the Fifth Generation project in Japan (1984) popularized Prolog
lots of offshoots: constraint logic programming: CLP languages, CHIP, Prolog III, Trilogy, HCLP, concurrent logic programming, etc.
Two modes: enter assertions; make queries
Suppose we have the following Prolog program in a file named basics.pl
likes(fred,beer). likes(fred,cheap_cigars). likes(fred,monday_night_football). likes(sue,jogging). likes(sue,yogurt). likes(sue,bicycling). likes(sue,amy_goodman). likes(mary,jogging). likes(mary,yogurt). likes(mary,bicycling). likes(mary,rush_limbaugh). health_freak(X) :- likes(X,yogurt), likes(X,jogging). left_wing(X) :- likes(X,amy_goodman). right_wing(X) :- likes(X,rush_limbaugh). low_life(X) :- likes(X,cheap_cigars).
File these in by saying
| ?- consult(basics).Make queries:
| ?- likes(fred,beer). true.
| ?- likes(fred,yogurt). false | ?- likes(fred,X). X = beerHowever, Fred likes other things besides beer. We can reject an answer by typing a semicolon, and get more by backtracking:
| ?- likes(fred,X). X = beer ; X = cheap_cigars ; X = monday_night_football. | ?- health_freak(Y). Y = sue ; Y = mary. /* is there anyone who is both left wing and a lowlife (known in our database, that is)? */ | ?- left_wing(X), low_life(X). falseHow about right wing and a lowlife? right wing and a health freak?
/* Some CSE majors courses and their prerequisites. This simplifies the actual CSE curriculum by assuming courses have at most one direct prerequisite. */ prerequisite(cse142,cse143). prerequisite(cse143,cse311). prerequisite(cse311,cse312). prerequisite(cse143,cse331). prerequisite(cse143,cse341). /* take_before(A,B) succeeds if you must take A before B */ take_before(X,Z) :- prerequisite(X,Z). take_before(X,Z) :- prerequisite(X,Y), take_before(Y,Z).Then we can issue queries such as:
take_before(cse142,cse341). take_before(cse341,cse311). take_before(X,cse341). prerequisite(X,Y).
 /* the empty list */  [10,11,12] [ [squid,octopus,clam], dolphin]
A = [4,5,6], B=[3|A]. /* then B =[3,4,5,6] */ A = [4,5,6], B=[3,A]. /* then B =[3,[4,5,6]] */The list notation is just shorthand for a set of structures, where "." plays the role of cons
.(4, .(5, ))is the same as [4,5]
point, line, . are unevaluated function symbols
fred unifies with fred
X unifies with fred (by substituting fred for X)
X unifies with Y (by substituting Y for X, or substituting 3 for X and 3 for Y)
point(A,10) unifies with point(B,C)
clam(X,X) unifies with clam(Y,3)
When Prolog unifies two terms, it picks the most general unification
point(A,A) unifies with point(B,C) by substituting A for B and A for C
Nit: the logical definition of unification also includes the "occurs check": a variable is not allowed to unify with a structure containing that variable. For example, X is not allowed to unify with f(X). However, most practical implementations of Prolog skip the occurs check for efficiency.
Unification can also be viewed as constraint solving, where the constraints are limited to equations over Prolog's data structures.
P :- Q1, Q2, Q3.means: if Q1 and Q2 and Q3 are true, then P is true.
a fact such as:
P.means P is true.
A goal G is satisfiable if there is a clause C such that
another way of describing this: variables in rules are UNIVERSALLY QUANTIFIED:
low_life(X) :- likes(X,cheap_cigars).means for every X, if likes(X,cheap_cigars) is true, then low_life(X) is true
variables in goals are EXISTENTIALLY QUANTIFIED:
?- likes(fred,X).means prove that there exists an X such that likes(fred,X)
A goal is satisfiable if it can be proven from the clauses.
take_before(X,Z) :- prerequisite(X,Z). take_before(X,Z) :- prerequisite(X,Y), take_before(Y,Z). Suppose instead it was written as: take_before(X,Z) :- take_before(Y,Z), prerequisite(X,Y).Declaratively this is fine, but procedurally a take_before goal would get stuck in an infinite search.
/* Definition of append (name changed to myappend to avoid colliding with built-in append rule) */ myappend(,Ys,Ys). myappend([X|Xs],Ys,[X|Zs]) :- myappend(Xs,Ys,Zs). /* SAMPLE GOALS */ | ?- myappend([1,2],[3,4,5],Q). | ?- myappend([1,2],M,[1,2,3,4,5,6]). | ?- myappend(A,B,[1,2,3]). | ?- myappend(A,B,C).If you're more used to an append function, the append rule may look confusing. Here is another version:
myappend(,Ys,Ys). myappend([X|Xs],Ys,Answer) :- myappend(Xs,Ys,Zs), Answer=[X|Zs].
The two versions work the same most of the time, but the first one is the standard way to write this rule in Prolog, and is considered better style. It also has a stronger implication that this is the append relation rather than the append function.
Also, there are cases where the nonstandard rule gets stuck in an infinite search, while the standard one works OK. If you try this goal:
?- myappend(A,B,[1,2])and backtrack through all the answers, the standard rule will give 3 answers and fail, while the non-standard one will give the same 3 answers and then get stuck in an infinite search. (Try tracing it to see why.)
/* DEFINITION OF MEMBER */ mymember(X,[X|_]). mymember(X,[_|Ys]) :- mymember(X,Ys). /* SAMPLE GOALS */ | ?- mymember(3,[1,2,3,4]). | ?- mymember(X,[1,2,3,4]). | ?- mymember(1,X).
X = 3+4, Y = 5*X.succeeds with X=3+4 and Y=5*(3+4). Or try:
X = 3+4+5, A+B=X.If you want to evaluate one of these tree structures, in other words do arithmetic, use the “is” operator. For example:
X is 3+4, Y is X*X.A little later we'll see how to do this in a cleaner and more general way using one of constraint libraries for SWI Prolog.
Some simple arithmetic examples:
fahrenheit(C,F) :- F is 1.8*C+32.0. myabs(X,X) :- X>=0. myabs(X,X1) :- X<0, X1 is -X. mymax(X,Y,X) :- X>=Y. mymax(X,Y,Y) :- X<Y. length of a list: mylength(,0). mylength([_|Xs],N1) :- mylength(Xs,N), N1 is N+1. factorial(0,1). factorial(N,F) :- N>0, N1 is N-1, factorial(N1,F1), F is N * F1.
/* CLAUSES TO FIND ALL PERMUTATIONS OF A LIST */ permute(,). permute([H|T],L) :- permute(T,U), insert(H,U,L). /* insert an element X somewhere in list L */ insert(X,L,[X|L]). insert(X,[H|T],[H|U]) :- insert(X,T,U). /* inefficient sort */ badsort(L,S) :- permute(L,S), sorted(S). sorted(). sorted([_]). sorted([A,B|R]) :- A=<B, sorted([B|R]). quicksort(,). quicksort([X|Xs],Sorted) :- partition(X,Xs,Smalls,Bigs), quicksort(Smalls,SortedSmalls), quicksort(Bigs,SortedBigs), myappend(SortedSmalls,[X|SortedBigs],Sorted). partition(_,,,). partition(Pivot,[X|Xs],[X|Ys],Zs) :- X =< Pivot, partition(Pivot,Xs,Ys,Zs). partition(Pivot,[X|Xs],Ys,[X|Zs]) :- X > Pivot, partition(Pivot,Xs,Ys,Zs).