1. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD LOGIC PROGRAMMING (WEEK 4) Eleni E. Mangina Department of Computer Science University College Dublin Equality and unification Arithmetic expressions Terminology Lists Structures

2. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lecture 10

3. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Terms So far, we have only encountered predicates which talk about simple values, called atomic constants eg. jane a 1 simple_term When we want to represent complicated, structured knowledge, this is reather limited Therefore, we are also allowed to use more general structures called terms

4. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Terms (2) A term is like a literal I.e. –It has a functor – a Prolog atom; –And maybe some arguments, each of which can be a term, or a variable Examples of terms: simple_term dog(bonzo) fat(X) lots(a,2,D,f(X,g)) ‘a string’(‘EVEN capitals!’) These are not terms: 2(X) X(2)

5. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Terms (3) The difference between literals and terms is: –Literals form individual goals to which a truth value can be assigned; –Terms are values in themselves and do not have a truth value. You can tell the difference by where there are found: –Literals appear as the outermost structure in heads and bodies of clauses and in goals, eg. ?- lit1( t_in_lit1 ), lit2( t_in_lit2 ). –Terms appear as arguments to literals eg. ?- literal( functor( arg1, arg2)). X = 2.

6. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Terms (4) We sometimes think of terms as tree structures (Trees in computer science grow downwards!) So the term functor( arg1, arg2 ) might be thought of as: And literal( atom, func( 1, 2 )) as: functor arg1arg2 literal atomfunc 12

7. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Terms (5) Examples of terms: % person( Name, Age, EyeCol, HairCol) person( george, 35, brown, fair). animal( type = dog, name = bonzo, hairyness = very). While terms are helpful in making the language more flexible, they are still not completely so – the number of arguments is fixed What happens if we want to represent a variable number of things in one place?

8. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Unification The “=” sign may seem like an equality test: | ?- 5 = 7. no | ?- 5 = 5. yes | ?- a = b. no Or it may seem like an assignment command: | ?- X = 7. X = 7 ? yes | ?- 7 = Y. Y = 7 ? yes

9. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD The “=” sign indicates unification – what we have been calling “matching”. Two constants unify if and only if they are identical. An unbound variable unifies with anything, and becomes bound to it. Two structures unify if they are the same kind of structure, have the same number of components, and each pair of corresponding components unifies; any variables involved in these unifications will become bound to whatever it unifies with.

10. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Arithmetic | ?- Num = 5 + 6. Num = 5 + 6 ? yes Arithmetical expressions are not automatically evaluated: They count as structures, and unify accordingly: | ?- X + Y = 5 + 6. X = 5, Y = 6 ? yes | ?- Z + W = a*b + c. W = c, Z = a*b ? yes

11. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD | ?- (3 + 4) * (7 + 9) = (A + 4) * M. A = 3, M = 7+9 ? yes | ?- (3 + 4) * (7 + 9) = (C + D) * (E + F). C = 3, D = 4, E = 7, F = 9 ?

12. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Evaluating arithmetic expressions The is operator will evaluate arithmetic expressions: | ?- N is 3 +1. N = 4 ? yes | ?- Total is (3 + 4) * (7 + 9). Total = 112 ? yes It uses unification, so the variable does not have to be unbound: | ?- M is 6, M is 3 * 2. M = 6 yes

13. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD | ?- Calculation = (2 * 3) + (5 * 4), Value is Calculation. Value = 26, Calculation = 2*3+5*4 ? yes | ?- Calculation = (2 * 3) + (5 * 4), Value is Calculation + 1. Value = 27, Calculation = 2*3+5*4 ? yes | ?- Calculation = (2 * 3) + (5 * 4), Value = Calculation + 1. Calculation = 2*3+5*4, V = 2*3+5*4+1 ? yes

14. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD This does not work: | ?- N is 24, N is N + 1. This would try to bind N to both 24 and 24 + 1 simultaneously.

15. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Types of object Also: variables (starting with capitals or with underscore); structures (arithmetic expressions, and others).

16. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lists A list is a collection of zero or more data-items, in order: [a] % a list of one element [34, 14, z] % a list of three elements [[a, b, c], Dummy] % a list of two elements, with the first % element being a list of three elements, % and the second element a variable Like any object, a list can be the value of a variable: | ?- [Any, list, of, items] = Avariable. Avariable = [Any,list,of,items] ? yes

17. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Two lists unify if they are the same length and all their elements unify: | ?- [a, b, c, d] = [Var1, b, Var2, d]. Var1 = a, Var2 = c ? yes | ?- [1, What, 2, X, 3] = [A, b, C, d, E]. A = 1, C = 2, E = 3, X = d, What = b ? yes

18. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD | ?- [(a + X),(Y + b)] = [(W + c),(d + b)]. W = a, X = c, Y = d ? yes | ?- [[X, a]] = [X,a]. no | ?- [[X, a]] = [[b, Y]]. X = b, Y = a ? yes Note the “unification-inside-unification” – recursion.

19. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lecture 11

20. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lists There is a special kind of term, called a list It can be represented in 2 ways – the internal representation or the syntactic sugar The internal representation uses 2 symbols:. (dot – a functor) [ ] (empty list – an atom). connects a term (on the left) with a list (on the right) NB this is not symmetrical The last list to be connected to any list is [ ]

21. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lists (2) Examples: [ ].(a,[ ]).(1,.(2,[ ])).(.(a, [ ]),.(.(b,.(c,[ ])),[ ])) However, thisi snot an easy notation Instead of., we write [A|B] where A is the term (head) and B is the list (tail) The same examples: [ ] [a|[ ] ] [1|[2|[ ] ] ] [ [a|[ ] ] | [ [b| [c| [ ] ] | [ ] ] ] ]

22. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lists (3) This is still not easy to read So we introduce simpler forms [A][A|[ ] ] [A,B][A|B|[ ] ] ] [A,B|C][A| [B|C] ] Now our examples read: [ ] [a] [1,2] [ [a],[b,c] ] Which is much better!

23. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lists (4) The different forms of list are all interchangeable, so ?- [a,b,c] =.(a,.(b,.(c, [ ]))) yes ?- [1,2] = [1| [2|[ ] ] ] yes Lists are important because: –They enable us to deal with collections of items –They enable us to control recursive programs

24. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Definition of a list The empty list, [ ], is a list. Adding an item to the front of an existing list makes a list. So, adding b to [ ] means that [b] is a list. Hence, [a, b] is a list. And so on. Or alternatively: The empty list, [ ], is a list. A structure of the form [X,...] is a list if X is any item and [...] is a list, possibly empty. So, to ask if [a, b] is a list, we consider whether [b] is a list, and to answer that we ask if [ ] is a list. It is, so the overall answer is that [a, b] is a list. That is, a list is a recursively defined structure.

25. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Bar notation in lists | ?- [a, b, c, d] = [X|Y]. X = a, Y = [b,c,d] ? yes | ?- [a, b, c, d] = [X|[Z|W]]. W = [c,d], X = a, Z = b ? yes | ?- [a|[b|[c|[ ]]]] = Wholelist. Wholelist = [a,b,c] ? no

26. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Structures To group a set of items into a structure, use a functor (a constant symbol) with the items as arguments. something(a, b, X, [1,2,3]) Functor is something, there are 4 arguments. Like a “record” in many traditional programming languages. A structure can be the value of a variable: | ?- Theman = person(mike, london, 36). Theman = person(mike, london, 36) ? yes

27. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Structure Unification Structures can unify, if same functor and same number of arguments, and arguments all unify: | ?- person(Nm, Addr, Age) = person(mike, london, 36). Age = 36, Nm = mike, Addr = london? yes | ?- person(Someone, _, 45) = person(harry, dundee, 45). Someone = harry? yes (The plain underscore does not receive any bindings.)

28. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD A structure may have another structure as an argument. addr(flat(23), street(140), postcode(2122)) Unification then works in the obvious way, recursively: ?- addr(flat(23),street(140),postcode(2122)) = addr(flat(F), _Str, Code). F = 23, Code = postcode(2122) ? yes ?- addr(flat(23),street(140),postcode(2122)) = addr(postcode(P), _Str, flat(F)). no (Any variable beginning with underscore is not reported by the interface).

29. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Arithmetic expressions as structures Arithmetic expressions are structures with +, *, etc. as functors. | ?- +(2, 3) = 2 + 3. yes They can be unified (recursively): | ?- +(2, *(5,6)) = X + 5 * Y. X = 2, Y = 6 ? yes They can be evaluated with is: | ?- Result is +(2, *(5,6)). Result = 32 ? yes

30. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lists as structures The special functor “.” holds lists together – a “join to the front” connector. | ?-.(a, [ ]) = [a]. yes | ?- List =.(a, [ ]). List = [a] ? yes | ?-.(a,.(b,.(c, []))) = Alist. Alist = [a,b,c] ? yes

31. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD | ?-.(a,.(b,.(c, []))) = [First,b,Last]. Last = c, First = a ? yes | ?-.(a,.(b,.(c, []))) = [a|.(b, [c])]. yes Mixing the various list notations is not recommended.

32. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Unification Now that we have terms, our original idea of unification is not adequate We need to be able to deal with more complex structures, eg person(Name, Age) = person(george,65) functor(X,a) = functor(Y,Y) [a,f(X,Y)] = [A|[f(A,B)]] We can think of unification as matching trees: functor Xa YY

33. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD First-order term Unification in Prolog To unify two terms –Compare their functors; if they do not match then fail; otherwise… –If the terms have different numbers of arguments, then fails; otherwise… * –If the terms have no arguments then succeed; otherwise… –For each pair of respective arguments If one is a variable, let it be identical to the other; otherwise… Unify the two arguments using this procedure (*) This is an efficiency measure in some systems A more formal version of this algorithm is given in “Foundations of Logic Programming” (John W. Lloyd, 1987, publ. Springer-Verlag)

34. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD First order term unification (2) It is important to understand that this algorithm is an approximation In one particular situation, it is unsound – I.e. logically incorrect That situation is when a variable is uninfied with a term strictly containing itself eg X = f(X) g(X) = g(p(X,Y)) In principle, we can test for this (the occurs check) but in practice doing so is too slow So we ignore it on the basis that such expressions are meaningless anyway and should never arise

35. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Summary The “=” symbol indicates unification (matching) Arithmetic expressions are not automatically evaluated The “is” operator evaluates arithmetic expressions A list is an ordered collection of items A list is made up of a first element and a further list of items. A structure is a general way of clustering data Arithmetic expressions and lists are special structures All structures unify by unifying their components, recursively.

36. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Lecture 12

37. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Input/Output (IO) Input/Output is a problem for declarative programming languages Output: we cannot give a truth value to the action of printing something Input: we could, maybe, view input as coming from a changing Prolog database, but this still gives us problems in understanding what the program means The problems get worse when we get on to flexible computation rules, later! In fact, there are ways to tell a declarative story about I/O, but we will not cover them here

38. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD IO facilities in SICStus Prolog Two ways of thinking about IO: –File-based –Stream-based File-based IO is nice and simple, but is not well-thought-out and can be confusing Stream-based IO is more complicated, but much more reliable In SICStus, file-based IO is implemented through stream-based IO

39. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD File-based IO in SICStus File-based IO is based on the idea of a “current file” (which may be the terminal) You can have severaql files open at once, but you can only read from or write to one at a time Each file has a pointer, which marks where the last operation took place

40. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD File-based IO in SICStus (2) We have nine basic predicates: see/1: choose the current reading file (and open it if necessary) seen/0: close the current reading file seeing/1: which is the current reading file? read/1: read a term from the current reading file tell/1: choose the current writing file (and open it if necessary) told/0: close the current writing file telling/1: which is the current writing file? write/1: wrute a term to the current existing file nl/0: write a newline to the current writing file The terminal is a file called user

41. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD File-based IO in SICStus Example: | ?- tell(example). yes | ?- write(example(term)), write( ‘.’). yes | ?- told yes | ?- see(example) yes | ?- seeing(example). File = example ? yes | ?- read(Term). Term = example(term)? yes | ?- seen, seeing (File). File = user ? yes

42. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Stream-based IO in SICStus We associate each open filewith an explicit pointer with which we refer to it subsequently There are too many predicates to learn usefully – see manual for details The basic streamm handling predicates are: open/3 arguments: a file specification (+); a mode(read/write/append) (+); a pointer (-) close/1 argument: a pointer (+) current_input/1 argument: a pointer (?) set_input/1 argument: a pointer(-) read/2 arguments: a pointer (+); a term(?) write/2 arguments: a pointer (+); a term(?)

43. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD General IO in SICStus Most of the reading and writing predicates come in two versions: –To the current file/stream (eg. Write/1) –To a named stream (eg. Write/2) The first argument is conventionally the stream pointer

44. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD The format predicate The most useful writing predicates are format/2 and format/3 Format/2 has two arguments –A format specification (atom or string) –A list of arguments For example the predicate call Format (‘v\n~w - ~w+\n’, [term1, term2]). Will print out to the terminal v temr1 – term2+ See the manual for more details of format specifications

45. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Arithmetic operators Recall that =/2 means unify We need arithmetic functions, even in logic programs Here are the basic arithmetic predicate is/2 computes the value of the arithmetic expression in its second argument (+) and unifies it with the first argument (?) >= > =:= =\= < =</2 all compute the respective comparison between the values of two arithmetic expressions (+,+) See the manual for more details

46. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Meta-Predicates Meta-predicates are predicates which work on data which is outside the logic of prolog Usually, they assign truth values to statements about the logic or the language They are mostly meant for programming where the data is a program…. … but they are often abused to write hacky prolog code

47. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Meta-Predicates (2) Example: var/1 var is a meta-predicate which tests whether or not its argument is a variable It is a meta-predicate because a variable is not a term – it may contain one, but it is not one… … so this predicate works on part of the external prolog languaage, not on its internal logic var/1 might be used in an implementation of unification to decide whether a variable had already been unified or not

48. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Misusing meta-predicates Here is how NOT to use ground/1, which succeeds if its argument is fully instantiated We want to test if two expressions are equal: equal (X,Y) :- ground (X), ground (Y), Y =:= X. equal (X,Y) :- ground (X), \+ ground (Y), Y is X. equal (X,Y) :- \+ ground (X), ground (Y), X is Y. equal (X,Y) :- \+ground(X), \+ground(Y), format(‘Error! \n’, [ ]).

49. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD To meta-program or not? Rule of thumb 1: if you have to use a meta- predicate and you are not sure why, there is something wrong Rule of thumb 2: if you have to use a meta- predicate and your data is not part of a program clause, there is something wrong Do not ever use meta-predicates to control the run-time behaviour of Prolog (as in the example), because: –It messes up the logic of your program –It makes your program very hard to analyse automatically –There are much better ways to do it

50. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Some safe, useful predicates There are three meta-predicates which are very useful and mostly safe logically They are concerned with finding multiple solutions to queries Findall/3 is exactly analogous to running a query and asking for all the solutions by hitting ; at the prompt For example, given a definition of ancestor/2. Findall(X, ancestor(john, X), Answers) instantiates Answers with a list of all the Xs such that ancestor (john, X) Is provable in the current database

51. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Some safe, useful meta- predicates (2) Findall/3 is very much a proof based prediate – it simulates exactly what prolog does under user control Answers appear in the list in the order that they would at the terminal NB this means that if there are infinitely many solutions, it will never terminate

52. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD Some safe, useful meta-predicates (3) Two more logically-oriented predicates are setof/3 and bagof/3 setof/3 instantiates its third argument to a list which represents an ordered set of all the answers generated for the term given in argument 1 by the goal given iin agrument 2. As with findall\3, compound structures can be given in argument 1, and compound goals in argument 2: setof(Place_Distance, (distance(edinburgh, Place, Distance), nice_to_visit(Place)), Possible_Venues) bagof/3 is the same as setof/3 but returns a multiset of answers

53. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD findall/3 differs from the other two in its treatment of uninstantiated variables in its goal which are not named in argument 1 It assumes that all variables in arguments which are not named in argument 1 are existentially quantified This means that they can take any (I.e. more than one) value, while the answers are generated setof/3 and bagof/3 require explicit existential quantification with the ^ operator Otherwise, each of the free variables takes a fixed value, with setof/3 and bagof/3 backtracking to produce all the possible answers Some safe, useful meta-predicates (4)

54. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD For example, these queries produce the same answers (but maybe not in the same order) findall (X, p(X,Y),L). bagof(X,Y^p(X,Y),L). But these may not (it depends on the definitionof p/2) findall (X,p(X,Y),L). bagof(X, p(X,Y), L). Note that if Y has a value when these goals are called, there is no difference in any of the behaviours Some safe, useful meta-predicates (5)

55. Dr Eleni Mangina – COURSE: LOGIC PROGRAMMING (during a joint degree with Fudan University in Software Engineering) DEPT. OF COMPUTER SCIENCE UCD For another example, consider the following program and query: p (a,b). p (c,b). p (d,e). ?- setof(X, p(X,Y), L). L = [a,b], Y = b?; L = [d], Y = e?; no Some safe, useful meta-predicates (6)