1. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering More Built-in Predicates Notes for Ch.7 of Bratko For CSCE 580 Sp03 Marco Valtorta

2. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Testing the Type of Terms var( X) succeeds if X is an uninstantiated variable nonvar( X) atom( X) succeeds if X currently stands for an atom integer( X) float( X) number( X) number (integer or float) atomic( X) number or atom compound( X) structure data objects (terms) simple objects Compound objects (structures) constantsvariables atomsnumbers

3. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Type of Terms in SWI-Prolog See section 4.5 of the manual There a few more built-in predicates, such as –string(+Term) –ground(+Term) succeeds if Term contains no uninstantiated variables

4. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Example: Counting Atoms ch7_1.pl We want to count actual occurrences of an atom, not terms that match an atom count1(Atom,List,Number) counts terms that match Atom 3 ?- count1(a,[a,b,X,Y],Na). X = a Y = a Na = 3 count2(Atom,List,Number) counts actual occurrences of Atom 5 ?- count2(a,[a,b,X,Y],Na). X = _G304 Y = _G307 Na = 1

5. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Cryptarithmetic Puzzle SEND + MORE = MONEY Assign distinct decimal digits to distinct letters so that the sum is valid Albert Newell and Herbert Simon studied in depth puzzle like these in their study of human problem solving (Human Problem Solving, Prentice Hall, 1972) People use a mixture of trial and error and constraint processing: e.g., M must be 1, S must be 8 or 9, O must be 0, etc.

6. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Cryptarithmetic Puzzle II sum( N1,N2,N) if N is N1+N2 Numbers are represented by lists of digits: the query is: ?-sum( [S,E,N,D],[M,O,R,E],[M,O,N,E,Y]). We need to define the sum relation; we generalize to a relation sum1, with Carry digit from the right (before summing, C1) Carry digit to the left (after summing, C) Set of digits available before summing (Digits1) Set of digits left after summing (Digits) sum1( N1,N2,N,C1,C,Digits1,Digits)

7. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Cryptarithmetic Puzzle III Example: 1 ?- sum1([H,E],[6,E],[U,S],1,1,[1,3,4,7,8,9],Digits). H = 8 E = 1 U = 4 S = 3 Digits = [7, 9] There are several (four, in fact) other answers. 1<- <-1 8 1 6 1 4 3

8. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Cryptarithmetic Puzzle IV We start off with all digits available, we do not want any carries at the end, and we do not care about which digits are left unused: sum(N1,N2,N) :- sum1(N1,N2,N,0,0,[0,1,2,3,4,5,6,7,8,9],_). We assume all three lists are of the same lengths, padding with zeros if necessary: ?- sum([0,S,E,N,D],[0,M,O,R,E],[M,O,N,E,Y]).

9. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Cryptarithmetic Puzzle V sum1( [], [], [], C, C, Digits, Digits). sum1( [D1|N1], [D2|N2], [D|N], C1, C, Digs1, Digs) :- sum1( N1, N2, N, C1, C2, Digs1, Digs2), digitsum( D1, D2, C2, D, C, Digs2, Digs). digitsum( D1, D2, C1, D, C, Digs1, Digs) :- del_var( D1, Digs1, Digs2), % Select an available digit for D1 del_var( D2, Digs2, Digs3), % Select an available digit for D2 del_var( D, Digs3, Digs), % Select an available digit for D S is D1 + D2 + C1, D is S mod 10, % Reminder C is S // 10. % Integer division

10. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Cryptarithmetic Puzzle VI Nonderministic deletion of variables del_var( A, L, L) :- nonvar(A), !. % A already instantiated del_var( A, [A|L], L). del_var( A, [B|L], [B|L1]) :- del_var(A, L, L1).

11. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Constructing and Decomposing Terms Clauses are terms too! As in LISP, data and programs have a common representation: S-expressions (atoms or lists) in LISP, terms in Prolog 2 ?- [user]. |: a. |: a :- b. 3 ?- clause(a,X). X = true ; X = b ; No

12. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Clauses are Terms The principal functor of a clause is its neck (:- ) 4 ?- [user]. |: :-(b,c). |: % user compiled 0.00 sec, 32 bytes Yes 5 ?- listing(b). b :- c. Yes

13. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering univ Term =.. L, if –L is a list containing the principal functor of Term, followed by Term’s argument –Example: fig7_3.pl substitute( Subterm,Term,Subterm1,Term1) ?-substitute( sin(x),2*sin(x)*f(sin(x)),t,F).

14. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering univ Example: –fig7_3.pl –substitute( Subterm,Term,Subterm1,Term1) –?-substitute( sin(x),2*sin(x)*f(sin(x)),t,F). An occurrence of Subterm in Term is something in Term that matches Subterm If Subterm = Term, then Term1 = Subterm1 Else if Term is atomic, then Term1 = Term Else carry out the substitution on the arguments of Term

15. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Dynamic Goals Goals may be created at run time, as in: Obtain( Functor), Compute( Arglist), Goal =.. [ Functor|Arglist], Goal. % works in SWI; with some Prologs, call( Goal) See ch7_2.pl for an example: try_call :- Goal =.. [ member| [a, [a,b,c]]], % Goal is a term Goal. % Goal is a predicate This is also an example of Prolog’s ambiguous syntax: the first Goal is a term (a variable), while the second Goal is a predicate

16. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Equality and Comparison X = Y matching (unification) X is E matches arithmetic value (discouraged in SWI) E1 =:= E2 arithmetic E1 =\= E2 arithmetic inequality T1 == T2 literal equality of terms T1 \== T2 not identical T1 @< T2 term comparison See section 4.6.1 of SWI manual for standard ordering

17. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Prolog Database Manipulation asserta/1 assertz/1 Same as assert/1 retract/1 More, described in section 4.13 of SWI manual Only dynamic predicates may be asserted, retracted, etc. dynamic +Functor/+Arity,... Section 4.14 of SWI manual

18. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering Control Facilities once( P) fail true not P (alternative syntax: \+ P) call( P) repeat, defined as: repeat. repeat :- repeat. dosquares example: ch7_3.pl

19. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering bagof, setof, and findall bagof( X,P,L) if L is the list of Xs such that P(X) holds setof( X,P,L) is like bagof, but without duplication Read ^ as “there exists” in bagof and setof findall( X,P,L) is like bagof but collects all objects X regardless of (possibly) different solutions for variables in P that are not shared with X Code for findall is in fig7_4.pl renamed findall1, because findall is built-in

20. UNIVERSITY OF SOUTH CAROLINA Department of Computer Science and Engineering bagof, etc. Examples fig7_4.pl: –age( peter,7). age( ann,5). age( pat,8). age( tom,5). ?- bagof( Child,age(Child,5),L). ?- bagof( Child,age(Child,Age),L). ?- bagof( Child,Age^age(Child,Age),L). ?- bagof( Age,Child^age(Child,Age),L). ?- setof( Age, Child^age(Child,Age),L). ?- setof( Age:Child,age(Child,Age),L). ?-findall( Child,age( Child,Age),L).