Prolog Recursion

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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
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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.

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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)

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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.

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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

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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).

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Recursion Analysis

• Base case
• 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)

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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).

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Accumulate text

• Without Accumulation
• 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)))

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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)))

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Adding Numbers

• adder(X, Y, Z)- Z is X Y.
• 10 ?- adder(1,2,X).
• X 3.
• 11 ?- adder(X,2,3).
• ERROR is/2 Arguments are not sufficiently
  instantiated

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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).

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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.
  
• ExamplethrowUntil_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).

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Exercise Count Edge Walk Recursions

• Count the number of possible steps between two
  points.
• countConnections(a,e,0,X).
• X 2
• X 3

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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