# ============================================================================ # BMI — ARC-style Body Mass Index example. # # This example turns a familiar health calculation into a small, inspectable # ARC program. It normalizes either metric or US inputs, computes BMI, assigns # a WHO adult category, and derives a healthy-range weight band for the given # height. The report explains the result and includes independent checks for # boundary handling and category behavior. # # For reproducibility and documentation only; not medical advice. # ============================================================================ @prefix : . @prefix log: . @prefix math: . @prefix string: . # -------------- # Editable input # -------------- :Input :unitSystem "metric"; :weight 72.0; :height 178.0. # US alternative: # :Input # :unitSystem "us"; # :weight 158.73; # :height 70.08. # --------------------------------- # Normalization and BMI calculation # --------------------------------- { :Input :unitSystem "metric"; :weight ?W; :height ?H. (?H 100.0) math:quotient ?M. } => { :Case :weightKg ?W; :heightM ?M. :Reason :units "Inputs were already metric, so kilograms stay kilograms and centimeters are divided by 100 to obtain meters.". } . { :Input :unitSystem "us"; :weight ?W; :height ?H. (?W 0.45359237) math:product ?Kg. (?H 0.0254) math:product ?M. } => { :Case :weightKg ?Kg; :heightM ?M. :Reason :units "US inputs were converted to SI units: pounds to kilograms and inches to meters.". } . { :Case :weightKg ?Kg; :heightM ?M. (?M ?M) math:product ?M2. (?Kg ?M2) math:quotient ?Bmi. (?Bmi 100.0) math:product ?BmiX100. ?BmiX100 math:rounded ?BmiRoundedInt. (?BmiRoundedInt 100.0) math:quotient ?BmiRounded. (18.5 ?M2) math:product ?HealthyMin. (24.9 ?M2) math:product ?HealthyMax. (?HealthyMin 10.0) math:product ?MinX10. (?HealthyMax 10.0) math:product ?MaxX10. ?MinX10 math:rounded ?MinRoundedInt. ?MaxX10 math:rounded ?MaxRoundedInt. (?MinRoundedInt 10.0) math:quotient ?HealthyMinRounded. (?MaxRoundedInt 10.0) math:quotient ?HealthyMaxRounded. } => { :Case :heightSquared ?M2; :bmi ?Bmi; :bmiRounded ?BmiRounded; :healthyMinKg ?HealthyMin; :healthyMaxKg ?HealthyMax; :healthyMinKgRounded ?HealthyMinRounded; :healthyMaxKgRounded ?HealthyMaxRounded. } . # ------------------------------------------ # WHO adult categories (half-open intervals) # ------------------------------------------ { :Case :bmi ?Bmi. ?Bmi math:lessThan 18.5. } => { :Decision :category "Underweight". } . { :Case :bmi ?Bmi. ?Bmi math:notLessThan 18.5. ?Bmi math:lessThan 25.0. } => { :Decision :category "Normal". } . { :Case :bmi ?Bmi. ?Bmi math:notLessThan 25.0. ?Bmi math:lessThan 30.0. } => { :Decision :category "Overweight". } . { :Case :bmi ?Bmi. ?Bmi math:notLessThan 30.0. ?Bmi math:lessThan 35.0. } => { :Decision :category "Obesity I". } . { :Case :bmi ?Bmi. ?Bmi math:notLessThan 35.0. ?Bmi math:lessThan 40.0. } => { :Decision :category "Obesity II". } . { :Case :bmi ?Bmi. ?Bmi math:notLessThan 40.0. } => { :Decision :category "Obesity III". } . # --------------------- # Answer and reason why # --------------------- { :Case :bmiRounded ?BmiRounded; :healthyMinKgRounded ?HealthyMinRounded; :healthyMaxKgRounded ?HealthyMaxRounded; :heightM ?M. :Decision :category ?Category. (?M 100.0) math:product ?Cm. ?Cm math:rounded ?CmRounded. } => { :Answer :bmi ?BmiRounded; :category ?Category; :healthyMinKg ?HealthyMinRounded; :healthyMaxKg ?HealthyMaxRounded; :heightCm ?CmRounded. } . { :Case :weightKg ?Kg; :heightM ?M; :heightSquared ?M2; :bmiRounded ?BmiRounded. :Reason :units ?Units. :Decision :category ?Category. } => { :Reason :formula "BMI is defined as weight in kilograms divided by height in meters squared."; :calculation "The normalized weight and height were used to compute BMI, then the result was mapped to the WHO adult category table."; :categoryRule ?Category; :unitsExplanation ?Units. } . # ------------------ # Independent checks # ------------------ { :Case :weightKg ?Kg; :heightM ?M. ?Kg math:greaterThan 0. ?M math:greaterThan 0. } => { :Check :c1 "OK - the input was normalized into positive SI values.". } . { :Case :heightM ?M; :heightSquared ?M2. (?M ?M) math:product ?M2. } => { :Check :c2 "OK - height squared was reconstructed from the normalized height.". } . { :Case :weightKg ?Kg; :heightSquared ?M2; :bmi ?Bmi. (?Kg ?M2) math:quotient ?Bmi. } => { :Check :c3 "OK - the BMI value matches the BMI = kg / m² formula.". } . { 18.49 math:lessThan 18.5. } => { :Check :c4 "OK - a BMI of 18.49 stays below the normal-weight threshold.". } . { 18.5 math:notLessThan 18.5. 18.5 math:lessThan 25.0. } => { :Check :c5 "OK - the lower boundary is half-open: BMI 18.5 is classified as Normal.". } . { 25.0 math:notLessThan 25.0. 25.0 math:lessThan 30.0. } => { :Check :c6 "OK - BMI 25.0 starts the Overweight category.". } . { 30.0 math:notLessThan 30.0. 30.0 math:lessThan 35.0. } => { :Check :c7 "OK - BMI 30.0 starts the Obesity I category.". } . { 22.0 math:notLessThan 18.5. 22.0 math:lessThan 25.0. 27.0 math:notLessThan 25.0. 27.0 math:lessThan 30.0. 41.0 math:notLessThan 40.0. } => { :Check :c8 "OK - classification behavior is monotonic across representative BMI values.". } . { :Case :heightSquared ?M2; :healthyMinKg ?Min; :healthyMaxKg ?Max. (18.5 ?M2) math:product ?Min. (24.9 ?M2) math:product ?Max. } => { :Check :c9 "OK - the healthy-weight band was reconstructed from BMI 18.5 to 24.9 at the same height.". } . # ----- # Fuses # ----- { :Decision :category ?Any. 1 log:notIncludes { :Check :c1 ?C1. :Check :c2 ?C2. :Check :c3 ?C3. :Check :c4 ?C4. :Check :c5 ?C5. :Check :c6 ?C6. :Check :c7 ?C7. :Check :c8 ?C8. :Check :c9 ?C9. }. } => false . { :Decision :category ?C1, ?C2. ?C1 log:notEqualTo ?C2. } => false . # --------------------------------------------- # ARC report (built from actual derived values) # --------------------------------------------- { :Answer :bmi ?BmiRounded; :category ?Category; :healthyMinKg ?HealthyMinRounded; :healthyMaxKg ?HealthyMaxRounded; :heightCm ?CmRounded. :Check :c1 ?C1. :Check :c2 ?C2. :Check :c3 ?C3. :Check :c4 ?C4. :Check :c5 ?C5. :Check :c6 ?C6. :Check :c7 ?C7. :Check :c8 ?C8. :Check :c9 ?C9. ( "BMI — ARC-style Body Mass Index example\n\n" "Answer\n" "BMI = " ?BmiRounded "\n" "Category = " ?Category "\n" "At height " ?CmRounded " cm, a healthy-weight range is about " ?HealthyMinRounded "–" ?HealthyMaxRounded " kg (BMI 18.5–24.9).\n\n" "Reason Why\n" "BMI is defined as weight in kilograms divided by height in meters squared. " "This program first normalizes the input to SI units, computes BMI, and then applies WHO adult categories as half-open intervals. " "The healthy-weight band is the weight range at the same height that corresponds to BMI 18.5 through 24.9.\n\n" "Check\n" "C1 " ?C1 "\n" "C2 " ?C2 "\n" "C3 " ?C3 "\n" "C4 " ?C4 "\n" "C5 " ?C5 "\n" "C6 " ?C6 "\n" "C7 " ?C7 "\n" "C8 " ?C8 "\n" "C9 " ?C9 "\n" ) string:concatenation ?Block. } => { :report log:outputString ?Block. } .