% Engineering example: cantilever beam tip deflection.
% The beam is modeled with load, span length, elastic modulus, and second moment
% of area.  The rules compute F*L^3/(3*E*I), convert meters to millimeters, and
% classify the design against a deflection limit.

%% goal: type(X0, X1)

%% goal: tipDeflection_m(X0, X1)

%% goal: tipDeflection_mm(X0, X1)

%% goal: limit_mm(X0, X1)

%% goal: status(X0, X1)


beam(beam1, force_N, 1200.0).
beam(beam1, length_m, 2.5).
beam(beam1, elasticModulus_Pa, 200000000000.0).
beam(beam1, secondMoment_m4, 0.000008).
limit(beam1, maxDeflection_mm, 5.0).

tip_deflection_m(Beam, Deflection) :-
  beam(Beam, force_N, Force),
  beam(Beam, length_m, Length),
  beam(Beam, elasticModulus_Pa, Elasticmodulus),
  beam(Beam, secondMoment_m4, Secondmoment),
  (Lengthcubed is Length ** 3.0),
  (Numerator is Force * Lengthcubed),
  (Threee is 3.0 * Elasticmodulus),
  (Denominator is Threee * Secondmoment),
  (Deflection is Numerator / Denominator).

tip_deflection_mm(Beam, Deflectionmm) :-
  tip_deflection_m(Beam, Deflectionm),
  (Deflectionmm is Deflectionm * 1000.0).

type(Beam, cantilever_beam) :-
  beam(Beam, force_N, _force).

tipDeflection_m(Beam, Deflectionm) :-
  tip_deflection_m(Beam, Deflectionm).

tipDeflection_mm(Beam, Deflectionmm) :-
  tip_deflection_mm(Beam, Deflectionmm).

limit_mm(Beam, Limit) :-
  limit(Beam, maxDeflection_mm, Limit).

status(Beam, within_deflection_limit) :-
  tip_deflection_mm(Beam, Deflectionmm),
  limit(Beam, maxDeflection_mm, Limit),
  (Deflectionmm =< Limit).