Snakes. Declarative Languages. Relation different. Overview. Negation as failure. Relation different

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1 Snakes Declarative Languages D7012E: Negation and solution gathering Fredrik Bengtsson "Mary like all animals but snakes" likes(mary, X):-snake(X),!,fail. likes(mary, X):-animal(X). observe the cut before fail otherwise prolog would backtrack! written as one clause likes(mary, X):- snake(x),!,fail animal(x). new operator: goal succeeds if either goal succeeds. Overview Negation as failure problems with cut and negation close world assumption Solution-gathering predicates bagof, setof, findall updating program database some meta-primitives Relation different define different(x,y) if X and Y do not match they are different if X and Y match different(x,y) is false if X and Y do not match different(x,y) is true How to implement? Negation as failure "Mary like all animals but snakes" expressed in prolog? easy to express one part "Mary likes any X if X is an animal". likes(mary, X):-animal(X) exclude snakes If X is snake then 'mary likes X' is not true otherwise if X is animal then mary likes X use special goal: fail always fails the goal we use a failure as negative logical expression Relation different different(x,x):-!,fail differen(x,y). or different(x,y):- X=Y,!,fail true. New goal true always succeeds 1

2 not Problems with cut and negation examples suggests nice to have unary predicate not not(goal) succeed if Goal fails and vice versa definition in prolog: not(p):- P,!,fail true. we will assume not is built-in prefix unary operator we can write: not snake(x) Usually not is written \+ example: \+ snake(x) depends on prolog implementation p :- a,b p :- c declarative meaning: p <=> (a & b) v c change order same meaning Our example Problems with cut and negotiation mary-example written with not: likes(mary,x):- animal(x), not snake(x). different: different(x,y):- not(x=y). much easier to read p :- a,!,b p :- c declarative meaning p <=> (a&b)v(~a&c) swap clauses p :- c p :- a,!,b declarative meaning p <=> c v (a & b) not the same meaning as before! using cut procedural meaning becomes important increases risk for programming error Cut Improve efficiency explicitly state other alternatives will not work called green cut Change behaviour of program specify mutually exclusive rules if P then Q otherwise R enhances expressive power called red cut problems with not?- not human(mary) answer will be "yes" indicating mary is not human this need not be the case! correct reading not enough information to conclude mary is human 2

3 problems with not if using failure as real logic negation Closed world assumption everything that is true is present in the program everything else is false no such thing as "not enough info" we usually does not assume "closed world" in this case not and fail is not the same in practice not Goal safe if variables instantiated prior to call of not Goal otherwise might not work as we expect more problems with not facts about restaurants good_standard(bbb). expensive(bbb). good_standard(centrum). reasonable(restaurant) :- not expensive(restaurant) now, we ask -? good_standard(x), reasonable(x). X=centrum Solution gathering primitives backtracking generate all possible solutions one by one only one solution at a time previous solutions thrown away If we want all solutions in a list? predicates bagof, setof, findall more problems with not ok, but if we ask -? reasonable(x), good_standard(x) no why is this? look at reasonable(x) subgoal not expensive(x) expensive(x) suceeds, X=bbb not expensive(bbb) fails resonable(x) fails good_standard(bbb). expensive(bbb). good_standard(centrum). reasonable(restaurant) :- not expensive(restaurant) bagof bagof(x, P, L) List L of objects X such that goal P satisfied only meaningful if P and X has common variables If no solutions bagof predicate fails age(peter, 7). age(ann, 5). age(pat, 8). age(tom, 5). question:?- bagof(child, age(child, 5), List). List=[ann, tom] 3

4 bagof more example: leave age unspecified?- bagof(child, age(child, Age), List). Age=7 List=[peter] Age=5 List=[ann, tom] Age=8 List=[pat] age(peter, 7). age(ann, 5). age(pat, 8). age(tom, 5). findall example Completely pointless 2?- findall(x, member(x, [1,2,3,4,5,6,7]), L). L = [1, 2, 3, 4, 5, 6, 7]. Not so pointless: Generate all sublists: allsublists1(l,al):-findall(x,sublist(x,l),al). Includes empty list several times sublist(s,l):- conc(l1,l2,l), conc(s,l3,l2). no Similar to bagof setof(x, P, L) setof duplicates removed objects ordered no restriction on object kind:?- setof(age/child, age(child, Age), List). List=[5/ann,5/tom,7/peter,8/pat] generate sublists Modify sublist: nonemptysublist(s,l):- conc(l1,l2,l), conc(s,l3,l2), length(s,n), N>0. Update allsublists: allsublists(l,al):-findall(x,nonemptysublist(x,l),al). Or! allsublists2(l,al):-findall(x,(sublist(x,l), length(x,n), N>0),AL). Or! allsublists3(l,sl):-setof(x,sublist(x,l),sl). include empty set once findall(x,p,l) findall find all solutions regardless of values of variables not common to P and X example (variable Age not common): findall(child, age(child, Age), List). List=[peter, ann, pat, tom] bagof gives one list per value of Age sublists of specified length fixlengthsublists(l,sl,n):- bagof(x,(nonemptysublist(x,l),length(x,n)),sl). What about fixlengthsublists([1,2,3],sl,n). Generate all sublists of increasing length! 4

5 Updating the database prolog program relational database How are bagof, setof and findall implemented? by means of updating the database assert add a clause retract remove a clause How does findall work? Run predicate repeatedly, save and backtrack find all predicate used for storage findall1( Template, Enumerator, List ) :- asserta( 'find all'( [] ) ), call( Enumerator ), asserta( 'find all'( {Template} ) ), fail 'all found'( [], List ). Example from The Craft of Prolog assert and retract The all found predicate assert(goal) Goal is a program clause retract(goal) remove Goal asserta(goal) add to beginnig of program assertz(goal) add to end of program example:?- crisis. no assert(crisis).?- crisis. yes retract(crisis).?- crisis. no Remove stored predicate copy to list 'all found'( SoFar, List ) :- retract( 'find all'( Item ) ),!, /* to stop retract looking for more Items. */ 'all found'( Item, SoFar, List ). 'all found'( [], List, List ). 'all found'( {Template}, SoFar, List ) :- 'all found'( [Template SoFar], List ). assert and retract example (swiprolog behaves a little different): fast(ann). slow(tom). slow(pat). assert( (faster(x,y):-fast(x),slow(y)) ). faster(a,b). A=ann. B=tom. retract(slow(x)). X=tom X=pat no some meta-predicates var(x) suceeds if X is uninstantiated nonvar(x) suceeds if X is not variable or if X is instantiated atom(x) X is an atom integer(x) X is an integer float(x) X is a float atomic(x) X is a number or an atom compound(x) X is a structure name(atom,list) List is characters from letters in Atom 5

6 a few words about I/O read(x) read from keyboard write(x) write to screen A string is a list of ascii-values can be denoted by quotes write('hello World.') 6