More Non-logical Features of Prolog

Transcription

1 More Non-logical Features of Prolog Prof. Geraint A. Wiggins Centre for Cognition, Computation and Culture Goldsmiths College, University of London Contents Commit operators Implementing Negation as Failure

2 Commit operators In logic programming, a commit operator allows us to choose a particular proof of a predicate over all others we commit to a particular choice Warning: commits are generally very difficult to account for logically, and it is often wise to avoid their use. Prolog has two commit operators,! cut prevents backtracking within the predicate in which it appears; -> local cut prevents backtracking into and within the goal to its left. Oddly, we write! as though it were a literal in Prolog, and not an operator Goldsmiths College, University of London 2

3 Cut Example p(a). p(a) :-!. p(b). p(b).?- p(x).?- p(x). X = a? ; X = a? ; X = b? ; no no Goldsmiths College, University of London 3

4 Cut (2) Example 2: p(a). p(a). p(b) :-!. p(b). p(c). p(c) :-!.?- p(x).?- p(x). X = a? ; X = a? ; X = b? ; X = b? ; no X = c? ; no Goldsmiths College, University of London 4

5 Cut (3) Example 3: p(a). p(a). p(b) :-!. p(b) :-!. p(c). p(c).?- p(c).?- ( X=b; X=c ), p(x). yes X = b? ; X = c? ; no Goldsmiths College, University of London 5

6 Guarded commit We can use! in a logically friendly way, by building clauses of this general form: p(x) :- guard1(x),!,call1(x). p(x) :- guard2(x),!,call2(x).. p(x) :- guardn(x),!,calln(x). where the guardi predicates are mutually exclusive. This is the commonest form of use of what we call a green cut As usual, green means go on, it s OK So a red cut is not acceptable Goldsmiths College, University of London 6

7 Red & Green Cuts A green cut is one which can be removed without changing the logical behaviour of the program For example, max( X, Y, X ) :- X > Y,!. max( X, Y, Y ) :- X =< Y. The effect here is purely procedural; we don t need to test the =< condition if > has succeeded So we save some processing power Be careful when using green cuts! Goldsmiths College, University of London 7

8 Red & Green Cuts (2) A red cut is one which can not be removed without changing the logical behaviour of the program For example, max( X, Y, X ) :- X > Y,!. max( X, Y, Y ). If we remove the!, we can get an incorrect result on backtracking, because the logical semantics of the program does not match the intended interpretation Do not use red cuts! Goldsmiths College, University of London 8

9 Local Cut Local cut -> can be even more unfriendly than! In some circumstances, -> behaves exactly like logical implies In others, it has no proper logical interpretation Example: p( X ) :- ( q( X ) -> r( X )). logically means p(x) is true if r(x) is true whenever q(x) is true In Prolog, it means find the first solution for q(x), and then try to prove r(x); if there is no solution for q(x), fail Goldsmiths College, University of London 9

10 Local Cut (2) Because of local cut s procedural behaviour, incorrect results can be obtained Example: p(a). p(b). q(b). p(b). p(a). q(b).?- p(x) -> q(x).?- p(x) -> q(x). no X = b? ; no Goldsmiths College, University of London 10

11 Local Cut (3) Local cut is commonly used to implement an if-then-else construction?- ( p(x) -> q(x); r(x) ). which is supposed to mean if p(x) is true, prove q(x); otherwise, prove r(x). However, this is only guaranteed to be correct if p(x) is fully instantiated when the call is made. In some Prologs, -> ; is a special ternary operator, which means (roughly) if-then-else. In some Prologs, backtracking on ; can give incorrect answers. Goldsmiths College, University of London 11

12 Implementing negation as failure Once we have!, we can implement NAF \+ Goal :- call( Goal ),!, fail. \+ Goal. call/1 attempts prove the goal given as its argument; fail/0 is always false. Of course, SWIProlog won t let you do this, because \+ is a built-in meta-predicate Goldsmiths College, University of London 12