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flachflach
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Search programs
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‎hanoi.pl

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% hanoi(N,A,B,C,Moves) <- Moves is the list of moves to
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% move N disks from peg A to peg C,
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% using peg B as intermediary peg
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hanoi(0,_,_,_,[]).
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hanoi(N,A,B,C,Moves):-
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N>0, N1 is N-1,
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hanoi(N1,A,C,B,Moves1),
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hanoi(N1,B,A,C,Moves2),
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append(Moves1,[A -> C|Moves2],Moves).
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hanoi(N,Moves):-
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hanoi(N,left,middle,right,Moves).
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/** &lt;examples&gt;
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?- hanoi(3,Moves).
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?- hanoi(5,Moves).
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*/

‎model.pl

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cl((bachelor(X);married(X):-man(X),adult(X))).
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cl((has_wife(X):-man(X),married(X))).
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%cl((false:-has_wife(paul))).
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cl((man(paul):-true)).
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cl((adult(paul):-true)).
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model(M0,M):-
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is_violated(Head,M0),!, % find instance of violated clause
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disj_element(L,Head), % select ground literal from the head
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model([L|M0],M). % and add it to the model
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model(M,M). % no more violated clauses
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is_violated(H,M):-
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cl((H:-B)),
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satisfied_body(B,M), % this will ground the variables
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not(satisfied_head(H,M)).
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satisfied_body(true,_M). % body is a conjunction
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satisfied_body(A,M):-
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member(A,M).
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satisfied_body((A,B),M):-
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member(A,M),
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satisfied_body(B,M).
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satisfied_head(A,M):- % head is a disjunction
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member(A,M).
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satisfied_head((A;_B),M):-
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member(A,M).
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satisfied_head((_A;B),M):-
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satisfied_head(B,M).
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disj_element(X,X):- % single-element disjunction
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not(X=false),not(X=(_;_)).
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disj_element(X,(X;_Ys)).
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disj_element(X,(_Y;Ys)):-
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disj_element(X,Ys).
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/** &lt;examples&gt;
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?- model([],M).
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*/

‎model_d.pl

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cl((append([],Y,Y):-list(Y))).
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cl((append([X|Xs],Ys,[X|Zs]):-thing(X),append(Xs,Ys,Zs))).
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cl((list([]):-true)).
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cl((list([X|Y]):-thing(X),list(Y))).
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cl((thing(a):-true)).
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cl((thing(b):-true)).
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%cl((thing(c):-true)).
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model_d(0,M,M).
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model_d(D,M0,M):-
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D>0,D1 is D-1,
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findall(H,is_violated(H,M0),Heads),
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satisfy_clauses(Heads,M0,M1),
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model_d(D1,M1,M).
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satisfy_clauses([],M,M).
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satisfy_clauses([H|Hs],M0,M):-
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disj_element(L,H),
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satisfy_clauses(Hs,[L|M0],M).
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is_violated(H,M):-
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cl((H:-B)),
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satisfied_body(B,M), % this will ground the variables
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not(satisfied_head(H,M)).
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satisfied_body(true,_M). % body is a conjunction
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satisfied_body(A,M):-
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member(A,M).
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satisfied_body((A,B),M):-
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member(A,M),
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satisfied_body(B,M).
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satisfied_head(A,M):- % head is a disjunction
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member(A,M).
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satisfied_head((A;_B),M):-
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member(A,M).
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satisfied_head((_A;B),M):-
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satisfied_head(B,M).
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disj_element(X,X):- % single-element disjunction
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not(X=false),not(X=(_;_)).
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disj_element(X,(X;_Ys)).
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disj_element(X,(_Y;Ys)):-
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disj_element(X,Ys).
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/** &lt;examples&gt;
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?- model_d(4,[],M).
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*/

‎path.pl

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path(SS):-
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width(W),height(H),empty_grid(W,H,Grid),
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setx_hor(5/3,4,Grid),setx_hor(7/6,2,Grid),setx_hor(3/9,4,Grid),
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setx_ver(2/5,3,Grid),setx_ver(4/4,3,Grid),setx_ver(7/7,2,Grid),
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search(Grid,SS),show_grid(Grid).
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width(8). height(10).
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entrance(1/1). exit(8/5). %exit(3/5).
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/*
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* Search predicates
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* move/2 enumerates all possible moves, ignoring whether cell is free
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* search/2 searches grid with various search strategies
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*/
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:-use_module(library(lists)).
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moves(X/Y,Moves):-
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bagof(X1/Y1,move(X/Y,X1/Y1),Moves).
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move(X/Y,X/Y1):-
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height(H),
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H>Y,Y1 is Y+1. % down
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move(X/Y,X1/Y):-
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width(W),
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W>X,X1 is X+1. % right
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move(X/Y,X/Y1):-
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Y>1,Y1 is Y-1. % up
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move(X/Y,X1/Y):-
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X>1,X1 is X-1. % left
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% for A* search: generates moves with increasing F-value
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moves_h(F/G:X/Y,Moves):-
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setof(F1/G1:X1/Y1,move_h(F/G:X/Y,F1/G1:X1/Y1),Moves).
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move_h(_/G:X/Y,F1/G1:X1/Y1):-
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move(X/Y,X1/Y1),
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h(X1/Y1,H1),
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G1 is G+1, % increase G-value from previous
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F1 is G1+H1. % add new H-value
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h(X/Y,H):-
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exit(XE/YE),
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H is abs(XE-X)+abs(YE-Y). % Manhattan distance
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search(Grid,SS):-
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entrance(X/Y),
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( SS=bt -> search_bt(0,X/Y,Grid) % backtracking search
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; SS=df -> search_df(0,[X/Y],Grid) % agenda-based depth-first
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; SS=bf -> search_bf(0,[X/Y],Grid) % agenda-based breadth-first
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; SS=as -> h(X/Y,H),search_as(0,[H/0:X/Y],Grid) % A* search
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).
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% backtracking search
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% only path found is indicated in grid
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search_bt(N,X/Y,Grid):-
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exit(X/Y),
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set(X/Y,Grid,N).
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search_bt(N,X/Y,Grid):-
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N1 is N+1,
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set(X/Y,Grid,N),
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move(X/Y,X1/Y1),
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search_bt(N1,X1/Y1,Grid).
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% agenda-based depth-first search
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% grid is used for loop-detection: if set/3 fails, it is either an obstacle
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% or we've been there already
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search_df(N,[X/Y|_],Grid):-
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exit(X/Y),
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set(X/Y,Grid,N).
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search_df(N,[X/Y|Agenda],Grid):-
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( set(X/Y,Grid,N) -> moves(X/Y,Moves),N1 is N+1,
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append(Moves,Agenda,NewAgenda)
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; otherwise -> NewAgenda=Agenda,N1=N % ignore: can't go there
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),search_df(N1,NewAgenda,Grid).
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% agenda-based breadth-first search
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search_bf(N,[X/Y|_],Grid):-
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exit(X/Y),
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set(X/Y,Grid,N).
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search_bf(N,[X/Y|Agenda],Grid):-
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( set(X/Y,Grid,N) -> moves(X/Y,Moves),N1 is N+1,
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append(Agenda,Moves,NewAgenda)
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; otherwise -> NewAgenda=Agenda,N1=N % ignore: can't go there
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),search_bf(N1,NewAgenda,Grid).
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% A* search: agenda contains F/G:X/Y with F=G+H evaluation of position X/Y
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search_as(N,[_:X/Y|_],Grid):-
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exit(X/Y),
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set(X/Y,Grid,N).
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search_as(N,[F/G:X/Y|Agenda],Grid):-
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( set(X/Y,Grid,N) -> moves_h(F/G:X/Y,Moves),N1 is N+1,
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merge_h(Moves,Agenda,NewAgenda)
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; otherwise -> NewAgenda=Agenda,N1=N % ignore: can't go there
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),search_as(N1,NewAgenda,Grid).
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merge_h([],Agenda,Agenda).
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merge_h(Moves,[],Moves).
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merge_h([F/G:X/Y|Moves],[F1/G1:X1/Y1|Agenda],[F/G:X/Y|NewAgenda]):-
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F1>F,
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merge_h(Moves,[F1/G1:X1/Y1|Agenda],NewAgenda).
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merge_h([F/G:X/Y|Moves],[F1/G1:X1/Y1|Agenda],[F1/G1:X1/Y1|NewAgenda]):-
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F>=F1,
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merge_h([F/G:X/Y|Moves],Agenda,NewAgenda).
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/*
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* Grid datastructure: list of H rows of length W.
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* A variable indicates cell is empty, so it can be
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* instantiated once with 'x' to indicate an obstacle
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* or with a number to indicate at which search iteration
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* it was explored.
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*/
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empty_grid(W,H,Grid):-
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length(Grid,H), % generate a list of variables of length H
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empty_rows(W,Grid). % and instantiate each variable to an empty row
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empty_rows(_,[]).
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empty_rows(W,[Row|Rows]):-
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length(Row,W), % generate a list of variables of length W
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empty_rows(W,Rows).
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get_row(N,Grid,Row):-
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nth1(N,Grid,Row).
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get_col(_,[],[]).
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get_col(N,[Row|Rows],[X|Col]):-
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nth1(N,Row,X),
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get_col(N,Rows,Col).
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% Create horizontal/vertical obstacles at position X/Y with length L
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setx_hor(X/Y,L,Grid):-
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get_row(Y,Grid,Row),
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setx(X,L,Row).
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setx_ver(X/Y,L,Grid):-
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get_col(X,Grid,Col),
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setx(Y,L,Col).
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setx(_,0,_).
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setx(X,L,Row):-
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L>0,L1 is L-1,X1 is X+1,
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nth1(X,Row,x),
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setx(X1,L1,Row).
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% Set cell X/Y to N; fails if cell has been set already
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set(X/Y,Grid,N):-
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get_row(Y,Grid,Row),
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nth1(X,Row,C),
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var(C),
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C=N.
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show_grid(Grid):-
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nl,
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show_rows(Grid),
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nl.
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show_rows([]).
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show_rows([Row|Rows]):-
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show_row(Row),
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show_rows(Rows).
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show_row([]):-nl.
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show_row([H|T]):-
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( var(H) -> format('~|~` t~w~3+ ',['.'])
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; H=x -> format('~|~` t~w~3+ ',[H])
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; otherwise -> format('~|~` t~d~3+ ',[H])
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),show_row(T).
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/** &lt;examples&gt;
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?- member(SS,[df,bf,as,bt]),path(SS).
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*/

‎prove_bf.pl

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% breadth-first version of prove_r/1
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% agenda items have the form a(CurrentQuery,OriginalQuery)
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% in order to obtain an answer substitution on termination
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prove_bf(Goal):-
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prove_bf_a([a(Goal,Goal)],Goal).
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prove_bf_a([a(true,Goal)|_Agenda],Goal).
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prove_bf_a([a((A,B),G)|Agenda],Goal):-!,
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findall(a(D,G),
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(cl(A,C),conj_append(C,B,D)),
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Children),
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append(Agenda,Children,NewAgenda), % breadth-first
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prove_bf_a(NewAgenda,Goal).
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prove_bf_a([a(A,G)|Agenda],Goal):-
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findall(a(B,G),cl(A,B),Children),
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append(Agenda,Children,NewAgenda), % breadth-first
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prove_bf_a(NewAgenda,Goal).
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% prove_r/1 included for comparison
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prove_r(A):-
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( A=true -> true
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; A=(B,C) -> cl(B,D),conj_append(D,C,E),prove_r(E)
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; otherwise -> cl(A,B),prove_r(B)
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).
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cl(brother(X,Y),brother(Y,X)).
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cl(brother(X,Y),(brother(X,Z),brother(Z,Y))).
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cl(brother(peter,paul),true).
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cl(brother(adrian,paul),true).
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%%% auxiliary predicates
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conj_append(A,B,C):-
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( A=true -> B=C
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; A=(A1,A2) -> C=(A1,C2),conj_append(A2,B,C2)
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; otherwise -> C=(A,B)
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).
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/** &lt;examples&gt;
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?- prove_bf(brother(peter,paul)).
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?- prove_r(brother(peter,paul)).
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?- prove_bf(brother(peter,Y)).
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?- prove_r(brother(peter,Y)).
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*/

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