%FILE: lp.p
%TYPE: Prolog Source
%Line: some generally useful list processing predicates
%Date: 10/17/2017

writelist([]).
writelist([H|T]) :- write(H), nl, writelist(T).

member(X,[X|_]).
member(X,[_|Y]) :- member(X,Y).

length([],0).
length([_|T],L) :- length(T,K),L is (1 + K).

item(N,[H|_],H) :- N = 0.
item(N,[_|T],E) :- N > 0, K is N - 1, item(K,T,E).

append([],L,L).
append([H|T1],L2,[H|T3]) :- append(T1,L2,T3).
append(L1,L2,L3,Result) :-
	append(L1,L2,L12),append(L12,L3,Result).
append(L1,L2,L3,L4,Result) :-
	append(L1,L2,L3,L123),append(L123,L4,Result).
	
last([H|[]],H).
last([_|T],Result) :- last(T,Result).

remove(_,[],[]).
remove(First,[First|Rest],Rest).
remove(Element,[First|Rest],[First|RestLessElement]) :-
	remove(Element,Rest,RestLessElement).

%remove(X, [X|Rest], Rest).
%remove(X, [First|Rest], Z) :-
%    X \= First, Rest \= [],
%    remove(X, Rest, RestRemoved),
%    Z = [First|RestRemoved].

replace(0,Object,[_|T],[Object|T]).
replace(ListPosition,Object,[H|T1],[H|T2]) :-
	K is ListPosition - 1,
	replace(K,Object,T1,T2).
	
makelist(0,_,[]).
makelist(Length,Element,[Element|Rest]) :-
	K is Length - 1,
	makelist(K,Element,Rest).
	
reverse([],[]).
reverse([H|T],R) :-
	reverse(T,Rev),lastput(H,Rev,R).

lastput(E,[],[E]).
lastput(E,[H|T],[H|L]) :- lastput(E,T,L).

pick(L,Item) :-
	length(L,Length),
	random(0,Length,RN),
	item(RN,L,Item).

take(List,Element,Rest) :-
	pick(List,Element),
	remove(Element,List,Rest).
	
iota(0,[]).
iota(N,IotaN) :-
	K is N - 1,
	iota(K,IotaK),
	lastput(N,IotaK,IotaN).
	
sum([],0).
sum([Head|Tail],Sum) :- 
	sum(Tail,SumOfTail),
	Sum is Head + SumOfTail.

min([H|[]],H).
min([H|T],Min) :- 
	min(T,CurrentMin),
	H < CurrentMin,
	Min = H.
min([H|T],Min) :- 
	min(T,CurrentMin),
	CurrentMin =< H,
	Min = CurrentMin. 

max([H|[]],H).
max([H|T],Max) :- 
	max(T,CurrentMax),
	H < CurrentMax,
	Max = CurrentMax.
max([H|T],Max) :- 
	max(T,CurrentMax),
	CurrentMax =< H,
	Max = H.
	
sort_inc([H|[]],[H]).
sort_inc(UnOrderedList,[H|OrderedTail]) :-
	min(UnOrderedList,H),
	remove(H,UnOrderedList,T),
	sort_inc(T,OrderedTail).
	
sort_dec([H|[]],[H]).
sort_dec(UnOrderedList,[H|OrderedTail]) :-
	max(UnOrderedList,H),
	remove(H,UnOrderedList,T),
	sort_dec(T,OrderedTail).
	
alist([],[],[]).
alist([H1|T1],[H2|T2],Alist):-
	length([H1|T1],L1),
	length([H2|T2],L2),
	L1 = L2,
	HeadPair = pair(H1,H2),
	alist(T1,T2,TailPairs),
	Alist = [HeadPair|TailPairs].
	
assoc([pair(K,V)|_],K,V).
assoc([_|T],K,V) :-
	assoc(T,K,V).
	
flatten([],[]).
flatten([[]|T],L) :-
	flatten(T,L).
flatten([H|T],L) :-
	atom(H),
	flatten(T,Tflattened),
	append([H],Tflattened,L).
flatten([H|T],L) :-
	flatten(H,FlatHead),
	flatten(T,FlatTail),
	append(FlatHead,FlatTail,L).