Last Week. Today. Prolog: recursion examples. Recursion in Prolog. CSC326 Programming Languages (Week 12,Friday)

Transcription

1 Last Week CSC326 Programming Languages (Week 12,Friday) Yilan Gu More on Prolog reasoning mechanism Operators Lists Today Recursion in Prolog (more examples) Negation as failure Misc Cut! (we leave it to the next lecture) 2 Recursion in Prolog Appending lists: Declarative Semantics: Appending an empty list to a n-empty list is the n-empty list else work on one list by removing its elements and adding it to the other list. Prolog append([],x,x). append([h X], Y, [H Z]) :- append(x,y,z). Member of a list: Declarative Semantics: X is a member of a list if X is equal to the first element, or a member of any sublist of that list Prolog: member(x,[x T]). member(x,[y T]):-member(X,T). 3 4

2 a b c d Blocks: Declarative Semantics: Block X is above block Y if X is placed on top of Y, or X is placed on top of some block Z that is above Y. Prolog: % first attempt above(x,y) :- on(x,y). (1) above(x,z) :- above(x,y), above(y,z). (2) on(a,b). (3) on(b,c). (4) on(c,d). (5)?- above(a,b). ;?- above(a,d). ;?- above(b,b). ;Infinite recursion! trace it to see why.?- above(c,a). ;Infinite recursion! trace it to see why. 5 a b c d Blocks: Declarative Semantics: Block X is above block Y if X is placed on top of Y, or X is placed on top of some block Z that is above Y. Prolog: % Second attempt above(x,y) :- on(x,y). (1) above(x,z) :- on(x,y), above(y,z). (2) on(a,b). (3) on(b,c). (4) on(c,d). (5)?- above(a,d). Yes 6 Note that sometimes changing the order of rules and/or rule premises can cause problems for Prolog above(x,z) :- above(y,z), on(x,y) (1) a b c d above(x,y) :- on(x,y). (2) on(a,b). (3) on(b,c). (4) on(c,d). (5)?- above(a,d). Infinite recursion: E.g. p :- p. %declaratively perfectly correct, but procedurally causes infinite loop What to do about infinite recursion? Rewrite the rules and facts (most widely used technique) Define a second n-recursive version (similar to a base case) Use! to stop the unification (more about this later). 7 8

3 Length of a list Exercises in Class Swap first two element in a list. Length of a list Exercises in Class % Solution 1: length([],0). length([x T], N):- length(t,n1),n is N1+1. % Solution 2: length(l,n):-length1(l,0,n). length1([h T], X, N):- X1 is X+1, length1(t,x1,n). length1([],n,n). Swap first two element in a list. swap([x,y T],[Y,X T]) Negatuion as Failure Negation as Failure No equivalent of logical t in Prolog: Prolog can only assert that something is true. Prolog cant assert that something is false. Prolog can assert that the given facts and rules do t allow something to be proven true. Assuming that something unprovable is false is called negation as failure. (Based on a closed world assumption.) The goal t(g) (or \+(G)) succeeds whenever the goal G fails. 11

4 Logical t ( ) blue(sky). father(sam, lee). We do t kw whether blue(earth). blue(earth). Negatuion as Failure Prolog t blue(sky). We kw?- blue(earth). false.?- t(blue(earth)). true. We can't state negative facts. Can t have a negative head, in the body only ( head :- body ) Can't declare a negative fact. Negatuion as Failure Example: Disjoint Sets overlap(s1,s2) :- member(x,s1),member(x,s2). disjoint(s1,s2) :- t(overlap(s1,s2)).?- overlap([a,b,c],[c,d,e]). true.?- overlap([a,b,c],[d,e,f]). false.?- disjoint([a,b,c],[c,d,e]). true.?- disjoint([a,b,c],[d,e,f]). true.?- disjoint([a,b,c],x). false. %< Not what we wanted Negatuion as Failure overlap(s1,s2) :- member(x,s1),member(x,s2). disjoint(s1,s2) :- t(overlap(s1,s2)).?- disjoint([a,b,c],x). No %< Not what we wanted [trace]?- disjoint([a,b,c],x). Call: (7) disjoint([a, b, c], _G293)? creep Call: (8) overlap([a, b, c], _G293)? creep Call: (9) lists:member(_l230, [a, b, c])? creep Exit: (9) lists:member(a, [a, b, c])? creep Call: (9) lists:member(a, _G293)? creep Exit: (9) lists:member(a, [a _G352])? creep Exit: (8) overlap([a, b, c], [a _G352])? creep Fail: (7) disjoint([a, b, c], _G293)? creep false. Proper Use of Negation as Failure t(g) works properly only in the following cases: 1. When G is fully instantiated at the time prolog processes the goal t(g). OR (In this case, t(g) is interpreted to mean goal G does t succeed.) 2. When all variables in G are unique to G, i.e., they don t appear elsewhere in the same clause. (In this case, t(g(x)) is interpreted to mean There is value of X that will make G(X) succeed.)

5 Proper Use of Negation as Failure Proper Use of Negation as Failure Use t to enforce semantics. loves(bill,x) :- pretty(x), female(x), t(loves(tom,x)). loves(tom,x):- famous(x), female(x), t(dead(x)). female(marilym-monroe). female(cindy-crawford). female(martha-stewart). female(girl-next-door). famous(marilym-monroe). famous(cindy-crawford). famous(martha-stewart). pretty(marilym-monroe). pretty(cindy-crawford). pretty(girl-next-door). dead(marilym-monroe). Using t is t always safe loves(bill,x) :- pretty(x), female(x), t(loves(tom,x)). loves(tom,x):- pretty(x), female(x), t(dead(x)). female(marilym-monroe). female(cindy-crawford). female(martha-stewart). female(girl-next-door). famous(marilym-monroe). famous(cindy-crawford). famous(martha-stewart). pretty(marilym-monroe). pretty(cindy-crawford). pretty(girl-next-door). dead(marilym-monroe). Consider the following rule: hates(tom,x):- t(loves(tom,x)). The answer is infinite, since for any P t mentioned in the database, We t infor loves(tom,p), so we must infer hates(tom,p). hates(tom, dog). hates(tom, meat).... This rule is said to be unsafe. Proper Use of Negation as Failure Using t is t always safe loves(bill,x) :- pretty(x), female(x), t(loves(tom,x)). loves(tom,x):- famous(x), female(x), t(dead(x)). female(marilym-monroe). female(cindy-crawford). female(martha-stewart). female(girl-next-door). famous(marilym-monroe). famous(cindy-crawford). famous(martha-stewart). pretty(marilym-monroe). pretty(cindy-crawford). pretty(girl-next-door). dead(marilym-monroe). hates(tom,x):- famous(x), female(x), t(loves(tom,x)). famous(x) and female(x) are called guards, prevend from getting unwanted inferences. Prolog: negation when to use? krispie( snap ). krispie( crackle ). krispie( pop ). breakfast(a,b,c) :- krispie(a), krispie(b), krispie(c).?- breakfast(x,y,z). Y = snap Z = snap ; Y = snap Z = crackle ; Y = snap Z = pop ; krispie( snap ). krispie( crackle ). krispie( pop ). breakfast(a,b,c) :- krispie(a), krispie(b), krispie(c), t(a=b), t(a=c), t(b=c).?- breakfast(x,y,z). Y = crackle Z = pop; Y = pop Z = crackle; X = crackle Y = snap Z = pop

6 Prolog: fail & true predicates That something is t true can be said in Prolog by using a special goal: fail, which always and immediately fails. That something is true can be said in Prolog by using the goal true, which always and immediately succeeds. Prolog: Misc The fail/true are inserted between goals as a pseudo-goal: head1(x) :- goal1a, goal1b, fail, goal1c. %rule 1 head2(x) :- true. %rule 2 Prolog: fail & true predicates Examples: How to represent Mary likes all animals but snakes? % If X is a snake then Mary likes X is t ture % otherwise if X is an animal then Mary likes X snake(cobra). cat(persian). animal(x):-snake(x);cat(x). likes(mary,x):-snake(x),fail. % rule 1 likes(mary,x):-animal(x). % rule 2?- likes(mary,cobra). % query % Why did we get a wrong answer? % rule 1 failed because of fail but % Prolog interpreter went on to unify % with rule 2 which succeeded so we % got snake(cobra). cat(persian). animal(x):-snake(x);cat(x). likes(mary,x):-snake(x),!,fail. % rule 1 likes(mary,x):-animal(x). % rule 2?- likes(mary,cobra). % query %Why did we get the right answer? % rule 1 failed because of fail and the! % told the interpreter t to try rule 2 % because since we have reached % there(aka to the!), it must be a snake Prolog: fail & true predicates Examples cont d: How to represent X and Y are different if they do t match? % If X and Y match then different(x,y) fails % otherwise different(x,y) succeeds different(x,y) :- X=Y,fail. %rule 1 different(x,y) :- true. %rule 2?- different(5,5). %query % Why did we get a wrong answer? % rule 1 failed because of fail but % Prolog interpreter unified with % rule 2 which succeeded so we got. How to represent t(goal) relation? % if Goal succeeds then t(goal) fails, % otherwise t(goal) succeeds t(p) :- P,!,fail. t(p) :- true. different(x,y) :- X=Y,!, fail. %rule 1 different(x,y) :- true. %rule 2?- different(5,5). %query % Why did we get the right answer? % rule 1 failed because of fail and % the! told the interpreter t to try % rule 2.

7 Prolog: input/output Reading from input: Read a term from the user read(x). Writing to output: output the term X write(x). New line nl. Output N spaces tab(n). Outputting a list: writelist([]). writelist([x L]) :- write(x), nl, writelist(l). Outputting a sequence of characters as * bars([]). bars([n L]) :- stars(n), nl, bars(l). stars(n) :- N > 0, write(*), N1 is N-1, stars(n1). stars(n):- N =< 0.?- writelist([12,14]) ?- bars([3,4,6,5]). *** **** ****** ***** Prolog: input/output Interactive program example: cube :- write( Next item, please: ),read(x),process(x). process(stop):-!. process(n) :- C is N * N * N, write( Cube of ), write(n), write( is ),write(c),nl,cube.?- cube. Next item, please: 5. Cube of 5 is 125 Next item, please: 10. Cube of 10 is 1000 Prolog: using write in debugging Prolog: dynamic programming What is it? Adding/removing rules: assert(c). % adds a clause to the database asserta(c). % adds a clause to the beginning of the database assertz(c). % adds a clause to the end of the database retract(c). % removes a clause from the database Examples:?- crisis.?- assert(crisis).?- crisis.?- retract(crisis).?- crisis. fast(ann). slow(tom). slow(pat).?- assert( (faster(x,y) :- fast(x), slow(y) ) ).?- faster(a,b)..?- retract( slow(x) ). X = tom; X = pat; faster( ann,_).

8 Prolog: pros & cons Cons: Horn clauses have limited expressive power Closed world assumptions (anything t mentioned is false) Ordering of clauses change the result Because horn clause is the basic construct, you must program carefully to avoid infinite loops and incorrect negation. There is 1-solution-fits-all for these problems Pros: Pattern matching Backtracking Unification Rules and goals are also data (dynamic programming). The logical model is powerful Logic vs. Imperative Languages