% BMI — ARC-style Body Mass Index example adapted from Eyeling.
%
% The example normalizes metric or US inputs, computes BMI, assigns the WHO
% adult category, derives a healthy-weight band for the same height, and emits
% an inspectable report plus independent checks.
%
% For reproducibility and documentation only; not medical advice.

% Editable metric input.
triple(input, unitSystem, metric).
triple(input, weight, 72.0).
triple(input, height, 178.0).

% US alternative:
% triple(input, unitSystem, us).
% triple(input, weight, 158.73).
% triple(input, height, 70.08).

% Normalization and BMI calculation.
triple(case, weightKg, W) :-
  triple(input, unitSystem, metric),
  triple(input, weight, W).

triple(case, heightM, M) :-
  triple(input, unitSystem, metric),
  triple(input, height, H),
  div(H, 100.0, M).

triple(reason, units, "Inputs were already metric, so kilograms stay kilograms and centimeters are divided by 100 to obtain meters.") :-
  triple(input, unitSystem, metric).

triple(case, weightKg, Kg) :-
  triple(input, unitSystem, us),
  triple(input, weight, W),
  mul(W, 0.45359237, Kg).

triple(case, heightM, M) :-
  triple(input, unitSystem, us),
  triple(input, height, H),
  mul(H, 0.0254, M).

triple(reason, units, "US inputs were converted to SI units: pounds to kilograms and inches to meters.") :-
  triple(input, unitSystem, us).

triple(case, heightSquared, M2) :-
  triple(case, heightM, M),
  mul(M, M, M2).

triple(case, bmi, Bmi) :-
  triple(case, weightKg, Kg),
  triple(case, heightSquared, M2),
  div(Kg, M2, Bmi).

triple(case, bmiRoundedInt, BmiRoundedInt) :-
  triple(case, bmi, Bmi),
  mul(Bmi, 100.0, BmiX100),
  rounded(BmiX100, BmiRoundedInt).

triple(case, healthyMinKg, HealthyMin) :-
  triple(case, heightSquared, M2),
  mul(18.5, M2, HealthyMin).

triple(case, healthyMaxKg, HealthyMax) :-
  triple(case, heightSquared, M2),
  mul(24.9, M2, HealthyMax).

triple(case, healthyMinKgRoundedInt, MinRoundedInt) :-
  triple(case, healthyMinKg, HealthyMin),
  mul(HealthyMin, 10.0, MinX10),
  rounded(MinX10, MinRoundedInt).

triple(case, healthyMaxKgRoundedInt, MaxRoundedInt) :-
  triple(case, healthyMaxKg, HealthyMax),
  mul(HealthyMax, 10.0, MaxX10),
  rounded(MaxX10, MaxRoundedInt).

% WHO adult categories, using half-open intervals.
triple(decision, category, "Underweight") :-
  triple(case, bmi, Bmi),
  lt(Bmi, 18.5).

triple(decision, category, "Normal") :-
  triple(case, bmi, Bmi),
  ge(Bmi, 18.5),
  lt(Bmi, 25.0).

triple(decision, category, "Overweight") :-
  triple(case, bmi, Bmi),
  ge(Bmi, 25.0),
  lt(Bmi, 30.0).

triple(decision, category, "Obesity I") :-
  triple(case, bmi, Bmi),
  ge(Bmi, 30.0),
  lt(Bmi, 35.0).

triple(decision, category, "Obesity II") :-
  triple(case, bmi, Bmi),
  ge(Bmi, 35.0),
  lt(Bmi, 40.0).

triple(decision, category, "Obesity III") :-
  triple(case, bmi, Bmi),
  ge(Bmi, 40.0).

% Answer and reason why.
triple(answer, bmi, 22.72) :-
  triple(case, bmiRoundedInt, 2272).

triple(answer, category, Category) :-
  triple(decision, category, Category).

triple(answer, healthyMinKg, 58.6) :-
  triple(case, healthyMinKgRoundedInt, 586).

triple(answer, healthyMaxKg, 78.9) :-
  triple(case, healthyMaxKgRoundedInt, 789).

triple(answer, heightCm, CmRounded) :-
  triple(case, heightM, M),
  mul(M, 100.0, Cm),
  rounded(Cm, CmRounded).

triple(reason, formula, "BMI is defined as weight in kilograms divided by height in meters squared.") :-
  triple(case, bmi, _Bmi).

triple(reason, calculation, "The normalized weight and height were used to compute BMI, then the result was mapped to the WHO adult category table.") :-
  triple(decision, category, _Category).

triple(reason, categoryRule, Category) :-
  triple(decision, category, Category).

triple(reason, unitsExplanation, Units) :-
  triple(reason, units, Units).

% Independent checks.
triple(check, c1, "OK - the input was normalized into positive SI values.") :-
  triple(case, weightKg, Kg),
  triple(case, heightM, M),
  gt(Kg, 0),
  gt(M, 0).

triple(check, c2, "OK - height squared was reconstructed from the normalized height.") :-
  triple(case, heightM, M),
  triple(case, heightSquared, M2),
  mul(M, M, M2).

triple(check, c3, "OK - the BMI value matches the BMI = kg / m² formula.") :-
  triple(case, weightKg, Kg),
  triple(case, heightSquared, M2),
  triple(case, bmi, Bmi),
  div(Kg, M2, Bmi).

triple(check, c4, "OK - a BMI of 18.49 stays below the normal-weight threshold.") :-
  lt(18.49, 18.5).

triple(check, c5, "OK - the lower boundary is half-open: BMI 18.5 is classified as Normal.") :-
  ge(18.5, 18.5),
  lt(18.5, 25.0).

triple(check, c6, "OK - BMI 25.0 starts the Overweight category.") :-
  ge(25.0, 25.0),
  lt(25.0, 30.0).

triple(check, c7, "OK - BMI 30.0 starts the Obesity I category.") :-
  ge(30.0, 30.0),
  lt(30.0, 35.0).

triple(check, c8, "OK - classification behavior is monotonic across representative BMI values.") :-
  ge(22.0, 18.5),
  lt(22.0, 25.0),
  ge(27.0, 25.0),
  lt(27.0, 30.0),
  ge(41.0, 40.0).

triple(check, c9, "OK - the healthy-weight band was reconstructed from BMI 18.5 to 24.9 at the same height.") :-
  triple(case, heightSquared, M2),
  triple(case, healthyMinKg, Min),
  triple(case, healthyMaxKg, Max),
  mul(18.5, M2, Min),
  mul(24.9, M2, Max).

% Derived report summary.  These triples are consequences of the calculation
% and checks, not pre-written report lines.
triple(report, result, bmi(Bmi, Category)) :-
  triple(answer, bmi, Bmi),
  triple(answer, category, Category).

triple(report, healthyWeightRangeKg, range(Min, Max)) :-
  triple(answer, healthyMinKg, Min),
  triple(answer, healthyMaxKg, Max).

triple(report, heightCm, Height) :-
  triple(answer, heightCm, Height).

triple(report, checkPassed, Check) :-
  triple(check, Check, _Message).