Prolog OR (disjunction) “;” is same as a logical OR “;” is same as a logical OR It is also equivalent to using separate clauses... It is also equivalent to using separate clauses... parent(X, Y) :- mother(X, Y). parent(X, Y) :- father(X, Y). SAME AS... parent(X, Y) :- mother(X, Y) ; father(X, Y). Although this saves writing some code, both versions are equivalent in efficiency. Although this saves writing some code, both versions are equivalent in efficiency. 1COSC 2P93 Prolog: Cut

Be careful with “;”! What is going on here? What is going on here? p(X) :- (q(X, Y) ; (r(Y), (s(U, Y); a(U), b(U)) ; r(X)), t(X, Y); w(X) ; z(A),z(B), etc... Too many or’s can make programs very hard to debug (trace)! Too many or’s can make programs very hard to debug (trace)! Rule of thumb: Don’t use or’s in order to reduce number of clauses. Rule of thumb: Don’t use or’s in order to reduce number of clauses. 2COSC 2P93 Prolog: Cut

Controlling Prolog execution Prolog exhaustively searches the computation tree for solutions Prolog exhaustively searches the computation tree for solutions If a goal fails, OR the user inputs ‘;’ at the prompt, then backtracking reverts to the last place in which a clause was chosen, and tries the next. If a goal fails, OR the user inputs ‘;’ at the prompt, then backtracking reverts to the last place in which a clause was chosen, and tries the next. There are lots of advantages of this scheme, most notably, searching for a solution, or multiple solutions, to a query. There are lots of advantages of this scheme, most notably, searching for a solution, or multiple solutions, to a query. However, it can be expensive: However, it can be expensive: Sometimes there is only one solution, and it is a waste of time searching for others -- they don’t exist! Sometimes there is only one solution, and it is a waste of time searching for others -- they don’t exist! Sometimes ‘failure’ after the first solution can take lots of time to infer Sometimes ‘failure’ after the first solution can take lots of time to infer Memory resources are used to contain the computation tree for backtracking. Memory resources are used to contain the computation tree for backtracking. Prolog permits some user control of execution, in order to reduce backtracking. Prolog permits some user control of execution, in order to reduce backtracking. 3COSC 2P93 Prolog: Cut

1. If-then-else (If -> Then ; Else) If goals in If are true, then do Then; else do Else If goals in If are true, then do Then; else do Else Once Then is executed, will go to Then or Else, but cannot backtrack from Then to Else, nor back to If. Once Then is executed, will go to Then or Else, but cannot backtrack from Then to Else, nor back to If. Backtracking will return multiple solutions in Then, and in Else. Backtracking will return multiple solutions in Then, and in Else. (If -> Then) This is equivalent to: (If -> Then ; fail) This is equivalent to: (If -> Then ; fail) 4COSC 2P93 Prolog: Cut

Example If-then-else If N is prime, return ‘prime’, Else ‘notprime’. If N is prime, return ‘prime’, Else ‘notprime’. idNum(N, prime) :- prime(N). idNum(N, notprime) :- idNum(N, notprime) :- \+ prime(N). Note that prime/N is called twice – with identical results! Note that prime/N is called twice – with identical results! Prime testing might be very slow for large integers, so this is very wasteful. Prime testing might be very slow for large integers, so this is very wasteful. 5COSC 2P93 Prolog: Cut

Example if-then-else filterNum(N, Ans) :- (prime(N) -> Ans = prime ; Ans = notprime). Here, prime/1 is called once. No backtracking into it. Here, prime/1 is called once. No backtracking into it. 6COSC 2P93 Prolog: Cut

2. once Often, we want just one solution from a predicate. Often, we want just one solution from a predicate. Multiple answers may slow execution, due to needless backtracking. Multiple answers may slow execution, due to needless backtracking.once(Goal): This calls Goal, and returns first solution. This calls Goal, and returns first solution. Backtracking will immediately fail. Backtracking will immediately fail. Built-in to Sicstus Prolog. Built-in to Sicstus Prolog. 7COSC 2P93 Prolog: Cut

Example of once/1 % delete(A, L, R): Delete A from L, resulting in R. delete(A, [A|T], T). delete(A, [B|T], [B|T2]) :- delete(A, T, T2). delete(A, T, T2). delete(_, [ ], [ ]). ?- delete(a, [a,b,a,c,a],L). L = [b,a,c,a] ? ; L = [a,b,c,a] ? ; L = [a,b,a,c] ? ; L = [a,b,a,c,a] ? ; ?- once( delete(a, [a,b,a,c,a],L) ). L = [b,a,c,a] ? ; no 8COSC 2P93 Prolog: Cut

3. The cut, ! The cut takes the form of a goal in a clause. The cut takes the form of a goal in a clause. Should use only one cut per clause. Should use only one cut per clause. A predicate can have one or more clauses with cuts. A predicate can have one or more clauses with cuts. Scheme : 1. all the clauses before the first clause with a cut are executed with normal backtracking. 2. if the goals before the cut fail, the cut does not activate, and the subsequent clause is used, as normal. 3. if the goals before the cut succeed, the cut activates: a) backtracking back to goals before the cut cannot occur b) backtracking to subsequent clauses after the one with the cut cannot occur --> that clause with the activated cut is “committed” c) the goals after the cut are executed with normal backtracking 9COSC 2P93 Prolog: Cut

The cut - example p(1). %1 p(1). %1 p(2). %2 p(2). %2 p(Y) :- q(3, Z), !, r(Z, Y). %3 p(Y) :- q(3, Z), !, r(Z, Y). %3 p(4). %4 p(4). %4 q(2, 4).r(5, 6). q(2, 4).r(5, 6). q(3, 5).r(5, 7). q(3, 5).r(5, 7). Clauses 1, 2 are executed as normal Clauses 1, 2 are executed as normal In 3, the goal q(3,Z) executes; if it succeeds, then the ! is activated, and the goal r is executed as normal. In 3, the goal q(3,Z) executes; if it succeeds, then the ! is activated, and the goal r is executed as normal. However, in activating this cut... However, in activating this cut... clause 4 will not execute for this particular execution call clause 4 will not execute for this particular execution call clause 3 will not backtrack to q again (in this goal inference) clause 3 will not backtrack to q again (in this goal inference) Note that backtracking in r(Z,Y) occurs as expected, and hence you can still get multiple solutions from clause 3 Note that backtracking in r(Z,Y) occurs as expected, and hence you can still get multiple solutions from clause 3 10COSC 2P93 Prolog: Cut

Green and red cuts There are two usages of cuts: There are two usages of cuts: (i) Green cuts (GOOD): cuts that prune execution branches that do not lead to useful solutions. (ii) Red cuts (BAD): cuts that prune valid solutions 11COSC 2P93 Prolog: Cut

Example: green cut % A list is bad if: (1) it is empty; (2) it has more than 100 items; or (3) it has an integer. test_list(L) :- test_if_bad(L), test_if_bad(L), !, !, write(‘Bad list,’), nl, fail. % print message and fail write(‘Bad list,’), nl, fail. % print message and fail test_list(L) :- write(‘Good list’), nl.% print message and succeed write(‘Good list’), nl.% print message and succeed test_if_bad([ ]). test_if_bad(L) :- length(L, N), N > 100. test_if_bad(L) :- member(X, L), integer(X). a “green cut”, because we know that only one of test_list clauses must succeed to say a list is bad. a “green cut”, because we know that only one of test_list clauses must succeed to say a list is bad. backtracking makes no sense with it. backtracking makes no sense with it. 12COSC 2P93 Prolog: Cut

Green cut Note that we could do the same with if-then-else... Note that we could do the same with if-then-else... test_list(L) :- (test_if_bad(L) -> (test_if_bad(L) -> write(‘Bad list,’), nl, fail; write(‘Good list’), nl ). write(‘Good list’), nl ). 13COSC 2P93 Prolog: Cut

Example: red cut A bad use of cut... A bad use of cut... parent(P, C) :- father(P, C), !. parent(P, C) :- mother(P, C). father(bob, sue). father(bob, kim). mother(mary, sue). mother(mary, kim). A red cut: we get the first solution from father, and never give another valid solution again, from either father or mother! A red cut: we get the first solution from father, and never give another valid solution again, from either father or mother! ?- parent(A, B). A = bob, B = sue ; no. 14COSC 2P93 Prolog: Cut

Red cut Variation: Variation: parent(P, C) :- !, father(P, C). parent(P, C) :- mother(P, C). (rest as before) ?- parent(A, B). A = bob, B = sue ; A = bob, B = kim ; no Same as... Same as... parent(P, C) :- father(P, C). 15COSC 2P93 : Cut

Implementation: If-then-else If-then-else is implemented with a cut: If-then-else is implemented with a cut: P :- (If -> Then;Else). Same as... P :- If, !,Then. P :- Else. 16COSC 2P93 Prolog: Cut

Implementation: once/1 once(P) :- call(P),!or... P,!. This is a “meta-logical” call. This is a “meta-logical” call. Usually built into Prolog. Usually built into Prolog. 17COSC 2P93 Prolog: Cut

More cut examples Example: a deterministic member/2: memberd/2 Example: a deterministic member/2: memberd/2 deterministic clause: one that returns one solution per call deterministic clause: one that returns one solution per call member(A, [A|_). member(A, [_|R]) :- member(A, R). memberd(A, [A|_]) :- !. memberd(A, [_ | R]) :- memberd(A, R). Here, as soon as memberd clause 1 finds a match, it succeeds Here, as soon as memberd clause 1 finds a match, it succeeds Subsequent backtracking to memberd then fails, due to the cut Subsequent backtracking to memberd then fails, due to the cut we prevent memberd clause 2 from finding another match we prevent memberd clause 2 from finding another match Note: memberd same as... ?- once(member(X,Y)). Note: memberd same as... ?- once(member(X,Y)). 18COSC 2P93 Prolog: Cut

Cut examples Example: sum the integers between 1 and n Example: sum the integers between 1 and n sum_to(1, 1) :- !. sum_to(N, Sum) :- M is N - 1, M is N - 1, sum_to(M, Tmp), sum_to(M, Tmp), Sum is Tmp + N. Sum is Tmp + N. Without the cut, backtracking proceeds to sum_to(0,_), sum_to(-1,...) etc Without the cut, backtracking proceeds to sum_to(0,_), sum_to(-1,...) etc with the cut, when the case sum_to(1,1) occurs, backtracking will not commence (via clause 2) with the cut, when the case sum_to(1,1) occurs, backtracking will not commence (via clause 2) again, a green cut: only one solution desired again, a green cut: only one solution desired BUT... simply checking size of N in 2 nd clause will prevent need for a cut... BUT... simply checking size of N in 2 nd clause will prevent need for a cut... 19COSC 2P93 Prolog: Cut

Take out the cut... sum_to(1, 1). sum_to(N, Sum) :- N > 1, N > 1, M is N - 1, sum_to(M, Tmp), sum_to(M, Tmp), Sum is Tmp + N. Sum is Tmp + N. 20COSC 2P93 Prolog: Cut

Cuts Cuts are extralogical: they almost always destroy a program’s logical “declarative” reading. Consider test_list example again... Cuts are extralogical: they almost always destroy a program’s logical “declarative” reading. Consider test_list example again... test_list(L) :- test_if_bad(L), test_if_bad(L), !, !, write(‘Bad list,’), nl, fail. write(‘Bad list,’), nl, fail. test_list(L) :- test_list(L) :- write(‘Good list’), nl. write(‘Good list’), nl. Read literally, the second clause says that all lists are good lists! Read literally, the second clause says that all lists are good lists! Hence we must now ascertain the meaning of this predicate by inspecting what the cut is doing. Hence we must now ascertain the meaning of this predicate by inspecting what the cut is doing. The second clause’s meaning is dependent upon the first clause. The second clause’s meaning is dependent upon the first clause. 21COSC 2P93 Prolog: Cut

Cuts Cuts are unavoidable in many programs. Without them, the program can become too large and inefficient Cuts are unavoidable in many programs. Without them, the program can become too large and inefficient However, cuts usually ruin a logic program’s readability However, cuts usually ruin a logic program’s readability Careless use of cuts can make a Prolog program unintelligible, and hard to debug. Careless use of cuts can make a Prolog program unintelligible, and hard to debug. 22COSC 2P93 Prolog: Cut

When to use cuts 1.Try to make a declarative predicate if feasible: correct, concise, efficient. 2.Else, use “->” (if-then-else) or once/1 if they help. 3.Else, use a cut if it is a green cut. 4.Red cut: use as rarely as possible. Document their function! 23COSC 2P93 Prolog: Cut