1. Prolog Recursion Pepper Major portions credited to :
Blackburn, Patrick, Johan Bos and Kristina Striegnitz. Learn Prolog Now.
London: College Publications, (ISBN )
Also available at

2. A rule with that calls itself
is_digesting(X,Y) :- just_ate(X,Y).
is_digesting(X,Y) :-
just_ate(X,Z),
is_digesting(Z,Y).
2 rules
You are digesting what you just ate
You are digesting whatever you ate just ate
And so on until you come to an animal that did not just eat something.

3. Use in a query
just_ate(mosquito,blood(john)). just_ate(frog,mosquito). just_ate(stork,frog). just_ate(person,cow). just_ate(cow,frog). is_digesting(person,X)"? Please answer 'y' or 'n'? yes X = cow ; X = frog ; X = mosquito ; X = blood(john) ;

4. Construction is_digesting(X,Y) :- just_ate(X,Y). is_digesting(X,Y) :-
just_ate(X,Z),
is_digesting(Z,Y).
Base case:
Does not use its own predicate.
Recursive rule:
Handles one case,
Recurses over the rest of the cases.

5. Proof Is_digesting(person,A).
What just_ate fact has person on the left side, then the right side can be X. : look for just_ate(person,A).
Look for just_ate(X,Z), is_digesting(Z,Y).
if just_ate (person,_1) and (_1, A)
so (person,cow) and (cow,frog) match
so A = frog

6. Recursion of descendants
 facts:
 child(anne,bridget).    child(bridget,caroline).    child(caroline,donna).    child(donna,emily).
Find descendants: - not far enough
   descend(X,Y)  :-  child(X,Y).        descend(X,Y)  :-  child(X,Z),                                      child(Z,Y).

7. Recursion Analysis Base case: Recursive rule:
Does not use its own predicate.
If y is a child of x, y descends from x
descend(X,Y)  :-  child(X,Y).
Recursive rule:
Handles one case,
Recurses over the rest of the cases.
If y is a child of a descendant of x, then y is a descendant of x
descend(X,Y) :- child (I,Y), descend(X,I)

8. Exercise graph Connected points
edge(a,b).
edge(b, c).
edge(b, d).
edge(b, e).
edge(d, e).
edge(y,x).
edge(x,z).
What points can you reach from a particular point? Assumes no circular connections.
connected(a,X).
connected (X, z).

9. Accumulate text Without Accumulation: With Accumulation: Query:
descend(X,Y)  :-  child(X,Y).
descend(X,Y) :- child (I,Y), descend(X,I)
With Accumulation:
descend(X,Y, childrel(X,Y)):- child(X,Y).
descend(X,Y,childrel(X,I,L)):- child(X,I),
descend(I,Y,L).
Query:
descend2(anne,donna,X).
X = parentChild(anne, bridget, parentChild(bridget, caroline, parentChild(caroline, donna))) ;

10. Exercise Walk the Graph
Given a list of edges
Show the path that connects from one edge to another
connectedPath(a,e,X).
Should give:
X = go(a, b, go(b, e)) ;
X = go(a, b, go(b, d, go(d, e))) ;

11. Adding Numbers adder(X, Y, Z):- Z is X + Y. 10 ?- adder(1,2,X). X = 3.
ERROR: is/2: Arguments are not sufficiently instantiated

12. Random Numbers
random/3 – given a range of numbers as the first 2 arguments, a random number starting from the first number but not including the last number. (for dice 1, 7)
makeroll(X) :- random(1,7,X).
adder(X,Y,Z):- Z is X + Y.
throw2(Z) :-
makeroll( X), makeroll( Y), Z is X + Y.
You can add writeln(Z).

13. Count Recursive Attempts
Need one variable to initialize to 0 when you start.
When you recurse, add 1 to the variable you initialized to 0
When you are done, add 1 to the accumulated list.
Example throwUntil_11(Count, FinalCount):-
FinalCount is Count + 1, throw2(11).
throwUntil_11(Count, FinalCount):-
throw2(Y), Z is Count + 1, Y \= 11
throwUntil_11(Z, FinalCount).
Example query: throwUntil_11(0,X).

14. Exercise Count Edge Walk Recursions
Count the number of possible steps between two points.
countConnections(a,e,0,X).
X = 2 ;
X = 3 ;

15. Recursion Summary How to declare a recursive rule
How to pair the recursive rule with a base case
How prolog proof leads to recursion
No base case – endless recursion
Random
Counting recursive steps