Part i:	Write recursive equations for Count, Shrink, and ScanC. State the base case(s) clearly.
Part ii:	Write the above functions in the Haskell language.

Logic Programming

We consider the following Prolog program in this question.

likes(john,soccer). male(john). male(peter). male(david). female(mary). female(amy). parent(john,peter). parent(john,david). parent(mary,peter). parent(mary,amy).

dad(X,Y) :- male(X), parent(X,Y). mum(X,Y) :- female(X), parent(X,Y).

sibling(X,Y) :- parent(Z,X), parent(Z,Y). hasChild(X) :- parent(X,_).

3(a) [10 marks]

Explain the binding of variables in the rule sibling.

3(b) [20 marks]

Now the user issues the following goal (or query) to the Prolog interpreter:

sibling ( peter, A ).

Draw the search tree used in the Prolog inference process for answering this goal.

Write all possible answers of A that are returned by the Prolog interpreter.

Question 3 Logic Programming We consider the following Prolog program in this question likes (john, soccer). male (john). male (peter). male (david) . female (mary) female (amy) . parent (john, peter). parent (john, david) parent (mary,peter). parent (mary,amy) . dad (X, Y) :- male (X), parent (X, Y) mum (X, Y)- sibling (X,Y) :- parent (Z, X), parent (Z,Y) . hasChild (X) :- parent (X,_) :- female (X), paren t (X, Y) 3(a) [10 marks] Explain the binding of variables in the rule sibling 3(b) [20 marks] Now the user issues the following goal (or query) to the Prolog interpreter: sibling peter, A ) . Draw the search tree used in the Prolog inference process for answering this goal Write all possible answers of A that are returned by the Prolog interpreter