Write a PROLOG program that will take grammar rules in the following format: NT (NT | T)* Where NT is any nonterminal, T is any terminal and Kleene star (*) signifies any number of repetitions, and generate the corresponding top-down parser, that is: sentence  noun-phrase, verb-phrase determiner  [the] will generate the following: sentence (I, O) :- noun-phrase(I,R), verb-phrase (R,O). determiner ([the|X], X) :- !.

24.Write a PROLOG program that will take grammar rules.

% PROLOG program that will take grammar rules.

%  below sets of  function is not predefined you can use any name as function

det([the|X],X):-!.

noun([sohan|X],X).

noun([frog|X],X).

verb([loves|X],X):-!.

sentence(P1,P3):- np(P1,P2),vp(P2,P3).

np(P1,P2):- noun(P1,P2).

np(P1,P3):- det(P1,P2),noun(P2,P3).

vp(P1,P3):- verb(P1,P2), np(P2,P3).

Write a program in PROLOG to implement merge (L1, L2, L3) where L1 is first ordered list and L2 is second ordered list and L3 represents the merged list.

23.Write a program in PROLOG to implement merge (L1, L2, L3) where L1 is first ordered list and L2 is second ordered list and L3 represents the merged list.

%PROLOG to implement merge (L1, L2, L3)

%  below merge function is not predefined you can use any name as function

merge([],[],[]).

merge([],L2,L2).

merge(L1,[],L1).

merge([H1|T1],[H2|T2],[H1|T3]):- H1=<H2,

merge(T1, [H2|T2], T3).

merge([H1|T1],[H2|T2],[H2|T3]):- merge([H1|T1], T2, T3).

% Output

Write a program in PROLOG to implement delete_all (X, L, R) where X denotes the element whose all occurrences has to be deleted from list L to obtain list R.

22.Write a program in PROLOG to implement delete_all (X, L, R) where X denotes the element whose all occurrences has to be deleted from list L to obtain list R.

%prolog program to implement delete_all(X,L,R)

%  below delete_all function is not predefined you can use any name as function

delete_all(X, [], []).

delete_all(X, [X|T], R):- delete_all(X, T, R).

delete_all(X, [H|T], [H|R]):- delete_all(X, T, R).

% Output

Write a Prolog program to implement delete_nth (N, L, R) that removes the element on Nth position from a list L to generate a list R.

21.Write a Prolog program to implement delete_nth (N, L, R) that removes the element on Nth position from a list L to generate a list R.

%Prolog program to implement delete_nth (N, L, R)

%  below delete_nth function is not predefined you can use any name as function

delete_nth(1, [H|T], T).

delete_nth(N, [H|T], [H|R]):- N1 is N-1,

delete_nth(N1, T, R).

% Output

Write a Program in PROLOG to implement sublist(S, L) that checks whether the list S is the sublist of list L or not. (Check for sequence or the part in the same order).

20.Write a Program in PROLOG to implement sublist(S, L) that checks whether the list S is the sublist of list L or not. (Check for sequence or the part in the same order).

%Program in PROLOG to implement sublist(S, L)

%  below subset function is not predefined you can use any name as function

subset([], L).

subset([E|Tail], [E|NTail]):-

subset(Tail, NTail).

subset([E|Tail], [D|NTail]):-

subset([E|Tail], NTail).

% Output

Write a prolog program to implement insert_nth(I, N, L, R) that inserts an item I into Nth position of list L to generate a list R.

19.Write a prolog program to implement insert_nth(I, N, L, R) that inserts an item I into Nth position of list L to generate a list R. 

%Write Prolog program to implement insert_nth(I, N, L, R) not.

%  below insert_nth function is not predefined you can use any name as function

insert_nth(I, 1, L, [I|L]).

insert_nth(I, N, [H|T], [H|R]):- N1 is N-1,insert_nth(I, N1, T, R).

% Output

Write a Prolog program to implement maxlist(L, M) so that M is the maximum number in the list.

18.Write a Prolog program to implement maxlist(L, M) so that M is the maximum number in the list. 

%Prolog program to implement maxlist(L, M)

%  below maxlist function is not predefined you can use any name as function

maxlist([H],H).

maxlist([H|T],R):-

 maxlist(T,M1),

 H>=M1,

 R is H.

maxlist([H|T],R):-

 maxlist(T,M1),

 H<M1, 

 R is M1.

% Output

Write a program in PROLOG to implement remove_dup (L, R) where L denotes the list with some duplicates and the list R denotes the list with duplicates removed.

17.Write a program in PROLOG to implement remove_dup (L, R) where L denotes the list with some duplicates and the list R denotes the list with duplicates removed. 

%PROLOG to implement remove_dup (L, R)

%  below is-member function is not predefined you can use any name as function

is_member(X,[X|_]).

is_member(X,[_|T]):- is_member(X,T).

remove_dups([],[]).

remove_dups([H|T], R):- is_member(H,T), remove_dups(T,R).

remove_dups([H|T],[H|R]):- \+(is_member(H,T)),remove_dups(T,R).

% Output

Write a Prolog program to implement nth_element (N, L, X) where N is the desired position, L is a list and X represents the Nth element of L.

16.Write a Prolog program to implement nth_element (N, L, X) where N is the desired position, L is a list and X represents the Nth element of L.

%Write Prolog program to implement nth_element (N, L, X) not.

%  below nth-element function is not predefined you can use any name as function

nth_element(1,[H|T],H).

nth_element(N,[H|T],X):- N1 is N-1,nth_element(N1,T,X).

% Output

Write a Prolog program to implement two predicates evenlength(List) and oddlength(List) so that they are true if their argument is a list of even or odd length respectively.

15.Write a Prolog program to implement two predicates evenlength(List) and oddlength(List) so that they are true if their argument is a list of even or odd length respectively.

%Write Write a Prolog program to implement two predicates evenlength(List) and 

oddlength(List) so that they are true if their argument is a list of even or 

odd length respectively.

%  below evenlength function is not predefined you can use any name as function

evenlength([]).

evenlength([_|T]):- oddlength(T).

oddlength([_]).

oddlength([_|T]):- evenlength(T).

% Output

Write a Prolog program to implement sumlist(L, S) so that S is the sum of a given list L.

14.Write a Prolog program to implement sumlist(L, S) so that S is the sum of a given list L.

% Write a Prolog program to implement sumlist(L, S) so that S is the sum of a given list L.

%  below sumlist function is not predefined you can use any name as function

sumlist([],0).

sumlist([H|T],S):- sumlist(T,S1),S is H+S1.

% Output

Write a Prolog program to implement reverse (L, R) where List L is original and List R is reversed list.

12.Write a Prolog program to implement reverse (L, R) where List L is original and List R is reversed list.

% Write a Prolog program to implement reverse (L, R) where List L is original 

  and List R is reversed list.

%  below reverse_list and reverse function is not predefined you can use any name as function

reverse_list(Inputlist,Outputlist):-

reverse(Inputlist,[],Outputlist).    

reverse([],Outputlist,Outputlist).    

reverse([Head|Tail],List1,List2):-

reverse(Tail,[Head|List1],List2).

% Output

Write a Prolog program to implement conc (L1, L2, L3) where L2 is the list to be appended with L1 to get the resulted list L3.

11.Write a Prolog program to implement conc (L1, L2, L3) where L2 is the list to be appended with L1 to get the resulted list L3.

% Write a Prolog program to implement conc (L1, L2, L3) where L2 is the 

  list to be appended with L1 to get the resulted list L3.

%  below conc function is not predefined you can use any name as function

conc([],L1,L1).

conc([X|T],L2,[X|T1]):- conc(T,L2,T1).

% Output

Write a Prolog program to implement memb(X, L): to check whether X is a member of L or not.

10. Write a Prolog program to implement memb(X, L): to check whether X is a member of L or not.

% Write a Prolog program to implement memb(X, L): to check whether

  X is a member of L or not.

%  below memb function is not predefined you can use any name as function

memb(X, [X|Tail]).

memb(X, [Head|Tail]):- memb(X, Tail).

% Output

Consider a cyclic directed graph [edge (p, q), edge (q, r), edge (q, r), edge (q, s), edge (s,t)] where edge (A,B) is a predicate indicating directed edge in a graph from a node A to a node B. Write a program to check whether there is a route from one node to another node.

9.Consider a cyclic directed graph [edge (p, q), edge (q, r), edge (q, r), edge (q, s), edge (s,t)] where edge (A,B) is a predicate indicating directed edge in a graph from a node A to a node B. Write a program to check whether there is a route from one node to another node.

% implement the cyclic directed graph.

%  below edge and path function is not predefined you can use any name as function

edge(p,q).

edge(q,r).

edge(r,s).

edge(s,t).

path(X,Y) :- edge(X,Y).

path(X,Y) :- edge(X,Z),

path(Z,Y).

% Output

Write a program in PROLOG to implement towerofhanoi (N) where N represents the number of discs.

8. Write a program in PROLOG to implement towerofhanoi (N) where N represents the number of discs.

% Write a program in PROLOG to implement towerofhanoi (N) where N 

  represents the number of discs.

%  below hanoi function is not predefined you can use any name as function

hanoi(N,F,T,A):-

( N=1 ->

( write('Move disk 1 from rod '),write(F),write(' to rod '),write(T),nl

)

;

Z is N-1,

hanoi(Z,F,A,T),

write('Move disk 1 from rod '),write(F),write(' to rod '),write(T),nl,

hanoi(Z,A,T,F)

).

% Output

Prolog program to implement multi (N1, N2, R) : where N1 and N2 denotes the numbers to be multiplied and R represents the result.

7. Write Prolog program to implement multi (N1, N2, R) : where N1 and N2 denotes the numbers to be multiplied and R represents the result.

% Write Prolog program to implement multi (N1, N2, R) : where N1 and N2 denotes the 

  numbers to be multiplied and R represents the result.

%  below m function is not predefined you can use any name as function

m(N,1,N).

m(N,M,A):-

T is M-1,

m(N,T,Y),

A is Y+N.

% Output

Write a Prolog program to implement power (Num,Pow, Ans) : where Num is raised to the power Pow to get Ans.

6. Write a Prolog program to implement power (Num,Pow, Ans) : where Num is raised to the power Pow to get Ans.

% Write a Prolog program to implement power (Num,Pow, Ans) : where 

  Num is raised to the power Pow to get Ans.

%  below power function is not predefined you can use any name as function

power(0,P,0):- P>0.

power(X,0,1):- X>0.

power(X,P,A):- X>0,P>0,P1 is P-1,

power(X,P1,Ans),

A is Ans*X.

% Output

Write a Prolog program to implement GCD of two numbers.

5. Write a Prolog program to implement GCD of two numbers.

%Write a Prolog program to implement GCD of two numbers.

%  below gcd function is not predefined you can use any name as function

gcd(X,Y):-

( X=0->

write(Y)

 ;

 Y=0->

write(X)

 ;

X=Y->

write(X)

;

X>Y ->

  ( Z is X-Y,

 gcd(Z,Y)

  )

  ;

Y>X ->

  (C is Y-X,

  gcd(X,C)

  )

).

% Output

Write a program in PROLOG to implement generate_fib(N,T) where T represents the Nth term of the fibonacci series.

4. Write a program in PROLOG to implement generate_fib(N,T) where T represents the Nth term of the fibonacci series.

% Write a program in PROLOG to implement generate_fib(N,T) where T 

  represents the Nth term of the fibonacci series.

%  below generate_fib function is not predefined you can use any name as function

generate_fib(0,1).

generate_fib(1,1).

generate_fib(N,T):- N1 is N-1, 

generate_fib(N1,T1),

N2 is N-2, 

generate_fib(N2,T2), 

T is T1+T2.

% Output