_of_arrays = arrays.size
  number_of_tails  = arrays.count{|array| has_tail?(array) }
  
  if number_of_tails.zero?
    unify_arrays_with_no_tails(arrays, arrays_goals, visited)
  elsif number_of_tails == number_of_arrays
    unify_arrays_with_all_tails(arrays, arrays_goals, visited)
  else
    unify_arrays_with_some_tails(arrays, arrays_goals, visited)
  end
end

#unify_tail_with_tail(arrays, arrays_goals, visited) ⇒ Array<Array, Array>?

Unifies Arrays where each Array is not a Head/Tail array.

Parameters:

  • arrays (Array<Array>) —

    the Arrays to be unified.

  • arrays_goals (Array<Porolog::Goal>) —

    the Goals of the Arrays to be unified.

  • visited (Array) —

    prevents infinite recursion.

Returns:

  • (Array<Array, Array>) —

    the merged Array and the unifications to be instantiated.

  • (nil) —

    if the Arrays cannot be unified.



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# File 'lib/porolog.rb', line 702

def unify_tail_with_tail(arrays, arrays_goals, visited)
  # -- Validate Arrays --
  unless arrays.map(&:headtail?).map(&:!).all?
    msg = "Wrong method called to unify #{arrays.inspect}"
    arrays_goals.uniq.each do |goal|
      goal.log << msg
    end
    return nil
  end
  
  # -- Variablise Arrays --
  arrays = arrays_goals.zip(arrays).map do |goal, array|
    goal.variablise(array)
  end
  
  # == [1,2,3]/:tail ~~ [1,2,3]/:tail ==
  # -- Extract Elements --
  merged       = []
  unifications = []
  
  arrays = arrays.sort_by{|array| -array.length }
  
  arrays[0].zip(*arrays[1..-1]).each_with_index do |values,index|
    if values.any?{|value| value.is_a?(Tail) }
      # -- Unify Remaining Values and Tails --
      tails = arrays.map{|array| expand_splat(array[index..-1]) }
      merged_tails = []
      tails.combination(2).each do |pair|
        next if pair.compact.size < 2
        if pair.any?{|tail| tail == UNKNOWN_ARRAY }
          merged_tails += pair.reject{|tail| tail == UNKNOWN_ARRAY }
          next
        end
        first_goal = nil
        last_goal  = nil
        first_goal = pair.first.goal if pair.first.respond_to?(:goal)
        last_goal  = pair.last.goal  if pair.last.respond_to?(:goal)
        m,u = unify_arrays(first_goal.variablise([pair.first]), last_goal.variablise([pair.last]), first_goal, last_goal, visited)
        return nil unless m
        m[-1] = UNKNOWN_TAIL if m[-1].nil?
        merged_tails += m
        unifications += u
      end
      merged_tails.uniq!
      merged_tails_unifications = []
      # TODO: Fix [first_goal] * arrays.size
      if merged_tails.size > 1
        merged_tails, merged_tails_unifications = unify_many_arrays(merged_tails, [arrays_goals.first] * arrays.size, visited)
      end
      merged       += merged_tails.flatten(1)
      unifications += merged_tails_unifications - unifications
      break
    else
      # -- Unify Values at Index --
      merged_value = []
      values.combination(2).each do |pair|
        if pair.any?(&:nil?)
          merged_value += pair.compact
          next
        end
        first_goal = nil
        last_goal  = nil
        first_goal = pair.first.goal if pair.first.respond_to?(:goal)
        last_goal  = pair.last.goal  if pair.last.respond_to?(:goal)
        
        m,u = unify_arrays([pair.first], [pair.last], first_goal, last_goal, visited)
        if m.nil?
          [first_goal, last_goal].uniq.each do |goal|
            goal.log << "Cannot unify #{pair.first.inspect} with #{pair.last.inspect}"
          end
          return nil
        end
        merged_value += m
        unifications += u
      end
      merged << merged_value.compact.uniq.first || nil
    end
  end
  
  [merged, unifications]
end