Family Age Gaps

README.md

@@ -15,7 +15,10 @@ The Jetisu Toolkit is exploring the possibility that the relational model can do
 
 <img width="100%" src="images/doing for rules what rm did for data.png">
 
-## Rules As Code examples
+## Puzzle Examples
+- [Family Age Gaps](puzzles/family_age_gaps.md)
+
+## Rules As Code Examples
 The examples are chosen to illustrate the benefits (and/or challenges) of using sigma complete relations to model rules as code.
 - [ACT Conveyance Duty](ACT_Conveyance_Duty.ipynb)
 - [Australian GST](Australian_GST.ipynb)

puzzles/family_age_gaps.md

@@ -0,0 +1,66 @@
+# How old is Donald?
+
+The following puzzle is from Peter Revesz's 1993 paper "A closed-form evaluation for Datalog queries with integer (gap)-order constraints." _Theoretical Computer Science, 116(1), 117–149._ https://doi.org/10.1016/0304-3975(93)90222-F
+
+> Alfred and Alice have children Bernard, Carl and Donald in this order.
+Bernard and Bernice have a child Edward. Donald and Denise have children Elise and
+Fred. Edward and Elise have a child, Gerald. Fred and Felice have a child, Harold. 
+Alfred is not yet 70, and Harold is already in school. Gerald was born just last
+month. Elise is over four years older than her younger brother Fred, and Bernard is over
+25 years older than his son Edward. Assuming that there is over 17 years difference between parents and their children
+and that no siblings are twins or born in the same year, how old is Donald?
+
+And here is a literate programming solution using a complete relation and SQL.
+
+```SQL
+SELECT Donald_age
+from COMPLETE(
+    Alfred_age int, Alice_age int, Bernard_age int,
+    Bernice_age int, Carl_age int, Donald_age int,
+    Denise_age int, Edward_age int, Elise_age int,
+    Fred_age int, Felice_age int, Gerald_age int,
+    Harold_age int
+  )
+WHERE
+    ---- Approach
+    ---- Given that no siblings are twins or born in the same year we will use > rather than >=
+    ---- Given the age gap between parents and their children we will add a generational gap test for each family
+
+    -- Alfred and Alice have children Bernard, Carl and Donald in this order.
+    Bernard_age > Carl_age
+    AND Carl_age > Donald_age
+    -- generational gap of >17 years
+    AND min(Alfred_age, Alice_age) - 17 > max(Bernard_age, Bernice_age, Carl_age, Donald_age)
+
+    -- Bernard and Bernice have child Edward.
+    -- generational gap of >17 years
+    AND min(Bernard_age, Bernice_age) - 17 > Edward_age
+
+    -- Donald and Denise have children Elise and Fred.
+    -- generational gap of >17 years
+    AND min(Donald_age, Denise_age) - 17 > max(Elise_age, Fred_age)
+
+    -- Edward and Elise have child Gerald.
+    -- generational gap of >17 years
+    AND min(Edward_age, Elise_age) - 17 > Gerald_age
+
+    -- Fred and Felice have child Harold
+    -- generational gap of >17 years
+    AND min(Fred_age, Felice_age) - 17 > Harold_age
+
+    -- Alfred is not yet 70
+    AND Alfred_age < 70
+
+    -- Harold is already in school
+    AND Harold_age > 5
+
+    -- Gerald was born just last month
+    AND Gerald_age = 0
+
+    -- Elise is over 4 years older than her younger brother Fred
+    AND Elise_age - 4 > Fred_age
+
+    -- Bernard is over 25 years older than his son Edward
+    AND Bernard_age - 25 > Edward_age;
+
+```