% enforce the relation between functions snf predicates
p_arity('NullaryPredicate', 0).
p_arity('UnaryPredicate', 1).
p_arity('BinaryPredicate', 2).
p_arity('TernaryPredicate', 3).
p_arity('QuaternaryPredicate', 4).
p_arity('QuinaryPredicate', 5).
p_arity('SenaryPredicate', 6).
p_arity('SeptenaryPredicate', 7).
p_arity('OctaryPredicate', 8).
p_arity('NonaryPredicate', 9).
p_arity('DenaryPredicate', 10).

f_arity('NullaryFunction', 0).
f_arity('UnaryFunction', 1).
f_arity('BinaryFunction', 2).
f_arity('TernaryFunction', 3).
f_arity('QuaternaryFunction', 4).
f_arity('QuinaryFunction', 5).
f_arity('SenaryFunction', 6).
f_arity('SeptenaryFunction', 7).
f_arity('OctaryFunction', 8).
f_arity('NonaryFunction', 9).

% Equivalent Types use this rule to spedifiy and enforce that they have the same instances as the other
(equivalentTypes(PredType,FunctType) ==>  
  (in(FunctorObject,PredType)
    <==>
   in(FunctorObject,FunctType))).

% generate some equivalency rules
((p_arity(PredType,PA), plus(FA,1,PA), f_arity(FunctType,FA))) 
  ==> equivalentTypes(PredType,FunctType).