eyeprolog

Body mass index

What is this person’s BMI, and which category does it fall in?

A weight and a height go in; a body mass index, its WHO adult category, and the healthy-weight band for the same height come out. Each number is derived by a rule, so the proof shows the full calculation, and nine independent checks confirm it.

Run it in the playground · Source

For reproducibility and documentation only; not medical advice.

The question

Body mass index is weight in kilograms divided by height in meters squared. The WHO adult table maps it to a category: below 18.5 is underweight, 18.5 up to 25 is normal, 25 up to 30 is overweight, and so on.

For 72 kg and 178 cm: what is the BMI, what is the category, and what weight range counts as healthy at this height?

The input

unitSystem(input, metric).
weight(input, 72.0).
height(input, 178.0).

The program also accepts US units (pounds and inches) and converts them to kilograms and meters before anything else is computed.

The calculation

heightSquared(case, M2) :-
  heightM(case, M),
  (M2 is M * M).

bmi(case, Bmi) :-
  weightKg(case, Kg),
  heightSquared(case, M2),
  (Bmi is Kg / M2).

category(decision, "Normal") :-
  bmi(case, Bmi),
  (Bmi >= 18.5),
  (Bmi < 25.0).

Each category is one rule over a half-open interval, so every BMI value falls into exactly one category.

The answer

eyeprolog examples/bmi.pl

bmi(case, 22.724403484408533).
bmi(answer, 22.72).
category(answer, "Normal").
result(report, bmi(22.72, "Normal")).
healthyWeightRangeKg(report, range(58.6, 78.9)).

The full output has 41 answers, including the explanation strings and the nine checkPassed/2 results.

The reason

step(bmi(case, 22.724403484408533),
     rule(19),
     ['Bmi' = 22.724403484408533, 'Kg' = 72.0, 'M2' = 3.1684],
     [weightKg(case, 72.0), heightSquared(case, 3.1684), 22.724403484408533 is 72.0 / 3.1684]).
step(category(decision, "Normal"),
     rule(26),
     ['Bmi' = 22.724403484408533],
     [bmi(case, 22.724403484408533), 22.724403484408533 >= 18.5, 22.724403484408533 < 25.0]).

The BMI is 72.0 divided by 3.1684 (1.78²), and “Normal” holds because that value is at least 18.5 and below 25.

The check

condition('C1', resolution, ok, 53).
condition('C5', re_decision, ok, 29).
trusted(0).
verdict(checked).

53 rule steps were replayed and all 29 arithmetic steps were recomputed independently. Nothing is taken on trust.

Try it

Switch to the US alternative in the source (158.73 lb, 70.08 in). The BMI becomes 22.72318149286574 and still rounds to 22.72, “Normal”.
Change the weight to 90.0 kg. The category becomes “Overweight”, but bmi(answer, …) and result(report, …) disappear. Find the rule with a hard-coded 2272 and make it general.
What answer does a BMI of exactly 25.0 get, and which rule decides it?

Learn more in The Art of EyeProlog, Chapters 6 and 14.

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