Prolog Recursion Pepper Major portions credited to : Blackburn, Patrick, Johan Bos and Kristina Striegnitz. Learn Prolog Now. London: College Publications, 2006. (ISBN 9781904987178) Also available at http://www.learnprolognow.org

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.

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) ;

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.

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

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).

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)

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).

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))) ;

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))) ;

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

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).

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).

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

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