Basic Prolog Demo

% L=[a,b,c,d,e,3,5,7,2,[8,6,9]].
% L=[X|T], X=a, T=[b,c,d.....].
% []

% X принадл. списку, если он - голова эт списка.
member(X, [X|_]).
% X принадлежит списку, если X принадл. хвосту списка.
member(X, [_|T]):-member(X,T).

% +List, -Sum
sum([], 0).
sum([X|T], S):- sum(T,ST), S = X + ST.

min([X],X).
min([X|T], X):-min(T,M), X<M.
min([X|T], M):-min(T,M), X>=M.

bs(L,S):-
	x(L,L1), !, bs(L1,S).
bs(L,L).
x([X,Y|T],[Y,X|T]):-X>Y,!.
x([X|T],[X|T1]):-x(T,T1).

t(1,1).
t(8,8).
t(0,0).
t(2,5).
t(5,2).
t(6,9).
t(9,6).
v(1).
v(8).
v(0).

p([X]):-v(X).
p([X,Y]):-t(X,Y).
p([X|T]):-t(X,Y),cut(T,Y, T1), p(T1).
cut([X],X,[]).
cut([Y|T],X,[Y|T1]):-cut(T,X,T1).

app([],L,L).
app([X|T1],L2,[X|T3]):-app(T1,L2,T3).


d(C,X,0):-atom(C), C\=X,!.
d(X,X,1):-!.

d(sin(E), X, cos(E)*DE):-
	d(E,X,DE).
d(cos(E), X, 0-sin(E)*DE):-
	d(E,X,DE).
d(ln(E), X, DE/E):-
	d(E,X,DE).

d(E^N, X, N*E^N1*DE):-
	d(E,X,DE), N1 is N-1.


d(A + B, X, DA + DB):-
	d(A, X, DA), d(B, X, DB).

d(A - B, X, DA - DB):-
	d(A, X, DA), d(B, X, DB).

d(A * B, X, A*DB + B*DA):-
	d(A, X, DA), d(B, X, DB).

d(A / B, X, (A*DB - B*DA)/(B^2)):-
	d(A, X, DA), d(B, X, DB).

red(E,E1):-
	r(E,E2),!,red(E2,E1).
red(E,E).

r(0*_,0).
r(_*0,0).
r(1*X,X).
r(X*1,X).
r(X+0,X).
r(0+X,X).
r(X*X, X^2).
r(X*X^N, X^N1):-N1 is N+1.



% article ::== "a" | "the"
% noun ::== "cow" | "tail"
% verb ::== "walks" | "shakes"
% -> sentence ::= noun_group verb_group
% noun_group ::== article noun
% verb_group ::== verb noun_group
% a cow shakes the tail
%

g(sentence, I, O):-
	g(noun_group,I,R),
	g(verb_group,R,O).

g(noun_group, I,O):-g(article,I,R), g(noun,R,O).
g(noun_group, I,O):-g(noun,I,O).

g(verb_group, I,O):-g(verb, I,R),g(noun_group,R,O).

g(noun, [X|T],T):-noun(X).
g(verb, [X|T],T):-verb(X).
g(article, [X|T],T):-article(X).

noun(cow).
noun(tail).
article(the).
article(a).
verb(shakes).
verb(walks).

num(X):-member(X,[0,1,2,3,4,5,6,7,8,9]).

lucky([A,B,C, D,E,F]):-
	A is F+B+C-D-E,
	num(A).

gen([]).
gen([X|T]):-gen(T),num(X).

lticket([A|L]):-L=[_,_, _,_,_],
	gen(L),lucky([A|L]).
tickets(N):-findall(X,lticket(X),L), len(L,N).
len([],0).
len([_|T],N):-len(T,M),N is M+1.