CS 360: Programming Language Concepts Lecture 15 Logic Programming

Transcription

1 Reference: Ch CS 360: Programming Language Concepts Lecture 15 Logic Programming I. Logic Programming (Generally) What is logic programming? A logic program is a collection of declarations, i.e. things that are true A logic program is executed by running queries against the program Most logic programing languages incorporate unification and backtracking What are some examples of logic programming languages? Prolog SQL Mercury ( Why would anyone program in a logic programming language? II. Prolog Many complex problems can be expressed as a queries against a set of declarations Unification and backtracking are applicable to a wide range of problems Example: the pegs game ( Overview of Prolog Untyped Uses top-down resolution, or backward-chaining Uses depth-first search 1

2 Syntax clause-seq clause clause-seq clause term opt-clause-tail. opt-clause-tail :- term-list term-list term, term-list term term CONST opt-args opt-args ( expr-list ) expr-list expr, expr-list expr expr [ opt-expr-list opt-list-tail ] ILIT CONST VAR _ opt-expr-list expr-list opt-list-tail expr ILIT = (SIGN ) DIGIT DIGIT VAR = UCHAR (UCHAR LCHAR _) CONST = LCHAR (UCHAR LCHAR _) SIGN = + - DIGIT = UCHAR = A... Z LCHAR = a... z The above is actually the syntax of programs. followed by a period (.). A query is just a term 2

3 Loading the file example.pl. [ example.pl ]. The Simpsons person(bart).?- person(bart).?- person(lisa).?- person(x). % X = bart Fathers and mothers father(grampa,homer). father(homer,bart). father(homer,lisa). father(homer,maggie). mother(marge,bart). mother(marge,lisa). mother(marge,maggie).?- father(homer,x). % X = bart?- mother(x,bart). % X = marge Parents parent(x,y) :- father(x,y). parent(x,y) :- mother(x,y).?- parent(x,bart). % X = homer? ; % X = marge 3

4 Mates (slightly broken) mated(x,y) :- father(x,z), mother(y,z).?- mated(homer,x). % X = marge? ; % X = marge? ; % X = marge?- mated(bart,x).?- mated(marge,x). Mates (slightly broken, but in a different way) mated(x,y) :- parent(x,z), parent(y,z).?- mated(homer,x). % X = homer? Mates (very broken) mated(x,y) :- father(x,z), mother(y,z). mated(x,y) :- mated(y,x).?- mated(homer,x). % X = marge??- mated(marge,x). % X = homer??- mated(bart,x). % hangs 4

5 Mates (fixed) mated(x,y) :- father(x,z), mother(y,z). mated(x,y) :- mother(x,z), father(y,z).?- mated(homer,x). % X = marge??- mated(marge,x). % X = homer??- mated(bart,x). Ancestors (broken) ancestor(x,y) :- parent(x,y). ancestor(x,y) :- ancestor(x,z), parent(z,y).?- ancestor(grampa,bart). % true??- ancestor(grampa,marge). % Fatal Error: local stack overflow... Ancestors (fixed) ancestor(x,y) :- parent(x,y). ancestor(x,y) :- parent(z,y), ancestor(x,z).?- ancestor(grampa,bart). % true??- ancestor(grampa,marge). 5

6 Lists member(x,[x _]). member(x,[_ YS]) :- member(x,ys).?- member(b,[a,b,c,d]).?- member(e,[a,b,c,d]). append([],ys,ys). append([x XS],YS,[X ZS]) :- append(xs,ys,zs).?- append([],[c,d],xs). % XS = [c,d]?- append([a,b],[c,d],xs). % XS = [a,b,c,d]?- append(xs,ys,[a,b,c,d]). % XS = [] % YS = [a,b,c,d]? ; % XS = [a] % YS = [b,c,d]? ; % XS = [a,b] % YS = [c,d]? ; % XS = [a,b,c] % YS = [d]? ; % XS = [a,b,c,d] % YS = []? ; 6

7 Insert-1 Insert-2 insert(x,ys,[x YS]). insert(x,[y YS],[Y ZS]) :- insert(x,ys,zs).?- insert(a,[b,c,d],xs). % XS = [a,b,c,d]? ; % XS = [b,a,c,d]? ; % XS = [b,c,a,d]? ; % XS = [b,c,d,a]? ;?- insert(x,ys,[a,b,c,d]). % X = a % YS = [b,c,d]? ; % X = b % YS = [a,c,d]? ; % X = c % YS = [a,b,d]? ; % X = d % YS = [a,b,c]? ; Arithmetic Predicates (<, =<, >, >=)?- 1 < 2.?- X < 2. % uncaught exception: error(instantiation_error,(<)/2) Permutations Permute-1 Permute-2 permute([],[]). permute([x XS],YS) :- permute(xs,zs), insert(x,zs,ys). Derivation tree for permute([a,b],[b,a]). (on following page) 7

8 Sorting (inefficient) sorted([]). sorted([_]). sorted([xa,xb XS]) :- XA =< XB, sorted([xb XS]). sort(xs,ys) :- permute(xs,ys), sorted(ys).?- sort([7,3,1,5,9],xs). % XS = [1,3,5,7,9]? Quick Sort qsort([],[]). qsort([x XS],YS) :- partition(x,xs,vs1,ws1), qsort(vs1,vs2), qsort(ws1,ws2), append(vs2,[x WS2],YS). partition(_,[],[],[]). partition(w,[x XS],[X YS],ZS) :- X < W, partition(w,xs,ys,zs). partition(w,[x XS],YS,[X ZS]) :- X >= W, partition(w,xs,ys,zs). Merge Sort msort([],[]). msort([x],[x]). msort([xa,xb XS],YS) :- split([xa,xb XS],VS1,WS1), msort(vs1,vs2), msort(ws1,ws2), merge(vs2,ws2,ys). split([],[],[]). split([x],[x],[]). split([xa,xb XS],[XA YS],[XB ZS]) :- split(xs,ys,zs). merge([],ys,ys). merge(xs,[],xs). merge([x XS],[Y YS],[X ZS]) :- X < Y, merge(xs,[y YS],ZS). merge([x XS],[Y YS],[Y ZS]) :- X >= Y, merge([x XS],YS,ZS). 8

9 Cut (!) assoc(x,[[x,y] _],Y). assoc(x,[_ YS],Z) :- assoc(x,ys,z). lookup(x,y) :- assoc(x,[[break,statement],[double,type], [int,type],[return,statement]],y),!. lookup(_,identifier). lookup(double,x). % X = type lookup(return,x). % X = statement lookup(filename,x). % X = identifier lookup(x,statement). % X = break What happened to return? 9